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Directional Auger and elastic peak electron spectroscopies: Versatile methods to reveal near-surface crystal structure
Accepted Manuscript Directional Auger and elastic peak electron spectroscopies: Versatile methods to reveal near-surface crystal structure I. Morawski, M. Nowicki PII:
S0167-5729(19)30011-1
DOI:
https://doi.org/10.1016/j.surfrep.2019.05.002
Reference:
SUSREP 469
To appear in:
Surface Science Reports
Received Date: 17 January 2019 Revised Date:
14 April 2019
Accepted Date: 15 April 2019
Please cite this article as: I. Morawski, M. Nowicki, Directional Auger and elastic peak electron spectroscopies: Versatile methods to reveal near-surface crystal structure, Surface Science Reports, https://doi.org/10.1016/j.surfrep.2019.05.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Directional Auger and elastic peak electron spectroscopies: Versatile methods to reveal near-surface crystal structure
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I. Morawski, M. Nowicki*
Institute of Experimental Physics, University of Wrocław,
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pl. M. Borna 9, 50-204 Wrocław, Poland
Abstract
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A review of directional Auger (DAES) and directional elastic peak electron spectroscopy (DEPES) for investigations of the short range order within a near-surface region, similar to XPD, is presented. The application of these techniques requires nothing more than a retarding field analyser (RFA), commonly applied for the observation of low energy electron
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diffraction (LEED) patterns and Auger electron spectroscopy (AES) measurements, for in depth structural investigations associated with the short range order within a near-surface region. The physical principles, experimental set-up, as well as examples of experimental and
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theoretical results, the latter obtained with the use of single scattering cluster (SSC) and multiple scattering (MS) calculations adopted for primary electron plane wave, are shown.
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The scattering geometry and details concerning the scattering events of primary electrons in crystalline solids described by SSC and MS approximations are presented. Furthermore, some issues related to computation parameters such as: maximal scattering order, the maximum radius around the emitter, the number of cluster layers, and the averaging range considered in the calculations are also addressed. The presentation of the data obtained for clean and covered substrates in the form of polar profiles and stereographic intensity distributions enables the straightforward identification of the crystalline structure within the first few
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ACCEPTED MANUSCRIPT sample layers. The data presented in the form of anisotropy maps enable the identification of interatomic axes formed between substrate and adsorbate atoms at the interface. The contribution of different sample layers to the final DEPES signal is discussed. The comparison of DAES results with those obtained by means of x-ray photoelectron diffraction
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(XPD) is also presented. The qualitative and quantitative data analysis, the latter achieved by the comparison of experimental data with theoretical results by means of an R-factor analysis, is shown. The application of DAES and DEPES enables the characterization of the crystalline
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structure of adsorption systems from one monolayer (1ML) up to thicknesses of the adsorbate limited by the inelastic mean free path of the registered electrons. Exemplary results are
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presented for adsorption systems, where the adsorbate and the substrate crystallize in the same (Ag/Cu, Pt/Cu, Cu/Pt) and in different (Cu/Ru) structures. The influence of the large unit cell of graphene formed on Ru(0001) on measured DEPES intensities is also shown. The detailed analysis of these results enables an identification of the short range order of atoms within the
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near-surface region, of adsorbate domains exhibiting different orientation with respect to the crystalline substrate, the determination of the domain populations, the relaxation and termination of the surface, the specific adsorption sites of adsorbed atoms, as well as the
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positions of atoms within a unit cell and their bond lengths (e.g. O Ru(10 1 0) ).
Keywords: electron spectroscopies, retarding field analyser (RFA), directional Auger electron spectroscopy (DAES), directional elastic peak electron spectroscopy (DEPES), crystalline structure, short range order, scattering of primary electrons, adsorbate growth, single scattering cluster (SSC) and multiple scattering (MS) calculations, adsorption sites, relaxation, surface termination, adatom coordinates, bond lengths.
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ACCEPTED MANUSCRIPT * corresponding author e-mail: [email protected]
Contents
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1. Introduction ………………………………………………………………………… 4 2. Experiment …………………………………………………………......................... 9
3. Theory ………………………………………………………………………………11
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3.1. Single scattering cluster (SSC) formalism ………………………………..14
3.2. Multiple scattering (MS) ………………………………………………….16
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3.3 Rmax ……………………………………………………………………….. 20 3.4. Averaging range ………………………………………………………….. 20 4. Results and discussion ……………………………………………………………. ...20 4.1. DAES and DEPES polar profiles ………………………………………. …21
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4.1.1. Cu(111), Cu(001), and Cu(110) ………………………………… 21 4.1.2. Comparison of DAES and XPD ………………………………… 24 4.1.3. Comparison of experimental and theoretical DEPES profiles ….. 25
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4.1.4. Ag/Cu(111) ………………………………………………………27 4.2. DEPES stereographic distributions ……………………………………….. 30
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4.2.1. Cu(111) ………………………………………………………….. 30 4.2.2. Contribution of layers and parameters of calculations – Pt(111) .. 31 4.2.3. Mo(110) …………………………………………………………. 34 4.2.4. Ru(0001) ………………………………………………………… 35 4.2.5. Graphene on Ru(0001) ………………………………………….. 37 4.2.6. Cu / Ru (10 1 0 ) …………………………………………………… 37
4.2.7. Pt/Cu(111) ……………………………………………………….. 41
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ACCEPTED MANUSCRIPT 4.2.8. Cu/Pt(111) ……………………………………………………….. 44 4.2.9. Determination of surface relaxation – Cu/Pt(111) ………………. 46 4.2.10. Determination of adatom coordinates - O Ru (10 1 0) ………….. 47 5. Conclusions ………………………………………………………………………….. 52
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Acknowledgments ……………………………………………………………………… 53 References ……………………………………………………………………………… 54
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1. Introduction
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The understanding of physicochemical processes taking place on solid surfaces requires the detailed knowledge about the chemical composition of surface layers, the growth mode of adsorbates, as well as the crystalline structure of surfaces and the order within a near-surface region. Therefore, it is extremely important to determine the structure of deposited layers
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already from the first stages of nucleation till the growth of a thicker adsorbate layer. The adsorbate growth is determined by the relation between the surface free energies of adsorbate γA, substrate γB, and interface γI [1,2]. Depending on the γ values a monolayer by monolayer
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(Frank-van der Merwe (FM)) growth mode, the formation of three dimensional (3D)
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adsorbate islands (Volmer-Weber (VW) growth mechanism), and an intermediate mode with the completion of the first monolayer followed by the growth of 3D islands (StranskiKrastanov (SK) growth) can be observed. The widely used method, which provides information about the so called long range order of surface atoms, determined by the coherence radius reaching few hundreds Å, is low energy electron diffraction (LEED) [3,4,5]. The observed diffraction pattern reflects the reciprocal lattice of the investigated surface. In turn, the so called short range order of atoms can be revealed by the application of x-ray photoelectron diffraction (XPD) and Auger electron
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ACCEPTED MANUSCRIPT diffraction (AED) [6,7,8,9,10,11,12,13,14,15,16,17,18]. Using the emitted photoelectrons [19,20,18] in XPD and Auger electrons [21,22,23] in AED both methods serve as a very powerful chemically sensitive tools for the determination of the order of nearest and next nearest neighbour atoms and molecules within a unit cell [24,25]. XPD and AED base on the
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scattering process of photo- and Auger electrons, respectively, of kinetic energies Ekin above 500 eV at atomic potentials, which results in the anisotropic distribution of the emitted electrons. The so called forward scattering [26,27] of emitted electrons of Ekin > 500 eV
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results in an enhancement of the recorded intensity of photoelectrons (XPD) and Auger
measured angular distributions [27].
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electrons (AED) along the direction of densely packed rows of atoms which shows up in the
The strong electron scattering at atomic cores is a universal phenomena, which concerns outgoing (emitted), as well as incoming (incident) electrons (independently on the direction of their propagation in solids). Historically, the experimental evidence for the scattering
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processes of primary electrons of energies above the LEED regime (several hundred eV) in crystalline solids was the observation of the brightness enhancements of the luminescent screen revealed while rotating the sample, when the direction of the primary electron beam
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coincides with densely packed atomic rows and planes of the sample [28]. Very similar effects were observed by the recording of Auger and elastically backscattered electrons as a
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function of the incidence beam direction [29,30,31,32,33,34]. The increase of the recorded intensity was observed in the case of a parallel alignment of the primary electron beam with densely packed atomic rows in the crystalline samples. This dependence is actually a nuisance in quantitative Auger analysis [35] of the concentration of different species in solids and the determination of the adsorbate coverage, because an Auger signal may change by 20%-30% by simply changing the incident beam direction. Moreover, this dependence concerns, in principle, also all secondary electrons emitted from crystalline samples including elastically
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ACCEPTED MANUSCRIPT and not elastically scattered electrons, the latter associated with e.g. plasmon excitations and ionisation losses [36,37]. It is this angular dependence, however, which in turn can be used to determine the sample crystallinity within the near-surface region with the use of different spectrometers [29,34,36,37,38, 39,40,41,42,43,44].
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The choice of the experimental geometry enables the observation of the scattering events of primary and secondary electrons separately [34]. The application of a small aperture spectrometer, such as a hemispherical analyser (HA) [18,45,46], enables the detection of
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electrons emitted in a small (few degrees) solid angle around the chosen direction. Therefore, a rotation of the sample enables the recording of angular distributions of emitted photo- and
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Auger electrons, which is applied in XPD and AED, respectively. The intensity maxima of the recorded signal observed along the direction of the densely packed rows of atoms make possible the identification of the near-surface crystalline structure of samples in a very straightforward way.
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The application of a large acceptance angle spectrometers, such as a retarding field analyser (RFA), commonly used for LEED pattern observations and Auger electron spectroscopy (AES) [22,23] measurements, in turn, integrates the angular distribution of emitted electrons
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within a large solid angle. Therefore, the contribution of the focussed scattering events of emitted Auger electrons, as well as elastically backscattered electrons is considerably
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reduced. Yet, the rotation of the sample with respect to the fixed axis of the electron gun and the recording of the signal of secondary electrons emitted from crystalline samples results in the observation of current modulations caused by the primary electron beam scattering effects in solids. The so called directional Auger (DAES) and directional elastic peak electron spectroscopy (DEPES) based on this effect enable structural investigations of the first few atomic layers of clean substrates and adsorption systems [40,42,47,48,49,50]. In DAES and DEPES the observed intensity maxima of Auger and elastically backscattered electrons,
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ACCEPTED MANUSCRIPT respectively, indicate the directions of densely packed rows of atoms in crystalline solids. Due to the forward scattering effect of primary electrons striking the sample the electrons are scattered along the incident direction. Depending on the mutual orientation of the incoming electron beam and the crystalline substrate the incident electrons strike the sample along
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densely or rarely occupied directions. Thus, the illumination of a given atom depends on the direction of the incidence beam. If the collimated incident beam is aligned with the direction of densely packed rows of atoms the electrons are focused (concentrated) onto atoms along
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these rows, which results in an increase of the number of elastic, as well as inelastic scattering events. The former leads to the increase of the current associated with elastically
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backscattered electrons and the latter with the increase of the probability of electron hole creation, which results in the enhancement of Auger electron emission. If, however, the primary electron beam strikes the sample along not densely packed directions there are no near atoms in forward direction, which leads to a reduction of the recorded signal. In view of
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the fact that the forward scattering is a very local effect, which extends to nearest and nextnearest neighbour atoms within a unit cell only, the information about the crystalline structure concerns the short range order, as in XPD and AED. The limited value of the inelastic
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electron mean free path and multiple scattering events, leading to a defocusing of electrons at energies in the range of 0.5-2.0 keV, cause that the information depth about the crystalline
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order concerns first few atomic layers. In DAES and DEPES first the scattering of primary electrons and then the emission of Auger and elastically backscattered electrons takes place, respectively. Therefore, both methods can be considered as time reversals of XPD, where first emission and then scattering of emitted photoelectrons occurs. In DAES and DEPES, however, no photons are associated with emitted Auger and elastically backscattered electrons. DAES and DEPES, thus, extend the applicability of an RFA analyser [51], which in spite of its limited resolution (∆E/E=0.01) becomes a very useful experimental tool. It can be
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ACCEPTED MANUSCRIPT used not only for investigations of the long range order (LEED) [ 52 , 53 , 54 ], chemical composition and growth mode of adsorbates by recording of Auger signals (AES) [23] from the adsorbate and the substrate during the continuous adsorption [55,56,57,58], but also of the short range order within the first few atomic layers of crystalline samples [40,42,47,48,49,50].
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The detection circuitry is uncomplicated and easy to assemble by each researcher familiar with electron spectroscopy methods and significantly facilitates experiments by changing the detection configuration and the measuring parameters. The direct measurement of the current
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maxima, associated with elastically backscattered electrons (DEPES) and Auger electrons (DAES) as a function of the incidence direction of the primary electron beam enables the
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straightforward determination of crystallographic directions of the investigated samples, as in XPD and AED. Moreover, the advantage of an RFA analyser concerns the continuous change of the primary electron beam energy Ep from the LEED regime till 2.0 keV, which makes experiments possible similar to those using a synchrotron radiation source. The dependence of
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the recorded signal on the primary electron energy at fixed incidence beam directions also contains information about the scattering geometry. The main idea of the present paper is to show how easily valuable crystallographic
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information can be extracted from simple experiments with the use of a standard experimental set-up available in almost every ultra high vacuum (UHV) system equipped with a relatively
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inexpensive and not sophisticated RFA spectrometer. This makes these experiments possible without any extra investment in the existing apparatus. The paper is organized as follows. First, the experimental details about DAES and DEPES measurements are presented. Then, the single scattering cluster (SSC) and multiple scattering (MS) approximations, describing the scattering events of the primary electron beam in crystalline solids, are presented. Next, a comparison of experimental DAES results with XPD data is shown. Finally, the comparison of experimental and theoretical results, the latter
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ACCEPTED MANUSCRIPT obtained with the use of the SSC and MS formalisms, are presented for different substrates and adsorbates exhibiting face centred cubic (fcc), body centred cubic (bcc), and hexagonal close packed (hcp) structures. The analysis of the experimental and theoretical data concerns i) the short range order of the first few atomic layers of the crystalline samples, ii) the
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contribution of individual atomic layers to the signal and, thus, the sensitivity of both methods, iii) the identification of adsorbate domains of different orientation with respect to the substrate, and the determination of their populations, iv) the identification of surface
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relaxation and termination, and v) the determination of adsorption geometries at the adsorbate-substrate interface concerning adsorption sites and positions of atoms within a unit
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cell, as well as bond lengths. In this work we show examples of DAES and DEPES investigations and refer to results published elsewhere.
2. Experiment
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Both experimental methods, DEPES and DAES, rely on the application of a large acceptance angle spectrometer. Therefore, the experiments were carried out in an UHV system equipped with a four grid RFA analyser (Fig.1) with an acceptance angle of about 110° [59], a precise
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sample manipulator, an argon sputtering gun, and adsorbate sources (Knudsen cells). The gas
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pressure during all measurements was lower than 1×10-8 Pa. The investigated samples were cleaned by repetitive cycles of Ar sputtering, annealing at elevated temperatures and flashing controlled by a thermocouple fastened at the sample edge, and, if necessary, by additional annealing in an oxygen atmosphere (Pt, Ru). The negative potential of the grids 2 and 3 (Fig.1) is given by the relation U = U 1 + U 0 cos(ωt ) , with U 1 and U 0 being a constant potential and the amplitude of the modulated potential, respectively, where the frequency ω is set by a generator. A signal amplification was obtained by the increase of the U 0 value, which was chosen to be in the range from 0.2V to 1V for DEPES, and in the range between 1.5V
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ACCEPTED MANUSCRIPT and 3V for AES and DAES measurements. AES was used to monitor the cleanliness of all samples. The recording of AES spectra and DAES profiles was performed in a differential dN(E)/dE mode of the RFA operation with the use of a Lock-in amplifier, by measuring the second derivative dI2(E)/dE2 of the collector current [51]. In the case of DEPES investigations
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the normal N(E) mode was used, where the first derivative dI(E)/dE of the collector current was recorded. Depending on the investigated system and the energy Ep the typical values of the primary electron beam current were in the range of 0.1-1 µA and few µA for DEPES and
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DAES respectively. In some cases the current below 0.1 µA can be used, which is, however, associated with the increase of the noise/signal ratio. In view of this fact DAES and DEPES
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methods can be applied to investigate metals, semiconductors, and strongly bound adsorbates such as chemisorbed oxygen, which do not undergo decomposition and desorption under the continuous electron bombardment.
The manipulator enables the annealing of the samples and precise rotation around two
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mutually perpendicular axes. The rotation of the sample around an axis within the sample surface ("polar axis"), enables the continuous change of the polar angle θ (Fig.1b) in the range from -θmax to θmax. The rotation of the sample around the surface normal ("azimuthal axis")
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(Fig.1b), allows the change of the azimuthal angle ϕ between 0º and 180º in arbitrary chosen
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steps ∆ϕ by researcher. Usually DEPES distributions were recorded for θmax =85° in steps of ∆θ=0.25º and ∆ϕ=2º, giving 61 380 measure points. In DAES and DEPES the Auger signal and the current of elastically backscattered electrons is recorded, respectively, as a function of the incidence angle of the primary electron beam at different beam energies Ep from 0.5keV till 2.0keV. The incidence angle of the electron beam was changed by the polar and azimuthal sample rotation. The DAES and DEPES results are presented in the form of polar profiles I(θ) or stereographic intensity distributions I(θ,ϕ). In order to present the data as stereographic plots the coordination transfer functions x=2tg(θ/2)sinϕ and y=2tg(θ/2)cosϕ were used. In the
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ACCEPTED MANUSCRIPT case of clean (111) surfaces of Cu and Pt monocrystals the symmetrization procedure of measured intensities was applied by the rotation of the I(θ,ϕ) recorded distribution by 60º and 120º and mirroring, according to the three-fold symmetry axis of the substrate, and averaging of signals. All intensities within each distribution were normalized with respect to the signal
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value at normal incidence (θ=0º). The intensities within each distribution were scaled by colour. In order to show the details of the intensity patterns related to crystalline structure of investigated sample a background subtraction procedure was applied [60]. The background in
(1)
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IBG = A⋅cos(B⋅θ) ,
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DEPES polar profiles was fitted by the cosine function of the polar angle θ:
where A and B are fitting parameters obtained by means of the least square analysis. The enhancement of signal changes within DEPES distributions under the influence of an adsorbed layer with respect to the signal from the substrate was obtained by the calculation of the signal anisotropy:
(I Ads−Sub − I Sub )
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A=
I Sub
,
(2)
where I Sub and I Ads − Sub represent intensities from the clean and adsorbate covered substrate at
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a given polar θ and azimuthal ϕ angle. The results were presented as anisotropy profiles A(θ)
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or stereographic anisotropy maps A(θ,ϕ), where the intensity maxima reflect changes of measured intensities caused by the adsorbate. Therefore, the anisotropy maxima reflect new interatomic directions formed between the adsorbate and the substrate atoms. In this way the geometry of the adsorption system already at 1ML coverage, assuming the FM growth mode, can be identified.
3. Theory
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ACCEPTED MANUSCRIPT In the literature different theoretical descriptions of electron scattering exist. The interpretation of the intensity patterns observed in scanning electron microscopy images [61,62] recorded at high electron energies in the range of tens of keV was possible by the consideration of the two-wave approximation [63] associated with channelling [64,65] and the
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Kikuchi effect [61, 66 , 67 ]. The intensity enhancements were associated with the Bragg reflections of the collimated electron beam passing through the atomic planes of a crystalline solid. Another approach used to describe the diffraction effects of the primary electron beam
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concerns the many-wave dynamic approximation [68,38]. At medium energies of electrons striking the sample in the range of 0.5-2.0 keV the enhancement of the Auger signal and the
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intensity of elastically backscattered electrons was observed when the primary electron beam passed “through” the densely packed rows of atoms as a result of the forward focusing effect [27] of the primary electrons. These effects were simulated by the use of single scattering cluster (SSC) [69,70,48] and multiple scattering (MS) approximations [71] in order to obtain
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theoretical DAES and DEPES polar profiles.
In the theoretical description of the scattering events of primary electrons different parameters need to be taken into account such as: the nature of the scattering atoms, the crystalline
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structure of the solid, lattice vibrations, the electron energy and its attenuation in the sample determined by the inelastic mean free path, as well as the incidence direction of the primary
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electron beam. These parameters serve as an input to calculate the wave field in a solid resulting from the coherent interference of the primary and scattered waves at different incidence angles and energies of the primary electron beam. The conditions of interference depend on the electron energy, the distance between atoms and the scattering angle, as well as on the atomic number Z. The scattering of an electron plane wave e ikr with the wave vector k, associated with primary electrons, at the atomic potential is schematically shown in Fig.2. The scattered wave in the
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ACCEPTED MANUSCRIPT form of a spherical wave eikr r is centred on the atomic core. The interference between the primary and the scattered waves leads to the enhancement of the wave amplitude along the forward direction (θS=0º). This well known forward scattering effect becomes significant at electron energies above 0.5 keV. According to the well known scattering theory described e.g.
a solid angle in which the particles are scattered and:
4π k2
∑ (2l + 1)sin l
2
δl =
4π Im{ f (k ,0 )} , k2
(3)
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σ (k ) =
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2
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in [3,5,13,14] f (k , θ S ) = dσ / dΩ is a differential scattering cross section, where Ω denotes
is the total elastic cross section, where δl represents the phase shifts for angular momentum l. f (k , θ S ) as a function of the scattering angle θS, where f (k ,θ S ) is the scattering factor, is 2
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shown together with the phase of the scattered wave for Cu at different electron energies in Fig.3 and for different scattering atoms and the same electron energy of 1000eV in Fig.4. In all cases f (k , θ S ) is large at small scattering angles, i.e. in the forward direction. The larger 2
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the energy of the incoming electrons and the larger the atomic number Z of the scattering atoms the forward scattering (θS=0º) becomes more effective. On the other hand,
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backscattering events (θS=180º) become significant at lower electron energies. An increase of the phase of the scattered wave is observed with increasing θS. Different scattering properties of scattering atoms with significantly different number Z can serve as an additional chemical contrast in measured and calculated intensities. Both the SSC and the MS formalism base on the same concept of electron scattering at an atomic potential in crystalline solids. In view of the fact that in our works we refer to both formalisms, the latter significantly expanded by functions, which take into account different
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ACCEPTED MANUSCRIPT scattering orders and the real experimental geometry, in the following sections we describe both approximations separately.
3.1. Single scattering cluster (SSC) formalism
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To first approximation the scattering processes of primary electrons can be described by the assumption that the electron wave in a crystalline solid undergoes only single scattering at atomic potentials, as it was also applied for emitted photoelectrons and Auger electrons in
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XPD and AED [8,9,13,14,15], respectively. The scattering geometry for the incoming electron beam used in single scattering cluster (SSC) calculations is schematically shown in
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Fig.5. Note that in Fig.5 θ’ and k’ denote the polar angle and the wave vector of the primary electron beam in vacuum and θ and k denote these values in the sample. In the case of electron energies in the range of 0.5-2.0keV used in DAES and DEPES experiments θ≈θ’ and
k≈k’ is assumed. The incoming electrons are represented by the plane wave ψ 0 = e ikr with
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the propagation vector k, which is scattered by the scatterer j. The resulting wave field in a crystal depends on the coherent interference of the primary ψ 0 and scattered ψ j waves.
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Taking into account all scattering atoms in a cluster the final wave function at the emitter site
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r in a crystal can be written in the SSC approximation as a sum of ψ 0 and ψ j [69,70,48]:
ikd e j − ikd − r / λ cos θ − d j / λ Ψ (k , r ) = eikr e − rZ / λ cos θ + ∑ e j e Zj e f j (k , d j , T ) kd j j
.
(4)
In Eq.(4) the sum concerns all scatterers j in the solid and the attenuation of the unscattered primary plane wave along rZ/cosθ and rZj/cosθ paths, and scattered waves are taken into account. λ is the inelastic electron mean free path, θ is the incidence angle defined relative to
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ACCEPTED MANUSCRIPT the surface normal, d j = r − r j defines the position of the scatterer j with respect to the emitter, T is the absolute temperature, and f j (k , d j , T ) is the scattering factor [72]. The latter factor involves the scattering amplitude, partial wave phase shifts calculated with the use of
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the muffin-tin approximation [3], and the curved character of the wave fronts at the emitter sites r [73]. The scattering factor can be written as [72]: ∞
f j (k , d, T ) = ∑ t lj (T )cl (kd j )(2l + 1) Pl (cos θ kd j ) .
(5)
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l =0
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Eq.(5) involves the scattering matrix tl j , which describes the scattering amplitude and vibrational properties of the scattering atom j [3], the polynomial factor cl that multiplies the asymptotic form of the spherical Hankel functions, the lth Legendre polynomial Pl , and the scattering angle θ kd j between vectors k and d j .
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The signal of Auger and elastically backscattered electrons in DAES and DEPES, respectively, integrated over the large acceptance angle Ω0 of the RFA analyser (Fig.5) is proportional to the sum of intensities of the incoming electrons over all emitters in the sample
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weighted with the escape probability of emitted electrons A [74,69]:
r 2 r I (k ) = ∑ Ψ (k , rS ) A Z S λout
.
(6)
In Eq.(6) the damping of outgoing electrons along their way to the surface is governed by the distance of an emitter to the surface rZ and the value of the inelastic mean free path of emitted electrons λout. The factor A integrates the inelastic damping of emitted electrons
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ACCEPTED MANUSCRIPT e − rZ / λout cos φ in a solid over all possible emission angles φ and to first approximation, can be written as [69]: − r ⋅t / λout ∞e Z = ∫ dt , t2 1
(7)
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r A Z λout
where the integration parameter t is equal to 1/cosφ.
Eqs. (4)-(7) enable to calculate DAES and DEPES profiles I(θ) and intensity distributions
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I(θ,ϕ) in the SSC approximation at different energies of the primary electron beam and emitted electrons by applying inelastic mean free path values λ and λout, respectively
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[75,76,77,78]. In the case of DEPES λout =λ. In DAES λout is associated with the emitted Auger electrons at energies significantly smaller than the primary electron beam, and in general λout < λ for Auger energies down to about 100 eV.
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3.2. Multiple scattering (MS)
Although the SSC approximation reflects the main intensity features observed in experimental
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DAES and DEPES data [48,49,69,70] the description of scattering processes taking place in a real system requires the consideration of different scattering orders of the primary wave,
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which is particularly desirable at electron energies above 0.5keV used in DAES and DEPES. Therefore, the multiple scattering (MS) approximation was developed [71] to describe scattering events of the primary electron beam, represented by a plane wave, in crystalline samples, which enables the calculation of theoretical DAES and DEPES distributions. In the literature the MS formalism is known to describe scattering events of secondary electrons, which are represented by spherical waves, such as emitted photoelectrons in XPD and Auger electrons in AED [79,80,81,82,83]. Multiple scattering events were also considered for the description of low energy electron diffraction [84,85].
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ACCEPTED MANUSCRIPT As in the SSC formalism, applied for DAES and DEPES, in the MS theory the small atom approximation [86,87] is used, where the atomic radius is considered to be small enough in order to make the curvature of the electron wave negligible. Similar to the SSC approach the wave field in a solid associated with the scattering events at atomic cores is calculated taking
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into account scattering properties of individual atom described by f (k ,θ S ) , the crystal structure, as well as the inelastic mean free path values associated with the electron energies. The MS approach requires, however, the consideration of different scattering orders in the
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final form of the wave function located at the emitter site. Therefore, taking into account all
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mentioned considerations the wave field at a site r in a crystal can be written as [71]:
(, , ) = (, ) + (, ) + (, ) + ⋯ + (, ) + ⋯ + (, ).
(8)
(, ) = ∙ represents the wave function of the primary electron, (, ), (1 ≤ p ≤ s),
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represents the wave function of electron which undergoes p consecutive scattering events before it reaches emitter site r. Index s denotes the highest scattering order considered in the MS approximation. According to the scattering model shown in Fig.6 each p-scattered wave
⋅ ⁄ ∑"#$
∑"#' … ∑"#* ⋅("#$ )"#' )⋯)"#*+ ( #$ ⁄ #' ⁄ … #* ⁄ + × /01 /01 /01 . #$ . #' . #* 2#$ ⁄ 2#' ⁄ 2#* ⁄ - 2 … 3 ( … + 4 4 … 4 "#$ "#$ "#' "#(*5$) "#* 2 2
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(, ) =
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component at the site r in the crystal can be expressed as follows [71]:
√
#$
(9)
#'
#*
where the sums concern all scattering atoms, N is the number of atoms in a cluster, 1 / N is the normalization factor, aj1, …, ajp are bond vectors, which define the relative positions of scattering atoms, e ik⋅r multiplied by ⋅("#$ )"#' )⋯)"#*+ describes the incidence plane wave at
the beginning of the bond vector aj1,, 62# 978 represents a spherical wave, which emanates
from the scattering atom at the beginning of the vector aj,, and 4"#$ 4"#$ "#' … 4"#(*5$)"#* are the
17
ACCEPTED MANUSCRIPT scattering factors [72] associated with the consecutive scattering events from 1st to pth. The damping of primary electrons is taken into account by the ⁄ and #⁄ factors, respectively, at the emitter site and the particular scattering atom j, while 2#⁄ describes damping of scattered electrons along aj vector; ξ and ξj represent the way of primary electrons
in a solid from the surface to the emitter and scatterer j, respectively; λ is the inelastic electron
calculated with the use of the recursion formula [71]:
√
√
∑"#(;5$) ⋅"#(;5$) #(;5$)⁄
∑"#(;5') ⋅"#(;5') #(;5')⁄
(10)
.
.
/01#(;5$)
2#(;5$)
/01#(;5')
2#(;5')
.
/01#;
2#;
2#;⁄ <4"#; +
2#(;5$)⁄ 4"#(;5$)"#; <4"#(;5$) +
2#(;5')⁄ 4"#(;5')"#(;5$) <4"#(;5') + ⋯
M AN U
:1 + ∑"#; ⋅"#; #;⁄
SC
(, , s) =
⋅ ⁄
RI PT
mean free path [75,76,77,78]. Finally the wave function at the site r of the emitter is
=>?@
Index s is the arbitrary chosen parameter, which reduces the summation, as well as allows the
TE D
comparison of the MS maps obtained for different maximal scattering orders. 4"# in Eq.(9) is the scattering factor associated with the first scattering of the incident plane wave at site aj
EP
[3,5,87]:
(11)
AC C
4"# = 6 ∑D(2B + 1)CD,"# (E)FD (E78 +GD HI J"# ,
while 4"#(*5$) "#* is the scattering factor associated with the pth scattering event (2 ≤ p ≤ s) at site ajp calculated by the formula:
4"#(*5$)"#* = 6 ∑D(2B + 1)CD,"#* (E)FD (E78 +FD (E78( ) +GD HI J"#(*5$)"#* .
(12)
In Eqs. (11) and (12) the matrix element CD,"# (E) = K KL MD NO describes the scattering amplitude and the vibrational properties of the scattering atoms taking into account partial-
18
ACCEPTED MANUSCRIPT wave phase shifts δl [3]; GD HI J"#
and GD HI J"#(*5$)"#* are the lth Legrende
polynomials of the cosine function of the angle between the k vector and the aj bond vector, as well as the angle between the aj(p-1) and ajp bond vectors, respectively; FD (E7) is the
FD (E7) = F(D ) (E7) −
D) 62
F(D ) (E7) ,
RI PT
polynomial part of the Hankel function written in recursion formula [87]:
F = 1,
F = 1 +
62
.
(13)
SC
As in SSC calculations the intensity of Auger or elastically backscattered electrons emitted from the sample towards the RFA analyser is proportional to the sum of the primary beam
M AN U
intensities over all emitters, enumerated by rn in the crystalline sample weighted with the escape probability B of the outgoing electrons [69,71]:
W
X
R(, s) ∝ ∑ , Θ X |(, U , s)| B
.
(14)
TE D
YZ[
B factor depends on the distance from the emitter to the surface, the inelastic mean free path
EP
of outgoing electrons λout, and the incident angle of the primary electron beam Θ associated
AC C
with a given wave vector k. The explicit formula of the B factor is given by the expression:
] "X , Θ = 2^ _` ξ
YZ[
abc
FJ exp f
ξ"
X
YZ[ ghi(j )`)
k
.
(15)
θRFA describes the acceptance angle of the RFA collector used in the experiments. This factor takes into account the real experimental geometry associated with the limited acceptance angle of the RFA analyser and the sample rotation with respect to the axial electron gun. Theoretical distributions I(θ,ϕ) were calculated taking into account the inelastic mean free path values of the primary electron beam λ, as well as the outgoing electrons λout, the latter
19
ACCEPTED MANUSCRIPT characteristic for emitted Auger and elastically backscattered electrons in DAES and DEPES, respectively [48]. The detailed analysis of the calculated signals, the contributions of particular emitters to the DEPES signal calculated at different scattering orders, as well as the defocusing factor associated with the multiple scattering events for selected atoms is
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presented in [71].
3.3. Rmax
SC
In the ideal case the infinitive number of scattering events and all atoms in a cluster should be taken into account in the MS calculations. On the other hand the strong damping of electrons
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in a solid causes that the contributions of scattered waves by atoms, located far away from the emitter, to the final form of the wave function are negligibly small. Therefore, the number of scattering atoms contributing appreciably to the wave function located at the emitter site can be arbitrary limited to the volume defined by the radius Rmax (Fig.7). The Rmax value is
TE D
expressed in units of the inelastic mean free path λ. It should assure a reasonable convergence of the simulated results. As shown in [88] this is achieved when Rmax falls in the range of 1.0-
EP
2.0 of λ.
AC C
3.4. Averaging range
In computations the primary electron beam is usually considered to be ideally parallel, i.e. the vector k is well defined, which is not the case in a real experiment. Electrons focused on a sample exhibit some angular divergence, which depends on the geometry of the electron gun, electrode potentials, and charge effects. That’s why theoretical intensities should be averaged over a small solid angle around the direction of the incidence beam [59,88]. Depending on the electron energy this angle varies from about 2° to 6°. This results in a smoothing of calculated intensities in theoretical DEPES maps.
20
ACCEPTED MANUSCRIPT
4. Results and discussion In this section examples of experimental results obtained with the use of the DAES and DEPES methods, as well as theoretical data received by SSC and MS calculations are
RI PT
presented in the form of polar I(θ) or anisotropy A(θ) profiles, as well as stereographic intensity I(θ,ϕ) or anisotropy A(θ,ϕ) distributions for surfaces of different substrates and
SC
adsorption systems.
4.1.1. Cu(111), Cu(001), and Cu(110)
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4.1. DAES and DEPES polar profiles
In Fig.8 the experimental DEPES polar profile recorded for Cu(111) at the primary electron
[ ] [
]
beam energy Ep=1.2 keV along the 112 − 1 1 2 azimuth is shown together with the model of the cross-section of an fcc(111) monocrystal. The characteristic intensity maxima of
TE D
elastically backscattered electrons are observed at incidence angles -35.3º, 0º, 19.5º, 35.3º, and 54.7º parallel to the atomic rows in the [110], [111], [112], [114], and [001] directions, respectively. The sample atoms act as scatterers, which scatter the primary electrons at this
EP
energy mainly along the forward direction (Fig.2). Thus, if the direction of the primary
AC C
electron beam and that of close packed atomic rows in the sample are aligned the primary electrons are focused along this row (Fig.8b), which leads to an increase of the number of elastic and inelastic scattering events. As a consequence the increase of the recorded current associated with the elastically backscattered electrons and Auger electrons is observed. If, however, the incidence electron beam strikes the sample along another direction, not parallel to close packed atomic rows, there are no near atoms in forward direction (Fig.8b). As a consequence at these incidence angles a decrease of the measured signal of elastically backscattered electrons and Auger electrons is noted. This dependence of the measured
21
ACCEPTED MANUSCRIPT current on the incidence beam direction visible in the DEPES polar profile (Fig.8a) serves as an indication of the sample crystallinity. In view of the fact that in the RFA analyser the energy Ep of the primary electrons can be changed continuously DEPES, as well as DAES profiles can be recorded at different Ep values in the range of 0.5-2.0keV, where the forward
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scattering is most effective. Examples of DEPES polar scans measured for Cu(111) at different energies Ep are shown in Fig.9. Since the energy of the primary electron beam influences the interference conditions of electrons in crystalline solids, some changes in the
SC
recorded intensities in DEPES and DAES profiles as a function of Ep value are expected. However, the position of the main intensity maxima associated with the [110], [112], and
M AN U
[001] directions does not change with Ep. The focusing of primary electrons onto atoms located along closely packed rows leads to the recording of well distinguished intensity maxima. The maximum associated with the [114] direction becomes noticeable above 1.0 keV. The characteristic intensity changes with energy Ep are mainly observed around the
TE D
[111] direction. A very similar dependence of the recorded signal on the incidence beam direction is observed in the DAES profiles (Fig.10), where the Auger signal for the MVV transition (66 eV) is measured at different primary electron beam energies. Due to the
EP
recording of Auger electrons the DAES method is chemically sensitive, which can be utilized in investigations of e.g. intermixing layers and order-disorder phase transitions within the
AC C
near-surface atomic layers as it was shown for Cu3Au(001) [ 89 ], as well as surface roughening as it was presented for Ni(110) [90]. Different scattering properties of atoms revealed by the dependence of the scattering factor on the scattering angle (Fig.4) can to some extend cause a chemical contrast also in DEPES profiles. The differences, however, in atomic numbers Z of scattering atoms e.g. in binary alloys such as Cu-Au should be, significant in order to distinguish their influence on the recorded intensities in DEPES [91]. As in DAES,
22
ACCEPTED MANUSCRIPT also in DEPES temperature effects enabled to reveal surface roughening of Cu(011) [92] and an order-disorder transition in Cu3Au(001) [93,89]. In Fig.11 a comparison of DAES and DEPES profiles recorded for Cu(001) at primary electron energies Ep=0.8, 1.0, and 1.2 keV is shown. At the same Ep values a very similar
RI PT
shape of the DAES and DEPES profiles is observed including the main [001] and [112] intensity maxima (note the splitting of the [001] maximum at Ep=1.0 keV), as well as small local intensity features. A change of the primary electron beam energy results in changes
SC
observed in both DAES and DEPES distributions, however, the overall character of the profiles at the chosen Ep value remains the same. This dependence was also confirmed by the
M AN U
recording of DAES polar scans for low (MVV, 66 eV) and high (LMM, 922 eV) energy Auger transitions and DEPES profiles at Ep=2.0 keV for Cu(001) and Cu(111) [70,48]. It must be noted that the angular distribution of low and high energy electrons is significantly different, as observed by XPD [94], because of the dependence of the scattering factor
TE D
f (k ,θ S ) and the inelastic mean free path λ on the electron energy. Therefore, the above discussed results prove that the intensity maxima originate from the scattering effects of the primary electron beam in the crystalline samples, and the integration of the recorded signal of
EP
Auger electrons in DAES and elastically backscattered electrons in DEPES over the large
AC C
acceptance angle of the RFA collector significantly minimizes the influence of the angular distribution of emitted electrons on the measured current. The information depth of the crystalline structure revealed by DAES and DEPES depends on the inelastic mean free path of primary (λ) and emitted (λout) electrons, as well as on the forward focusing, which takes place within the first few atomic layers because the subsequent scattering events of primary electrons along an atomic row cause a defocusing effect [71]. At the same Ep value the difference between DAES and DEPES results from different inelastic mean free paths of outgoing electrons, because in a case of DEPES λout =λ, but in DAES λout<
23
ACCEPTED MANUSCRIPT λ usually for energy down to about 100 eV. Moreover, in DEPES only elastically backscattered electrons contribute to the recorded signal. In DAES, however, the emission of Auger electrons results from the ionisation of atoms, which can be excited by the primary electron beam, elastically and
inelastically scattered electrons, as well as by secondary
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electrons of sufficient energy [68], which contribute to the backscattering factor in Auger electron emission. In this context the information received by the use of DAES relates also to the probability of electron hole creation and the initiation of the Auger transition, which
SC
underlies the measured intensities. The signal modulation observed in polar scans is usually smaller for DAES than for DEPES, which is reflected by the signal anisotropy values given
M AN U
on the left hand side of each profile (Fig.11). The signal anisotropy is defined as A=(ImaxImin)/Imax, where Imax and Imin represent the maximal and minimal signal within the polar scan.
4.1.2. Comparison of DAES and XPD
TE D
In Fig.12 the comparison of DAES and XPD polar profiles is shown for more or less similar energies of primary electrons in DAES and emitted photoelectrons in XPD scattered at a Cu(111) sample. In the case of DAES the Auger transition MVV (Auger electrons of kinetic
EP
energy 66eV) was excited by primary electrons of Ep=800, 1000, and 1200 keV. In the case of
AC C
XPD the angular distributions of emitted photoelectrons at energies 807 eV, 1178 eV, and 1617 eV were recorded. The DAES and XPD profiles exhibit a very similar distribution of intensity maxima, which in case of DAES results from the scattering events of primary electrons striking the sample but in XPD from scattering events of emitted photoelectrons. The results presented in Fig.12 were obtained independently by two groups (XPD at the University of Fribourg and DAES at the University of Wrocław) and confirm that similar information about the crystalline order of samples can be obtained with the use both methods. The strength of the signal modulation in XPD is higher than in DAES, which results from a
24
ACCEPTED MANUSCRIPT lower probing depth of the Auger electrons than of the photoelectrons and the higher background intensity in DAES. In XPD, first the emission of photoelectrons excited by x-rays following scattering of these electrons at atoms occurs, which results in the anisotropic distribution of the emitted
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photoelectrons. In DAES, however, first the scattering of primary electrons along the incidence direction and then the emission of Auger electrons takes place. Because of the experimental geometry discussed in the introduction section associated with the use of a small
SC
aperture HA analyser in XPD and a large acceptance angle RFA analyser in DAES, the scattering events of secondary and primary electrons are monitored, respectively. A more
SSC results can be found in [69].
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detailed discussion about the comparison of XPD and DAES data, as well as corresponding
4.1.3. Comparison of experimental and theoretical DEPES profiles
TE D
To first approximation the description of scattering events of primary electrons in crystalline solids can be performed with the use of a single scattering cluster (SSC) model [69]. This formalism enables to calculate theoretical DAES and DEPES profiles [48,49,69,70] and to
EP
compare them with experimental data. In Fig.13 experimental and theoretical DEPES polar scans for Cu(001) are presented for primary electron beam energies Ep in the range of 0.5-1.5
AC C
keV. Similar distributions of intensity maxima are observed in both the theoretical and the experimental data. The SSC theory reproduces the majority of intensity maxima associated with the [001] direction at the incidence angle of 0º, as well as the shift of the maximum near the [112] direction at -35º at low primary electron energies. The increase of the Ep value leads to the gradual appearance of the maxima at -54º and -19º associated with the [111] and [114] directions, respectively, in both the experimental and the theoretical scans. The correspondence between measured and computed DEPES profiles is also visible in the
25
ACCEPTED MANUSCRIPT characteristic splitting of the main [001] maximum at Ep=0.9, and 1.0 keV. The main discrepancies between the experimental and theoretical results concern the relative height of the main intensity maxima, reflected by the anisotropy values, and the presence of local peaks observed within the whole scanning range. Some intensity features are more pronounced in
RI PT
the theoretical than in the experimental scans. Moreover, the [001] maximum at 0º in the experimental DEPES profile exhibits three components at Ep=0.5 keV, which is not reproduced in the theoretical distribution, and at Ep=0.7 keV this theoretical maximum splits
SC
but is sharp in the experiment. A more detailed discussion about experimental and computed DEPES data for Cu(001) with the use of the SSC formalism can be found in [70]. Similar
M AN U
observations can be made by the comparison of experimental and theoretical DAES results [48,69].
The comparison of experimental and calculated DEPES profiles for the low index (001), (111), and (110) surfaces of a copper monocrystal is shown in Fig.14. The azimuth of each
TE D
sample was chosen in such a way that the primary electron beam strikes the copper monocrystal parallel to the (1 10) plane, as it is indicated in Fig.15. This enables to reach all densely packed rows of an fcc structure for different substrate symmetries and sample
EP
orientations with respect to an axial electron gun of the RFA analyser. The distribution of the
AC C
main intensity maxima observed in the profiles (Fig.14) corresponds to the crystalline directions within an fcc monocrystal shown in Fig.15. DEPES polar profiles for the Cu(001) and Cu(110) sample are symmetrical as expected for four-fold and two-fold symmetry axes of these surfaces, respectively. The unsymmetrical DEPES scan for Cu(111) is associated with the three-fold symmetry axis of this surface. The SSC theory reflects almost all intensity maxima observed experimentally. The characteristic background observed in all profiles results from the increased damping of primary and emitted electrons towards grazing angles. Therefore, the relative intensity of e.g. the [001] maximum is higher for Cu(001) than for
26
ACCEPTED MANUSCRIPT Cu(111). The same concerns the [110] maximum observed in DEPES profiles for Cu(111) and Cu(110). This maximum is inclined towards grazing angles for Cu(111), while that for Cu(110) is symmetrical. As in Fig.13 the splitting of the [001] maximum for Cu(001) is observed in experiment and theory, which is not the case for the experimental DEPES scan
RI PT
for Cu(111). The lack of this splitting is rather caused by the experimental geometry associated with the limited collector aperture than with the diffraction processes in the sample. It must be noted that a decrease of the effective aperture of the RFA analyser occurs
SC
at incidence angles larger than ±52º, half of the acceptance angle of the collector equal to 104º, in this particular experiment, which causes the additional decrease of the recorded
M AN U
current. Therefore, the limited analyser aperture affects the measured signal before the [001] maximum at -54º is reached for Cu(111). Similar intensity maxima are observed in the experimental and theoretical DAES profiles for other low index surfaces of the copper monocrystal [48]. An overall agreement between experimental and theoretical DEPES and
TE D
DAES scans can been found. Examples of DAES and DEPES profiles recorded for Cu(111),
4.1.4. Ag/Cu(111)
EP
Cu(011), and Cu(001) can be found e.g. in [95,96,97,98,99].
DAES and DEPES can also be used to study the structure of adsorbed layers. While regular
AC C
AES provides information about the thickness of deposited layers and their growth mode LEED yields information mainly about the long range order of surface atoms. The sensitivity of the DAES and DEPES methods to the short range order within a near surface layers can be exploited to add information about the local bond geometry of adsorbed atoms at the adsorbate/substrate interface in the incipient and further stages of adsorbate growth. All this complex information can be received with the use of just one and the same RFA analyser.
27
ACCEPTED MANUSCRIPT In Fig.16 the DEPES polar profiles recorded for clean Cu(111) and different Ag coverages from 1 ML till 12 ML at Ep=1.0keV are presented. The DEPES scan measured for clean
[
] [ ]
Cu(111) along the 1 1 2 − 112 azimuth exhibits pronounced intensity maxima associated with [001], [112], and [110] close packed atomic rows of the fcc structure as observed in Figs.
RI PT
8, 9, and 10. The adsorption of Ag layers causes significant changes in the measured profiles. The presence of the silver layers at different thicknesses leads to the decrease of some intensity maxima and simultaneous appearance of other peaks, which reflect directions at the
SC
Ag/Cu interface and within the newly formed Ag overlayer. The detailed analysis of the DEPES data enables to find maxima, which correspond to Ag(111) domains mutually rotated
M AN U
by 180º, which is indicated in Fig.16 by the distribution of directions within the silver overlayer and illustrated in Fig.17. The growth of an unrotated, with respect to the substrate, Ag domain results in the same distribution of directions as it is shown in Fig.17a. Therefore, the DEPES profile for this domain should reflect a similar but not identical distribution of
TE D
intensity maxima as for the substrate, as it is observed for e.g. Co/Cu(001) [97] and Co/Cu(110) [98]. Different lattice parameters of the Ag overlayer and scattering properties of individual silver atoms in comparison to the copper substrate cause differences in the
EP
recorded intensities and shapes of particular maxima. For this situation the stacking sequence
AC C
along the surface normal at the Ag/Cu(111) interface is CBA/CBA. If, however, the stacking sequence at the adsorbate/substrate interface is CAB/CBA, as shown in Fig.17b, the growth of the 180º rotated domain occurs. For this domain the distribution of directions is reflected with respect to the [111] direction. The recorded DEPES intensities in Fig.16, in fact, correspond to two mutually rotated adsorbate domains. Moreover, the dominant [011] maximum of the Ag overlayer suggests different populations of rotated and unrotated Ag domains. In order to obtain information about the domain growth a quantitative data analysis with the use of an R-
28
ACCEPTED MANUSCRIPT factor can be performed [49]. The experimental polar profiles can be compared with a linear combination of theoretical scans obtained for two mutually rotated domains:
2
I Th = ∑ ni I Th ,i ,
(16)
RI PT
i =1
where ITh,i is the calculated intensity at given polar angle for domain i and ni represents its
condition. We used the following R-factor [100]:
∫ (L
− L Ex ) dθ 2
∫ (L
2 Th
)
+ L2Ex dθ .
M AN U
R=
∑
SC
population. In the calculations the ni values are varied by 1% steps and fulfil the
Th
2
i =1
ni = 1
(17)
In Eq. (17) LTh and LEx are L=I’/I ratios obtained for theoretical and experimental results at a given incidence angle, where I and I’ represent the signal and its derivative with respect to
TE D
polar angle θ, respectively. The calculation of L values assures that the R-factor is affected by the relative shape and position of intensity maxima observed in DEPES profiles without any
EP
influence of the relative intensity scale. Perfect fit between experimental and theoretical data is obtained when R=0, while at R=1 no correspondence between the results is found.
AC C
In Fig.18 the R-factor calculated for experimental and theoretical DEPES scans at Ep=0.8keV is presented as a function of adsorbate domain populations n1 and n2. The best fit of the Rfactor minimum at 0.29 was obtained for n1=75% and n2=25% of rotated and unrotated Ag(111) domains, respectively. The comparison of experimental and theoretical DEPES profiles, the latter obtained for the best fit with the use of Eq. (16), is shown in Fig.19. This result proofs the preferred growth of rotated Ag domains, which is also confirmed by DEPES and DAES results obtained at different energies Ep [49]. The not uniform growth of rotated and unrotated adsorbate domains is most likely associated with the presence of atomic steps,
29
ACCEPTED MANUSCRIPT which are oriented along a certain direction on the Cu(111) surface as a result of the sample miscut. When the nucleation process starts at step edges the preferred adsorption sites enforce the sequence of Ag atoms at the Ag/Cu interface. In the case of the Ag growth on flat terraces both sequences shown in Fig.17a and Fig.17b are equally possible, which results in the
RI PT
nucleation of rotated and unrotated domains. The presence of unsymmetrical DEPES profiles was also found for Ag/Cu(001), which again indicates the preferred growth of one domain [70]. In the case of the Ag/Cu adsorption system the γ A + γ I < γ S relation predicts a wetting
SC
of Cu by Ag. The orientation of Ag domains is determined by the first stages of growth. Therefore, the presence of steps on the Cu substrate can enforce the sequence of atoms in the
M AN U
Ag overlayer. Similar information about the domain populations was obtained with the use of XPD [101,102]. The preferred adsorption sites at step edges were also reported for oxygen on stepped copper surfaces such as Cu(410) and Cu(211) [103]. It must be noted, that the rotation of the fcc(111) domain by 180º leads to the observation of the same LEED pattern,
TE D
which makes a quantitative analysis difficult. Only the application of I(V) measurements of diffracted electron beams [3,104,105,106] can be used to obtain similar information about the domain populations as with DEPES and XPD. In the case of I(V) investigations, however, the
EP
detailed knowledge about the intensity-energy spectrum of diffraction spots of a single
AC C
adsorbate domain is required. The combined detection of polar DEPES profiles, LEED patterns, and AES signals with the use of one and the same RFA analyser has also enabled to find the short and long range order, as well as the growth mode, respectively, for other adsorption systems such as: Ag/Cu(011) [95], Ag/Cu(001) [70,96], Co/Cu(001) [97], Co/Cu(110) [98], Co/Cu(111) [99], Au/Ni(111) [107], Ag/Au(111) [108], Pb/Ni(111) [109].
4.2. DEPES stereographic distributions
30
ACCEPTED MANUSCRIPT The manipulator, which enables the precise polar and azimuthal rotation of the sample (Fig.1b), can be applied to record DEPES profiles at different azimuths. The presentation of such results in the form of the stereographic projection I(θ,ϕ) with the use of the coordination transfer function defined in section 2 reflects the scattering geometry in real space, which
RI PT
enables the direct identification of the sample crystallinity. Therefore, in this section the interpretation of two dimensional DEPES distributions recorded and calculated in a wide
SC
angular range is presented.
4.2.1. Cu(111)
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In Fig.20a the experimental DEPES stereographic distribution for Cu(111) at Ep=1.5 keV is shown. The characteristic threefold symmetric intensity pattern reflects the sample crystallinity. The intensity maxima correspond to the 110 , 112 , 114 , and 100 directions of the sample shown in the stereographic projection of an fcc(111) monocrystal
TE D
(Fig.20c). The detailed analysis of the DEPES distribution enables to find intensity bands associated with atomic planes, as well as the characteristic central maximum with satellite peaks associated with the [111] direction, which strongly depend on the energy Ep of the
EP
primary electron beam. The intensity features observed in the theoretical distribution
AC C
(Fig.20b) also reflect densely packed atomic rows in Cu(111). The background level is higher in the experiment than in theory, which is reflected by the colour scale, as was also observed for other samples [110,111]. Therefore, the background subtraction procedure described in section 2 was often applied in the quantitative data analysis. In Fig.21 DEPES distributions are shown for Cu(111) at different Ep values [ 112 ]. A narrowing of the intensity maxima with increasing energy is observed, which is associated with the dependence of the scattering factor on the electron energy (Fig.3). Moreover, at higher Ep values the inelastic mean free path increases. Therefore, the DEPES maps at
31
ACCEPTED MANUSCRIPT increased electron energies are characterised by the more detailed intensity pattern with intensity bands reflecting atomic plains. A similar dependence is observed in the theoretical DEPES distributions. The signal changes within each map are reflected by contrast values C defined as: C = 2(Imax −Imin)/(Imax + Imin), where Imax and Imin are the maximal and minimal
RI PT
signal intensities within the area surrounded by the dashed circle (θmax=60°) on the experimental map at 0.6 keV. An increase of contrast is observed with increasing energy. C values of the theoretical data are about 1.5 times larger than of experimental results, which
M AN U
performed for Au(111) can be found in [114,115].
SC
originates from a larger background level of the recorded maps [113]. A similar analysis
4.2.2. Contribution of layers and parameters of calculations - Pt(111) As it has been already mentioned both DAES and DEPES are sensitive to the short range order of atoms within the near-surface region. In order to find the contribution of different
TE D
sample layers to the DEPES intensity plot in MS calculations we took into account all scattering atoms in the cluster and considered emitters only in one individual layer. The result of such calculations for Pt(111) at Ep=1.2 keV is shown in Fig.22. A similar analysis at
EP
Ep=1.1keV can be found in [116]. The same intensity scale enables a direct comparison of
AC C
intensities among all partial maps. The contribution of the first layer of Pt(111) is almost isotropic, which results from the lack of scattering atoms above this layer. A small signal modulation results from backscattering events of primary electron wave in the sample. The appearing intensity maxima in the partial plots arrising from deeper layers in Fig.22 are associated with rows of atoms along 110 , 112 , 114 , and 100 directions formed above the considered layer of emitters (Fig.8b). The 110 and 100 intensity maxima originate already from the first and second layer (Fig.22b). The third layer adds contribution to these maxima, but gives also rise to the intensities associated with the 112 peak (Fig.22c). The
32
ACCEPTED MANUSCRIPT 114
and 111 maxima originate from emitters in the fourth layer (Fig.22d). The
characteristic satellite maxima of the [111] peak, which form a threefold symmetric pattern in the center of the DEPES distributions visible in Fig.20a, are associated with scattering of electrons from the 4th and 5th layer. The damping of electrons in a solid as well as the
RI PT
defocusing of electrons [13,79,80,82,117], which is a consequence of multiple scattering events, results in a steady decrease of intensities from deeper layers. The detailed analysis of the scattering and damping of electrons in Cu(111) and Pt(111) is discussed in [111]. The
SC
above results confirm the contribution of few topmost sample layers to the DEPES signal.
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The application of the MS formalism described in section 3.2 enables also the consideration of different scattering orders of primary electrons in solids. We compared two computed DEPES profiles obtained at s-1 and s maximal scattering orders, associated with consecutive number of scattering events, by calculating the data convergence factor expressed by the formula:
1
I s (θ ) − I s −1 (θ )
TE D
Conv =
2
θ
(18)
where, Is(θ) and Is-1(θ) represent the intensities at a given polar angle θ for s and s-1 scattering
EP
orders, respectively. The mean value of the module of intensity differences at s and s-1 is calculated over all polar angles associated with the DEPES polar scans. The convergence
AC C
factor indicates the number of scattering events, which should be taken into account in MS calculations, which assure the negligible intensity differences of computed DEPES intensities at s-1 and s scattering orders. In Fig.23 the convergence factor is shown as a function of the scattering order. The convergence factor, calculated for Is(θ) and Is-1(θ), is shown for the index s of the pair (s, s-1). The consideration of the scattering order in the range from 3 to 5 already ensures the sufficient convergence of computed results, which on the other hand significantly reduces the computation time. As expected at lower Ep a better correspondence
33
ACCEPTED MANUSCRIPT between theoretical DEPES data obtained at s and s-1 scattering orders is achieved because of the lower λ values. As mentioned in section 3.3 the number of scattering atoms, which contribute to the wave function at the emitter site can be limited by the sphere with radius Rmax around the emitter
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(Fig.7). The scatterers in this volume give the main contribution to the final wave function, while the contribution of scatterers outside this sphere plays a minor role, therefore the latter atoms are not taken into account in calculations. In Fig.24 the convergence factor (Eq.18)
SC
calculated for two DEPES intensities obtained for consecutive values of Rmax with 0.1 increments is shown. Rmax is expressed in units of the inelastic mean free path. The
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consideration of Rmax values in the range of 1.0-2.0 ensures a sufficient convergence of theoretical data obtained within a reasonable computation time.
In Fig.25 the convergence factor is shown as a function of the number of layers taken into account in MS calculations. As in the case of the scattering order and Rmax the convergence
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factor was calculated taken two theoretical intensities associated with consecutive number of cluster layers. For Pt(111) at Ep=1.2keV the consideration of the first 20 layers of the
electrons.
EP
crystalline sample seems to be sufficient to simulate the scattering events of primary
In calculations the angular distribution of the primary electrons leaving the electron gun is
AC C
taken into account by the consideration of a divergence ∆θ of the primary electrons (averaging range) around the incidence direction (section 3.4). In Fig.26 the calculated DEPES distributions for Pt(111) are shown at different averaging ranges ∆θ. A smoothing of intensities is observed with increasing ∆θ value. As shown in [59] a decrease of the averaging range is observed with the electron beam energy, which results from the better focusing of electrons in the electron gun at higher Ep values. Depending on the energy Ep the ∆θ values reach few degrees [59].
34
ACCEPTED MANUSCRIPT
4.2.3. Mo(110) In Fig.27a the experimental DEPES distribution recorded at the primary electron beam energy Ep=1.8 keV is presented for the Mo(110) monocrystal. The two-fold symmetry intensity
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pattern corresponds to the distribution of close packed atomic rows within a body centred cubic structure shown in the stereographic projection (Fig.27e). The characteristic intensity bands, which become more pronounced at higher primary electron beam energies Ep (Fig.21),
SC
reflect the atomic planes within the Mo(110) crystal. In the case of the bcc structure the
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increase of DEPES intensities is observed at the 111 , 100 , and 110 directions because they represent the most densely packed rows of atoms within this structure. This observation is also confirmed by the theoretical DEPES map obtained with the use of the MS formalism (Fig.27c). The experimental DAES plot recorded for the MNN transition (Auger electrons of energy 190 eV) at Ep=1.8 keV (Fig.27b) also reflects the well pronounced maxima associated
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with the directions shown in Fig.27e. The current of Auger electrons recorded in DAES gives additional information about the chemical composition of the sample. The theoretical DAES plot shown in Fig.27d reflects the similar distribution of maxima as the theoretical DEPES
EP
map. The differences in the signal intensities between theoretical DEPES and DAES plots
AC C
result from the lower value of the inelastic mean free path of Auger electrons in DAES than elastically backscattered electrons in DEPES. In Fig.27f the experimental DAES distribution recorded for the C KLL Auger transition (275eV) at the trace amounts of carbon on Mo(110) and the same primary electron beam energy Ep=1.8keV does not show any intensity maxima, which could indicate an order within the adsorbate. One can, however, notice the characteristic pattern of the background intensities in the centre of this distribution similar to the pattern observed in DEPES (Fig.27a) and DAES (Fig.27b) plots for Mo(110). This pattern
35
ACCEPTED MANUSCRIPT results from the contribution of elastically backscattered electrons in the substrate in the Auger emission from carbon.
4.2.4. Ru(0001)
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An fcc(111) monocrystal exhibits a ABCABC stacking of atomic layers along the surface normal as shown in Fig.28a. As a result the termination of an fcc(111) surface such as Pt(111) does not influence the contribution of the [110] , [111] , [112] , [114] , and [001] directions to
SC
DEPES intensities. In other words, the same DEPES intensity plot shown in Fig.20 is obtained for A, B, and C terminated Pt(111) surface. In the case of an hcp(0001) monocrystal,
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however, the stacking sequence is ABAB as presented in Fig.28b. This sequence determines the distribution of intensity maxima in DEPES maps. Depending on the terrace termination A
[
]
[
] [
]
[
]
or B the contribution of 10 1 2 and 1 011 or 10 1 1 and 1 012 directions predominates in DEPES plots, respectively, which results from the attenuation of electrons in a solid. In
TE D
Fig.29a the theoretical DEPES plot for an A terminated Ru(0001) surface at Ep=1.3 keV is shown. A threefold symmetry intensity pattern is observed. For symmetry reasons mentioned above the intensity pattern (not shown) obtained for B terminated Ru(0001) surface is rotated
EP
by 180º with respect to the pattern of the A terminated surface. The experimental DEPES
AC C
distribution shown in Fig.29c, however, exhibits six-fold symmetry pattern. Similar intensity features were also observed in angular distributions of Ru 3d photoemission from Ru(0001) in XPD [ 118 ]. This six-fold symmetry intensity pattern is associated with the uniform distribution of A and B terminated terraces, which are separated by monoatomic steps. Both A and B terraces of the Ru(0001) surface give similar contribution to the overall recorded intensities. A quantitative analysis of the experimental and theoretical DEPES plots performed with the use of an R-factor analysis enables to find the populations of A and B terminated terraces. Taking into account theoretical intensities I th , A and I th , B at given polar
36
ACCEPTED MANUSCRIPT and azimuthal angles and terrace populations n A and n B for terraces A and B, respectively, the theoretical intensity can be written as I th = n A I th , A + nB I th , B . The calculations were performed to fulfil the n A + n B = 100% condition by changing the population values in steps
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0.1%. Theoretical DEPES distributions were calculated considering different phase shifts as proposed by NIST [119], Clementi at al. [120], and Barbieri et al. [121]. Experimental and theoretical DEPES distributions were compared with the use of an R-factor defined as:
R = 1−
i =1
∑ (I N
exi
)(
− I ex I thi − I th
− I ex
) ∑ (I 2
N
i =1
)
,
thi
− I th
)
(19)
2
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i =1
exi
SC
∑ (I N
where, I ex and I th are the experimental and theoretical signals, respectively. The results of this analysis at Ep=1.6 keV are summarized in Fig.30. The minimum of an R-factor associated
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with the best fit was obtained at nA=46.8 % and nB=53.2 % irrespective of the source of the phase shifts. Taking into account phase shifts from [121] assures the best correspondence between experiment and theory. Very similar mean values of populations namely
EP
nA=48.9±1.6% and nB=51.1±1.6% [59], obtained at different energies of the primary electrons confirm the uniform distribution of A and B terminated terraces. The latter is confirmed by
[
] [
]
AC C
the almost symmetrical polar DEPES profile recorded along the 0 1 10 − 01 1 0 azimuth (Fig.29e). For comparison this profile is shown together with the polar plot recorded for the polycrystalline Fe, which exhibits the clear lack of intensity maxima. The latter distribution shows background intensities, which are determined by the attenuation of electrons in a solid.
4.2.5. Graphene on Ru(0001) The Ru(0001) surface is often used as a support to form a graphene (Gr) layer [122,123,124,125,126]. The long range order within the Gr layer is well reflected by sharp
37
ACCEPTED MANUSCRIPT diffraction spots in LEED observations, which yield a large (12×12) Moiré unit cell, consistent with a (11×11) mash of the Ru substrate lattice. After formation of the Gr layer the changes of the DEPES signal are not noticeable in the DEPES plot shown on the absolute scale of intensities because of the large contribution of the substrate to the recorded signal
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associated with the large inelastic mean free path of the primary electrons and the large scattering cross section of Ru atoms with respect to C atoms. However, subtle signal changes caused by the presence of the thin Gr layer on Ru(0001) can be revealed by the calculation of
SC
the signal anisotropy (Eq.2). In Fig.31 the anisotropy distribution A(θ, φ ) at Ep=1.2keV is
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presented. The six-fold symmetry pattern of smeared intensities is observed without any pronounced maxima, which indicates a number of different interatomic axes formed by the C and Ru atoms within a large unit cell of the corrugated Gr layer.
4.2.6. Cu / Ru (10 1 0 )
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In contrast to the Ag/Cu(111) adsorption system discussed in section 4.1.4, where silver and copper crystallize in the same fcc structure, the Cu / Ru (10 1 0 ) system is characterized by
EP
different structures of the Cu adsorbate (fcc) and the Ru substrate (hcp) in their bulk form. Depending on the adsorbate-substrate and adsorbate-adsorbate interactions different surface
AC C
structures can be observed. In the case of strong interaction between substrate and adsorbate atoms the formation of a pseudomorphic adsorbate layer is expected. If, however, the interaction between the adatoms prevails, which usually occurs within the overlayer at larger coverages, the formation of the structure characteristic for the adsorbate bulk phase can be observed. The latter is associated with lattice mismatch and a break of the symmetry, which is reflected in the recorded DEPES intensity patterns.
38
ACCEPTED MANUSCRIPT The experimental DEPES plot obtained for Ru (10 1 0 ) at Ep=1.2 keV is shown in Fig.32a. The two twofold symmetry of the intensity pattern characteristic for the Ru (10 1 0 ) substrate with
[
]
[
]
two main intensity maxima at θ = ±30° corresponding to the 2 1 1 0 and 1120 directions is
[
] [
clearly observed (Fig.32c,d). Other low intensity maxima visible along the 1210 − 1 2 1 0
][
]
[
]
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[
]
azimuth correspond to the 1 1 00 , 10 1 0 , and 01 1 0 directions of the hcp structure. The theoretical DEPES distribution (Fig.32b) reflects almost all intensity features observed
SC
experimentally. The other low intensity features correspond to the crystalline directions within the area surrounded by the blue dashed line in Fig.32c.
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Auger measurements from the substrate (Ru NVV transition, 40eV) during the continuous Cu deposition show first the growth of two Cu bilayers [127,110,128] followed by the nucleation of 3D islands. One bilayer (1BL=2ML) corresponds to two p(1×1) copper monolayers separated by 0.78 Ǻ along the surface normal [127]. LEED patterns recorded during the first
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stages of Cu growth exhibit the same distribution of reflexes as for the uncovered Ru substrate, which proves the formation of a pseudomorphic Cu overlayer [127]. LEED observations performed at coverages above 2BL, however, reflect a six-fold symmetry of the
EP
Cu deposit characteristic for the fcc(111) surface [110]. These experimental observations agree with results of density functional theory (DFT) calculations, which indicate the
AC C
energetic stability of the first two Cu pseudomorphic bilayers, while the third bilayer is thermodynamically metastable [128]. The change of the adsorbate symmetry revealed by LEED is particularly interesting from the point of view of DEPES measurements because of the short range order sensitivity of the latter method. The DEPES distribution recorded at Ep=1.5 keV for Cu coverage equivalent to about 7BL on
Ru (10 1 0) is presented in Fig.33 before and after background subtraction. The background of a DEPES polar scan was obtained by the fitting with a cosine function given by the
39
ACCEPTED MANUSCRIPT expression I BG = A ⋅ cos(Bθ ) [60,110] (lower panel of Fig.33a) with A and B determined by a least square analysis applied to the mean polar profile over all scans of a considered DEPES distribution. The DEPES polar profile after the background subtraction given by the
I * (θ ) = I (θ ) − I BG (θ ) = I (θ ) − A cos(Bθ ) , together with the DEPES map are shown in Fig.33b.
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expression: (20)
SC
The intensity pattern shows maxima associated with 110 , 112 , 114 and 100 atomic rows characteristic for two fcc(111) domains mutually rotated by 180º, as well as some low
[
] [
] [
] [
]
[
]
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intensity maxima, which correspond to the 10 1 0 , 1120 , 21 1 0 , 10 1 1 and 2021
directions of the hcp(10 1 0) structure. The orientation of the two fcc(111) adsorbate domains with respect to the Ru (10 1 0 ) substrate is described by the [2 1 1 ](111)Cu and [2 11](111)Cu
[0001](10 1 0 )Ru
[0001](10 1 0 )Ru
relations. The above analysis leads to a picture of the
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adsorption geometry as shown in Fig.34. The first two Cu bilayers reflect the hcp(10 1 0) structure. The growth of the subsequent layers is characterized by an fcc(111) structure,
EP
which exhibits two equivalent ABC and ACB stacking sequences and the resulting mutual rotation of copper domains by 180º. Small violet rings in Fig.34 show the most probable
AC C
hollow adsorption sites on the second Cu (10 1 0 ) bilayer. Because of the symmetry break the growth of a particular Cu(111) domain is likely to be associated with the choice of one of the two equivalent adsorption sites. The DEPES distributions reveal more intensive maxima associated with one Cu(111) domain, which is particularly visible after the background subtraction (Fig.33b). This suggests different domain populations, which can be determined by an R-factor analysis. As it was already shown for DEPES results obtained for Ag/Cu(111) [49] and Ru(0001) [59] a similar quantitative analysis can be performed for Cu/ Ru (10 1 0)
40
ACCEPTED MANUSCRIPT taking into account the contributions of the first two pseudomorphic Cu p(1×1) bilayers, as well as the rotated and unrotated Cu(111) domains with the use of the formula:
* I sim =
∑ (m ⋅ I
* hcp
* * + p ⋅ I fcc _ 0 + q ⋅ I fcc _ 180 ) ,
(21)
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m, p,q
where, I*hcp , I*fcc_0 , and I*fcc_180 indicate intensities associated with the simulated distribution of hcp structure, as well as unrotated and rotated fcc domains, respectively, weighted by m, p, and q populations, which range from 0% to 100% while fulfilling the condition
SC
m + p + q = 100 % . At coverages as large as 7BL the contribution of the pseudomorphic Cu
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and the Ru substrate in the recorded DEPES signal is governed by the inelastic mean free path. The results of such R-factor analysis performed with the use of experimental and theoretical component distributions (I*hcp , I*fcc_0 , I*fcc_180) at Ep=1.2 keV are shown in Fig.35. The best fit of the experimental component maps to the recorded DEPES distribution
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at Ep=1.2 keV associated with the R-factor minimum was found for m=24%, p=41% and q=35% (Fig.35b). The same analysis performed for the theoretical component distributions leads to the m=19 %, p=46 % and q=35 % populations (Fig.35d). The resulting DEPES plots
EP
are shown in Fig.35c and Fig.35e. Very similar results were obtained at Ep=1.5keV [110]. As already mentioned in the case of Ag/Cu(111) different population values of rotated and
AC C
unrotated domains are likely to be associated with nonequivalent adsorption sites. It is worth noticing that because of symmetry reasons LEED patterns exhibit the same distribution of diffraction reflexes for rotated and unrotated Cu(111) domains [110] as in the case of the Ag/Cu(111) system described in section 4.1.4.
4.2.7. Pt/Cu(111) The information concerning the surface composition and structure is crucial for a knowledge based materials design. This information seems to be particularly important for catalytically
41
ACCEPTED MANUSCRIPT active systems such as Cu/Pt and Pt/Cu. Usually, the bimetallic adsorption systems demonstrate other catalytic properties than their components alone [ 129 , 130 , 131 ]. The breaking and formation of new bonds between metal atoms lead to changes in electronic structure, which can influence the stability, activity, and selectivity of catalysts. The Cu-Pt
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system, for instance, was used to investigate the reforming of hydrocarbons and the hydrogenolysis of pentane [132,133]. The Pt/Cu(111) is an example of an often investigated bimetalic system, where a number of experimental [134,135,136,137,138,139,140,141] and
SC
theoretical [142,143,144] methods was applied. Because of an 8% lattice mismatch between the two metals pronounced lattice strain occurs at the interface. At room temperature (RT) the
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Frank-van der Merwe growth mechanism was observed [137,145,141] and the epitaxial Pt layer on Cu(111) exhibiting an fcc stacking sequence was reported [145]. In view of the exothermic heat of mixing three bulk alloy phases are possible CuPt3, CuPt, and Cu3Pt [146]. Experimental investigations with the use of ion scattering revealed that the Cu3Pt(111) phase
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is formed within a few near-surface layers after the thermal treatment of a Pt/Cu(111) system [134,135]. The resultant Cu3Pt(111) surface is characterized by a p(2×2) platinum superstructure. A site exchange process at step edges was found to be responsible for the
EP
intermixing at the Pt/Cu interface with the use of scanning tunneling microscopy [140]. DFT investigations support the formation of a surface alloy [142].
AC C
Because of the sensitivity of DEPES to the short range order the local configuration of adsorbate atoms of the first monolayer with respect to the crystalline substrate can be identified [141]. Different adsorption sites of deposited atoms result in the formation of associated directions between adsorbate and substrate atoms, which influences the DEPES signal. Therefore, DEPES can be applied to investigate ultrathin adsorbate layers formed on crystalline substrates. In Fig.36a the experimental DEPES distribution at 1ML coverage of Pt on Cu(111) is shown. A background subtraction procedure [60,110] was applied to all
42
ACCEPTED MANUSCRIPT distributions in Fig.36 in order to enhance weak intensity features. The observed intensity pattern is very similar to the DEPES map measured for the uncovered substrate shown in Fig.20a (note that the experimental DEPES map in Fig.20a represents the Cu(111) substrate rotated by 180° compared to the one covered by a Pt monolayer shown in Fig.36a). The
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theoretical DEPES distributions were calculated for different geometries at the adsorbate/substrate interface. The presence of domains with Pt atoms at different positions such as A and B hollows, on top (C), and bridge sites on Cu(111) shown in Fig.37 was
SC
considered in the MS calculations regardless of their energetic rationalization. The calculations were performed for not dissolved and dissolved Pt in the first layer of the copper
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substrate taking into account the Pt-Cu bond length. In a case of the intermixing layer the Cu3Pt alloy, which exhibits the p(2×2) structure in the top most Cu layer, and the presence of the Pt monolayer at different adsorption sites was considered (Fig.37e). As expected the formation of a pseudomorphic monolayer with Pt atoms at sites of A type (Fig.36b), which
TE D
causes the continuation of stacking sequence characteristic for fcc structure at the interface, namely A/CBA, results in almost the same intensity features as observed for the uncovered substrate observed in Fig.20b (note again that the theoretical DEPES map in Fig.20b
EP
represents Cu(111) substrate rotated by 180º with respect to Pt covered one in Fig.36b). The differences in intensities observed for the clean and Pt covered copper substrate are associated
AC C
with the individual scattering properties of Pt and Cu atoms considered in the simulations by the appropriate scattering factors f (θ S ) (Fig.4). Because of the forward scattering the signal in DEPES depends mainly on the f (θ S ) maximum (θS<20º). From Fig.4 it is evident that a Pt atom scatters the electron wave more effectively than Cu, which scales with the values of the scattering cross section of these atoms. Therefore, the chemical composition of the investigated sample within the near-surface region influences to some extent the intensities in DEPES. As it is visible in Fig.36c the intermixing of Pt and Cu leads to a smoothing of the
43
ACCEPTED MANUSCRIPT intensity maxima. The consideration of adsorption at B sites (Fig.37b) leads to three layers of B/CB stacking sequence at the adsorbate/substrate interface characteristic for hcp structure. This arrangement is reflected in the theoretical DEPES plot (Fig.36d) by additional intensity maxima. Taking into account the mixed Pt-Cu layer an enhancement of the 110 intensity
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maxima associated with the Pt(B) terminated surface is observed (Fig.36e). If, however, ontop Pt atoms (Fig.37c) are considered an intense maximum in the center of the distribution and weak intensity features at large polar angles are observed (Fig.36f). A suppression of the
SC
low intensity maxima is noted for the Pt-Cu surface alloy (Fig.36g). Adsorption at bridge sites
M AN U
(Fig.37d) requires the consideration of three mutually rotated Pt domains and results in additional intensity features (Fig.36h), which are not observed in the other distributions. Again, the low intensity features are suppressed in the case of the intermixed layer (Fig.36i). The results of the quantitative analysis obtained with the use of an R-factor, where the contribution of different adsorbate domains to the DEPES signal was considered (see section
TE D
4.2.6), are shown in Fig.38. The best fit (Rmin=0.125) was obtained for the presence of Pt(A) and Pt(B) terminated Pt domains at nA=58% and nB=42% populations on the mixed Pt-Cu layer at the interface. Differently terminated adsorbate domains within the first layer influence
EP
the further growth, which results in a nucleation of rotated and unrotated Pt islands on
AC C
Cu(111) [141]. The use of the experimental and the theoretical distributions of component domains in the R-factor analysis results in almost the same domain population values. The above analysis shows that surface alloying occurs for the Pt/Cu(111) system already at 330K, which is also confirmed by previous scanning tunneling microscopy (STM) investigations at 315K [140]. Medium energy ion scattering (MEIS) measurements reveal the intermixing at even lower temperature 225K [135], which is far below 550K characteristic for the formation of Cu3Pt bulk alloy. The examples of theoretical DEPES data obtained for other alloys such as
44
ACCEPTED MANUSCRIPT AuCu(001) and AuCu3(001), as well as pure components Cu(001) and Au(001) can be found in [91].
4.2.8. Cu/Pt(111)
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The above presented analysis concerns the DEPES maps measured and calculated at 1ML coverage of the adsorbate, and showed that the position of adsorbate atoms within the first monolayer with respect to the crystalline substrate can be revealed by the comparison of
SC
experimental and theoretical DEPES distributions, the latter obtained for different adsorption sites. Another approach used to reveal the adsorption geometry of atoms at the interface
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concerns the calculation of the signal anisotropy. The anisotropy defined by Eq. (2) reflects the relative change of intensities caused by the adsorbed layer with respect to the signal from the substrate underneath. Therefore, the considerable enhancement of intensity features caused by the formation of adsorbate-substrate atomic axes can be obtained if the data are
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presented as anisotropy maps. An example of such investigations concerning the Cu/Pt(111) adsorption system is presented in [ 147 ]. The anisotropy distributions A(θ,ϕ) from experimental DEPES maps obtained after the adsorption of Cu at 330K and 450K,
EP
respectively, and theoretical plots, the latter simulated for a Cu(A), Cu(B), and Cu on top (C)
AC C
terminated Cu monolayer, as well as a misfit layer are shown in Fig.39 and Fig.40. The same models for A and B hollow sites, as well as for on-top (C)-sites shown in Fig.37a,b,c for the inverse Pt/Cu(111) system and additional model of the misfit layer (Fig.41) were applied for Cu/Pt(111). The quantitative analysis of the anisotropy distributions was made by the calculation of R-factor values [60] given in Fig.39 and Fig.40. The comparison of the data in Fig.39 shows that after the adsorption of Cu at 330K the misfit layer is formed, which is also confirmed by the lowest value of Rmin=0.52 among all R-factor values, as well as by a Moiré like distribution of LEED reflexes [147]. The R-factor minimum for A and B threefold
45
ACCEPTED MANUSCRIPT hollow, as well as C (on-top) sites are equal to 0.81, 1.48, and 0.69 respectively. At larger coverages the DEPES distributions reflect the same order within the adsorbate as for bulk Cu(111), which is also reflected in LEED patterns. A different relative intensity pattern in the experimental anisotropy DEPES distribution is
RI PT
observed after the adsorption of Cu at T=450K (Fig.40). The comparison of experimental and theoretical anisotropy plots obtained at Ep=0.8 keV clearly indicates the nucleation of a pseudomorphic Cu monolayer exhibiting adsorption sites of type A. The A/CBA sequence of
SC
atoms along the surface normal at the adsorbate/substrate interface (Fig.37a) results in the lowest value of Rmin=0.8 (Fig.40b). Other adsorption sites such as B and on-top, as well as a
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misfit layer exhibit larger values of Rmin=1.32, 1.37, and 1.24, respectively. As it was mentioned earlier, DEPES intensities depend on the short range order within the near-surface region, and are determined by the scattering properties of the individual atoms in the solids, which is demonstrated by the scattering factor values in Fig.4. Therefore, in the case of a
TE D
pseudomorphic monolayer exhibiting the A/CBA stacking sequence, characteristic for the continuation of the substrate structure in the adsorbed layer, the anisotropy values are governed only by different scattering properties of the deposited and the substrate atoms as in
EP
the case of 1ML of Cu on Pt(111) (Fig.40b). The A/CBA stacking sequence at the Cu/Pt(111) interface is also confirmed by DEPES investigations performed at other energies of primary
AC C
electron beam such as Ep=1.4 keV [50]. Again, it must be noted that in the case of a pseudomorphic adsorbate monolayer the same pattern of LEED reflexes for the uncovered as well as the covered substrate surface with A, B, and on-top (C) termination is expected. By contrast, DEPES anisotropy maps reveal the geometry at the interface and, in addition, enable to determine straightforwardly the adsorption sites (Fig.40) [147].
46
ACCEPTED MANUSCRIPT 4.2.9. Determination of surface relaxation – Cu/Pt(111) In view of the fact that the signal in DEPES originates from the first few sample layers (see e.g. Fig.22 and Fig.36) the position of intensity maxima should be influenced by any changes of interplanar distances associated with surface relaxation schematically shown in Fig.42. The
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[110] and [001] intensity maxima, which originate already from the two topmost layers (Fig.22b), are expected to be mostly affected by the relaxation. Therefore, the analysis of experimental DEPES distributions and the comparison of measured results with theoretical
SC
intensity plots, the latter obtained for different interplanar spacings, should lead to the determination of the surface relaxation. An example of such investigations, where the shift of
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intensity maxima in DEPES plots serves as a measure of relaxation, is presented in [116]. In this analysis the displacement is virtually limited to the first layer and described by the relaxation value ∆1,2 (Fig.42), which is measured with respect to the ideally terminated surface. In Fig.43 the polar cut of an experimental DEPES distribution, recorded along the
TE D
[112] − [1 1 2] azimuth of Pt(111) at Ep = 0.8 keV, is shown together with theoretical polar scans calculated for the unrelaxed surface (∆1,2 = 0%), as well as an inward (∆1,2 = –10%) and outward (∆1,2 = +10%) relaxation of the outermost layer. The inward displacement of the first
EP
layer leads to the shift of peaks in the DEPES profile away from the [111] maximum, while
AC C
the outward displacement results in a shift of the maxima towards the centre at θ = 0° (Fig.43), as it is indicated in Fig.42b. Experimental DEPES plots were recorded at Ep=0.8, 1.1, and 1.4 keV and compared to theoretical data with the use of an R-factor. MS calculations were performed for ∆1,2 displacements ranging from –10% to +10% of the distance between neighbouring bulk-like (111) layers in steps of 1% and the Ep values used in the experiment. The results obtained at Ep = 1.4 keV are presented in Fig.44. The best fit between experimental and simulated DEPES distributions, indicated by the R-factor minimum, is obtained at ∆1,2 = +0.6%. This result reveals a small increase of the interplanar
47
ACCEPTED MANUSCRIPT distance between the first two layers of Pt(111) with respect to the bulk distances between (111) planes, which confirms the literature data obtained with the use of different experimental methods [148,149,150,151,152,153,154,155]. The mean value of the relaxation derived from DEPES results obtained at different Ep values is equal to +0.7%.
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A similar analysis can be applied to one pseudomorphic Cu monolayer on Pt(111) in order to find the distance between the adsorbed layer and the topmost substrate layer. LEED observations performed after the formation of a Cu monolayer at 450K indicate the same
SC
symmetry and distances between diffraction spots as for the uncovered Pt(111) surface, which proves the formation of the (1×1) adsorbate structure [116]. DEPES investigations applied to
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1ML of Cu on Pt(111) proved that at 450K Cu atoms are adsorbed at threefold A type fcc hollow sites (Fig.40) [147]. Taking into account the above considerations the only remaining parameter to be determined by the quantitative analysis is the interlayer distance between the Cu monolayer and the first Pt layer, described as d0,1 = (1 + ∆0,1)d. The results of this analysis
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at Ep = 1.4 keV are shown in Fig.45. The minimum of an R-factor indicating the best fit was found at ∆0,1 = –7.3%, which shows a smaller distance between the Cu layer and the Pt(111) surface in comparison to the interlayer distances of bulk platinum (111) planes. The mean
EP
value of the Cu-Pt separation distance obtained from DEPES at different Ep equals to -6.9%, which scales with the smaller size of Cu atom in comparison to Pt. The distances between two
AC C
topmost layers revealed by DEPES for uncovered and Cu covered Pt(111) are similar to results obtained with the use of DFT [116,156,157].
4.2.10. Determination of adatom coordinates – O Ru (10 1 0) The usefulness of the DEPES data analysis by means of anisotropy values is shown in Fig.46. The theoretical DEPES distributions were calculated for a model of one adsorbate and three substrate atoms. The position of the adsorbate atom is defined by the angle θad varying from
48
ACCEPTED MANUSCRIPT 10º to 50º (Fig.46a). For comparison the data are presented as theoretical I(θ,ϕ) DEPES and A(θ,ϕ) anisotropy stereographic plots. The low intensity features caused by the adsorbate visible in the DEPES distributions are significantly enhanced on the anisotropy scale. The high intensity central maximum visible in all DEPES distributions originating from a row of
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substrate atoms is represented by the anisotropy minimum. In other words the minimum of the anisotropy reflects the lack of an adsorbate atom along the chain of substrate atoms. The anisotropy maximum reveals the newly formed interatomic axis between adsorbate and
SC
substrate atoms. A shift of the intensity maximum with θad indicating the new direction formed between adsorbate and substrate atoms is noted. Because of the interference of
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electron waves characteristic intensity rings are noted in all stereographic plots. Therefore, the analysis of the maxima in A(θ,ϕ) distributions can lead to the identification of the adsorption geometry at the interface, as it was already shown in Figs.31, 39, and 40. The comparison of DEPES distributions obtained at the same primary electron beam energy
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Ep for the clean substrate and after the formation of the adsorbate monolayer by means of the anisotropy values for the O Ru (10 1 0) system is presented in [158,50]. The DEPES results
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were used to determine the structure, the positions of the oxygen atoms in the unit cell, as well as bond lengths. As it is known from LEED experiments oxygen forms a long range
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ordered (2 × 1)p2mg structure on Ru (10 1 0 ) [159,158]. It must be noted that at energies used in DEPES above LEED regime the primary electron beam penetrates several atomic layers of the investigated sample because of the large inelastic mean free path. Moreover, the lower values of the scattering cross section for O than for Ru cause that the signal from the substrate predominates in the recorded intensities. Therefore, the DEPES distributions I(θ,ϕ) recorded before and after oxygen adsorption are almost identical if the absolute intensity scale is used [158]. The relative signal changes caused by the saturated adsorbate overlayer are, however, well reflected in the anisotropy distribution A(θ,ϕ) shown in Fig.47. Well distinguished
49
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[
]
anisotropy maxima observed along the 000 1 − [0001] azimuth of the substrate at θ=±26° reveal the interatomic axes between O and Ru atoms. These maxima originate from the focusing of primary electrons along O-Ru atomic pairs, which leads to the enhancement of the DEPES signal along this newly formed interatomic directions. The DEPES polar profiles
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recorded before and after oxygen adsorption are shown in the upper panel of Fig.48. Small but measurable signal changes of the recorded DEPES intensities caused by the adsorbate layer are well visible in the anisotropy profiles shown in the lower panel of Fig.48. The
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anisotropy maxima, which do not correlate with the DEPES signal from the substrate, originate from the formation of the O-Ru atomic pairs after the oxygen adsorption, which is
[
]
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well reflected in the anisotropy profile along the 000 1 − [0001] substrate azimuth. The anisotropy values change within ±15 %, which is well above the experimental uncertainty of the measured DEPES signal of 0.5 %. The anisotropy profile obtained along the [1210] − [1210]
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azimuth, also shown in the lower panel of Fig.48, does not exhibit any maxima because of the lack of O-Ru pairs along this azimuth. Other maxima of the anisotropy noticeable in Fig.47 are associated with the orientation of other interatomic bonds formed between O and Ru
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atoms.
In order to confirm the origin of the anisotropy maxima observed at θ=±26° (Fig.47 and
[
]
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Fig.48) the DEPES polar profiles along the 000 1 − [0001] azimuth of Ru (10 1 0 ) were recorded for a gradual increase of the oxygen coverage. The obtained anisotropy profiles are presented in Fig.49. The steady increase of these maxima with increasing oxygen dose is observed till the coverage saturates. All anisotropy changes are very reproducible including the main maxima at θ=±26°. Further adsorption (above 4 Langmuirs) does not influence the DEPES profiles anymore, which confirms that after the formation of the first saturated oxygen monolayer further adsorption does not take place. The presence of LEED diffraction
50
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azimuthal (ϕ) angles, obtained from the A(θ,ϕ) plot can serve as input parameters for the quantitative determination of the positions of O atoms within the unit cell of the two dimensional (2 × 1)p2mg structure, as well as of the O-Ru bond length [158]. The observed
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LEED patterns together with the anisotropy polar profiles (Fig.48) and the stereographic distribution (Fig.47) indicate that the oxygen structure is commensurate with respect to the
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Ru (10 1 0) lattice. The oxygen atoms belong to the (1 2 1 0) plane perpendicular to the Ru (10 1 0) surface containing substrate atoms and occupy two equivalent adsorption sites symmetrically located along the [0001] − [0001] azimuth, with the O-Ru axis being inclined
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26º with respect to the surface normal. The resulting model of the O /Ru(10 1 0) system is shown in Fig.47b. These conclusions are consistent with the observed LEED patterns, results
[159].
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of LEED I(V) measurements, as well as density functional theory (DFT) data presented in
From the data shown in Figs.46, 47, and 48 it is evident that the anisotropy gives information
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about the orientation of O-Ru axes with respect to the substrate structure underneath. The direct observation of the anisotropy maxima in Fig.47, however, does not, give any information concerning the adatom coordinates within a surface unit cell. Therefore, the above conclusions do not permit a discrimination between the two cases: (1) oxygen atoms are located symmetrically only in the pI plane (Fig.47b) with respect to the Ru atom; (2) the presence of two oxygen domains mutually rotated by 180º with oxygen atoms adsorbed only on one side of the ruthenium atom within the pI and pI’ atomic planes as shown in Fig.47b.
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maxima in the anisotropy distribution (Fig.47a) and used their angular coordinates (θ,ϕ) to determine the interatomic axes (angular directions) between O and Ru atoms. In Fig.50 only two of these directions are presented for clarity. Other intensity features noted in the
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anisotropy distribution A(θ,ϕ) (Fig.47) restrict the adsorption sites of oxygen to two planes marked as pI and pII in Fig.47b. Then, the following evaluation procedure was applied: For
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the angular direction (θ,ϕ) revealed by the experimental data and an assumed (Y,Z) atom position the distance D between this atom and that direction (dashed blue line) was determined (Fig.50). In this evaluation the first three layers of the Ru (10 1 0 ) cluster and the surface relaxation of the substrate [159] were considered. In the next step the distance D was
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used as an argument of the Gaussian functions. Finally, the mean values of Gaussian functions for all considered angular directions (θ,ϕ) were calculated at different (Y,Z)
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coordinates of the oxygen atom within the rectangle (4.28 Å × 2.71 Å) defined by the size of the substrate unit cell. The normalized, to the highest mean value of Gaussians, results of this
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evaluation, which was performed simultaneously for both pI and pI’ planes, are shown in Fig.51a. The value of a Gaussian function, given by the colour scale, is a measure of a probability of the adatom location. Therefore, the maxima at (1.33 Å, 1.08 Å) and (2.95 Å, 1.08 Å) reveal the positions of oxygen atoms in the pI and pI’ planes, respectively. These maxima are mirror reflected with respect to the [1210] − [1210] substrate azimuth, which is consistent with the conclusions drawn from the experimental data (Fig.47). The analysis performed for the pII plane results in the same position of O and Ru atoms at the corners of the unit cell (Fig.51b), which is unrealistic. In this evaluation procedure the uncertainty of the
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analysis enables to find the interatomic distances between O and Ru atoms. The bond lengths between oxygen and ruthenium atoms of the first and second substrate layers are equal to 2.19Å and 2.06Å, respectively, and agree with 2.01 Å and 2.04 Å obtained with the use of
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LEED, as well as 2.11 Å and 2.11 Å revealed from DFT calculations [159]. It should be mentioned that also different relative values of the anisotropy are most likely associated with
however, requires further verification.
5. Conclusions
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different bond lengths, which may serve as an indication of interatomic distances. This,
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Due to the prevalent focused forward scattering of primary electron beam of kinetic energies above 500 eV DAES and DEPES experiments provide information about the crystallinity of the first few layers at solid surfaces as well as about the local bond geometry of adsorbed
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atoms, similar to XPD. DAES and DEPES experiments can be carried out in a standard UHV
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chamber equipped with a simple RFA analyser and a sample manipulator which enables a precise polar and azimuthal rotation of the sample. For a chosen angle of polar (azimuthal) incidence of the primary electron beam the total current of emitted Auger and elastically backscattered electrons is recorded within the acceptance cone of the RFA analyser. Using a lock-in amplifier any variation of this total current as a function of the (ϴ,φ) orientation of the sample surface is discriminated from the isotropic background and represents the desired data. The angles ϴ and φ associated with these characteristic directions are simply read out from the manipulator. Due to the limited mean free path length of electrons in solids and the
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DAES and DEPES powerful sources of quantitative information about the crystallinity of solid surfaces and adsorbed layers on them. Thus, a simple classical RFA analyser, available in every surface science laboratory, can be used not only to investigate the long-range surface
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order by means of LEED patterns, and to study the composition and growth mode of surface layers by means of AES, but may simultaneously serve as detector for local bond geometries
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at surfaces by performing DAES and DEPES measurements.
Acknowledgments
We thank the Universty of Wrocław for the financial support under the 1010/S/IFD project.
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We acknowledge prof. Stefan Mróz and prof. Klaus Wandelt for numerous discussions. We would like to thank Michał Jurczyszyn, Andrzej Miszczuk, and Zbigniew Jankowski for fruitful cooperation and technical support. MS computations were carried out in the Wrocław
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Centre for Networking and Supercomputing (www.wcss.wroc.pl).
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Figure captions
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Figure 1. (a) Detection circuit for DEPES and DAES measurements using an RFA analyser. (b) Rotation of the sample with respect to the polar (within the sample surface) and azimuthal
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(perpendicular to the sample surface) axes. The polar angle (θ) was changed between -θmax and θmax in steps of ∆θ=0.25º. The azimuthal angle (ϕ) was changed between 0º and 180º in steps of ∆ϕ=2º. Adopted with permission from [59].
55
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Figure 2. Scattering of an electron plane wave e ikr with the wave vector k, representing
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primary electrons, at the atomic potential. f (k ,θ S ) is the scattering factor and θ S is the
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scattering angle. Angular dependence of f (k ,θ S ) shown as a polar plot.
Figure 3. f (k , θ S ) and phase of the scattered wave as a function of the scattering angle θ S 2
for Cu at different electron energies. Because of high electron energies used in DEPES, in comparison to LEED, partial waves up to the angular momentum l=40 were taken into
56
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backscattering of incoming electrons, respectively.
Figure 4. f (k , θ S ) and phase of the scattered wave as a function of the scattering angle θ S
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2
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for O, Cu, and Pt scattering atoms at electron energy 1000eV.
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Figure 5. Scattering geometry of primary electrons striking the crystalline solid used in single scattering cluster (SSC) calculations. Please note that at electron energies in the range of 0.5-
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2.0keV used in DAES and DEPES θ≈θ’ and k≈k’ is assumed.
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ACCEPTED MANUSCRIPT Figure 6. The model applied in MS calculations, where s defines the highest scattering order, k is the wave vector of primary electrons, aj1, …, aj(s-1) represent vectors, which describe the relative positions of scattering atoms in a cluster, and ajS describes the position of an emitter
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with respect to the sth scatterer.
Figure 7. Volume of a cluster determined by the radius Rmax expressed in units of the
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inelastic mean free path λ. Adopted with permission from [59].
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Figure 8. (a) Experimental DEPES polar profile I(θ) recorded for Cu(111) along the
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[112] − [1 1 2] azimuth at Ep=1.2 keV. (b) Visualisation of the scattering process of primary electrons in the crystalline sample. Two incidence beam directions parallel (left hand side)
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and not parallel (right hand side) to the close packed rows of atoms of the fcc(111) sample are
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shown. Adopted with permission from [50].
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Figure 9. Experimental DEPES polar profiles I(θ) recorded for Cu(111) along the
[1 1 2] − [112]
azimuth at different primary electron beam energies Ep. Adopted with
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permission from [40].
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[
] [ ]
(66eV) Auger transition along the 1 1 2 − 112 azimuth at different primary electron beam
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energies Ep. Adopted with permission from [40].
Figure 11. DAES (MVV Auger transition, 66eV) and DEPES polar profiles I(θ) recorded for
[
]
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Cu(001) along the [110] − 1 1 0 azimuth at primary electron beam energies Ep=0.8, 1.0, and 1.2 keV. The signal anisotropy defined as A=(Imax-Imin)/Imax, where Imax and Imin represent the maximal and minimal signal within the polar scan, is given on the left hand side of each profile. Adopted with permission from [70].
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Figure 12. Experimental DAES (MVV Auger transition, 66eV) and XPD polar profiles I(θ)
[ ] [
]
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recorded for Cu(111) along the 112 − 1 1 2 azimuth at more or less similar energies of the scattered electrons, in DAES primary electrons at energies 800 eV, 1200 eV, 1500 eV and in
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XPD energies of emitted photoelectrons 807 eV, 1178 eV, and 1617 eV. The signal anisotropy values are given on the left hand side. Adopted with permission from [69].
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Figure 13. Experimental DEPES polar profiles I(θ) (lower panel) obtained for Cu(001) along
[
]
the [110] − 1 1 0 azimuth at different primary electron beam energies and corresponding theoretical profiles (upper panel) obtained using the SSC theory. The signal anisotropy is indicated on the left hand side of each polar profile. Adopted with permission from [70].
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Figure 14. Comparison of experimental (red) and theoretical (black) DEPES polar profiles
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I(θ), the latter obtained with the use of the SSC theory, for Cu(001), Cu(111), and Cu(110)
[
]
[
] [ ]
[ ]
along the 1 1 0 − [110] , 1 1 2 − 112 , and [001] − 00 1 azimuths, respectively. For all DEPES profiles the incident electron beam strikes the Cu(001), Cu(111), and Cu(110) samples along the (1 10) plane (Fig.15). For each profile the signal anisotropy is given on the left hand side. Adopted with permission from [48].
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Figure 15. The cut of the fcc structure along the (1 10) plane with indicated atomic
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dashed lines.
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directions. The (001), (111), and (110) planes perpendicular to the paper plane are denoted by
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Figure 16. DEPES polar profiles I(θ) recorded for the Cu(111) substrate along the at different Ag coverages from 1ML till 12 ML at Ep=1.0 keV.
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[1 1 2] − [112] azimuth
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Adopted with permission from [40].
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Figure 17. Ball models of an fcc structure at the adsorbate/substrate interface indicating the growth of an unrotated adsorbate domain (a) exhibiting a CBA/CBA stacking sequence along the surface normal, and an adsorbate domain rotated by 180º (b) associated with the CAB/CBA stacking sequence. Black and grey circles represent the substrate and adsorbate
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atoms, respectively.
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ACCEPTED MANUSCRIPT Figure 18. R-factor values obtained for experimental and theoretical DEPES profiles at Ep=0.8keV. The best fit at Rmin obtained for n1=75% and n2=25% populations of rotated and
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unrotated domains, respectively. Adopted with permission from [4947].
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Figure 19. Experimental DEPES polar profile I(θ) (lower curve) recorded for Ag/Cu(111) at
[
] [ ]
12ML coverage along the 1 1 2 − 112 substrate azimuth and Ep=0.8 keV. Theoretical
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profile (upper curve) obtained with the use of the SSC theory for the best fit at n1=75% and n2=25% populations of rotated and unrotated Ag domains, respectively (Figs.17, 18). Signal anisotropy is given on the left hand side of each profile. Adopted with permission from [49].
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Figure 20. Experimental (a) and theoretical (b) DEPES stereographic intensity plots I(θ,ϕ) obtained for a copper monocrystal (111) at Ep=1.5 keV. Stereographic projection of directions in an fcc(111) monocrystal (c). The area surrounded by the dashed line in (c) indicates incidence beam directions (θ ranges from -72º to 72º) used in (b). In (a) θ ranges from -72º to 70º. Adopted with permission from [59].
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Figure 21. Experimental and theoretical DEPES maps I(θ,ϕ) for Cu(111) at Ep=0.6, 1.2, and 1.8 keV. The intensities within the area surrounded by the dashed circle on the experimental
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permission from [112].
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plot at 0.6 keV (θmax=60°) were used to calculate the contrast for each map. Adopted with
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Figure 22. Calculated contributions of the 1st (a), 2nd (b), 3rd (c), 4th (d), 5th (e), and 6th (f)
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layers to the DEPES signal from Pt(111) at Ep=1.2 keV. The intensity maxima are associated
[
] [ ]
with rows formed by atoms above the considered layer of emitters (Fig.8b). The 1 1 2 − 112 azimuth is indicated by dashed lines (Fig.20c).
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Figure 23. Convergence factor as a function of the scattering order calculated for DEPES profiles obtained for Pt(111) at different primary electron beam energies. The convergence
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order s.
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factor (Eq.(18)), calculated for Is(θ) and Is-1(θ), is shown for the higher considered scattering
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Figure 24. Convergence factor as a function of Rmax value (Fig.7) at different energies of primary electrons Ep. The Rmax value is expressed in units of the inelastic mean free path. The ordinate was calculated for two DEPES intensities obtained for subsequent values of Rmax
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higher Rmax value.
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with 0.1 increments. The convergence factor is indicated at the abscissa corresponding to the
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Figure 25. Convergence factor as a function of the number of layers in Pt(111) considered in MS calculations at Ep=1200eV. The ordinate was calculated for two DEPES intensities
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obtained for consecutive number of layers. The convergence factor is indicated at the abscissa
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corresponding to the larger number of layers.
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Figure 26. Theoretical DEPES maps I(θ,ϕ) obtained for Pt(111) at Ep=1.2 keV and different
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averaging ranges ∆θ around the incidence beam direction: a) 0º, b) 1º, c) 3º, c) 5º.
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Figure 27. Experimental DEPES (a) and DAES (Mo MNN Auger transition, 190 eV) (b) distributions recorded for Mo(110). Theoretical DEPES (c) and DAES (d) maps obtained with the use of the MS formalism for Mo(110). Stereographic projection of directions in a
77
ACCEPTED MANUSCRIPT bcc(111) monocrystal (e). The dashed line surrounds the incidence beam directions within the range of polar angles θ from -80º to 80º used in (a), (c), (d), and (f). In (b) θ ranges from -80º to 75º. Experimental DAES distribution (C KLL Auger transition, 275 eV) for trace amounts of carbon on Mo(110) (f). All DEPES and DAES distributions are presented at the primary
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electron beam energy Ep=1.8 keV.
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[ ] [
]
Figure 28. (a) Side view of an fcc(111) monocrystal along the 112 − 1 1 2 azimuth. Because of the ABCABC stacking sequence the terrace termination does not influence the contribution of the [110] , [111] , [112] , [114] , and [001] directions to DEPES intensities. (b)
[
] [
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Side view of an hcp(0001) monocrystal along the 10 1 0 − 1 010 azimuth. In view of the
[
] [
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ABAB stacking sequence along the surface normal the contribution of the 10 1 2 , 1 011
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[
] [
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and 10 1 1 , 1 012 directions to the DEPES signal depends on the terrace termination.
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Adopted with permission from [59].
Figure 29. (a) Theoretical DEPES distribution I(θ,ϕ) for Ru(0001) and Ep=1.3 keV calculated for A terminated terrace (Fig.27b). (b) Stereographic projection for an hcp(0001)
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ACCEPTED MANUSCRIPT monocrystal. The dashed line surrounds the area of incidence electron beam directions available in experiment (the polar angle θ ranges from -78º till 78º). (c) Experimental DEPES plot recorded for Ru(0001) and Ep=1.3 keV. (d) The calculated DEPES distribution for the best fit obtained during an R-factor analysis (Fig.29) of experimental and theoretical maps at
[
] [
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nA=48,7 % and nB=51,3 % populations of A and B terminated terraces, respectively. e)
]
DEPES polar profile recorded for Ru(0001) along the 0 1 10 − 01 1 0 azimuth and polar plot
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recorded for polycrystalline Fe. Adopted with permission from [59].
Figure 30. R-factor calculated for experimental and theoretical DEPES distributions at Ep=1.6 keV as a function of population nA and nB of A and B terminated terraces of a Ru(0001) surface. Different sources of phase shifts were used to obtain theoretical DEPES
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Adopted with permission from [59].
Figure 31. Experimental anisotropy distribution A(θ, φ ) for Gr/Ru(0001) at 1.2keV.
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Figure 32. (a) Experimental DEPES distribution I(θ,ϕ) recorded for Ru (10 1 0 ) at Ep=1.2 keV. (b) Corresponding theoretical DEPES plot obtained with the use of the MS theory. (c) Stereographic projection of a (10 1 0) terminated hcp monocrystal. The dashed line indicates the range of incidence angles available in experiment (θ: from −73° to 73°,ϕ: from 0° to
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180°). (d) Side and top view of an hcp(10 1 0) structure. Adopted with permission from [50].
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Figure 33. Experimental DEPES stereographic plot I(θ,ϕ) at Ep = 1.5 keV and a coverage
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equivalent to about 7 BL of Cu on Ru (10 1 0 ) before (a) and after (b) subtraction of the
[
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background. The polar profiles are taken along the 12 10 - 1 2 1 0 azimuth. Adopted with
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permission from [110].
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Figure 34. Ball model of Cu layers on Ru (10 1 0 ). Violet rings indicate two most probable adsorption sites of copper forming Cu (111) islands on the second pseudomorphic Cu (10 1 0 )
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bilayer. The arrows show the directions within the hcp(10 1 0) and fcc(111) planes. Adopted
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with permission from [110].
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Figure 35. (a) DEPES distribution I(θ,ϕ) recorded at Ep=1.2 keV and 7 BL of Cu on
Ru (10 1 0) after the background subtraction. (b) R-factor calculated for different contributions
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of the experimental plots for: hcp(10 1 0) structure, unrotated fcc(111)0° and rotated fcc(111)180° Cu domains. (c) The computed DEPES distribution obtained for experimental component maps at the minimum of an R-factor at m=24%, p=41%, and q=35 %. The same
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analysis performed for the theoretical component plots is shown in (d) and (e). The best fit for
[110].
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theoretical maps obtained at m=19%, p=46%, and q=35 %. Adopted with permission from
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Figure 36. (a) Experimental DEPES plot I(θ,ϕ) measured for 1ML of Pt on Cu(111) and Ep=1.1keV. Theoretical DEPES maps I(θ,ϕ) for 1ML of Pt on Cu(111) at: (b-c) A - hollow
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site, (d-e) B - hollow site, (f-g) on-top (C-site), (h-i) bridge site (three mutually rotated Pt domains considered), (j-k) best fit (Fig.38) obtained for two mutually rotated domains at A
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and B adsorption sites shown in Fig.37. The theoretical distributions were calculated for not dissolved (not diss.), and dissolved (diss.) Pt in the first Cu layer. A mixed layer in the form of the Cu3Pt alloy and the presence of a topmost Pt monolayer was considered. The background subtraction procedure was applied for each distribution with the maximum polar angle θmax= 76°. Adopted with permission from [141].
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Figure 37. Ball models of 1ML of Pt on Cu(111) taken into account in MS calculations. (a) A-hollow site. (b) B-hollow site. (c) On-top (C-site). (d) Bridge site (for clarity only one from three possible adsorbate domains is presented). (e) A-hollow site configuration on the first Cu3Pt alloy layer showing the p(2×2) structure at the Pt/Cu interface. All configurations of adsorbate atoms on not dissolved and dissolved Pt were taken into account in calculations of DEPES distributions. The same models (a-c) were used to the inverse system Cu/Pt(111). Adopted with permission from [141].
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Figure 38. R-factor values at different domain populations ni with Pt atoms at A and B, A and bridge, as well as A and on-top adsorption sites at 1ML of Pt on Cu(111) (Fig.37). The best correspondence between theoretical and experimental data is obtained for the coexistence of domains A and B of nA=58% and nB=42% populations when dissolved Pt in Cu is taken into account. Adopted with permission from [141].
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Figure 39. (a) Experimental DEPES anisotropy distribution A(θ,ϕ) recorded for 1 ML of Cu
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on Pt(111) after Cu adsorption at T=330K. Theoretical DEPES anisotropy plots for 1 ML of Cu calculated for: (b) A hollow site layer, (c) B hollow site layer, (d) on-top (C-site) layer, and (e) misfit Cu(13×13) overlayer on Pt(12×12). R-factor values are indicated. Each DEPES distribution obtained at Ep = 1.1 keV. Adopted with permission from [147].
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Figure 40. (a) Experimental DEPES anisotropy plot A(θ,ϕ) for 1 ML of Cu on Pt(111) after
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Cu adsorption at T=450K. Theoretical DEPES anisotropy distributions for 1 ML of Cu simulated for: (b) A hollow site layer, (c) B hollow site layer, (d) on-top (C-site) layer, and (e)
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misfit Cu(13×13) overlayer on Pt(12×12). R-factor values are given. Each DEPES distribution obtained at Ep = 0.8 keV. Adopted with permission from [147].
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Figure 41. Ball model of Cu misfit monolayer on Pt(111). Models of A and B hollow sites, as well as on-top (C-sites) were considered as for the inverse adsorption system Pt/Cu(111)
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shown in Fig.36. Adopted with permission from [147].
[ ] [
Figure 42. Side view of an unrelaxed (a) and relaxed (b) surface along the 112 − 1 1 2
]
azimuth of an fcc(111) monocrystal. An outward relaxation of the first layer results in a displacement of the interatomic directions between the first and second layer, which leads to the shift of DEPES maxima. Adopted with permission from [116].
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Figure 43. Experimental and theoretical DEPES polar profiles for Pt(111) along the
[112] − [1 1 2] azimuth at Ep = 0.8 keV. Simulated polar scans were obtained taking into account: no surface relaxation (∆1,2 = 0%, blue dashed line), contraction of topmost layer by
∆1,2 = –10% (black solid line), and expansion of topmost layer by ∆1,2 = +10% (red solid line). The corresponding shift of maxima is explained in Fig.42. Adopted with permission from [116].
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Figure 44. Values of an R-factor calculated for experimental and theoretical DEPES
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distributions for Pt(111) at Ep = 1.4 keV. Theoretical results were obtained for different relaxation ∆1,2 values of the topmost layer considered in MS simulations (Fig.41). Adopted
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Figure 45. R-factor values obtained for experimental and theoretical DEPES plots for a
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pseudomorphic 1ML of Cu on Pt(111) at Ep = 1.4 keV. Theoretical data were obtained for the Pt(111) surface covered by a pseudomorphic 1 ML of Cu at different relative separation ∆0,1
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[116].
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of the Cu layer taken into account in MS calculations (Fig.42). Adopted with permission from
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Figure 46. (a) Model used in MS simulations. An oxygen atom (red) and three ruthenium
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atoms (black) at different θad angles are shown. (b), (c), (d) DEPES intensity I(θ,ϕ) and anisotropy A(θ,ϕ) distributions calculated at θad=10°, 30°, and 50°, respectively. Adopted
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Figure 47. (a) Experimental DEPES anisotropy plot A(θ,ϕ) obtained from the clean
Ru (10 1 0) substrate and after the formation of the (2 × 1)p2mg oxygen structure at Ep = 1.2 keV. The orientation of the Ru (10 1 0 ) substrate underneath the oxygen monolayer is the same as in Fig.32. The polar angle θ ranges from −73° to 73°. The maxima (dashed black circles)
[
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observed at θ = ±26° along the 000 1 − [0001] azimuth reveal the interatomic axes formed between Ru and O atoms. (b) Model of the (2 × 1)p2mg oxygen structure on Ru (10 1 0 ) . Adopted with permission from [50].
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Figure 48. Experimental DEPES profiles I(θ) (upper panel) recorded for clean (black solid
[0001] − [0001]
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line) and oxygen covered (red dotted line) Ru (10 1 0 ) substrate at Ep = 1.2 keV along the substrate azimuth. Anisotropy profiles A(θ) (lower panel) along the
[0001] − [0001] (solid black line) and [1210] − [1210] (doted blue line) azimuths of Ru (10 1 0).
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The anisotropy maxima at θ = ±26° are noted only along the [0001] − [0001] azimuth. Adopted
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Figure 49. Anisotropy profiles A(θ) along the [0001] − [0001] azimuth of Ru (10 1 0 ) obtained at increased oxygen coverage. The applied oxygen doses are given in Langmuirs (L).
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Figure 50. The scheme used to determine the position of the oxygen atom within a unit cell. At defined (Y,Z) coordinates of an adsorbate atom the direction, read out from the
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ACCEPTED MANUSCRIPT experimental anisotropy distribution marked by the blue dashed line, passes a substrate atom by a certain distance D. The Gaussian function of D is used as a fitting parameter of the (Y,Z) position with respect to the ruthenium atoms. For the sake of simplicity only two directions along the [0001] − [0001] substrate azimuth are
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indicated. Adopted with permission from [158].
Figure 51. The coordinates (Y,Z) of an adsorbate atom determined with the use of the fitting procedure shown in Fig.50 along pI and pI’ (a) and pII (b) planes (Fig.47b). The maxima in (a) indicate the coordinates of oxygen atoms simultaneously in pI and pI’ planes. The maxima at corners in (b) show the position of substrate atoms (for details see the text). Adopted with permission from [158].
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DOI:
https://doi.org/10.1016/j.surfrep.2019.05.002
Reference:
SUSREP 469
To appear in:
Surface Science Reports
Received Date: 17 January 2019 Revised Date:
14 April 2019
Accepted Date: 15 April 2019
Please cite this article as: I. Morawski, M. Nowicki, Directional Auger and elastic peak electron spectroscopies: Versatile methods to reveal near-surface crystal structure, Surface Science Reports, https://doi.org/10.1016/j.surfrep.2019.05.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Directional Auger and elastic peak electron spectroscopies: Versatile methods to reveal near-surface crystal structure
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I. Morawski, M. Nowicki*
Institute of Experimental Physics, University of Wrocław,
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pl. M. Borna 9, 50-204 Wrocław, Poland
Abstract
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A review of directional Auger (DAES) and directional elastic peak electron spectroscopy (DEPES) for investigations of the short range order within a near-surface region, similar to XPD, is presented. The application of these techniques requires nothing more than a retarding field analyser (RFA), commonly applied for the observation of low energy electron
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diffraction (LEED) patterns and Auger electron spectroscopy (AES) measurements, for in depth structural investigations associated with the short range order within a near-surface region. The physical principles, experimental set-up, as well as examples of experimental and
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theoretical results, the latter obtained with the use of single scattering cluster (SSC) and multiple scattering (MS) calculations adopted for primary electron plane wave, are shown.
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The scattering geometry and details concerning the scattering events of primary electrons in crystalline solids described by SSC and MS approximations are presented. Furthermore, some issues related to computation parameters such as: maximal scattering order, the maximum radius around the emitter, the number of cluster layers, and the averaging range considered in the calculations are also addressed. The presentation of the data obtained for clean and covered substrates in the form of polar profiles and stereographic intensity distributions enables the straightforward identification of the crystalline structure within the first few
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ACCEPTED MANUSCRIPT sample layers. The data presented in the form of anisotropy maps enable the identification of interatomic axes formed between substrate and adsorbate atoms at the interface. The contribution of different sample layers to the final DEPES signal is discussed. The comparison of DAES results with those obtained by means of x-ray photoelectron diffraction
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(XPD) is also presented. The qualitative and quantitative data analysis, the latter achieved by the comparison of experimental data with theoretical results by means of an R-factor analysis, is shown. The application of DAES and DEPES enables the characterization of the crystalline
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structure of adsorption systems from one monolayer (1ML) up to thicknesses of the adsorbate limited by the inelastic mean free path of the registered electrons. Exemplary results are
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presented for adsorption systems, where the adsorbate and the substrate crystallize in the same (Ag/Cu, Pt/Cu, Cu/Pt) and in different (Cu/Ru) structures. The influence of the large unit cell of graphene formed on Ru(0001) on measured DEPES intensities is also shown. The detailed analysis of these results enables an identification of the short range order of atoms within the
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near-surface region, of adsorbate domains exhibiting different orientation with respect to the crystalline substrate, the determination of the domain populations, the relaxation and termination of the surface, the specific adsorption sites of adsorbed atoms, as well as the
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positions of atoms within a unit cell and their bond lengths (e.g. O Ru(10 1 0) ).
Keywords: electron spectroscopies, retarding field analyser (RFA), directional Auger electron spectroscopy (DAES), directional elastic peak electron spectroscopy (DEPES), crystalline structure, short range order, scattering of primary electrons, adsorbate growth, single scattering cluster (SSC) and multiple scattering (MS) calculations, adsorption sites, relaxation, surface termination, adatom coordinates, bond lengths.
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ACCEPTED MANUSCRIPT * corresponding author e-mail: [email protected]
Contents
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1. Introduction ………………………………………………………………………… 4 2. Experiment …………………………………………………………......................... 9
3. Theory ………………………………………………………………………………11
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3.1. Single scattering cluster (SSC) formalism ………………………………..14
3.2. Multiple scattering (MS) ………………………………………………….16
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3.3 Rmax ……………………………………………………………………….. 20 3.4. Averaging range ………………………………………………………….. 20 4. Results and discussion ……………………………………………………………. ...20 4.1. DAES and DEPES polar profiles ………………………………………. …21
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4.1.1. Cu(111), Cu(001), and Cu(110) ………………………………… 21 4.1.2. Comparison of DAES and XPD ………………………………… 24 4.1.3. Comparison of experimental and theoretical DEPES profiles ….. 25
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4.1.4. Ag/Cu(111) ………………………………………………………27 4.2. DEPES stereographic distributions ……………………………………….. 30
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4.2.1. Cu(111) ………………………………………………………….. 30 4.2.2. Contribution of layers and parameters of calculations – Pt(111) .. 31 4.2.3. Mo(110) …………………………………………………………. 34 4.2.4. Ru(0001) ………………………………………………………… 35 4.2.5. Graphene on Ru(0001) ………………………………………….. 37 4.2.6. Cu / Ru (10 1 0 ) …………………………………………………… 37
4.2.7. Pt/Cu(111) ……………………………………………………….. 41
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ACCEPTED MANUSCRIPT 4.2.8. Cu/Pt(111) ……………………………………………………….. 44 4.2.9. Determination of surface relaxation – Cu/Pt(111) ………………. 46 4.2.10. Determination of adatom coordinates - O Ru (10 1 0) ………….. 47 5. Conclusions ………………………………………………………………………….. 52
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Acknowledgments ……………………………………………………………………… 53 References ……………………………………………………………………………… 54
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1. Introduction
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The understanding of physicochemical processes taking place on solid surfaces requires the detailed knowledge about the chemical composition of surface layers, the growth mode of adsorbates, as well as the crystalline structure of surfaces and the order within a near-surface region. Therefore, it is extremely important to determine the structure of deposited layers
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already from the first stages of nucleation till the growth of a thicker adsorbate layer. The adsorbate growth is determined by the relation between the surface free energies of adsorbate γA, substrate γB, and interface γI [1,2]. Depending on the γ values a monolayer by monolayer
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(Frank-van der Merwe (FM)) growth mode, the formation of three dimensional (3D)
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adsorbate islands (Volmer-Weber (VW) growth mechanism), and an intermediate mode with the completion of the first monolayer followed by the growth of 3D islands (StranskiKrastanov (SK) growth) can be observed. The widely used method, which provides information about the so called long range order of surface atoms, determined by the coherence radius reaching few hundreds Å, is low energy electron diffraction (LEED) [3,4,5]. The observed diffraction pattern reflects the reciprocal lattice of the investigated surface. In turn, the so called short range order of atoms can be revealed by the application of x-ray photoelectron diffraction (XPD) and Auger electron
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ACCEPTED MANUSCRIPT diffraction (AED) [6,7,8,9,10,11,12,13,14,15,16,17,18]. Using the emitted photoelectrons [19,20,18] in XPD and Auger electrons [21,22,23] in AED both methods serve as a very powerful chemically sensitive tools for the determination of the order of nearest and next nearest neighbour atoms and molecules within a unit cell [24,25]. XPD and AED base on the
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scattering process of photo- and Auger electrons, respectively, of kinetic energies Ekin above 500 eV at atomic potentials, which results in the anisotropic distribution of the emitted electrons. The so called forward scattering [26,27] of emitted electrons of Ekin > 500 eV
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results in an enhancement of the recorded intensity of photoelectrons (XPD) and Auger
measured angular distributions [27].
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electrons (AED) along the direction of densely packed rows of atoms which shows up in the
The strong electron scattering at atomic cores is a universal phenomena, which concerns outgoing (emitted), as well as incoming (incident) electrons (independently on the direction of their propagation in solids). Historically, the experimental evidence for the scattering
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processes of primary electrons of energies above the LEED regime (several hundred eV) in crystalline solids was the observation of the brightness enhancements of the luminescent screen revealed while rotating the sample, when the direction of the primary electron beam
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coincides with densely packed atomic rows and planes of the sample [28]. Very similar effects were observed by the recording of Auger and elastically backscattered electrons as a
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function of the incidence beam direction [29,30,31,32,33,34]. The increase of the recorded intensity was observed in the case of a parallel alignment of the primary electron beam with densely packed atomic rows in the crystalline samples. This dependence is actually a nuisance in quantitative Auger analysis [35] of the concentration of different species in solids and the determination of the adsorbate coverage, because an Auger signal may change by 20%-30% by simply changing the incident beam direction. Moreover, this dependence concerns, in principle, also all secondary electrons emitted from crystalline samples including elastically
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ACCEPTED MANUSCRIPT and not elastically scattered electrons, the latter associated with e.g. plasmon excitations and ionisation losses [36,37]. It is this angular dependence, however, which in turn can be used to determine the sample crystallinity within the near-surface region with the use of different spectrometers [29,34,36,37,38, 39,40,41,42,43,44].
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The choice of the experimental geometry enables the observation of the scattering events of primary and secondary electrons separately [34]. The application of a small aperture spectrometer, such as a hemispherical analyser (HA) [18,45,46], enables the detection of
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electrons emitted in a small (few degrees) solid angle around the chosen direction. Therefore, a rotation of the sample enables the recording of angular distributions of emitted photo- and
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Auger electrons, which is applied in XPD and AED, respectively. The intensity maxima of the recorded signal observed along the direction of the densely packed rows of atoms make possible the identification of the near-surface crystalline structure of samples in a very straightforward way.
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The application of a large acceptance angle spectrometers, such as a retarding field analyser (RFA), commonly used for LEED pattern observations and Auger electron spectroscopy (AES) [22,23] measurements, in turn, integrates the angular distribution of emitted electrons
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within a large solid angle. Therefore, the contribution of the focussed scattering events of emitted Auger electrons, as well as elastically backscattered electrons is considerably
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reduced. Yet, the rotation of the sample with respect to the fixed axis of the electron gun and the recording of the signal of secondary electrons emitted from crystalline samples results in the observation of current modulations caused by the primary electron beam scattering effects in solids. The so called directional Auger (DAES) and directional elastic peak electron spectroscopy (DEPES) based on this effect enable structural investigations of the first few atomic layers of clean substrates and adsorption systems [40,42,47,48,49,50]. In DAES and DEPES the observed intensity maxima of Auger and elastically backscattered electrons,
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ACCEPTED MANUSCRIPT respectively, indicate the directions of densely packed rows of atoms in crystalline solids. Due to the forward scattering effect of primary electrons striking the sample the electrons are scattered along the incident direction. Depending on the mutual orientation of the incoming electron beam and the crystalline substrate the incident electrons strike the sample along
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densely or rarely occupied directions. Thus, the illumination of a given atom depends on the direction of the incidence beam. If the collimated incident beam is aligned with the direction of densely packed rows of atoms the electrons are focused (concentrated) onto atoms along
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these rows, which results in an increase of the number of elastic, as well as inelastic scattering events. The former leads to the increase of the current associated with elastically
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backscattered electrons and the latter with the increase of the probability of electron hole creation, which results in the enhancement of Auger electron emission. If, however, the primary electron beam strikes the sample along not densely packed directions there are no near atoms in forward direction, which leads to a reduction of the recorded signal. In view of
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the fact that the forward scattering is a very local effect, which extends to nearest and nextnearest neighbour atoms within a unit cell only, the information about the crystalline structure concerns the short range order, as in XPD and AED. The limited value of the inelastic
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electron mean free path and multiple scattering events, leading to a defocusing of electrons at energies in the range of 0.5-2.0 keV, cause that the information depth about the crystalline
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order concerns first few atomic layers. In DAES and DEPES first the scattering of primary electrons and then the emission of Auger and elastically backscattered electrons takes place, respectively. Therefore, both methods can be considered as time reversals of XPD, where first emission and then scattering of emitted photoelectrons occurs. In DAES and DEPES, however, no photons are associated with emitted Auger and elastically backscattered electrons. DAES and DEPES, thus, extend the applicability of an RFA analyser [51], which in spite of its limited resolution (∆E/E=0.01) becomes a very useful experimental tool. It can be
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ACCEPTED MANUSCRIPT used not only for investigations of the long range order (LEED) [ 52 , 53 , 54 ], chemical composition and growth mode of adsorbates by recording of Auger signals (AES) [23] from the adsorbate and the substrate during the continuous adsorption [55,56,57,58], but also of the short range order within the first few atomic layers of crystalline samples [40,42,47,48,49,50].
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The detection circuitry is uncomplicated and easy to assemble by each researcher familiar with electron spectroscopy methods and significantly facilitates experiments by changing the detection configuration and the measuring parameters. The direct measurement of the current
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maxima, associated with elastically backscattered electrons (DEPES) and Auger electrons (DAES) as a function of the incidence direction of the primary electron beam enables the
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straightforward determination of crystallographic directions of the investigated samples, as in XPD and AED. Moreover, the advantage of an RFA analyser concerns the continuous change of the primary electron beam energy Ep from the LEED regime till 2.0 keV, which makes experiments possible similar to those using a synchrotron radiation source. The dependence of
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the recorded signal on the primary electron energy at fixed incidence beam directions also contains information about the scattering geometry. The main idea of the present paper is to show how easily valuable crystallographic
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information can be extracted from simple experiments with the use of a standard experimental set-up available in almost every ultra high vacuum (UHV) system equipped with a relatively
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inexpensive and not sophisticated RFA spectrometer. This makes these experiments possible without any extra investment in the existing apparatus. The paper is organized as follows. First, the experimental details about DAES and DEPES measurements are presented. Then, the single scattering cluster (SSC) and multiple scattering (MS) approximations, describing the scattering events of the primary electron beam in crystalline solids, are presented. Next, a comparison of experimental DAES results with XPD data is shown. Finally, the comparison of experimental and theoretical results, the latter
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ACCEPTED MANUSCRIPT obtained with the use of the SSC and MS formalisms, are presented for different substrates and adsorbates exhibiting face centred cubic (fcc), body centred cubic (bcc), and hexagonal close packed (hcp) structures. The analysis of the experimental and theoretical data concerns i) the short range order of the first few atomic layers of the crystalline samples, ii) the
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contribution of individual atomic layers to the signal and, thus, the sensitivity of both methods, iii) the identification of adsorbate domains of different orientation with respect to the substrate, and the determination of their populations, iv) the identification of surface
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relaxation and termination, and v) the determination of adsorption geometries at the adsorbate-substrate interface concerning adsorption sites and positions of atoms within a unit
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cell, as well as bond lengths. In this work we show examples of DAES and DEPES investigations and refer to results published elsewhere.
2. Experiment
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Both experimental methods, DEPES and DAES, rely on the application of a large acceptance angle spectrometer. Therefore, the experiments were carried out in an UHV system equipped with a four grid RFA analyser (Fig.1) with an acceptance angle of about 110° [59], a precise
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sample manipulator, an argon sputtering gun, and adsorbate sources (Knudsen cells). The gas
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pressure during all measurements was lower than 1×10-8 Pa. The investigated samples were cleaned by repetitive cycles of Ar sputtering, annealing at elevated temperatures and flashing controlled by a thermocouple fastened at the sample edge, and, if necessary, by additional annealing in an oxygen atmosphere (Pt, Ru). The negative potential of the grids 2 and 3 (Fig.1) is given by the relation U = U 1 + U 0 cos(ωt ) , with U 1 and U 0 being a constant potential and the amplitude of the modulated potential, respectively, where the frequency ω is set by a generator. A signal amplification was obtained by the increase of the U 0 value, which was chosen to be in the range from 0.2V to 1V for DEPES, and in the range between 1.5V
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ACCEPTED MANUSCRIPT and 3V for AES and DAES measurements. AES was used to monitor the cleanliness of all samples. The recording of AES spectra and DAES profiles was performed in a differential dN(E)/dE mode of the RFA operation with the use of a Lock-in amplifier, by measuring the second derivative dI2(E)/dE2 of the collector current [51]. In the case of DEPES investigations
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the normal N(E) mode was used, where the first derivative dI(E)/dE of the collector current was recorded. Depending on the investigated system and the energy Ep the typical values of the primary electron beam current were in the range of 0.1-1 µA and few µA for DEPES and
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DAES respectively. In some cases the current below 0.1 µA can be used, which is, however, associated with the increase of the noise/signal ratio. In view of this fact DAES and DEPES
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methods can be applied to investigate metals, semiconductors, and strongly bound adsorbates such as chemisorbed oxygen, which do not undergo decomposition and desorption under the continuous electron bombardment.
The manipulator enables the annealing of the samples and precise rotation around two
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mutually perpendicular axes. The rotation of the sample around an axis within the sample surface ("polar axis"), enables the continuous change of the polar angle θ (Fig.1b) in the range from -θmax to θmax. The rotation of the sample around the surface normal ("azimuthal axis")
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(Fig.1b), allows the change of the azimuthal angle ϕ between 0º and 180º in arbitrary chosen
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steps ∆ϕ by researcher. Usually DEPES distributions were recorded for θmax =85° in steps of ∆θ=0.25º and ∆ϕ=2º, giving 61 380 measure points. In DAES and DEPES the Auger signal and the current of elastically backscattered electrons is recorded, respectively, as a function of the incidence angle of the primary electron beam at different beam energies Ep from 0.5keV till 2.0keV. The incidence angle of the electron beam was changed by the polar and azimuthal sample rotation. The DAES and DEPES results are presented in the form of polar profiles I(θ) or stereographic intensity distributions I(θ,ϕ). In order to present the data as stereographic plots the coordination transfer functions x=2tg(θ/2)sinϕ and y=2tg(θ/2)cosϕ were used. In the
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ACCEPTED MANUSCRIPT case of clean (111) surfaces of Cu and Pt monocrystals the symmetrization procedure of measured intensities was applied by the rotation of the I(θ,ϕ) recorded distribution by 60º and 120º and mirroring, according to the three-fold symmetry axis of the substrate, and averaging of signals. All intensities within each distribution were normalized with respect to the signal
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value at normal incidence (θ=0º). The intensities within each distribution were scaled by colour. In order to show the details of the intensity patterns related to crystalline structure of investigated sample a background subtraction procedure was applied [60]. The background in
(1)
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IBG = A⋅cos(B⋅θ) ,
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DEPES polar profiles was fitted by the cosine function of the polar angle θ:
where A and B are fitting parameters obtained by means of the least square analysis. The enhancement of signal changes within DEPES distributions under the influence of an adsorbed layer with respect to the signal from the substrate was obtained by the calculation of the signal anisotropy:
(I Ads−Sub − I Sub )
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A=
I Sub
,
(2)
where I Sub and I Ads − Sub represent intensities from the clean and adsorbate covered substrate at
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a given polar θ and azimuthal ϕ angle. The results were presented as anisotropy profiles A(θ)
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or stereographic anisotropy maps A(θ,ϕ), where the intensity maxima reflect changes of measured intensities caused by the adsorbate. Therefore, the anisotropy maxima reflect new interatomic directions formed between the adsorbate and the substrate atoms. In this way the geometry of the adsorption system already at 1ML coverage, assuming the FM growth mode, can be identified.
3. Theory
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ACCEPTED MANUSCRIPT In the literature different theoretical descriptions of electron scattering exist. The interpretation of the intensity patterns observed in scanning electron microscopy images [61,62] recorded at high electron energies in the range of tens of keV was possible by the consideration of the two-wave approximation [63] associated with channelling [64,65] and the
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Kikuchi effect [61, 66 , 67 ]. The intensity enhancements were associated with the Bragg reflections of the collimated electron beam passing through the atomic planes of a crystalline solid. Another approach used to describe the diffraction effects of the primary electron beam
SC
concerns the many-wave dynamic approximation [68,38]. At medium energies of electrons striking the sample in the range of 0.5-2.0 keV the enhancement of the Auger signal and the
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intensity of elastically backscattered electrons was observed when the primary electron beam passed “through” the densely packed rows of atoms as a result of the forward focusing effect [27] of the primary electrons. These effects were simulated by the use of single scattering cluster (SSC) [69,70,48] and multiple scattering (MS) approximations [71] in order to obtain
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theoretical DAES and DEPES polar profiles.
In the theoretical description of the scattering events of primary electrons different parameters need to be taken into account such as: the nature of the scattering atoms, the crystalline
EP
structure of the solid, lattice vibrations, the electron energy and its attenuation in the sample determined by the inelastic mean free path, as well as the incidence direction of the primary
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electron beam. These parameters serve as an input to calculate the wave field in a solid resulting from the coherent interference of the primary and scattered waves at different incidence angles and energies of the primary electron beam. The conditions of interference depend on the electron energy, the distance between atoms and the scattering angle, as well as on the atomic number Z. The scattering of an electron plane wave e ikr with the wave vector k, associated with primary electrons, at the atomic potential is schematically shown in Fig.2. The scattered wave in the
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ACCEPTED MANUSCRIPT form of a spherical wave eikr r is centred on the atomic core. The interference between the primary and the scattered waves leads to the enhancement of the wave amplitude along the forward direction (θS=0º). This well known forward scattering effect becomes significant at electron energies above 0.5 keV. According to the well known scattering theory described e.g.
a solid angle in which the particles are scattered and:
4π k2
∑ (2l + 1)sin l
2
δl =
4π Im{ f (k ,0 )} , k2
(3)
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σ (k ) =
SC
2
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in [3,5,13,14] f (k , θ S ) = dσ / dΩ is a differential scattering cross section, where Ω denotes
is the total elastic cross section, where δl represents the phase shifts for angular momentum l. f (k , θ S ) as a function of the scattering angle θS, where f (k ,θ S ) is the scattering factor, is 2
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shown together with the phase of the scattered wave for Cu at different electron energies in Fig.3 and for different scattering atoms and the same electron energy of 1000eV in Fig.4. In all cases f (k , θ S ) is large at small scattering angles, i.e. in the forward direction. The larger 2
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the energy of the incoming electrons and the larger the atomic number Z of the scattering atoms the forward scattering (θS=0º) becomes more effective. On the other hand,
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backscattering events (θS=180º) become significant at lower electron energies. An increase of the phase of the scattered wave is observed with increasing θS. Different scattering properties of scattering atoms with significantly different number Z can serve as an additional chemical contrast in measured and calculated intensities. Both the SSC and the MS formalism base on the same concept of electron scattering at an atomic potential in crystalline solids. In view of the fact that in our works we refer to both formalisms, the latter significantly expanded by functions, which take into account different
13
ACCEPTED MANUSCRIPT scattering orders and the real experimental geometry, in the following sections we describe both approximations separately.
3.1. Single scattering cluster (SSC) formalism
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To first approximation the scattering processes of primary electrons can be described by the assumption that the electron wave in a crystalline solid undergoes only single scattering at atomic potentials, as it was also applied for emitted photoelectrons and Auger electrons in
SC
XPD and AED [8,9,13,14,15], respectively. The scattering geometry for the incoming electron beam used in single scattering cluster (SSC) calculations is schematically shown in
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Fig.5. Note that in Fig.5 θ’ and k’ denote the polar angle and the wave vector of the primary electron beam in vacuum and θ and k denote these values in the sample. In the case of electron energies in the range of 0.5-2.0keV used in DAES and DEPES experiments θ≈θ’ and
k≈k’ is assumed. The incoming electrons are represented by the plane wave ψ 0 = e ikr with
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the propagation vector k, which is scattered by the scatterer j. The resulting wave field in a crystal depends on the coherent interference of the primary ψ 0 and scattered ψ j waves.
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Taking into account all scattering atoms in a cluster the final wave function at the emitter site
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r in a crystal can be written in the SSC approximation as a sum of ψ 0 and ψ j [69,70,48]:
ikd e j − ikd − r / λ cos θ − d j / λ Ψ (k , r ) = eikr e − rZ / λ cos θ + ∑ e j e Zj e f j (k , d j , T ) kd j j
.
(4)
In Eq.(4) the sum concerns all scatterers j in the solid and the attenuation of the unscattered primary plane wave along rZ/cosθ and rZj/cosθ paths, and scattered waves are taken into account. λ is the inelastic electron mean free path, θ is the incidence angle defined relative to
14
ACCEPTED MANUSCRIPT the surface normal, d j = r − r j defines the position of the scatterer j with respect to the emitter, T is the absolute temperature, and f j (k , d j , T ) is the scattering factor [72]. The latter factor involves the scattering amplitude, partial wave phase shifts calculated with the use of
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the muffin-tin approximation [3], and the curved character of the wave fronts at the emitter sites r [73]. The scattering factor can be written as [72]: ∞
f j (k , d, T ) = ∑ t lj (T )cl (kd j )(2l + 1) Pl (cos θ kd j ) .
(5)
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l =0
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Eq.(5) involves the scattering matrix tl j , which describes the scattering amplitude and vibrational properties of the scattering atom j [3], the polynomial factor cl that multiplies the asymptotic form of the spherical Hankel functions, the lth Legendre polynomial Pl , and the scattering angle θ kd j between vectors k and d j .
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The signal of Auger and elastically backscattered electrons in DAES and DEPES, respectively, integrated over the large acceptance angle Ω0 of the RFA analyser (Fig.5) is proportional to the sum of intensities of the incoming electrons over all emitters in the sample
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EP
weighted with the escape probability of emitted electrons A [74,69]:
r 2 r I (k ) = ∑ Ψ (k , rS ) A Z S λout
.
(6)
In Eq.(6) the damping of outgoing electrons along their way to the surface is governed by the distance of an emitter to the surface rZ and the value of the inelastic mean free path of emitted electrons λout. The factor A integrates the inelastic damping of emitted electrons
15
ACCEPTED MANUSCRIPT e − rZ / λout cos φ in a solid over all possible emission angles φ and to first approximation, can be written as [69]: − r ⋅t / λout ∞e Z = ∫ dt , t2 1
(7)
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r A Z λout
where the integration parameter t is equal to 1/cosφ.
Eqs. (4)-(7) enable to calculate DAES and DEPES profiles I(θ) and intensity distributions
SC
I(θ,ϕ) in the SSC approximation at different energies of the primary electron beam and emitted electrons by applying inelastic mean free path values λ and λout, respectively
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[75,76,77,78]. In the case of DEPES λout =λ. In DAES λout is associated with the emitted Auger electrons at energies significantly smaller than the primary electron beam, and in general λout < λ for Auger energies down to about 100 eV.
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3.2. Multiple scattering (MS)
Although the SSC approximation reflects the main intensity features observed in experimental
EP
DAES and DEPES data [48,49,69,70] the description of scattering processes taking place in a real system requires the consideration of different scattering orders of the primary wave,
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which is particularly desirable at electron energies above 0.5keV used in DAES and DEPES. Therefore, the multiple scattering (MS) approximation was developed [71] to describe scattering events of the primary electron beam, represented by a plane wave, in crystalline samples, which enables the calculation of theoretical DAES and DEPES distributions. In the literature the MS formalism is known to describe scattering events of secondary electrons, which are represented by spherical waves, such as emitted photoelectrons in XPD and Auger electrons in AED [79,80,81,82,83]. Multiple scattering events were also considered for the description of low energy electron diffraction [84,85].
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ACCEPTED MANUSCRIPT As in the SSC formalism, applied for DAES and DEPES, in the MS theory the small atom approximation [86,87] is used, where the atomic radius is considered to be small enough in order to make the curvature of the electron wave negligible. Similar to the SSC approach the wave field in a solid associated with the scattering events at atomic cores is calculated taking
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into account scattering properties of individual atom described by f (k ,θ S ) , the crystal structure, as well as the inelastic mean free path values associated with the electron energies. The MS approach requires, however, the consideration of different scattering orders in the
SC
final form of the wave function located at the emitter site. Therefore, taking into account all
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mentioned considerations the wave field at a site r in a crystal can be written as [71]:
(, , ) = (, ) + (, ) + (, ) + ⋯ + (, ) + ⋯ + (, ).
(8)
(, ) = ∙ represents the wave function of the primary electron, (, ), (1 ≤ p ≤ s),
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represents the wave function of electron which undergoes p consecutive scattering events before it reaches emitter site r. Index s denotes the highest scattering order considered in the MS approximation. According to the scattering model shown in Fig.6 each p-scattered wave
⋅ ⁄ ∑"#$
∑"#' … ∑"#* ⋅("#$ )"#' )⋯)"#*+ ( #$ ⁄ #' ⁄ … #* ⁄ + × /01 /01 /01 . #$ . #' . #* 2#$ ⁄ 2#' ⁄ 2#* ⁄ - 2 … 3 ( … + 4 4 … 4 "#$ "#$ "#' "#(*5$) "#* 2 2
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(, ) =
EP
component at the site r in the crystal can be expressed as follows [71]:
√
#$
(9)
#'
#*
where the sums concern all scattering atoms, N is the number of atoms in a cluster, 1 / N is the normalization factor, aj1, …, ajp are bond vectors, which define the relative positions of scattering atoms, e ik⋅r multiplied by ⋅("#$ )"#' )⋯)"#*+ describes the incidence plane wave at
the beginning of the bond vector aj1,, 62# 978 represents a spherical wave, which emanates
from the scattering atom at the beginning of the vector aj,, and 4"#$ 4"#$ "#' … 4"#(*5$)"#* are the
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ACCEPTED MANUSCRIPT scattering factors [72] associated with the consecutive scattering events from 1st to pth. The damping of primary electrons is taken into account by the ⁄ and #⁄ factors, respectively, at the emitter site and the particular scattering atom j, while 2#⁄ describes damping of scattered electrons along aj vector; ξ and ξj represent the way of primary electrons
in a solid from the surface to the emitter and scatterer j, respectively; λ is the inelastic electron
calculated with the use of the recursion formula [71]:
√
√
∑"#(;5$) ⋅"#(;5$) #(;5$)⁄
∑"#(;5') ⋅"#(;5') #(;5')⁄
(10)
.
.
/01#(;5$)
2#(;5$)
/01#(;5')
2#(;5')
.
/01#;
2#;
2#;⁄ <4"#; +
2#(;5$)⁄ 4"#(;5$)"#; <4"#(;5$) +
2#(;5')⁄ 4"#(;5')"#(;5$) <4"#(;5') + ⋯
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:1 + ∑"#; ⋅"#; #;⁄
SC
(, , s) =
⋅ ⁄
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mean free path [75,76,77,78]. Finally the wave function at the site r of the emitter is
=>?@
Index s is the arbitrary chosen parameter, which reduces the summation, as well as allows the
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comparison of the MS maps obtained for different maximal scattering orders. 4"# in Eq.(9) is the scattering factor associated with the first scattering of the incident plane wave at site aj
EP
[3,5,87]:
(11)
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4"# = 6 ∑D(2B + 1)CD,"# (E)FD (E78 +GD HI J"# ,
while 4"#(*5$) "#* is the scattering factor associated with the pth scattering event (2 ≤ p ≤ s) at site ajp calculated by the formula:
4"#(*5$)"#* = 6 ∑D(2B + 1)CD,"#* (E)FD (E78 +FD (E78( ) +GD HI J"#(*5$)"#* .
(12)
In Eqs. (11) and (12) the matrix element CD,"# (E) = K KL MD NO describes the scattering amplitude and the vibrational properties of the scattering atoms taking into account partial-
18
ACCEPTED MANUSCRIPT wave phase shifts δl [3]; GD HI J"#
and GD HI J"#(*5$)"#* are the lth Legrende
polynomials of the cosine function of the angle between the k vector and the aj bond vector, as well as the angle between the aj(p-1) and ajp bond vectors, respectively; FD (E7) is the
FD (E7) = F(D ) (E7) −
D) 62
F(D ) (E7) ,
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polynomial part of the Hankel function written in recursion formula [87]:
F = 1,
F = 1 +
62
.
(13)
SC
As in SSC calculations the intensity of Auger or elastically backscattered electrons emitted from the sample towards the RFA analyser is proportional to the sum of the primary beam
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intensities over all emitters, enumerated by rn in the crystalline sample weighted with the escape probability B of the outgoing electrons [69,71]:
W
X
R(, s) ∝ ∑ , Θ X |(, U , s)| B
.
(14)
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YZ[
B factor depends on the distance from the emitter to the surface, the inelastic mean free path
EP
of outgoing electrons λout, and the incident angle of the primary electron beam Θ associated
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with a given wave vector k. The explicit formula of the B factor is given by the expression:
] "X , Θ = 2^ _` ξ
YZ[
abc
FJ exp f
ξ"
X
YZ[ ghi(j )`)
k
.
(15)
θRFA describes the acceptance angle of the RFA collector used in the experiments. This factor takes into account the real experimental geometry associated with the limited acceptance angle of the RFA analyser and the sample rotation with respect to the axial electron gun. Theoretical distributions I(θ,ϕ) were calculated taking into account the inelastic mean free path values of the primary electron beam λ, as well as the outgoing electrons λout, the latter
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ACCEPTED MANUSCRIPT characteristic for emitted Auger and elastically backscattered electrons in DAES and DEPES, respectively [48]. The detailed analysis of the calculated signals, the contributions of particular emitters to the DEPES signal calculated at different scattering orders, as well as the defocusing factor associated with the multiple scattering events for selected atoms is
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presented in [71].
3.3. Rmax
SC
In the ideal case the infinitive number of scattering events and all atoms in a cluster should be taken into account in the MS calculations. On the other hand the strong damping of electrons
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in a solid causes that the contributions of scattered waves by atoms, located far away from the emitter, to the final form of the wave function are negligibly small. Therefore, the number of scattering atoms contributing appreciably to the wave function located at the emitter site can be arbitrary limited to the volume defined by the radius Rmax (Fig.7). The Rmax value is
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expressed in units of the inelastic mean free path λ. It should assure a reasonable convergence of the simulated results. As shown in [88] this is achieved when Rmax falls in the range of 1.0-
EP
2.0 of λ.
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3.4. Averaging range
In computations the primary electron beam is usually considered to be ideally parallel, i.e. the vector k is well defined, which is not the case in a real experiment. Electrons focused on a sample exhibit some angular divergence, which depends on the geometry of the electron gun, electrode potentials, and charge effects. That’s why theoretical intensities should be averaged over a small solid angle around the direction of the incidence beam [59,88]. Depending on the electron energy this angle varies from about 2° to 6°. This results in a smoothing of calculated intensities in theoretical DEPES maps.
20
ACCEPTED MANUSCRIPT
4. Results and discussion In this section examples of experimental results obtained with the use of the DAES and DEPES methods, as well as theoretical data received by SSC and MS calculations are
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presented in the form of polar I(θ) or anisotropy A(θ) profiles, as well as stereographic intensity I(θ,ϕ) or anisotropy A(θ,ϕ) distributions for surfaces of different substrates and
SC
adsorption systems.
4.1.1. Cu(111), Cu(001), and Cu(110)
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4.1. DAES and DEPES polar profiles
In Fig.8 the experimental DEPES polar profile recorded for Cu(111) at the primary electron
[ ] [
]
beam energy Ep=1.2 keV along the 112 − 1 1 2 azimuth is shown together with the model of the cross-section of an fcc(111) monocrystal. The characteristic intensity maxima of
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elastically backscattered electrons are observed at incidence angles -35.3º, 0º, 19.5º, 35.3º, and 54.7º parallel to the atomic rows in the [110], [111], [112], [114], and [001] directions, respectively. The sample atoms act as scatterers, which scatter the primary electrons at this
EP
energy mainly along the forward direction (Fig.2). Thus, if the direction of the primary
AC C
electron beam and that of close packed atomic rows in the sample are aligned the primary electrons are focused along this row (Fig.8b), which leads to an increase of the number of elastic and inelastic scattering events. As a consequence the increase of the recorded current associated with the elastically backscattered electrons and Auger electrons is observed. If, however, the incidence electron beam strikes the sample along another direction, not parallel to close packed atomic rows, there are no near atoms in forward direction (Fig.8b). As a consequence at these incidence angles a decrease of the measured signal of elastically backscattered electrons and Auger electrons is noted. This dependence of the measured
21
ACCEPTED MANUSCRIPT current on the incidence beam direction visible in the DEPES polar profile (Fig.8a) serves as an indication of the sample crystallinity. In view of the fact that in the RFA analyser the energy Ep of the primary electrons can be changed continuously DEPES, as well as DAES profiles can be recorded at different Ep values in the range of 0.5-2.0keV, where the forward
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scattering is most effective. Examples of DEPES polar scans measured for Cu(111) at different energies Ep are shown in Fig.9. Since the energy of the primary electron beam influences the interference conditions of electrons in crystalline solids, some changes in the
SC
recorded intensities in DEPES and DAES profiles as a function of Ep value are expected. However, the position of the main intensity maxima associated with the [110], [112], and
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[001] directions does not change with Ep. The focusing of primary electrons onto atoms located along closely packed rows leads to the recording of well distinguished intensity maxima. The maximum associated with the [114] direction becomes noticeable above 1.0 keV. The characteristic intensity changes with energy Ep are mainly observed around the
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[111] direction. A very similar dependence of the recorded signal on the incidence beam direction is observed in the DAES profiles (Fig.10), where the Auger signal for the MVV transition (66 eV) is measured at different primary electron beam energies. Due to the
EP
recording of Auger electrons the DAES method is chemically sensitive, which can be utilized in investigations of e.g. intermixing layers and order-disorder phase transitions within the
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near-surface atomic layers as it was shown for Cu3Au(001) [ 89 ], as well as surface roughening as it was presented for Ni(110) [90]. Different scattering properties of atoms revealed by the dependence of the scattering factor on the scattering angle (Fig.4) can to some extend cause a chemical contrast also in DEPES profiles. The differences, however, in atomic numbers Z of scattering atoms e.g. in binary alloys such as Cu-Au should be, significant in order to distinguish their influence on the recorded intensities in DEPES [91]. As in DAES,
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ACCEPTED MANUSCRIPT also in DEPES temperature effects enabled to reveal surface roughening of Cu(011) [92] and an order-disorder transition in Cu3Au(001) [93,89]. In Fig.11 a comparison of DAES and DEPES profiles recorded for Cu(001) at primary electron energies Ep=0.8, 1.0, and 1.2 keV is shown. At the same Ep values a very similar
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shape of the DAES and DEPES profiles is observed including the main [001] and [112] intensity maxima (note the splitting of the [001] maximum at Ep=1.0 keV), as well as small local intensity features. A change of the primary electron beam energy results in changes
SC
observed in both DAES and DEPES distributions, however, the overall character of the profiles at the chosen Ep value remains the same. This dependence was also confirmed by the
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recording of DAES polar scans for low (MVV, 66 eV) and high (LMM, 922 eV) energy Auger transitions and DEPES profiles at Ep=2.0 keV for Cu(001) and Cu(111) [70,48]. It must be noted that the angular distribution of low and high energy electrons is significantly different, as observed by XPD [94], because of the dependence of the scattering factor
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f (k ,θ S ) and the inelastic mean free path λ on the electron energy. Therefore, the above discussed results prove that the intensity maxima originate from the scattering effects of the primary electron beam in the crystalline samples, and the integration of the recorded signal of
EP
Auger electrons in DAES and elastically backscattered electrons in DEPES over the large
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acceptance angle of the RFA collector significantly minimizes the influence of the angular distribution of emitted electrons on the measured current. The information depth of the crystalline structure revealed by DAES and DEPES depends on the inelastic mean free path of primary (λ) and emitted (λout) electrons, as well as on the forward focusing, which takes place within the first few atomic layers because the subsequent scattering events of primary electrons along an atomic row cause a defocusing effect [71]. At the same Ep value the difference between DAES and DEPES results from different inelastic mean free paths of outgoing electrons, because in a case of DEPES λout =λ, but in DAES λout<
23
ACCEPTED MANUSCRIPT λ usually for energy down to about 100 eV. Moreover, in DEPES only elastically backscattered electrons contribute to the recorded signal. In DAES, however, the emission of Auger electrons results from the ionisation of atoms, which can be excited by the primary electron beam, elastically and
inelastically scattered electrons, as well as by secondary
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electrons of sufficient energy [68], which contribute to the backscattering factor in Auger electron emission. In this context the information received by the use of DAES relates also to the probability of electron hole creation and the initiation of the Auger transition, which
SC
underlies the measured intensities. The signal modulation observed in polar scans is usually smaller for DAES than for DEPES, which is reflected by the signal anisotropy values given
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on the left hand side of each profile (Fig.11). The signal anisotropy is defined as A=(ImaxImin)/Imax, where Imax and Imin represent the maximal and minimal signal within the polar scan.
4.1.2. Comparison of DAES and XPD
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In Fig.12 the comparison of DAES and XPD polar profiles is shown for more or less similar energies of primary electrons in DAES and emitted photoelectrons in XPD scattered at a Cu(111) sample. In the case of DAES the Auger transition MVV (Auger electrons of kinetic
EP
energy 66eV) was excited by primary electrons of Ep=800, 1000, and 1200 keV. In the case of
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XPD the angular distributions of emitted photoelectrons at energies 807 eV, 1178 eV, and 1617 eV were recorded. The DAES and XPD profiles exhibit a very similar distribution of intensity maxima, which in case of DAES results from the scattering events of primary electrons striking the sample but in XPD from scattering events of emitted photoelectrons. The results presented in Fig.12 were obtained independently by two groups (XPD at the University of Fribourg and DAES at the University of Wrocław) and confirm that similar information about the crystalline order of samples can be obtained with the use both methods. The strength of the signal modulation in XPD is higher than in DAES, which results from a
24
ACCEPTED MANUSCRIPT lower probing depth of the Auger electrons than of the photoelectrons and the higher background intensity in DAES. In XPD, first the emission of photoelectrons excited by x-rays following scattering of these electrons at atoms occurs, which results in the anisotropic distribution of the emitted
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photoelectrons. In DAES, however, first the scattering of primary electrons along the incidence direction and then the emission of Auger electrons takes place. Because of the experimental geometry discussed in the introduction section associated with the use of a small
SC
aperture HA analyser in XPD and a large acceptance angle RFA analyser in DAES, the scattering events of secondary and primary electrons are monitored, respectively. A more
SSC results can be found in [69].
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detailed discussion about the comparison of XPD and DAES data, as well as corresponding
4.1.3. Comparison of experimental and theoretical DEPES profiles
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To first approximation the description of scattering events of primary electrons in crystalline solids can be performed with the use of a single scattering cluster (SSC) model [69]. This formalism enables to calculate theoretical DAES and DEPES profiles [48,49,69,70] and to
EP
compare them with experimental data. In Fig.13 experimental and theoretical DEPES polar scans for Cu(001) are presented for primary electron beam energies Ep in the range of 0.5-1.5
AC C
keV. Similar distributions of intensity maxima are observed in both the theoretical and the experimental data. The SSC theory reproduces the majority of intensity maxima associated with the [001] direction at the incidence angle of 0º, as well as the shift of the maximum near the [112] direction at -35º at low primary electron energies. The increase of the Ep value leads to the gradual appearance of the maxima at -54º and -19º associated with the [111] and [114] directions, respectively, in both the experimental and the theoretical scans. The correspondence between measured and computed DEPES profiles is also visible in the
25
ACCEPTED MANUSCRIPT characteristic splitting of the main [001] maximum at Ep=0.9, and 1.0 keV. The main discrepancies between the experimental and theoretical results concern the relative height of the main intensity maxima, reflected by the anisotropy values, and the presence of local peaks observed within the whole scanning range. Some intensity features are more pronounced in
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the theoretical than in the experimental scans. Moreover, the [001] maximum at 0º in the experimental DEPES profile exhibits three components at Ep=0.5 keV, which is not reproduced in the theoretical distribution, and at Ep=0.7 keV this theoretical maximum splits
SC
but is sharp in the experiment. A more detailed discussion about experimental and computed DEPES data for Cu(001) with the use of the SSC formalism can be found in [70]. Similar
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observations can be made by the comparison of experimental and theoretical DAES results [48,69].
The comparison of experimental and calculated DEPES profiles for the low index (001), (111), and (110) surfaces of a copper monocrystal is shown in Fig.14. The azimuth of each
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sample was chosen in such a way that the primary electron beam strikes the copper monocrystal parallel to the (1 10) plane, as it is indicated in Fig.15. This enables to reach all densely packed rows of an fcc structure for different substrate symmetries and sample
EP
orientations with respect to an axial electron gun of the RFA analyser. The distribution of the
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main intensity maxima observed in the profiles (Fig.14) corresponds to the crystalline directions within an fcc monocrystal shown in Fig.15. DEPES polar profiles for the Cu(001) and Cu(110) sample are symmetrical as expected for four-fold and two-fold symmetry axes of these surfaces, respectively. The unsymmetrical DEPES scan for Cu(111) is associated with the three-fold symmetry axis of this surface. The SSC theory reflects almost all intensity maxima observed experimentally. The characteristic background observed in all profiles results from the increased damping of primary and emitted electrons towards grazing angles. Therefore, the relative intensity of e.g. the [001] maximum is higher for Cu(001) than for
26
ACCEPTED MANUSCRIPT Cu(111). The same concerns the [110] maximum observed in DEPES profiles for Cu(111) and Cu(110). This maximum is inclined towards grazing angles for Cu(111), while that for Cu(110) is symmetrical. As in Fig.13 the splitting of the [001] maximum for Cu(001) is observed in experiment and theory, which is not the case for the experimental DEPES scan
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for Cu(111). The lack of this splitting is rather caused by the experimental geometry associated with the limited collector aperture than with the diffraction processes in the sample. It must be noted that a decrease of the effective aperture of the RFA analyser occurs
SC
at incidence angles larger than ±52º, half of the acceptance angle of the collector equal to 104º, in this particular experiment, which causes the additional decrease of the recorded
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current. Therefore, the limited analyser aperture affects the measured signal before the [001] maximum at -54º is reached for Cu(111). Similar intensity maxima are observed in the experimental and theoretical DAES profiles for other low index surfaces of the copper monocrystal [48]. An overall agreement between experimental and theoretical DEPES and
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DAES scans can been found. Examples of DAES and DEPES profiles recorded for Cu(111),
4.1.4. Ag/Cu(111)
EP
Cu(011), and Cu(001) can be found e.g. in [95,96,97,98,99].
DAES and DEPES can also be used to study the structure of adsorbed layers. While regular
AC C
AES provides information about the thickness of deposited layers and their growth mode LEED yields information mainly about the long range order of surface atoms. The sensitivity of the DAES and DEPES methods to the short range order within a near surface layers can be exploited to add information about the local bond geometry of adsorbed atoms at the adsorbate/substrate interface in the incipient and further stages of adsorbate growth. All this complex information can be received with the use of just one and the same RFA analyser.
27
ACCEPTED MANUSCRIPT In Fig.16 the DEPES polar profiles recorded for clean Cu(111) and different Ag coverages from 1 ML till 12 ML at Ep=1.0keV are presented. The DEPES scan measured for clean
[
] [ ]
Cu(111) along the 1 1 2 − 112 azimuth exhibits pronounced intensity maxima associated with [001], [112], and [110] close packed atomic rows of the fcc structure as observed in Figs.
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8, 9, and 10. The adsorption of Ag layers causes significant changes in the measured profiles. The presence of the silver layers at different thicknesses leads to the decrease of some intensity maxima and simultaneous appearance of other peaks, which reflect directions at the
SC
Ag/Cu interface and within the newly formed Ag overlayer. The detailed analysis of the DEPES data enables to find maxima, which correspond to Ag(111) domains mutually rotated
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by 180º, which is indicated in Fig.16 by the distribution of directions within the silver overlayer and illustrated in Fig.17. The growth of an unrotated, with respect to the substrate, Ag domain results in the same distribution of directions as it is shown in Fig.17a. Therefore, the DEPES profile for this domain should reflect a similar but not identical distribution of
TE D
intensity maxima as for the substrate, as it is observed for e.g. Co/Cu(001) [97] and Co/Cu(110) [98]. Different lattice parameters of the Ag overlayer and scattering properties of individual silver atoms in comparison to the copper substrate cause differences in the
EP
recorded intensities and shapes of particular maxima. For this situation the stacking sequence
AC C
along the surface normal at the Ag/Cu(111) interface is CBA/CBA. If, however, the stacking sequence at the adsorbate/substrate interface is CAB/CBA, as shown in Fig.17b, the growth of the 180º rotated domain occurs. For this domain the distribution of directions is reflected with respect to the [111] direction. The recorded DEPES intensities in Fig.16, in fact, correspond to two mutually rotated adsorbate domains. Moreover, the dominant [011] maximum of the Ag overlayer suggests different populations of rotated and unrotated Ag domains. In order to obtain information about the domain growth a quantitative data analysis with the use of an R-
28
ACCEPTED MANUSCRIPT factor can be performed [49]. The experimental polar profiles can be compared with a linear combination of theoretical scans obtained for two mutually rotated domains:
2
I Th = ∑ ni I Th ,i ,
(16)
RI PT
i =1
where ITh,i is the calculated intensity at given polar angle for domain i and ni represents its
condition. We used the following R-factor [100]:
∫ (L
− L Ex ) dθ 2
∫ (L
2 Th
)
+ L2Ex dθ .
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R=
∑
SC
population. In the calculations the ni values are varied by 1% steps and fulfil the
Th
2
i =1
ni = 1
(17)
In Eq. (17) LTh and LEx are L=I’/I ratios obtained for theoretical and experimental results at a given incidence angle, where I and I’ represent the signal and its derivative with respect to
TE D
polar angle θ, respectively. The calculation of L values assures that the R-factor is affected by the relative shape and position of intensity maxima observed in DEPES profiles without any
EP
influence of the relative intensity scale. Perfect fit between experimental and theoretical data is obtained when R=0, while at R=1 no correspondence between the results is found.
AC C
In Fig.18 the R-factor calculated for experimental and theoretical DEPES scans at Ep=0.8keV is presented as a function of adsorbate domain populations n1 and n2. The best fit of the Rfactor minimum at 0.29 was obtained for n1=75% and n2=25% of rotated and unrotated Ag(111) domains, respectively. The comparison of experimental and theoretical DEPES profiles, the latter obtained for the best fit with the use of Eq. (16), is shown in Fig.19. This result proofs the preferred growth of rotated Ag domains, which is also confirmed by DEPES and DAES results obtained at different energies Ep [49]. The not uniform growth of rotated and unrotated adsorbate domains is most likely associated with the presence of atomic steps,
29
ACCEPTED MANUSCRIPT which are oriented along a certain direction on the Cu(111) surface as a result of the sample miscut. When the nucleation process starts at step edges the preferred adsorption sites enforce the sequence of Ag atoms at the Ag/Cu interface. In the case of the Ag growth on flat terraces both sequences shown in Fig.17a and Fig.17b are equally possible, which results in the
RI PT
nucleation of rotated and unrotated domains. The presence of unsymmetrical DEPES profiles was also found for Ag/Cu(001), which again indicates the preferred growth of one domain [70]. In the case of the Ag/Cu adsorption system the γ A + γ I < γ S relation predicts a wetting
SC
of Cu by Ag. The orientation of Ag domains is determined by the first stages of growth. Therefore, the presence of steps on the Cu substrate can enforce the sequence of atoms in the
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Ag overlayer. Similar information about the domain populations was obtained with the use of XPD [101,102]. The preferred adsorption sites at step edges were also reported for oxygen on stepped copper surfaces such as Cu(410) and Cu(211) [103]. It must be noted, that the rotation of the fcc(111) domain by 180º leads to the observation of the same LEED pattern,
TE D
which makes a quantitative analysis difficult. Only the application of I(V) measurements of diffracted electron beams [3,104,105,106] can be used to obtain similar information about the domain populations as with DEPES and XPD. In the case of I(V) investigations, however, the
EP
detailed knowledge about the intensity-energy spectrum of diffraction spots of a single
AC C
adsorbate domain is required. The combined detection of polar DEPES profiles, LEED patterns, and AES signals with the use of one and the same RFA analyser has also enabled to find the short and long range order, as well as the growth mode, respectively, for other adsorption systems such as: Ag/Cu(011) [95], Ag/Cu(001) [70,96], Co/Cu(001) [97], Co/Cu(110) [98], Co/Cu(111) [99], Au/Ni(111) [107], Ag/Au(111) [108], Pb/Ni(111) [109].
4.2. DEPES stereographic distributions
30
ACCEPTED MANUSCRIPT The manipulator, which enables the precise polar and azimuthal rotation of the sample (Fig.1b), can be applied to record DEPES profiles at different azimuths. The presentation of such results in the form of the stereographic projection I(θ,ϕ) with the use of the coordination transfer function defined in section 2 reflects the scattering geometry in real space, which
RI PT
enables the direct identification of the sample crystallinity. Therefore, in this section the interpretation of two dimensional DEPES distributions recorded and calculated in a wide
SC
angular range is presented.
4.2.1. Cu(111)
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In Fig.20a the experimental DEPES stereographic distribution for Cu(111) at Ep=1.5 keV is shown. The characteristic threefold symmetric intensity pattern reflects the sample crystallinity. The intensity maxima correspond to the 110 , 112 , 114 , and 100 directions of the sample shown in the stereographic projection of an fcc(111) monocrystal
TE D
(Fig.20c). The detailed analysis of the DEPES distribution enables to find intensity bands associated with atomic planes, as well as the characteristic central maximum with satellite peaks associated with the [111] direction, which strongly depend on the energy Ep of the
EP
primary electron beam. The intensity features observed in the theoretical distribution
AC C
(Fig.20b) also reflect densely packed atomic rows in Cu(111). The background level is higher in the experiment than in theory, which is reflected by the colour scale, as was also observed for other samples [110,111]. Therefore, the background subtraction procedure described in section 2 was often applied in the quantitative data analysis. In Fig.21 DEPES distributions are shown for Cu(111) at different Ep values [ 112 ]. A narrowing of the intensity maxima with increasing energy is observed, which is associated with the dependence of the scattering factor on the electron energy (Fig.3). Moreover, at higher Ep values the inelastic mean free path increases. Therefore, the DEPES maps at
31
ACCEPTED MANUSCRIPT increased electron energies are characterised by the more detailed intensity pattern with intensity bands reflecting atomic plains. A similar dependence is observed in the theoretical DEPES distributions. The signal changes within each map are reflected by contrast values C defined as: C = 2(Imax −Imin)/(Imax + Imin), where Imax and Imin are the maximal and minimal
RI PT
signal intensities within the area surrounded by the dashed circle (θmax=60°) on the experimental map at 0.6 keV. An increase of contrast is observed with increasing energy. C values of the theoretical data are about 1.5 times larger than of experimental results, which
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performed for Au(111) can be found in [114,115].
SC
originates from a larger background level of the recorded maps [113]. A similar analysis
4.2.2. Contribution of layers and parameters of calculations - Pt(111) As it has been already mentioned both DAES and DEPES are sensitive to the short range order of atoms within the near-surface region. In order to find the contribution of different
TE D
sample layers to the DEPES intensity plot in MS calculations we took into account all scattering atoms in the cluster and considered emitters only in one individual layer. The result of such calculations for Pt(111) at Ep=1.2 keV is shown in Fig.22. A similar analysis at
EP
Ep=1.1keV can be found in [116]. The same intensity scale enables a direct comparison of
AC C
intensities among all partial maps. The contribution of the first layer of Pt(111) is almost isotropic, which results from the lack of scattering atoms above this layer. A small signal modulation results from backscattering events of primary electron wave in the sample. The appearing intensity maxima in the partial plots arrising from deeper layers in Fig.22 are associated with rows of atoms along 110 , 112 , 114 , and 100 directions formed above the considered layer of emitters (Fig.8b). The 110 and 100 intensity maxima originate already from the first and second layer (Fig.22b). The third layer adds contribution to these maxima, but gives also rise to the intensities associated with the 112 peak (Fig.22c). The
32
ACCEPTED MANUSCRIPT 114
and 111 maxima originate from emitters in the fourth layer (Fig.22d). The
characteristic satellite maxima of the [111] peak, which form a threefold symmetric pattern in the center of the DEPES distributions visible in Fig.20a, are associated with scattering of electrons from the 4th and 5th layer. The damping of electrons in a solid as well as the
RI PT
defocusing of electrons [13,79,80,82,117], which is a consequence of multiple scattering events, results in a steady decrease of intensities from deeper layers. The detailed analysis of the scattering and damping of electrons in Cu(111) and Pt(111) is discussed in [111]. The
SC
above results confirm the contribution of few topmost sample layers to the DEPES signal.
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The application of the MS formalism described in section 3.2 enables also the consideration of different scattering orders of primary electrons in solids. We compared two computed DEPES profiles obtained at s-1 and s maximal scattering orders, associated with consecutive number of scattering events, by calculating the data convergence factor expressed by the formula:
1
I s (θ ) − I s −1 (θ )
TE D
Conv =
2
θ
(18)
where, Is(θ) and Is-1(θ) represent the intensities at a given polar angle θ for s and s-1 scattering
EP
orders, respectively. The mean value of the module of intensity differences at s and s-1 is calculated over all polar angles associated with the DEPES polar scans. The convergence
AC C
factor indicates the number of scattering events, which should be taken into account in MS calculations, which assure the negligible intensity differences of computed DEPES intensities at s-1 and s scattering orders. In Fig.23 the convergence factor is shown as a function of the scattering order. The convergence factor, calculated for Is(θ) and Is-1(θ), is shown for the index s of the pair (s, s-1). The consideration of the scattering order in the range from 3 to 5 already ensures the sufficient convergence of computed results, which on the other hand significantly reduces the computation time. As expected at lower Ep a better correspondence
33
ACCEPTED MANUSCRIPT between theoretical DEPES data obtained at s and s-1 scattering orders is achieved because of the lower λ values. As mentioned in section 3.3 the number of scattering atoms, which contribute to the wave function at the emitter site can be limited by the sphere with radius Rmax around the emitter
RI PT
(Fig.7). The scatterers in this volume give the main contribution to the final wave function, while the contribution of scatterers outside this sphere plays a minor role, therefore the latter atoms are not taken into account in calculations. In Fig.24 the convergence factor (Eq.18)
SC
calculated for two DEPES intensities obtained for consecutive values of Rmax with 0.1 increments is shown. Rmax is expressed in units of the inelastic mean free path. The
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consideration of Rmax values in the range of 1.0-2.0 ensures a sufficient convergence of theoretical data obtained within a reasonable computation time.
In Fig.25 the convergence factor is shown as a function of the number of layers taken into account in MS calculations. As in the case of the scattering order and Rmax the convergence
TE D
factor was calculated taken two theoretical intensities associated with consecutive number of cluster layers. For Pt(111) at Ep=1.2keV the consideration of the first 20 layers of the
electrons.
EP
crystalline sample seems to be sufficient to simulate the scattering events of primary
In calculations the angular distribution of the primary electrons leaving the electron gun is
AC C
taken into account by the consideration of a divergence ∆θ of the primary electrons (averaging range) around the incidence direction (section 3.4). In Fig.26 the calculated DEPES distributions for Pt(111) are shown at different averaging ranges ∆θ. A smoothing of intensities is observed with increasing ∆θ value. As shown in [59] a decrease of the averaging range is observed with the electron beam energy, which results from the better focusing of electrons in the electron gun at higher Ep values. Depending on the energy Ep the ∆θ values reach few degrees [59].
34
ACCEPTED MANUSCRIPT
4.2.3. Mo(110) In Fig.27a the experimental DEPES distribution recorded at the primary electron beam energy Ep=1.8 keV is presented for the Mo(110) monocrystal. The two-fold symmetry intensity
RI PT
pattern corresponds to the distribution of close packed atomic rows within a body centred cubic structure shown in the stereographic projection (Fig.27e). The characteristic intensity bands, which become more pronounced at higher primary electron beam energies Ep (Fig.21),
SC
reflect the atomic planes within the Mo(110) crystal. In the case of the bcc structure the
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increase of DEPES intensities is observed at the 111 , 100 , and 110 directions because they represent the most densely packed rows of atoms within this structure. This observation is also confirmed by the theoretical DEPES map obtained with the use of the MS formalism (Fig.27c). The experimental DAES plot recorded for the MNN transition (Auger electrons of energy 190 eV) at Ep=1.8 keV (Fig.27b) also reflects the well pronounced maxima associated
TE D
with the directions shown in Fig.27e. The current of Auger electrons recorded in DAES gives additional information about the chemical composition of the sample. The theoretical DAES plot shown in Fig.27d reflects the similar distribution of maxima as the theoretical DEPES
EP
map. The differences in the signal intensities between theoretical DEPES and DAES plots
AC C
result from the lower value of the inelastic mean free path of Auger electrons in DAES than elastically backscattered electrons in DEPES. In Fig.27f the experimental DAES distribution recorded for the C KLL Auger transition (275eV) at the trace amounts of carbon on Mo(110) and the same primary electron beam energy Ep=1.8keV does not show any intensity maxima, which could indicate an order within the adsorbate. One can, however, notice the characteristic pattern of the background intensities in the centre of this distribution similar to the pattern observed in DEPES (Fig.27a) and DAES (Fig.27b) plots for Mo(110). This pattern
35
ACCEPTED MANUSCRIPT results from the contribution of elastically backscattered electrons in the substrate in the Auger emission from carbon.
4.2.4. Ru(0001)
RI PT
An fcc(111) monocrystal exhibits a ABCABC stacking of atomic layers along the surface normal as shown in Fig.28a. As a result the termination of an fcc(111) surface such as Pt(111) does not influence the contribution of the [110] , [111] , [112] , [114] , and [001] directions to
SC
DEPES intensities. In other words, the same DEPES intensity plot shown in Fig.20 is obtained for A, B, and C terminated Pt(111) surface. In the case of an hcp(0001) monocrystal,
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however, the stacking sequence is ABAB as presented in Fig.28b. This sequence determines the distribution of intensity maxima in DEPES maps. Depending on the terrace termination A
[
]
[
] [
]
[
]
or B the contribution of 10 1 2 and 1 011 or 10 1 1 and 1 012 directions predominates in DEPES plots, respectively, which results from the attenuation of electrons in a solid. In
TE D
Fig.29a the theoretical DEPES plot for an A terminated Ru(0001) surface at Ep=1.3 keV is shown. A threefold symmetry intensity pattern is observed. For symmetry reasons mentioned above the intensity pattern (not shown) obtained for B terminated Ru(0001) surface is rotated
EP
by 180º with respect to the pattern of the A terminated surface. The experimental DEPES
AC C
distribution shown in Fig.29c, however, exhibits six-fold symmetry pattern. Similar intensity features were also observed in angular distributions of Ru 3d photoemission from Ru(0001) in XPD [ 118 ]. This six-fold symmetry intensity pattern is associated with the uniform distribution of A and B terminated terraces, which are separated by monoatomic steps. Both A and B terraces of the Ru(0001) surface give similar contribution to the overall recorded intensities. A quantitative analysis of the experimental and theoretical DEPES plots performed with the use of an R-factor analysis enables to find the populations of A and B terminated terraces. Taking into account theoretical intensities I th , A and I th , B at given polar
36
ACCEPTED MANUSCRIPT and azimuthal angles and terrace populations n A and n B for terraces A and B, respectively, the theoretical intensity can be written as I th = n A I th , A + nB I th , B . The calculations were performed to fulfil the n A + n B = 100% condition by changing the population values in steps
RI PT
0.1%. Theoretical DEPES distributions were calculated considering different phase shifts as proposed by NIST [119], Clementi at al. [120], and Barbieri et al. [121]. Experimental and theoretical DEPES distributions were compared with the use of an R-factor defined as:
R = 1−
i =1
∑ (I N
exi
)(
− I ex I thi − I th
− I ex
) ∑ (I 2
N
i =1
)
,
thi
− I th
)
(19)
2
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i =1
exi
SC
∑ (I N
where, I ex and I th are the experimental and theoretical signals, respectively. The results of this analysis at Ep=1.6 keV are summarized in Fig.30. The minimum of an R-factor associated
TE D
with the best fit was obtained at nA=46.8 % and nB=53.2 % irrespective of the source of the phase shifts. Taking into account phase shifts from [121] assures the best correspondence between experiment and theory. Very similar mean values of populations namely
EP
nA=48.9±1.6% and nB=51.1±1.6% [59], obtained at different energies of the primary electrons confirm the uniform distribution of A and B terminated terraces. The latter is confirmed by
[
] [
]
AC C
the almost symmetrical polar DEPES profile recorded along the 0 1 10 − 01 1 0 azimuth (Fig.29e). For comparison this profile is shown together with the polar plot recorded for the polycrystalline Fe, which exhibits the clear lack of intensity maxima. The latter distribution shows background intensities, which are determined by the attenuation of electrons in a solid.
4.2.5. Graphene on Ru(0001) The Ru(0001) surface is often used as a support to form a graphene (Gr) layer [122,123,124,125,126]. The long range order within the Gr layer is well reflected by sharp
37
ACCEPTED MANUSCRIPT diffraction spots in LEED observations, which yield a large (12×12) Moiré unit cell, consistent with a (11×11) mash of the Ru substrate lattice. After formation of the Gr layer the changes of the DEPES signal are not noticeable in the DEPES plot shown on the absolute scale of intensities because of the large contribution of the substrate to the recorded signal
RI PT
associated with the large inelastic mean free path of the primary electrons and the large scattering cross section of Ru atoms with respect to C atoms. However, subtle signal changes caused by the presence of the thin Gr layer on Ru(0001) can be revealed by the calculation of
SC
the signal anisotropy (Eq.2). In Fig.31 the anisotropy distribution A(θ, φ ) at Ep=1.2keV is
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presented. The six-fold symmetry pattern of smeared intensities is observed without any pronounced maxima, which indicates a number of different interatomic axes formed by the C and Ru atoms within a large unit cell of the corrugated Gr layer.
4.2.6. Cu / Ru (10 1 0 )
TE D
In contrast to the Ag/Cu(111) adsorption system discussed in section 4.1.4, where silver and copper crystallize in the same fcc structure, the Cu / Ru (10 1 0 ) system is characterized by
EP
different structures of the Cu adsorbate (fcc) and the Ru substrate (hcp) in their bulk form. Depending on the adsorbate-substrate and adsorbate-adsorbate interactions different surface
AC C
structures can be observed. In the case of strong interaction between substrate and adsorbate atoms the formation of a pseudomorphic adsorbate layer is expected. If, however, the interaction between the adatoms prevails, which usually occurs within the overlayer at larger coverages, the formation of the structure characteristic for the adsorbate bulk phase can be observed. The latter is associated with lattice mismatch and a break of the symmetry, which is reflected in the recorded DEPES intensity patterns.
38
ACCEPTED MANUSCRIPT The experimental DEPES plot obtained for Ru (10 1 0 ) at Ep=1.2 keV is shown in Fig.32a. The two twofold symmetry of the intensity pattern characteristic for the Ru (10 1 0 ) substrate with
[
]
[
]
two main intensity maxima at θ = ±30° corresponding to the 2 1 1 0 and 1120 directions is
[
] [
clearly observed (Fig.32c,d). Other low intensity maxima visible along the 1210 − 1 2 1 0
][
]
[
]
RI PT
[
]
azimuth correspond to the 1 1 00 , 10 1 0 , and 01 1 0 directions of the hcp structure. The theoretical DEPES distribution (Fig.32b) reflects almost all intensity features observed
SC
experimentally. The other low intensity features correspond to the crystalline directions within the area surrounded by the blue dashed line in Fig.32c.
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Auger measurements from the substrate (Ru NVV transition, 40eV) during the continuous Cu deposition show first the growth of two Cu bilayers [127,110,128] followed by the nucleation of 3D islands. One bilayer (1BL=2ML) corresponds to two p(1×1) copper monolayers separated by 0.78 Ǻ along the surface normal [127]. LEED patterns recorded during the first
TE D
stages of Cu growth exhibit the same distribution of reflexes as for the uncovered Ru substrate, which proves the formation of a pseudomorphic Cu overlayer [127]. LEED observations performed at coverages above 2BL, however, reflect a six-fold symmetry of the
EP
Cu deposit characteristic for the fcc(111) surface [110]. These experimental observations agree with results of density functional theory (DFT) calculations, which indicate the
AC C
energetic stability of the first two Cu pseudomorphic bilayers, while the third bilayer is thermodynamically metastable [128]. The change of the adsorbate symmetry revealed by LEED is particularly interesting from the point of view of DEPES measurements because of the short range order sensitivity of the latter method. The DEPES distribution recorded at Ep=1.5 keV for Cu coverage equivalent to about 7BL on
Ru (10 1 0) is presented in Fig.33 before and after background subtraction. The background of a DEPES polar scan was obtained by the fitting with a cosine function given by the
39
ACCEPTED MANUSCRIPT expression I BG = A ⋅ cos(Bθ ) [60,110] (lower panel of Fig.33a) with A and B determined by a least square analysis applied to the mean polar profile over all scans of a considered DEPES distribution. The DEPES polar profile after the background subtraction given by the
I * (θ ) = I (θ ) − I BG (θ ) = I (θ ) − A cos(Bθ ) , together with the DEPES map are shown in Fig.33b.
RI PT
expression: (20)
SC
The intensity pattern shows maxima associated with 110 , 112 , 114 and 100 atomic rows characteristic for two fcc(111) domains mutually rotated by 180º, as well as some low
[
] [
] [
] [
]
[
]
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intensity maxima, which correspond to the 10 1 0 , 1120 , 21 1 0 , 10 1 1 and 2021
directions of the hcp(10 1 0) structure. The orientation of the two fcc(111) adsorbate domains with respect to the Ru (10 1 0 ) substrate is described by the [2 1 1 ](111)Cu and [2 11](111)Cu
[0001](10 1 0 )Ru
[0001](10 1 0 )Ru
relations. The above analysis leads to a picture of the
TE D
adsorption geometry as shown in Fig.34. The first two Cu bilayers reflect the hcp(10 1 0) structure. The growth of the subsequent layers is characterized by an fcc(111) structure,
EP
which exhibits two equivalent ABC and ACB stacking sequences and the resulting mutual rotation of copper domains by 180º. Small violet rings in Fig.34 show the most probable
AC C
hollow adsorption sites on the second Cu (10 1 0 ) bilayer. Because of the symmetry break the growth of a particular Cu(111) domain is likely to be associated with the choice of one of the two equivalent adsorption sites. The DEPES distributions reveal more intensive maxima associated with one Cu(111) domain, which is particularly visible after the background subtraction (Fig.33b). This suggests different domain populations, which can be determined by an R-factor analysis. As it was already shown for DEPES results obtained for Ag/Cu(111) [49] and Ru(0001) [59] a similar quantitative analysis can be performed for Cu/ Ru (10 1 0)
40
ACCEPTED MANUSCRIPT taking into account the contributions of the first two pseudomorphic Cu p(1×1) bilayers, as well as the rotated and unrotated Cu(111) domains with the use of the formula:
* I sim =
∑ (m ⋅ I
* hcp
* * + p ⋅ I fcc _ 0 + q ⋅ I fcc _ 180 ) ,
(21)
RI PT
m, p,q
where, I*hcp , I*fcc_0 , and I*fcc_180 indicate intensities associated with the simulated distribution of hcp structure, as well as unrotated and rotated fcc domains, respectively, weighted by m, p, and q populations, which range from 0% to 100% while fulfilling the condition
SC
m + p + q = 100 % . At coverages as large as 7BL the contribution of the pseudomorphic Cu
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and the Ru substrate in the recorded DEPES signal is governed by the inelastic mean free path. The results of such R-factor analysis performed with the use of experimental and theoretical component distributions (I*hcp , I*fcc_0 , I*fcc_180) at Ep=1.2 keV are shown in Fig.35. The best fit of the experimental component maps to the recorded DEPES distribution
TE D
at Ep=1.2 keV associated with the R-factor minimum was found for m=24%, p=41% and q=35% (Fig.35b). The same analysis performed for the theoretical component distributions leads to the m=19 %, p=46 % and q=35 % populations (Fig.35d). The resulting DEPES plots
EP
are shown in Fig.35c and Fig.35e. Very similar results were obtained at Ep=1.5keV [110]. As already mentioned in the case of Ag/Cu(111) different population values of rotated and
AC C
unrotated domains are likely to be associated with nonequivalent adsorption sites. It is worth noticing that because of symmetry reasons LEED patterns exhibit the same distribution of diffraction reflexes for rotated and unrotated Cu(111) domains [110] as in the case of the Ag/Cu(111) system described in section 4.1.4.
4.2.7. Pt/Cu(111) The information concerning the surface composition and structure is crucial for a knowledge based materials design. This information seems to be particularly important for catalytically
41
ACCEPTED MANUSCRIPT active systems such as Cu/Pt and Pt/Cu. Usually, the bimetallic adsorption systems demonstrate other catalytic properties than their components alone [ 129 , 130 , 131 ]. The breaking and formation of new bonds between metal atoms lead to changes in electronic structure, which can influence the stability, activity, and selectivity of catalysts. The Cu-Pt
RI PT
system, for instance, was used to investigate the reforming of hydrocarbons and the hydrogenolysis of pentane [132,133]. The Pt/Cu(111) is an example of an often investigated bimetalic system, where a number of experimental [134,135,136,137,138,139,140,141] and
SC
theoretical [142,143,144] methods was applied. Because of an 8% lattice mismatch between the two metals pronounced lattice strain occurs at the interface. At room temperature (RT) the
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Frank-van der Merwe growth mechanism was observed [137,145,141] and the epitaxial Pt layer on Cu(111) exhibiting an fcc stacking sequence was reported [145]. In view of the exothermic heat of mixing three bulk alloy phases are possible CuPt3, CuPt, and Cu3Pt [146]. Experimental investigations with the use of ion scattering revealed that the Cu3Pt(111) phase
TE D
is formed within a few near-surface layers after the thermal treatment of a Pt/Cu(111) system [134,135]. The resultant Cu3Pt(111) surface is characterized by a p(2×2) platinum superstructure. A site exchange process at step edges was found to be responsible for the
EP
intermixing at the Pt/Cu interface with the use of scanning tunneling microscopy [140]. DFT investigations support the formation of a surface alloy [142].
AC C
Because of the sensitivity of DEPES to the short range order the local configuration of adsorbate atoms of the first monolayer with respect to the crystalline substrate can be identified [141]. Different adsorption sites of deposited atoms result in the formation of associated directions between adsorbate and substrate atoms, which influences the DEPES signal. Therefore, DEPES can be applied to investigate ultrathin adsorbate layers formed on crystalline substrates. In Fig.36a the experimental DEPES distribution at 1ML coverage of Pt on Cu(111) is shown. A background subtraction procedure [60,110] was applied to all
42
ACCEPTED MANUSCRIPT distributions in Fig.36 in order to enhance weak intensity features. The observed intensity pattern is very similar to the DEPES map measured for the uncovered substrate shown in Fig.20a (note that the experimental DEPES map in Fig.20a represents the Cu(111) substrate rotated by 180° compared to the one covered by a Pt monolayer shown in Fig.36a). The
RI PT
theoretical DEPES distributions were calculated for different geometries at the adsorbate/substrate interface. The presence of domains with Pt atoms at different positions such as A and B hollows, on top (C), and bridge sites on Cu(111) shown in Fig.37 was
SC
considered in the MS calculations regardless of their energetic rationalization. The calculations were performed for not dissolved and dissolved Pt in the first layer of the copper
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substrate taking into account the Pt-Cu bond length. In a case of the intermixing layer the Cu3Pt alloy, which exhibits the p(2×2) structure in the top most Cu layer, and the presence of the Pt monolayer at different adsorption sites was considered (Fig.37e). As expected the formation of a pseudomorphic monolayer with Pt atoms at sites of A type (Fig.36b), which
TE D
causes the continuation of stacking sequence characteristic for fcc structure at the interface, namely A/CBA, results in almost the same intensity features as observed for the uncovered substrate observed in Fig.20b (note again that the theoretical DEPES map in Fig.20b
EP
represents Cu(111) substrate rotated by 180º with respect to Pt covered one in Fig.36b). The differences in intensities observed for the clean and Pt covered copper substrate are associated
AC C
with the individual scattering properties of Pt and Cu atoms considered in the simulations by the appropriate scattering factors f (θ S ) (Fig.4). Because of the forward scattering the signal in DEPES depends mainly on the f (θ S ) maximum (θS<20º). From Fig.4 it is evident that a Pt atom scatters the electron wave more effectively than Cu, which scales with the values of the scattering cross section of these atoms. Therefore, the chemical composition of the investigated sample within the near-surface region influences to some extent the intensities in DEPES. As it is visible in Fig.36c the intermixing of Pt and Cu leads to a smoothing of the
43
ACCEPTED MANUSCRIPT intensity maxima. The consideration of adsorption at B sites (Fig.37b) leads to three layers of B/CB stacking sequence at the adsorbate/substrate interface characteristic for hcp structure. This arrangement is reflected in the theoretical DEPES plot (Fig.36d) by additional intensity maxima. Taking into account the mixed Pt-Cu layer an enhancement of the 110 intensity
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maxima associated with the Pt(B) terminated surface is observed (Fig.36e). If, however, ontop Pt atoms (Fig.37c) are considered an intense maximum in the center of the distribution and weak intensity features at large polar angles are observed (Fig.36f). A suppression of the
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low intensity maxima is noted for the Pt-Cu surface alloy (Fig.36g). Adsorption at bridge sites
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(Fig.37d) requires the consideration of three mutually rotated Pt domains and results in additional intensity features (Fig.36h), which are not observed in the other distributions. Again, the low intensity features are suppressed in the case of the intermixed layer (Fig.36i). The results of the quantitative analysis obtained with the use of an R-factor, where the contribution of different adsorbate domains to the DEPES signal was considered (see section
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4.2.6), are shown in Fig.38. The best fit (Rmin=0.125) was obtained for the presence of Pt(A) and Pt(B) terminated Pt domains at nA=58% and nB=42% populations on the mixed Pt-Cu layer at the interface. Differently terminated adsorbate domains within the first layer influence
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the further growth, which results in a nucleation of rotated and unrotated Pt islands on
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Cu(111) [141]. The use of the experimental and the theoretical distributions of component domains in the R-factor analysis results in almost the same domain population values. The above analysis shows that surface alloying occurs for the Pt/Cu(111) system already at 330K, which is also confirmed by previous scanning tunneling microscopy (STM) investigations at 315K [140]. Medium energy ion scattering (MEIS) measurements reveal the intermixing at even lower temperature 225K [135], which is far below 550K characteristic for the formation of Cu3Pt bulk alloy. The examples of theoretical DEPES data obtained for other alloys such as
44
ACCEPTED MANUSCRIPT AuCu(001) and AuCu3(001), as well as pure components Cu(001) and Au(001) can be found in [91].
4.2.8. Cu/Pt(111)
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The above presented analysis concerns the DEPES maps measured and calculated at 1ML coverage of the adsorbate, and showed that the position of adsorbate atoms within the first monolayer with respect to the crystalline substrate can be revealed by the comparison of
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experimental and theoretical DEPES distributions, the latter obtained for different adsorption sites. Another approach used to reveal the adsorption geometry of atoms at the interface
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concerns the calculation of the signal anisotropy. The anisotropy defined by Eq. (2) reflects the relative change of intensities caused by the adsorbed layer with respect to the signal from the substrate underneath. Therefore, the considerable enhancement of intensity features caused by the formation of adsorbate-substrate atomic axes can be obtained if the data are
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presented as anisotropy maps. An example of such investigations concerning the Cu/Pt(111) adsorption system is presented in [ 147 ]. The anisotropy distributions A(θ,ϕ) from experimental DEPES maps obtained after the adsorption of Cu at 330K and 450K,
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respectively, and theoretical plots, the latter simulated for a Cu(A), Cu(B), and Cu on top (C)
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terminated Cu monolayer, as well as a misfit layer are shown in Fig.39 and Fig.40. The same models for A and B hollow sites, as well as for on-top (C)-sites shown in Fig.37a,b,c for the inverse Pt/Cu(111) system and additional model of the misfit layer (Fig.41) were applied for Cu/Pt(111). The quantitative analysis of the anisotropy distributions was made by the calculation of R-factor values [60] given in Fig.39 and Fig.40. The comparison of the data in Fig.39 shows that after the adsorption of Cu at 330K the misfit layer is formed, which is also confirmed by the lowest value of Rmin=0.52 among all R-factor values, as well as by a Moiré like distribution of LEED reflexes [147]. The R-factor minimum for A and B threefold
45
ACCEPTED MANUSCRIPT hollow, as well as C (on-top) sites are equal to 0.81, 1.48, and 0.69 respectively. At larger coverages the DEPES distributions reflect the same order within the adsorbate as for bulk Cu(111), which is also reflected in LEED patterns. A different relative intensity pattern in the experimental anisotropy DEPES distribution is
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observed after the adsorption of Cu at T=450K (Fig.40). The comparison of experimental and theoretical anisotropy plots obtained at Ep=0.8 keV clearly indicates the nucleation of a pseudomorphic Cu monolayer exhibiting adsorption sites of type A. The A/CBA sequence of
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atoms along the surface normal at the adsorbate/substrate interface (Fig.37a) results in the lowest value of Rmin=0.8 (Fig.40b). Other adsorption sites such as B and on-top, as well as a
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misfit layer exhibit larger values of Rmin=1.32, 1.37, and 1.24, respectively. As it was mentioned earlier, DEPES intensities depend on the short range order within the near-surface region, and are determined by the scattering properties of the individual atoms in the solids, which is demonstrated by the scattering factor values in Fig.4. Therefore, in the case of a
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pseudomorphic monolayer exhibiting the A/CBA stacking sequence, characteristic for the continuation of the substrate structure in the adsorbed layer, the anisotropy values are governed only by different scattering properties of the deposited and the substrate atoms as in
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the case of 1ML of Cu on Pt(111) (Fig.40b). The A/CBA stacking sequence at the Cu/Pt(111) interface is also confirmed by DEPES investigations performed at other energies of primary
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electron beam such as Ep=1.4 keV [50]. Again, it must be noted that in the case of a pseudomorphic adsorbate monolayer the same pattern of LEED reflexes for the uncovered as well as the covered substrate surface with A, B, and on-top (C) termination is expected. By contrast, DEPES anisotropy maps reveal the geometry at the interface and, in addition, enable to determine straightforwardly the adsorption sites (Fig.40) [147].
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ACCEPTED MANUSCRIPT 4.2.9. Determination of surface relaxation – Cu/Pt(111) In view of the fact that the signal in DEPES originates from the first few sample layers (see e.g. Fig.22 and Fig.36) the position of intensity maxima should be influenced by any changes of interplanar distances associated with surface relaxation schematically shown in Fig.42. The
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[110] and [001] intensity maxima, which originate already from the two topmost layers (Fig.22b), are expected to be mostly affected by the relaxation. Therefore, the analysis of experimental DEPES distributions and the comparison of measured results with theoretical
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intensity plots, the latter obtained for different interplanar spacings, should lead to the determination of the surface relaxation. An example of such investigations, where the shift of
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intensity maxima in DEPES plots serves as a measure of relaxation, is presented in [116]. In this analysis the displacement is virtually limited to the first layer and described by the relaxation value ∆1,2 (Fig.42), which is measured with respect to the ideally terminated surface. In Fig.43 the polar cut of an experimental DEPES distribution, recorded along the
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[112] − [1 1 2] azimuth of Pt(111) at Ep = 0.8 keV, is shown together with theoretical polar scans calculated for the unrelaxed surface (∆1,2 = 0%), as well as an inward (∆1,2 = –10%) and outward (∆1,2 = +10%) relaxation of the outermost layer. The inward displacement of the first
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layer leads to the shift of peaks in the DEPES profile away from the [111] maximum, while
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the outward displacement results in a shift of the maxima towards the centre at θ = 0° (Fig.43), as it is indicated in Fig.42b. Experimental DEPES plots were recorded at Ep=0.8, 1.1, and 1.4 keV and compared to theoretical data with the use of an R-factor. MS calculations were performed for ∆1,2 displacements ranging from –10% to +10% of the distance between neighbouring bulk-like (111) layers in steps of 1% and the Ep values used in the experiment. The results obtained at Ep = 1.4 keV are presented in Fig.44. The best fit between experimental and simulated DEPES distributions, indicated by the R-factor minimum, is obtained at ∆1,2 = +0.6%. This result reveals a small increase of the interplanar
47
ACCEPTED MANUSCRIPT distance between the first two layers of Pt(111) with respect to the bulk distances between (111) planes, which confirms the literature data obtained with the use of different experimental methods [148,149,150,151,152,153,154,155]. The mean value of the relaxation derived from DEPES results obtained at different Ep values is equal to +0.7%.
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A similar analysis can be applied to one pseudomorphic Cu monolayer on Pt(111) in order to find the distance between the adsorbed layer and the topmost substrate layer. LEED observations performed after the formation of a Cu monolayer at 450K indicate the same
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symmetry and distances between diffraction spots as for the uncovered Pt(111) surface, which proves the formation of the (1×1) adsorbate structure [116]. DEPES investigations applied to
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1ML of Cu on Pt(111) proved that at 450K Cu atoms are adsorbed at threefold A type fcc hollow sites (Fig.40) [147]. Taking into account the above considerations the only remaining parameter to be determined by the quantitative analysis is the interlayer distance between the Cu monolayer and the first Pt layer, described as d0,1 = (1 + ∆0,1)d. The results of this analysis
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at Ep = 1.4 keV are shown in Fig.45. The minimum of an R-factor indicating the best fit was found at ∆0,1 = –7.3%, which shows a smaller distance between the Cu layer and the Pt(111) surface in comparison to the interlayer distances of bulk platinum (111) planes. The mean
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value of the Cu-Pt separation distance obtained from DEPES at different Ep equals to -6.9%, which scales with the smaller size of Cu atom in comparison to Pt. The distances between two
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topmost layers revealed by DEPES for uncovered and Cu covered Pt(111) are similar to results obtained with the use of DFT [116,156,157].
4.2.10. Determination of adatom coordinates – O Ru (10 1 0) The usefulness of the DEPES data analysis by means of anisotropy values is shown in Fig.46. The theoretical DEPES distributions were calculated for a model of one adsorbate and three substrate atoms. The position of the adsorbate atom is defined by the angle θad varying from
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ACCEPTED MANUSCRIPT 10º to 50º (Fig.46a). For comparison the data are presented as theoretical I(θ,ϕ) DEPES and A(θ,ϕ) anisotropy stereographic plots. The low intensity features caused by the adsorbate visible in the DEPES distributions are significantly enhanced on the anisotropy scale. The high intensity central maximum visible in all DEPES distributions originating from a row of
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substrate atoms is represented by the anisotropy minimum. In other words the minimum of the anisotropy reflects the lack of an adsorbate atom along the chain of substrate atoms. The anisotropy maximum reveals the newly formed interatomic axis between adsorbate and
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substrate atoms. A shift of the intensity maximum with θad indicating the new direction formed between adsorbate and substrate atoms is noted. Because of the interference of
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electron waves characteristic intensity rings are noted in all stereographic plots. Therefore, the analysis of the maxima in A(θ,ϕ) distributions can lead to the identification of the adsorption geometry at the interface, as it was already shown in Figs.31, 39, and 40. The comparison of DEPES distributions obtained at the same primary electron beam energy
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Ep for the clean substrate and after the formation of the adsorbate monolayer by means of the anisotropy values for the O Ru (10 1 0) system is presented in [158,50]. The DEPES results
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were used to determine the structure, the positions of the oxygen atoms in the unit cell, as well as bond lengths. As it is known from LEED experiments oxygen forms a long range
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ordered (2 × 1)p2mg structure on Ru (10 1 0 ) [159,158]. It must be noted that at energies used in DEPES above LEED regime the primary electron beam penetrates several atomic layers of the investigated sample because of the large inelastic mean free path. Moreover, the lower values of the scattering cross section for O than for Ru cause that the signal from the substrate predominates in the recorded intensities. Therefore, the DEPES distributions I(θ,ϕ) recorded before and after oxygen adsorption are almost identical if the absolute intensity scale is used [158]. The relative signal changes caused by the saturated adsorbate overlayer are, however, well reflected in the anisotropy distribution A(θ,ϕ) shown in Fig.47. Well distinguished
49
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[
]
anisotropy maxima observed along the 000 1 − [0001] azimuth of the substrate at θ=±26° reveal the interatomic axes between O and Ru atoms. These maxima originate from the focusing of primary electrons along O-Ru atomic pairs, which leads to the enhancement of the DEPES signal along this newly formed interatomic directions. The DEPES polar profiles
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recorded before and after oxygen adsorption are shown in the upper panel of Fig.48. Small but measurable signal changes of the recorded DEPES intensities caused by the adsorbate layer are well visible in the anisotropy profiles shown in the lower panel of Fig.48. The
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anisotropy maxima, which do not correlate with the DEPES signal from the substrate, originate from the formation of the O-Ru atomic pairs after the oxygen adsorption, which is
[
]
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well reflected in the anisotropy profile along the 000 1 − [0001] substrate azimuth. The anisotropy values change within ±15 %, which is well above the experimental uncertainty of the measured DEPES signal of 0.5 %. The anisotropy profile obtained along the [1210] − [1210]
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azimuth, also shown in the lower panel of Fig.48, does not exhibit any maxima because of the lack of O-Ru pairs along this azimuth. Other maxima of the anisotropy noticeable in Fig.47 are associated with the orientation of other interatomic bonds formed between O and Ru
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atoms.
In order to confirm the origin of the anisotropy maxima observed at θ=±26° (Fig.47 and
[
]
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Fig.48) the DEPES polar profiles along the 000 1 − [0001] azimuth of Ru (10 1 0 ) were recorded for a gradual increase of the oxygen coverage. The obtained anisotropy profiles are presented in Fig.49. The steady increase of these maxima with increasing oxygen dose is observed till the coverage saturates. All anisotropy changes are very reproducible including the main maxima at θ=±26°. Further adsorption (above 4 Langmuirs) does not influence the DEPES profiles anymore, which confirms that after the formation of the first saturated oxygen monolayer further adsorption does not take place. The presence of LEED diffraction
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ACCEPTED MANUSCRIPT spots associated with the (2 × 1)p2mg oxygen structure after the DEPES experiments was confirmed. The position of the maxima observed in the anisotropy distribution (Fig.46) depend on the adsorbate-substrate geometry. Therefore, the angular coordinates, namely the polar (θ) and
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azimuthal (ϕ) angles, obtained from the A(θ,ϕ) plot can serve as input parameters for the quantitative determination of the positions of O atoms within the unit cell of the two dimensional (2 × 1)p2mg structure, as well as of the O-Ru bond length [158]. The observed
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LEED patterns together with the anisotropy polar profiles (Fig.48) and the stereographic distribution (Fig.47) indicate that the oxygen structure is commensurate with respect to the
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Ru (10 1 0) lattice. The oxygen atoms belong to the (1 2 1 0) plane perpendicular to the Ru (10 1 0) surface containing substrate atoms and occupy two equivalent adsorption sites symmetrically located along the [0001] − [0001] azimuth, with the O-Ru axis being inclined
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26º with respect to the surface normal. The resulting model of the O /Ru(10 1 0) system is shown in Fig.47b. These conclusions are consistent with the observed LEED patterns, results
[159].
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of LEED I(V) measurements, as well as density functional theory (DFT) data presented in
From the data shown in Figs.46, 47, and 48 it is evident that the anisotropy gives information
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about the orientation of O-Ru axes with respect to the substrate structure underneath. The direct observation of the anisotropy maxima in Fig.47, however, does not, give any information concerning the adatom coordinates within a surface unit cell. Therefore, the above conclusions do not permit a discrimination between the two cases: (1) oxygen atoms are located symmetrically only in the pI plane (Fig.47b) with respect to the Ru atom; (2) the presence of two oxygen domains mutually rotated by 180º with oxygen atoms adsorbed only on one side of the ruthenium atom within the pI and pI’ atomic planes as shown in Fig.47b.
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ACCEPTED MANUSCRIPT The cases (1) and (2) are, however, not confirmed by LEED, as well as can be questioned in view of the repulsive character of the interaction between oxygen atoms. In order to determine the coordinates of adsorbed atoms within a surface unit cell a quantitative data analysis was performed. We choose the more pronounced anisotropy
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maxima in the anisotropy distribution (Fig.47a) and used their angular coordinates (θ,ϕ) to determine the interatomic axes (angular directions) between O and Ru atoms. In Fig.50 only two of these directions are presented for clarity. Other intensity features noted in the
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anisotropy distribution A(θ,ϕ) (Fig.47) restrict the adsorption sites of oxygen to two planes marked as pI and pII in Fig.47b. Then, the following evaluation procedure was applied: For
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the angular direction (θ,ϕ) revealed by the experimental data and an assumed (Y,Z) atom position the distance D between this atom and that direction (dashed blue line) was determined (Fig.50). In this evaluation the first three layers of the Ru (10 1 0 ) cluster and the surface relaxation of the substrate [159] were considered. In the next step the distance D was
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used as an argument of the Gaussian functions. Finally, the mean values of Gaussian functions for all considered angular directions (θ,ϕ) were calculated at different (Y,Z)
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coordinates of the oxygen atom within the rectangle (4.28 Å × 2.71 Å) defined by the size of the substrate unit cell. The normalized, to the highest mean value of Gaussians, results of this
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evaluation, which was performed simultaneously for both pI and pI’ planes, are shown in Fig.51a. The value of a Gaussian function, given by the colour scale, is a measure of a probability of the adatom location. Therefore, the maxima at (1.33 Å, 1.08 Å) and (2.95 Å, 1.08 Å) reveal the positions of oxygen atoms in the pI and pI’ planes, respectively. These maxima are mirror reflected with respect to the [1210] − [1210] substrate azimuth, which is consistent with the conclusions drawn from the experimental data (Fig.47). The analysis performed for the pII plane results in the same position of O and Ru atoms at the corners of the unit cell (Fig.51b), which is unrealistic. In this evaluation procedure the uncertainty of the
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ACCEPTED MANUSCRIPT coordinate values depend on the standard deviation of the Gaussian distribution, which was chosen to be 0.5Å. It should be noted that the values of the coordinates obtained from the quantitative analysis of the experimental anisotropy plots are comparable to LEED (1.13±0.05Å, 0.96±0.02Å) and DFT (1.19Å, 1.06Å) results [159]. Moreover, the above
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analysis enables to find the interatomic distances between O and Ru atoms. The bond lengths between oxygen and ruthenium atoms of the first and second substrate layers are equal to 2.19Å and 2.06Å, respectively, and agree with 2.01 Å and 2.04 Å obtained with the use of
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LEED, as well as 2.11 Å and 2.11 Å revealed from DFT calculations [159]. It should be mentioned that also different relative values of the anisotropy are most likely associated with
however, requires further verification.
5. Conclusions
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different bond lengths, which may serve as an indication of interatomic distances. This,
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Due to the prevalent focused forward scattering of primary electron beam of kinetic energies above 500 eV DAES and DEPES experiments provide information about the crystallinity of the first few layers at solid surfaces as well as about the local bond geometry of adsorbed
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atoms, similar to XPD. DAES and DEPES experiments can be carried out in a standard UHV
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chamber equipped with a simple RFA analyser and a sample manipulator which enables a precise polar and azimuthal rotation of the sample. For a chosen angle of polar (azimuthal) incidence of the primary electron beam the total current of emitted Auger and elastically backscattered electrons is recorded within the acceptance cone of the RFA analyser. Using a lock-in amplifier any variation of this total current as a function of the (ϴ,φ) orientation of the sample surface is discriminated from the isotropic background and represents the desired data. The angles ϴ and φ associated with these characteristic directions are simply read out from the manipulator. Due to the limited mean free path length of electrons in solids and the
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ACCEPTED MANUSCRIPT prevalent forward scattering of the incoming primary electrons at nearest and next-nearest neighbor atoms DAES and DEPES provide information about the local atomic short range order within the surface-nearest layers. Comparison of the measured angular intensity distributions with simulated ones based on the SSC and/or MS formalism, therefore, makes
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DAES and DEPES powerful sources of quantitative information about the crystallinity of solid surfaces and adsorbed layers on them. Thus, a simple classical RFA analyser, available in every surface science laboratory, can be used not only to investigate the long-range surface
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order by means of LEED patterns, and to study the composition and growth mode of surface layers by means of AES, but may simultaneously serve as detector for local bond geometries
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at surfaces by performing DAES and DEPES measurements.
Acknowledgments
We thank the Universty of Wrocław for the financial support under the 1010/S/IFD project.
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We acknowledge prof. Stefan Mróz and prof. Klaus Wandelt for numerous discussions. We would like to thank Michał Jurczyszyn, Andrzej Miszczuk, and Zbigniew Jankowski for fruitful cooperation and technical support. MS computations were carried out in the Wrocław
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Centre for Networking and Supercomputing (www.wcss.wroc.pl).
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Figure captions
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Figure 1. (a) Detection circuit for DEPES and DAES measurements using an RFA analyser. (b) Rotation of the sample with respect to the polar (within the sample surface) and azimuthal
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(perpendicular to the sample surface) axes. The polar angle (θ) was changed between -θmax and θmax in steps of ∆θ=0.25º. The azimuthal angle (ϕ) was changed between 0º and 180º in steps of ∆ϕ=2º. Adopted with permission from [59].
55
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Figure 2. Scattering of an electron plane wave e ikr with the wave vector k, representing
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primary electrons, at the atomic potential. f (k ,θ S ) is the scattering factor and θ S is the
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scattering angle. Angular dependence of f (k ,θ S ) shown as a polar plot.
Figure 3. f (k , θ S ) and phase of the scattered wave as a function of the scattering angle θ S 2
for Cu at different electron energies. Because of high electron energies used in DEPES, in comparison to LEED, partial waves up to the angular momentum l=40 were taken into
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ACCEPTED MANUSCRIPT account. Maxima of f (k , θ S ) at 0º an 180º correspond to the forward scattering and 2
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backscattering of incoming electrons, respectively.
Figure 4. f (k , θ S ) and phase of the scattered wave as a function of the scattering angle θ S
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2
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for O, Cu, and Pt scattering atoms at electron energy 1000eV.
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Figure 5. Scattering geometry of primary electrons striking the crystalline solid used in single scattering cluster (SSC) calculations. Please note that at electron energies in the range of 0.5-
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2.0keV used in DAES and DEPES θ≈θ’ and k≈k’ is assumed.
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ACCEPTED MANUSCRIPT Figure 6. The model applied in MS calculations, where s defines the highest scattering order, k is the wave vector of primary electrons, aj1, …, aj(s-1) represent vectors, which describe the relative positions of scattering atoms in a cluster, and ajS describes the position of an emitter
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with respect to the sth scatterer.
Figure 7. Volume of a cluster determined by the radius Rmax expressed in units of the
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inelastic mean free path λ. Adopted with permission from [59].
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Figure 8. (a) Experimental DEPES polar profile I(θ) recorded for Cu(111) along the
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[112] − [1 1 2] azimuth at Ep=1.2 keV. (b) Visualisation of the scattering process of primary electrons in the crystalline sample. Two incidence beam directions parallel (left hand side)
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and not parallel (right hand side) to the close packed rows of atoms of the fcc(111) sample are
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shown. Adopted with permission from [50].
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Figure 9. Experimental DEPES polar profiles I(θ) recorded for Cu(111) along the
[1 1 2] − [112]
azimuth at different primary electron beam energies Ep. Adopted with
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permission from [40].
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ACCEPTED MANUSCRIPT Figure 10. Experimental DAES polar profiles I(θ) recorded for Cu(111) and the MVV
[
] [ ]
(66eV) Auger transition along the 1 1 2 − 112 azimuth at different primary electron beam
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energies Ep. Adopted with permission from [40].
Figure 11. DAES (MVV Auger transition, 66eV) and DEPES polar profiles I(θ) recorded for
[
]
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Cu(001) along the [110] − 1 1 0 azimuth at primary electron beam energies Ep=0.8, 1.0, and 1.2 keV. The signal anisotropy defined as A=(Imax-Imin)/Imax, where Imax and Imin represent the maximal and minimal signal within the polar scan, is given on the left hand side of each profile. Adopted with permission from [70].
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Figure 12. Experimental DAES (MVV Auger transition, 66eV) and XPD polar profiles I(θ)
[ ] [
]
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recorded for Cu(111) along the 112 − 1 1 2 azimuth at more or less similar energies of the scattered electrons, in DAES primary electrons at energies 800 eV, 1200 eV, 1500 eV and in
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XPD energies of emitted photoelectrons 807 eV, 1178 eV, and 1617 eV. The signal anisotropy values are given on the left hand side. Adopted with permission from [69].
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Figure 13. Experimental DEPES polar profiles I(θ) (lower panel) obtained for Cu(001) along
[
]
the [110] − 1 1 0 azimuth at different primary electron beam energies and corresponding theoretical profiles (upper panel) obtained using the SSC theory. The signal anisotropy is indicated on the left hand side of each polar profile. Adopted with permission from [70].
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Figure 14. Comparison of experimental (red) and theoretical (black) DEPES polar profiles
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I(θ), the latter obtained with the use of the SSC theory, for Cu(001), Cu(111), and Cu(110)
[
]
[
] [ ]
[ ]
along the 1 1 0 − [110] , 1 1 2 − 112 , and [001] − 00 1 azimuths, respectively. For all DEPES profiles the incident electron beam strikes the Cu(001), Cu(111), and Cu(110) samples along the (1 10) plane (Fig.15). For each profile the signal anisotropy is given on the left hand side. Adopted with permission from [48].
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Figure 15. The cut of the fcc structure along the (1 10) plane with indicated atomic
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dashed lines.
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directions. The (001), (111), and (110) planes perpendicular to the paper plane are denoted by
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Figure 16. DEPES polar profiles I(θ) recorded for the Cu(111) substrate along the at different Ag coverages from 1ML till 12 ML at Ep=1.0 keV.
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[1 1 2] − [112] azimuth
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Adopted with permission from [40].
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Figure 17. Ball models of an fcc structure at the adsorbate/substrate interface indicating the growth of an unrotated adsorbate domain (a) exhibiting a CBA/CBA stacking sequence along the surface normal, and an adsorbate domain rotated by 180º (b) associated with the CAB/CBA stacking sequence. Black and grey circles represent the substrate and adsorbate
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atoms, respectively.
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ACCEPTED MANUSCRIPT Figure 18. R-factor values obtained for experimental and theoretical DEPES profiles at Ep=0.8keV. The best fit at Rmin obtained for n1=75% and n2=25% populations of rotated and
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unrotated domains, respectively. Adopted with permission from [4947].
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Figure 19. Experimental DEPES polar profile I(θ) (lower curve) recorded for Ag/Cu(111) at
[
] [ ]
12ML coverage along the 1 1 2 − 112 substrate azimuth and Ep=0.8 keV. Theoretical
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profile (upper curve) obtained with the use of the SSC theory for the best fit at n1=75% and n2=25% populations of rotated and unrotated Ag domains, respectively (Figs.17, 18). Signal anisotropy is given on the left hand side of each profile. Adopted with permission from [49].
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Figure 20. Experimental (a) and theoretical (b) DEPES stereographic intensity plots I(θ,ϕ) obtained for a copper monocrystal (111) at Ep=1.5 keV. Stereographic projection of directions in an fcc(111) monocrystal (c). The area surrounded by the dashed line in (c) indicates incidence beam directions (θ ranges from -72º to 72º) used in (b). In (a) θ ranges from -72º to 70º. Adopted with permission from [59].
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Figure 21. Experimental and theoretical DEPES maps I(θ,ϕ) for Cu(111) at Ep=0.6, 1.2, and 1.8 keV. The intensities within the area surrounded by the dashed circle on the experimental
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permission from [112].
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plot at 0.6 keV (θmax=60°) were used to calculate the contrast for each map. Adopted with
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Figure 22. Calculated contributions of the 1st (a), 2nd (b), 3rd (c), 4th (d), 5th (e), and 6th (f)
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layers to the DEPES signal from Pt(111) at Ep=1.2 keV. The intensity maxima are associated
[
] [ ]
with rows formed by atoms above the considered layer of emitters (Fig.8b). The 1 1 2 − 112 azimuth is indicated by dashed lines (Fig.20c).
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Figure 23. Convergence factor as a function of the scattering order calculated for DEPES profiles obtained for Pt(111) at different primary electron beam energies. The convergence
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order s.
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factor (Eq.(18)), calculated for Is(θ) and Is-1(θ), is shown for the higher considered scattering
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Figure 24. Convergence factor as a function of Rmax value (Fig.7) at different energies of primary electrons Ep. The Rmax value is expressed in units of the inelastic mean free path. The ordinate was calculated for two DEPES intensities obtained for subsequent values of Rmax
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higher Rmax value.
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Figure 25. Convergence factor as a function of the number of layers in Pt(111) considered in MS calculations at Ep=1200eV. The ordinate was calculated for two DEPES intensities
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corresponding to the larger number of layers.
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Figure 26. Theoretical DEPES maps I(θ,ϕ) obtained for Pt(111) at Ep=1.2 keV and different
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Figure 27. Experimental DEPES (a) and DAES (Mo MNN Auger transition, 190 eV) (b) distributions recorded for Mo(110). Theoretical DEPES (c) and DAES (d) maps obtained with the use of the MS formalism for Mo(110). Stereographic projection of directions in a
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electron beam energy Ep=1.8 keV.
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Figure 28. (a) Side view of an fcc(111) monocrystal along the 112 − 1 1 2 azimuth. Because of the ABCABC stacking sequence the terrace termination does not influence the contribution of the [110] , [111] , [112] , [114] , and [001] directions to DEPES intensities. (b)
[
] [
]
Side view of an hcp(0001) monocrystal along the 10 1 0 − 1 010 azimuth. In view of the
[
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ABAB stacking sequence along the surface normal the contribution of the 10 1 2 , 1 011
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[
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and 10 1 1 , 1 012 directions to the DEPES signal depends on the terrace termination.
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Adopted with permission from [59].
Figure 29. (a) Theoretical DEPES distribution I(θ,ϕ) for Ru(0001) and Ep=1.3 keV calculated for A terminated terrace (Fig.27b). (b) Stereographic projection for an hcp(0001)
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[
] [
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nA=48,7 % and nB=51,3 % populations of A and B terminated terraces, respectively. e)
]
DEPES polar profile recorded for Ru(0001) along the 0 1 10 − 01 1 0 azimuth and polar plot
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recorded for polycrystalline Fe. Adopted with permission from [59].
Figure 30. R-factor calculated for experimental and theoretical DEPES distributions at Ep=1.6 keV as a function of population nA and nB of A and B terminated terraces of a Ru(0001) surface. Different sources of phase shifts were used to obtain theoretical DEPES
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Figure 31. Experimental anisotropy distribution A(θ, φ ) for Gr/Ru(0001) at 1.2keV.
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Figure 32. (a) Experimental DEPES distribution I(θ,ϕ) recorded for Ru (10 1 0 ) at Ep=1.2 keV. (b) Corresponding theoretical DEPES plot obtained with the use of the MS theory. (c) Stereographic projection of a (10 1 0) terminated hcp monocrystal. The dashed line indicates the range of incidence angles available in experiment (θ: from −73° to 73°,ϕ: from 0° to
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180°). (d) Side and top view of an hcp(10 1 0) structure. Adopted with permission from [50].
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Figure 33. Experimental DEPES stereographic plot I(θ,ϕ) at Ep = 1.5 keV and a coverage
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equivalent to about 7 BL of Cu on Ru (10 1 0 ) before (a) and after (b) subtraction of the
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background. The polar profiles are taken along the 12 10 - 1 2 1 0 azimuth. Adopted with
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Figure 34. Ball model of Cu layers on Ru (10 1 0 ). Violet rings indicate two most probable adsorption sites of copper forming Cu (111) islands on the second pseudomorphic Cu (10 1 0 )
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bilayer. The arrows show the directions within the hcp(10 1 0) and fcc(111) planes. Adopted
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with permission from [110].
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Figure 35. (a) DEPES distribution I(θ,ϕ) recorded at Ep=1.2 keV and 7 BL of Cu on
Ru (10 1 0) after the background subtraction. (b) R-factor calculated for different contributions
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of the experimental plots for: hcp(10 1 0) structure, unrotated fcc(111)0° and rotated fcc(111)180° Cu domains. (c) The computed DEPES distribution obtained for experimental component maps at the minimum of an R-factor at m=24%, p=41%, and q=35 %. The same
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analysis performed for the theoretical component plots is shown in (d) and (e). The best fit for
[110].
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theoretical maps obtained at m=19%, p=46%, and q=35 %. Adopted with permission from
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Figure 36. (a) Experimental DEPES plot I(θ,ϕ) measured for 1ML of Pt on Cu(111) and Ep=1.1keV. Theoretical DEPES maps I(θ,ϕ) for 1ML of Pt on Cu(111) at: (b-c) A - hollow
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site, (d-e) B - hollow site, (f-g) on-top (C-site), (h-i) bridge site (three mutually rotated Pt domains considered), (j-k) best fit (Fig.38) obtained for two mutually rotated domains at A
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and B adsorption sites shown in Fig.37. The theoretical distributions were calculated for not dissolved (not diss.), and dissolved (diss.) Pt in the first Cu layer. A mixed layer in the form of the Cu3Pt alloy and the presence of a topmost Pt monolayer was considered. The background subtraction procedure was applied for each distribution with the maximum polar angle θmax= 76°. Adopted with permission from [141].
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Figure 37. Ball models of 1ML of Pt on Cu(111) taken into account in MS calculations. (a) A-hollow site. (b) B-hollow site. (c) On-top (C-site). (d) Bridge site (for clarity only one from three possible adsorbate domains is presented). (e) A-hollow site configuration on the first Cu3Pt alloy layer showing the p(2×2) structure at the Pt/Cu interface. All configurations of adsorbate atoms on not dissolved and dissolved Pt were taken into account in calculations of DEPES distributions. The same models (a-c) were used to the inverse system Cu/Pt(111). Adopted with permission from [141].
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Figure 38. R-factor values at different domain populations ni with Pt atoms at A and B, A and bridge, as well as A and on-top adsorption sites at 1ML of Pt on Cu(111) (Fig.37). The best correspondence between theoretical and experimental data is obtained for the coexistence of domains A and B of nA=58% and nB=42% populations when dissolved Pt in Cu is taken into account. Adopted with permission from [141].
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Figure 39. (a) Experimental DEPES anisotropy distribution A(θ,ϕ) recorded for 1 ML of Cu
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on Pt(111) after Cu adsorption at T=330K. Theoretical DEPES anisotropy plots for 1 ML of Cu calculated for: (b) A hollow site layer, (c) B hollow site layer, (d) on-top (C-site) layer, and (e) misfit Cu(13×13) overlayer on Pt(12×12). R-factor values are indicated. Each DEPES distribution obtained at Ep = 1.1 keV. Adopted with permission from [147].
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Figure 40. (a) Experimental DEPES anisotropy plot A(θ,ϕ) for 1 ML of Cu on Pt(111) after
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Cu adsorption at T=450K. Theoretical DEPES anisotropy distributions for 1 ML of Cu simulated for: (b) A hollow site layer, (c) B hollow site layer, (d) on-top (C-site) layer, and (e)
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misfit Cu(13×13) overlayer on Pt(12×12). R-factor values are given. Each DEPES distribution obtained at Ep = 0.8 keV. Adopted with permission from [147].
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Figure 41. Ball model of Cu misfit monolayer on Pt(111). Models of A and B hollow sites, as well as on-top (C-sites) were considered as for the inverse adsorption system Pt/Cu(111)
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shown in Fig.36. Adopted with permission from [147].
[ ] [
Figure 42. Side view of an unrelaxed (a) and relaxed (b) surface along the 112 − 1 1 2
]
azimuth of an fcc(111) monocrystal. An outward relaxation of the first layer results in a displacement of the interatomic directions between the first and second layer, which leads to the shift of DEPES maxima. Adopted with permission from [116].
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Figure 43. Experimental and theoretical DEPES polar profiles for Pt(111) along the
[112] − [1 1 2] azimuth at Ep = 0.8 keV. Simulated polar scans were obtained taking into account: no surface relaxation (∆1,2 = 0%, blue dashed line), contraction of topmost layer by
∆1,2 = –10% (black solid line), and expansion of topmost layer by ∆1,2 = +10% (red solid line). The corresponding shift of maxima is explained in Fig.42. Adopted with permission from [116].
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Figure 44. Values of an R-factor calculated for experimental and theoretical DEPES
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distributions for Pt(111) at Ep = 1.4 keV. Theoretical results were obtained for different relaxation ∆1,2 values of the topmost layer considered in MS simulations (Fig.41). Adopted
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with permission from [116].
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Figure 45. R-factor values obtained for experimental and theoretical DEPES plots for a
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pseudomorphic 1ML of Cu on Pt(111) at Ep = 1.4 keV. Theoretical data were obtained for the Pt(111) surface covered by a pseudomorphic 1 ML of Cu at different relative separation ∆0,1
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[116].
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of the Cu layer taken into account in MS calculations (Fig.42). Adopted with permission from
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Figure 46. (a) Model used in MS simulations. An oxygen atom (red) and three ruthenium
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atoms (black) at different θad angles are shown. (b), (c), (d) DEPES intensity I(θ,ϕ) and anisotropy A(θ,ϕ) distributions calculated at θad=10°, 30°, and 50°, respectively. Adopted
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with permission from [50].
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Figure 47. (a) Experimental DEPES anisotropy plot A(θ,ϕ) obtained from the clean
Ru (10 1 0) substrate and after the formation of the (2 × 1)p2mg oxygen structure at Ep = 1.2 keV. The orientation of the Ru (10 1 0 ) substrate underneath the oxygen monolayer is the same as in Fig.32. The polar angle θ ranges from −73° to 73°. The maxima (dashed black circles)
[
]
observed at θ = ±26° along the 000 1 − [0001] azimuth reveal the interatomic axes formed between Ru and O atoms. (b) Model of the (2 × 1)p2mg oxygen structure on Ru (10 1 0 ) . Adopted with permission from [50].
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Figure 48. Experimental DEPES profiles I(θ) (upper panel) recorded for clean (black solid
[0001] − [0001]
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line) and oxygen covered (red dotted line) Ru (10 1 0 ) substrate at Ep = 1.2 keV along the substrate azimuth. Anisotropy profiles A(θ) (lower panel) along the
[0001] − [0001] (solid black line) and [1210] − [1210] (doted blue line) azimuths of Ru (10 1 0).
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The anisotropy maxima at θ = ±26° are noted only along the [0001] − [0001] azimuth. Adopted
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Figure 49. Anisotropy profiles A(θ) along the [0001] − [0001] azimuth of Ru (10 1 0 ) obtained at increased oxygen coverage. The applied oxygen doses are given in Langmuirs (L).
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The largest dose 4.0L corresponds to the saturated coverage of oxygen.
Figure 50. The scheme used to determine the position of the oxygen atom within a unit cell. At defined (Y,Z) coordinates of an adsorbate atom the direction, read out from the
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indicated. Adopted with permission from [158].
Figure 51. The coordinates (Y,Z) of an adsorbate atom determined with the use of the fitting procedure shown in Fig.50 along pI and pI’ (a) and pII (b) planes (Fig.47b). The maxima in (a) indicate the coordinates of oxygen atoms simultaneously in pI and pI’ planes. The maxima at corners in (b) show the position of substrate atoms (for details see the text). Adopted with permission from [158].
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