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Probing the surface structure of quasicrystals via angle-resolved low-energy ion scattering
Progress in Surface Science 75 (2004) 147–160 www.elsevier.com/locate/progsurf
Probing the surface structure of quasicrystals via angle-resolved low-energy ion scattering Cynthia J. Jenks a
a,*
, Robert Bastasz
b
Department of Chemistry and Ames Laboratory, Iowa State University, Ames, IA 50011-3020, USA b Sandia National Laboratories, Livermore, CA 94551-0969, USA
Abstract Angle-resolved low-energy ion scattering is a valuable technique for examining the topmost surface layers of materials. Using this technique, information about both composition and structure can be obtained. We discuss the physical basis of this technique and present our findings for the fivefold surface of icosahedral (i-) Al–Pd–Mn. Our results clearly show that the exposed surface has a higher Al content than the bulk and can have fivefold periodicity. Information about frequently occurring interatomic distances on the surface can also be obtained by this technique. We discuss the results and compare them to recent scanning tunneling microscopy studies and to bulk structure models. Ó 2004 Published by Elsevier Ltd.
Contents 1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
2.
LEED-IV findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.
Low-energy ion scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.1. Surface composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 4.2. Surface structure and comparison to STM and bulk models . . . . . . . . . 156
*
Corresponding author. Tel.: +1-515-294-8486; fax: +1-515-294-4709. E-mail address: [email protected] (C.J. Jenks).
0079-6816/$ - see front matter Ó 2004 Published by Elsevier Ltd. doi:10.1016/j.progsurf.2004.05.008
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5.
Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
1. Introduction We talk in surface science about the surface sensitivity of our experiments, but what does this mean? For techniques such as Auger electron spectroscopy and X-ray photoelectron spectroscopy this usually means several atomic layers. Few analysis techniques are truly surface sensitive in the sense that they are specific only to the topmost atoms. Scanning tunneling microscopy (STM) is one such technique. STM is invaluable for understanding the surface structure of complex materials such as quasicrystals. Although low-energy electron diffraction (LEED) per se does not provide such surface sensitivity, LEED in combination with dynamical scattering calculations, collectively known as dynamical LEED or LEED-IV analysis, does provide such information. Dynamical LEED work has lead to many valuable insights into the surface structure of materials. In this chapter we discuss the application to quasicrystals of a less widely used technique, angle-resolved low-energy ion scattering (LEIS) and why this technique is particularly well suited to examine i-Al– Pd–Mn. This ultrahigh vacuum (UHV) technique probes both the topmost surface composition of materials and its average local atomic structure. LEIS is complementary to both STM and LEED. Like LEED, LEIS provides information about the overall symmetry of the atom configuration. However, LEIS measurements are directly related to real-space atomic coordinates, whereas LEED views reciprocal space. Like STM, LEIS can provide information about bond distances, but also provides some information about the local surface environment of particular elements.
2. LEED-IV findings The impetus for this work arose from dynamical LEED studies of quasicrystalline Al–Pd–Mn by Gierer et al. published in 1997 and 1998 [1,2]. Dynamical LEED has been used extensively for periodic materials, but the work by Gierer et al. was the first to tackle aperiodic surfaces using dynamical LEED calculations. All previous such work assumed a periodic structure for the initial starting structure. Quasicrystals, lacking a 3D unit cell, made such calculations impossible. Thus a new construct for such calculations had to be devised. The structure optimization of Gierer et al. began with the bulk structure model of Boudard and co-workers [3,4]. This model can be broken down into layers parallel to the surface of interest, each having its own composition and density. In a traditional crystal each atom within a
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unit cell has a unique scattering factor and the number of different scattering factors is limited by the existence of the unit cell; in a quasicrystal there is no limit to the number of different scattering characteristics of each type of atom because each has a unique environment. The aperiodic construct developed approximates the scattering factors by assuming that all atoms within a specific plane have identical scattering properties. The scattering factor used for each plane is weighted using the chemical composition of the plane. An average neighborhood approximation is then applied to handle multiple scattering. Despite the essentially infinite number of different layer compositions and densities that can be identified in the bulk model, many of these layers have certain characteristics in common. The optimum surface layers identified in the dynamical LEED work are all rich in aluminum (on average 93 at.% Al) relative to the average bulk composition, which is about Al72 Pd21 Mn7 , and below each of these layers resides a layer with a 50:50 mixture of Al and Pd. The distance between the first and which is a contraction of 0.10 A relative to the second layer is only 0.38 0.13 A, bulk spacing [1,2]. Additionally the average atomic density of the two closely spaced 2 [2]. Interestingly, this is comlayers of the favored terminations is 0.136 atoms/A 2 . This composition parable to the density of Al(1 1 1), which is 0.141 atoms/A information provides insight as to why the surface reacts much like Al [5–7]. In comparison, both Auger electron spectroscopy and X-ray photoelectron spectroscopy, which probe several layers deep, reveal a composition inline with the average bulk composition of about Al72 Pd21 Mn7 [7,8]. The bulk model data, starting with a favored termination determined by LEED-IV, do yield the average bulk composition into the bulk). Thus, if one averages the composition of at least 11 layers (>7 A significant differences are expected between AES and XPS composition results and other more surface-sensitive techniques. Hence a technique that enables one to distinguish top layer composition directly is critical to confirm the dynamic LEED results.
3. Low-energy ion scattering LEIS has long been used to study the composition and structure of ordered surfaces [9,10]. It works by measuring the energy loss of ions reflected from a sample. In the ‘‘low-energy’’ range from about 0.5 to 5 keV, collisions between atomic particles are well approximated as binary events that can be described by classical two-body kinematics. The energy loss is a function of the incident ion mass, the surface atom mass, and the scattering angle. By using a well-characterized ion beam (i.e., monoenergetic and mass selected) and observing scattered ions at a known observation angle, it is possible to assign the peaks seen in an ion energy spectrum to collisions between the incident ions and surface atoms of particular masses. Consequently, an energy spectrum of the scattered ions provides a mass spectrum of the surface atoms. An example of a scattered-ion energy spectrum is shown in Fig. 1.
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Fig. 1. Ion energy spectrum of 1 keV Heþ scattered from a sputter-cleaned i-Al–Pd–Mn single grain sample at room temperature. The ion beam was at 68° incidence and ions were detected at a scattering angle of 75°. Scattering from the component elements present on the surface of the alloy produces three peaks in the spectrum. A small amount of oxygen is also detected on the surface.
The advantage of LEIS over other surface analysis techniques is an ability to obtain top-layer mass analysis. This is possible when low-energy inert-gas ions are used to probe the surface since they have a high neutralization rate especially when scattered from subsurface layers. Only scattering from the top atomic layer yields an appreciable ion fraction, so detecting scattered ions (but not scattered neutral atoms) is the key to making measurements of the outer atomic layer. The extreme surface specificity of low-energy inert-gas ion scattering comes at a price: quantification is difficult due to uncertainties in knowing the neutralization rate of ions scattered from different surface atoms. This problem is circumvented in certain systems where neutralization rates appear to be relatively constant [11] or by empirical calibration using standards [12]. Other problems encountered with LEIS are surface damage caused by the ion beam probe and poor mass resolution. The energy of the probe ion beam must be at least ’100 eV to ensure the scattering process predominantly consists of binary collisions between the incident ions and the sample atoms, rather than multiple-atom collisions, which prevail at lower energies and do not convey clear atomic mass information. Ions used for LEIS have sufficient momentum to sputter atoms from a surface, thereby creating surface damage and altering sample composition. To minimize sample damage, selecting a light probe ion, keeping the beam energy low, and reducing the beam flux to the sample are helpful. Lowering the beam energy as much as practical is especially useful, as it reduces sputtering and increases the scattered ion signal intensity, due to the inverse dependence of the scattering cross section on energy. Another strategy for reducing beam damage is to make LEIS
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measurements at small observation angles, since scattering cross sections strongly increase with decreasing scattering angle. However, the mass resolution of LEIS decreases with observation angle and also depends upon the probe ion mass. The mass resolution (m=dm) is often not much better than 1–10, so this can be a severe constraint. Consequently, tradeoffs among sample damage, signal intensity, and mass resolution must be carefully considered when setting up the conditions for a LEIS measurement. The drawbacks mentioned above have prevented LEIS from becoming a widely used, general surface analysis technique. However, in certain cases, LEIS proves very useful. A fortuitous circumstance arises in general for quasicrystals, and particularly so for i-Al–Pd–Mn. There appears to be a near absence of the so-called matrix effect, which usually results from variations in the neutralization rate of ions scattered from different surface atoms or along different trajectories. We speculate that the unusual electronic structure of quasicrystal surfaces is responsible for an apparent regularity of scattered ion survival probabilities. In any event, quantification of LEIS data from quasicrystal surfaces does not seem as problematic as from some other materials. In addition, Al–Pd–Mn is perhaps the best suited of the numerous quasicrystal materials for LEIS measurements, due to the large mass difference between each of its elemental components. This allows LEIS measurements to be made with clearly resolved scattering peaks from each constituent at small scattering angles, where signal intensities are large enough to permit good spectra to be recorded with a low incident ion fluence, thereby making beam damage effects negligible. In the study of quasicrystals, the most attractive feature of LEIS is the ability to obtain direct structural information about the surface from angular measurements. This ability results from shadowing and blocking of ion trajectories by surface atoms. An example of shadowing is shown in Fig. 2, which depicts a family of trajectories for 1 keV He projectiles passing by an initially stationary Al atom. The trajectories form an envelope around the Al atom, referred to as a shadow cone.
Fig. 2. A 2D trajectory plot for 1 keV Heþ scattering from an Al atom initially at rest. A shadowed area, whose boundary is described by the function y ¼ kðx þ aÞl , forms behind the initial target atom position. For this case, using the ZBL screened Coulomb potential, a ¼ 0:16, k ¼ 0:64, and l ¼ 0:29. In 3D, the shadowed region has a cone shape.
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Incident particles cannot penetrate the region inside a shadow cone (at least in the absence of other scattering events). So, if another atom is located inside a shadow cone, it is effectively invisible to the incident beam. On a surface, a shadow cone forms behind each exposed surface atom and at particular beam orientations, atoms on the surface can be either outside or inside the shadow cone formed by a neighboring atom. For example, consider a probe ion beam striking a surface at a selected incidence angle. At normal incidence, all surface atoms are visible, while at glancing incidence nearly all of the surface atoms are shadowed. At an intermediate angle, shadow cone edges will pass across neighboring surface atoms and the scattered ion intensity will strongly change with incidence angle. If one monitors the scattered ion intensity as a function of incidence angle on an ordered surface, the angle at which atoms become shadowed can be measured. Then, knowing the shape of the shadow cone, it is possible to determine interatomic distances on the surface. This is illustrated in Fig. 3 for the case of a shadow cone intersecting a neighboring atom. The shape of a shadow cone depends on the atomic number and mass of the colliding particles, their relative energy, and the interatomic potential. In the lowenergy range, a screened Coulomb potential is used to model binary atomic collisions. Suitable screened Coulomb potentials enable one to easily calculate the details of the scattering process and derive expressions for the shape of the shadow cone in the low-energy range for any pair of collision partners. Currently, a popular potential for this purpose is the ZBL potential, sometimes referred to as the universal potential [13]. The derived expressions typically give the shadow cone radius as a function of distance from the target atom, the so-called scattering center. It is also possible to obtain information from LEIS about the local geometric arrangement of atoms on the surface of a sample. This is done with an oblique incidence angle beam that produces shadowing and then rotating the sample in front of the beam. As surface atoms become shadowed or exposed, variations in the LEIS signal intensity can be observed. The signal periodicity is a direct indication of the
Fig. 3. Interatomic distances on a surface can be found from simple geometry when the shadow cone radius r ¼ f ðxÞ is known as well as the angle a at which the shadow cone-edge intersects neighboring atoms.
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Fig. 4. Azimuthal variation of signal intensity of 0.5 keV Heþ scattered from an Al(1 1 1) sample at an oblique incidence angle shows the sixfold symmetry of the surface.
local surface symmetry. Further, by selecting the energy of the scattering signal, information about the local environment of particular types of surface atoms can be obtained. As an example, the variation in signal intensity with sample rotation angle for 1 keV Heþ scattering from Al(1 1 1) is shown in Fig. 4 [14]. The obvious sixfold symmetry of the surface plane results from shadowing of nearest-neighbor atoms, as illustrated in Fig. 5. An analogy may be a helpful way to sum up the characteristics of angle-resolved LEIS analysis. In a sense, LEIS is like surveying land (at least, before the advent of global positioning systems). To survey a field of land or an atomic surface, one needs to identify objects, measure distances, and measure directions. Energy spectra provide identification of surface atoms much like visual sighting identifies objects in surveying. Distances are measured in LEIS through observations of shadowing as a function of the beam angle-of-incidence. The equivalent method in surveying is to use a tape measure or, nowadays, a laser range meter. Directions in LEIS are measured through observations of shadowing as a function of sample azimuthal rotation angle. In surveying, one uses a compass. With either survey data or LEIS data, one can apply the same principles of cartography. The result in one case might be, for example, a map showing the location of trees in an orchard, and in the other, the location of atoms on a quasicrystal surface.
4. Results We thought these features of LEIS made it an attractive technique to use for studying the surface structure of quasicrystals, so we set out to survey the surface of
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Fig. 5. At oblique incidence angles of the probe beam, shadow cones pass over nearest-neighbor atoms when the beam is aligned along closed-packed directions on this fcc(1 1 1) surface plane. The plot is of 0.5 keV Heþ incident on Al(1 1 1) at a ¼ 68°.
a large single grain of i-Al–Pd–Mn grown by Tom Lograsso and colleagues at the Ames Laboratory. We measured the surface composition, structure and local symmetry of the atoms for this sample and the results are described in the following sections. 4.1. Surface composition Initial LEIS results were included with the LEED-IV work [2], and they showed indeed that the topmost surface is Al-rich relative to the bulk average. More detailed LEIS measurements of i-Al–Pd–Mn were made to find out what elements are present at the alloy surface as received and after sputtering. A series of ion energy spectra after various amounts of sputter cleaning is shown in Fig. 6. Looking at an untreated sample, it appears that O and Al cover much of the surface. Only a small signal from Pd is seen and Mn is not in evidence. The ion beam probe used for the analysis was also used to sputter clean the sample. With continued sputtering, surface oxygen decreases and the three alloy components become visible. The Mn signal strength, however, is much smaller than that of Al and Pd. Following sputter cleaning, the sample was annealed up to 525 °C to reorder the surface. Several sputter/anneal cycles were needed to produce a clean, ordered surface. The result is shown in Fig. 1, where almost no O remains on the surface. A quantitative estimate of the surface composition, assuming the absence of matrix effects, can be made by measuring the peak area of each scattering signal and scaling the value according to the scattering cross section for the corresponding element. Scattering cross sections can be calculated to within a few percent accuracy by evaluating the scattering integral (also known as the deflection function) for an
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Fig. 6. A series of ion energy spectra for 1 keV Heþ scattering from i-Al–Pd–Mn (h ¼ 75°, a ¼ 68°) taken during sputter cleaning of the sample at room temperature. The cumulative ion dose to the sample is listed for each spectrum. Initially, oxygen and aluminum cover much of the surface. With continued sputtering, surface oxygen decreases and the three alloy components become visible.
Fig. 7. Angle-of-incidence (a) dependence of Heþ signal intensity scattered from an i-Al–Pd–Mn fivefold surface at three energies, corresponding to collisions with Al, Mn and Pd surface atoms. The Al signal peaks at a higher a than does the Pd signal, indicating that Pd atoms are beneath Al atoms. The angle a is measured with respect to the surface normal. Reprinted from Ref. [20], Copyright (2002), with permission from Elsevier.
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appropriate interatomic potential, such as the ZBL screened Coulomb potential. When this was done, the surface composition was found to be Al86 Pd13 Mn0:8 with the oxygen concentration estimated to be <1%. Compared to its average bulk composition of Al71 Pd20 Mn9 as determined by inductively coupled-plasma atomicemission spectroscopy, the surface of the i-Al–Pd–Mn sample was substantially enriched in Al. In addition to top layer analysis, which is conducted with the incident ion beam striking the sample at an oblique incidence angle, it is possible to probe exposed subsurface layers by directing the beam onto the sample at more normal incidence. The manipulator we use for LEIS measurements allows the sample to be rotated to give beam angles of incidence, a, from 0° to 90°. Monitoring scattered ion intensities from each alloy species as a function of a, provides a means to determine the relative heights of the exposed atoms. Fig. 7 illustrates such a measurement on the i-Al–Pd– Mn surface. At the more glancing angles of incidence, the Al signal dominates. However, at steeper angles of incidence the Pd signal increases and peaks near a ¼ 50°. It should be mentioned that the scattering cross section of Pd is about three times greater than that of Al under these conditions, so that the raw signal intensities do not correspond to atomic concentrations. Nevertheless, the Pd signal dependence on a indicates that exposed Pd atoms are located below the Al atoms. The Mn signal dependence suggests in a similar manner that the majority of exposed Mn atoms reside below the topmost Al layer. 4.2. Surface structure and comparison to STM and bulk models Perhaps the most intriguing LEIS data on i-Al–Pd–Mn were obtained when the sample was azimuthally rotated while probing the surface at an oblique angle of
Fig. 8. Azimuthal (/) dependence of Heþ signal intensity scattered from an i-Al–Pd–Mn fivefold surface at energies corresponding to collisions with Al, Mn and Pd surface atoms. A 72° periodic variation (marked by arrows) in the signal strength is clearly seen for Heþ scattered by Al surface atoms. The Pd atom signal also appears to exhibit fivefold symmetry. Reprinted from Ref. [20], Copyright (2002), with permission from Elsevier.
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incidence. The results are shown in Fig. 8. For a properly prepared surface, we found that the scattering signals from Al and Pd surface atoms exhibited maxima every 72° for a ¼ 67:5°. This is direct evidence that the exposed surface atoms in i-Al–Pd–Mn can reside in locales with fivefold symmetry. Examination of the model of Boudard and de Boissieu and the LEED-IV findings suggests that 10-fold symmetry, rather than fivefold symmetry, should be observed. However, given that the second layer is in close proximity to the first, the effect of this layer must be considered. It turns out that the Pd atoms in the second layer all reside below and in the center of Al pentagons in the first layer and those pentagons are all oriented in the same direction as shown in Fig. 9. At a sufficiently oblique angle of incidence, the shadow cones of the Pd atoms intersect the Al atoms in the first layer. Thus the fivefold symmetry observed is actually induced by the second layer arrangement of atoms relative to the first layer! What about atom separations? As mentioned using LEIS scattered ion intensities from each alloy species can be monitored as a function of a. Such studies yield results pertaining to distances between surface atoms by looking for an inflection in the
Fig. 9. Favored termination of the bulk model of Boudard and de Boissieu based on LEED-IV calcu below the first. Solid black circles represent lation. Two layers are shown. The second layer is only 0.38 A Al in the first layer, the open circles represent Al in the second layer, the solid grey circles represent Pd in the second layer and the circles with x in the middle represent Mn in the first layer. This figure illustrates the important relationship between Pd atom positions in the second layer and Al atoms in the first layer.
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signal as one goes from a ¼ 90° to a ¼ 0°. This inflection point represents the angle at which a shadow cone from one atom skims a neighboring atom, at which point the atom is no longer being shadowed. As noted in Fig. 2, ions are focused along the edge of this shadow cone. Thus additional signal arises because of this as soon as the cone is no longer shadowing a particular atom. From these results, LEIS reveal a 0.5 A. We also find an A1–A1 separation of 3.0 predominant separation of 7.6 A A 0.2 A. These separations show up prominently in both the model of Boudard and de Boissieu and that of Katz, Gratias and Elser, and STM data. Ledieu and coworkers have published some stunning STM images of i-Al–Pd–Mn [15,16]. Analysis of a high resolution STM image shows maxima in the radial distribution function calculated from the autocorrelation function of the STM image, at 7.3, below 15 A,
Fig. 10. Top: radial distribution function calculated from the autocorrelation of a high resolution STM image. Reprinted from Ref. [15]. Copyright (2002) by the American Physical Society. Middle: histogram of atomic separations for a favored termination of a bulk model of i-Al–Pd–Mn by Boudard and de Boissieu. Bottom: histogram of atomic separations for a favored termination of a bulk model of i-Al–Pd–Mn by Katz, Gratias and Elser.
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[15]. Using the raw data for both the bulk model of Katz and co-workers and 12.1 A [17,18] and the bulk model Boudard and co-workers [3,4] we can calculate distances between all atoms of preferred terminations. Fig. 10 shows the resulting histograms in comparison to the radial distribution function calculated by Ledieu and co workers [15]. The Katz, Gratias and Elser model has atoms separated (below 15 A) most commonly by 3.0, 4.8, 7.8, 12.0, and 12.6 A. Similarly the Boudard and de The distriBoissieu model has atomic separations of 3.0, 4.8, 7.8,10.3, and 12.6 A. bution of the separations in Fig. 10 are not the same for the models as for the STM data but this is not unexpected given that STM does not image atoms per se. However, the separations found for both models and the STM results are consistent and are also consistent with our results. Thus, LEIS provides additional evidence that the surface is essentially bulk terminated.
5. Future prospects The potential for using LEIS to study the surfaces of quasicrystals has only just begun to be explored. We discussed here only results for i-Al–Pd–Mn. Taking into account the mass resolution of LEIS, the availability of single grain samples, and their UHV compatibility, some potential candidates for further LEIS investigations are Al–Pd–Mn–Ga, Al–Cu–Ru and Al–Li–Cu. In addition to examining other compositions and orientations, molecular adsorption sites can be explored using LEIS. Looking at i-Al–Pd–Mn should prove interesting. For example, while molecular hydrogen does not dissociate on the surface of i-Al–Pd–Mn [6], H atoms should adsorb. Data about H adsorption on i-Al–Pd–Mn can then be compared to H atom adsorption on pure Al(1 1 1) [19]. Metal overlayer formation studies are another potential focus area. Much work on this is being done by STM, but additional elemental information may be obtainable by LEIS about the sites where metal atoms tend to deposit, which would help to better understand the chemical properties of such systems.
Acknowledgements This manuscript has been authored by Iowa State University of Science and Technology under Contract No. W-7405-ENG-82 with the US Department of Energy and by Sandia National Laboratories under Contract No. DE-AC0494AL85000 also with the US Department of Energy.
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Probing the surface structure of quasicrystals via angle-resolved low-energy ion scattering Cynthia J. Jenks a
a,*
, Robert Bastasz
b
Department of Chemistry and Ames Laboratory, Iowa State University, Ames, IA 50011-3020, USA b Sandia National Laboratories, Livermore, CA 94551-0969, USA
Abstract Angle-resolved low-energy ion scattering is a valuable technique for examining the topmost surface layers of materials. Using this technique, information about both composition and structure can be obtained. We discuss the physical basis of this technique and present our findings for the fivefold surface of icosahedral (i-) Al–Pd–Mn. Our results clearly show that the exposed surface has a higher Al content than the bulk and can have fivefold periodicity. Information about frequently occurring interatomic distances on the surface can also be obtained by this technique. We discuss the results and compare them to recent scanning tunneling microscopy studies and to bulk structure models. Ó 2004 Published by Elsevier Ltd.
Contents 1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
2.
LEED-IV findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.
Low-energy ion scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.1. Surface composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 4.2. Surface structure and comparison to STM and bulk models . . . . . . . . . 156
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Corresponding author. Tel.: +1-515-294-8486; fax: +1-515-294-4709. E-mail address: [email protected] (C.J. Jenks).
0079-6816/$ - see front matter Ó 2004 Published by Elsevier Ltd. doi:10.1016/j.progsurf.2004.05.008
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Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
1. Introduction We talk in surface science about the surface sensitivity of our experiments, but what does this mean? For techniques such as Auger electron spectroscopy and X-ray photoelectron spectroscopy this usually means several atomic layers. Few analysis techniques are truly surface sensitive in the sense that they are specific only to the topmost atoms. Scanning tunneling microscopy (STM) is one such technique. STM is invaluable for understanding the surface structure of complex materials such as quasicrystals. Although low-energy electron diffraction (LEED) per se does not provide such surface sensitivity, LEED in combination with dynamical scattering calculations, collectively known as dynamical LEED or LEED-IV analysis, does provide such information. Dynamical LEED work has lead to many valuable insights into the surface structure of materials. In this chapter we discuss the application to quasicrystals of a less widely used technique, angle-resolved low-energy ion scattering (LEIS) and why this technique is particularly well suited to examine i-Al– Pd–Mn. This ultrahigh vacuum (UHV) technique probes both the topmost surface composition of materials and its average local atomic structure. LEIS is complementary to both STM and LEED. Like LEED, LEIS provides information about the overall symmetry of the atom configuration. However, LEIS measurements are directly related to real-space atomic coordinates, whereas LEED views reciprocal space. Like STM, LEIS can provide information about bond distances, but also provides some information about the local surface environment of particular elements.
2. LEED-IV findings The impetus for this work arose from dynamical LEED studies of quasicrystalline Al–Pd–Mn by Gierer et al. published in 1997 and 1998 [1,2]. Dynamical LEED has been used extensively for periodic materials, but the work by Gierer et al. was the first to tackle aperiodic surfaces using dynamical LEED calculations. All previous such work assumed a periodic structure for the initial starting structure. Quasicrystals, lacking a 3D unit cell, made such calculations impossible. Thus a new construct for such calculations had to be devised. The structure optimization of Gierer et al. began with the bulk structure model of Boudard and co-workers [3,4]. This model can be broken down into layers parallel to the surface of interest, each having its own composition and density. In a traditional crystal each atom within a
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unit cell has a unique scattering factor and the number of different scattering factors is limited by the existence of the unit cell; in a quasicrystal there is no limit to the number of different scattering characteristics of each type of atom because each has a unique environment. The aperiodic construct developed approximates the scattering factors by assuming that all atoms within a specific plane have identical scattering properties. The scattering factor used for each plane is weighted using the chemical composition of the plane. An average neighborhood approximation is then applied to handle multiple scattering. Despite the essentially infinite number of different layer compositions and densities that can be identified in the bulk model, many of these layers have certain characteristics in common. The optimum surface layers identified in the dynamical LEED work are all rich in aluminum (on average 93 at.% Al) relative to the average bulk composition, which is about Al72 Pd21 Mn7 , and below each of these layers resides a layer with a 50:50 mixture of Al and Pd. The distance between the first and which is a contraction of 0.10 A relative to the second layer is only 0.38 0.13 A, bulk spacing [1,2]. Additionally the average atomic density of the two closely spaced 2 [2]. Interestingly, this is comlayers of the favored terminations is 0.136 atoms/A 2 . This composition parable to the density of Al(1 1 1), which is 0.141 atoms/A information provides insight as to why the surface reacts much like Al [5–7]. In comparison, both Auger electron spectroscopy and X-ray photoelectron spectroscopy, which probe several layers deep, reveal a composition inline with the average bulk composition of about Al72 Pd21 Mn7 [7,8]. The bulk model data, starting with a favored termination determined by LEED-IV, do yield the average bulk composition into the bulk). Thus, if one averages the composition of at least 11 layers (>7 A significant differences are expected between AES and XPS composition results and other more surface-sensitive techniques. Hence a technique that enables one to distinguish top layer composition directly is critical to confirm the dynamic LEED results.
3. Low-energy ion scattering LEIS has long been used to study the composition and structure of ordered surfaces [9,10]. It works by measuring the energy loss of ions reflected from a sample. In the ‘‘low-energy’’ range from about 0.5 to 5 keV, collisions between atomic particles are well approximated as binary events that can be described by classical two-body kinematics. The energy loss is a function of the incident ion mass, the surface atom mass, and the scattering angle. By using a well-characterized ion beam (i.e., monoenergetic and mass selected) and observing scattered ions at a known observation angle, it is possible to assign the peaks seen in an ion energy spectrum to collisions between the incident ions and surface atoms of particular masses. Consequently, an energy spectrum of the scattered ions provides a mass spectrum of the surface atoms. An example of a scattered-ion energy spectrum is shown in Fig. 1.
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Fig. 1. Ion energy spectrum of 1 keV Heþ scattered from a sputter-cleaned i-Al–Pd–Mn single grain sample at room temperature. The ion beam was at 68° incidence and ions were detected at a scattering angle of 75°. Scattering from the component elements present on the surface of the alloy produces three peaks in the spectrum. A small amount of oxygen is also detected on the surface.
The advantage of LEIS over other surface analysis techniques is an ability to obtain top-layer mass analysis. This is possible when low-energy inert-gas ions are used to probe the surface since they have a high neutralization rate especially when scattered from subsurface layers. Only scattering from the top atomic layer yields an appreciable ion fraction, so detecting scattered ions (but not scattered neutral atoms) is the key to making measurements of the outer atomic layer. The extreme surface specificity of low-energy inert-gas ion scattering comes at a price: quantification is difficult due to uncertainties in knowing the neutralization rate of ions scattered from different surface atoms. This problem is circumvented in certain systems where neutralization rates appear to be relatively constant [11] or by empirical calibration using standards [12]. Other problems encountered with LEIS are surface damage caused by the ion beam probe and poor mass resolution. The energy of the probe ion beam must be at least ’100 eV to ensure the scattering process predominantly consists of binary collisions between the incident ions and the sample atoms, rather than multiple-atom collisions, which prevail at lower energies and do not convey clear atomic mass information. Ions used for LEIS have sufficient momentum to sputter atoms from a surface, thereby creating surface damage and altering sample composition. To minimize sample damage, selecting a light probe ion, keeping the beam energy low, and reducing the beam flux to the sample are helpful. Lowering the beam energy as much as practical is especially useful, as it reduces sputtering and increases the scattered ion signal intensity, due to the inverse dependence of the scattering cross section on energy. Another strategy for reducing beam damage is to make LEIS
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measurements at small observation angles, since scattering cross sections strongly increase with decreasing scattering angle. However, the mass resolution of LEIS decreases with observation angle and also depends upon the probe ion mass. The mass resolution (m=dm) is often not much better than 1–10, so this can be a severe constraint. Consequently, tradeoffs among sample damage, signal intensity, and mass resolution must be carefully considered when setting up the conditions for a LEIS measurement. The drawbacks mentioned above have prevented LEIS from becoming a widely used, general surface analysis technique. However, in certain cases, LEIS proves very useful. A fortuitous circumstance arises in general for quasicrystals, and particularly so for i-Al–Pd–Mn. There appears to be a near absence of the so-called matrix effect, which usually results from variations in the neutralization rate of ions scattered from different surface atoms or along different trajectories. We speculate that the unusual electronic structure of quasicrystal surfaces is responsible for an apparent regularity of scattered ion survival probabilities. In any event, quantification of LEIS data from quasicrystal surfaces does not seem as problematic as from some other materials. In addition, Al–Pd–Mn is perhaps the best suited of the numerous quasicrystal materials for LEIS measurements, due to the large mass difference between each of its elemental components. This allows LEIS measurements to be made with clearly resolved scattering peaks from each constituent at small scattering angles, where signal intensities are large enough to permit good spectra to be recorded with a low incident ion fluence, thereby making beam damage effects negligible. In the study of quasicrystals, the most attractive feature of LEIS is the ability to obtain direct structural information about the surface from angular measurements. This ability results from shadowing and blocking of ion trajectories by surface atoms. An example of shadowing is shown in Fig. 2, which depicts a family of trajectories for 1 keV He projectiles passing by an initially stationary Al atom. The trajectories form an envelope around the Al atom, referred to as a shadow cone.
Fig. 2. A 2D trajectory plot for 1 keV Heþ scattering from an Al atom initially at rest. A shadowed area, whose boundary is described by the function y ¼ kðx þ aÞl , forms behind the initial target atom position. For this case, using the ZBL screened Coulomb potential, a ¼ 0:16, k ¼ 0:64, and l ¼ 0:29. In 3D, the shadowed region has a cone shape.
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Incident particles cannot penetrate the region inside a shadow cone (at least in the absence of other scattering events). So, if another atom is located inside a shadow cone, it is effectively invisible to the incident beam. On a surface, a shadow cone forms behind each exposed surface atom and at particular beam orientations, atoms on the surface can be either outside or inside the shadow cone formed by a neighboring atom. For example, consider a probe ion beam striking a surface at a selected incidence angle. At normal incidence, all surface atoms are visible, while at glancing incidence nearly all of the surface atoms are shadowed. At an intermediate angle, shadow cone edges will pass across neighboring surface atoms and the scattered ion intensity will strongly change with incidence angle. If one monitors the scattered ion intensity as a function of incidence angle on an ordered surface, the angle at which atoms become shadowed can be measured. Then, knowing the shape of the shadow cone, it is possible to determine interatomic distances on the surface. This is illustrated in Fig. 3 for the case of a shadow cone intersecting a neighboring atom. The shape of a shadow cone depends on the atomic number and mass of the colliding particles, their relative energy, and the interatomic potential. In the lowenergy range, a screened Coulomb potential is used to model binary atomic collisions. Suitable screened Coulomb potentials enable one to easily calculate the details of the scattering process and derive expressions for the shape of the shadow cone in the low-energy range for any pair of collision partners. Currently, a popular potential for this purpose is the ZBL potential, sometimes referred to as the universal potential [13]. The derived expressions typically give the shadow cone radius as a function of distance from the target atom, the so-called scattering center. It is also possible to obtain information from LEIS about the local geometric arrangement of atoms on the surface of a sample. This is done with an oblique incidence angle beam that produces shadowing and then rotating the sample in front of the beam. As surface atoms become shadowed or exposed, variations in the LEIS signal intensity can be observed. The signal periodicity is a direct indication of the
Fig. 3. Interatomic distances on a surface can be found from simple geometry when the shadow cone radius r ¼ f ðxÞ is known as well as the angle a at which the shadow cone-edge intersects neighboring atoms.
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Fig. 4. Azimuthal variation of signal intensity of 0.5 keV Heþ scattered from an Al(1 1 1) sample at an oblique incidence angle shows the sixfold symmetry of the surface.
local surface symmetry. Further, by selecting the energy of the scattering signal, information about the local environment of particular types of surface atoms can be obtained. As an example, the variation in signal intensity with sample rotation angle for 1 keV Heþ scattering from Al(1 1 1) is shown in Fig. 4 [14]. The obvious sixfold symmetry of the surface plane results from shadowing of nearest-neighbor atoms, as illustrated in Fig. 5. An analogy may be a helpful way to sum up the characteristics of angle-resolved LEIS analysis. In a sense, LEIS is like surveying land (at least, before the advent of global positioning systems). To survey a field of land or an atomic surface, one needs to identify objects, measure distances, and measure directions. Energy spectra provide identification of surface atoms much like visual sighting identifies objects in surveying. Distances are measured in LEIS through observations of shadowing as a function of the beam angle-of-incidence. The equivalent method in surveying is to use a tape measure or, nowadays, a laser range meter. Directions in LEIS are measured through observations of shadowing as a function of sample azimuthal rotation angle. In surveying, one uses a compass. With either survey data or LEIS data, one can apply the same principles of cartography. The result in one case might be, for example, a map showing the location of trees in an orchard, and in the other, the location of atoms on a quasicrystal surface.
4. Results We thought these features of LEIS made it an attractive technique to use for studying the surface structure of quasicrystals, so we set out to survey the surface of
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Fig. 5. At oblique incidence angles of the probe beam, shadow cones pass over nearest-neighbor atoms when the beam is aligned along closed-packed directions on this fcc(1 1 1) surface plane. The plot is of 0.5 keV Heþ incident on Al(1 1 1) at a ¼ 68°.
a large single grain of i-Al–Pd–Mn grown by Tom Lograsso and colleagues at the Ames Laboratory. We measured the surface composition, structure and local symmetry of the atoms for this sample and the results are described in the following sections. 4.1. Surface composition Initial LEIS results were included with the LEED-IV work [2], and they showed indeed that the topmost surface is Al-rich relative to the bulk average. More detailed LEIS measurements of i-Al–Pd–Mn were made to find out what elements are present at the alloy surface as received and after sputtering. A series of ion energy spectra after various amounts of sputter cleaning is shown in Fig. 6. Looking at an untreated sample, it appears that O and Al cover much of the surface. Only a small signal from Pd is seen and Mn is not in evidence. The ion beam probe used for the analysis was also used to sputter clean the sample. With continued sputtering, surface oxygen decreases and the three alloy components become visible. The Mn signal strength, however, is much smaller than that of Al and Pd. Following sputter cleaning, the sample was annealed up to 525 °C to reorder the surface. Several sputter/anneal cycles were needed to produce a clean, ordered surface. The result is shown in Fig. 1, where almost no O remains on the surface. A quantitative estimate of the surface composition, assuming the absence of matrix effects, can be made by measuring the peak area of each scattering signal and scaling the value according to the scattering cross section for the corresponding element. Scattering cross sections can be calculated to within a few percent accuracy by evaluating the scattering integral (also known as the deflection function) for an
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Fig. 6. A series of ion energy spectra for 1 keV Heþ scattering from i-Al–Pd–Mn (h ¼ 75°, a ¼ 68°) taken during sputter cleaning of the sample at room temperature. The cumulative ion dose to the sample is listed for each spectrum. Initially, oxygen and aluminum cover much of the surface. With continued sputtering, surface oxygen decreases and the three alloy components become visible.
Fig. 7. Angle-of-incidence (a) dependence of Heþ signal intensity scattered from an i-Al–Pd–Mn fivefold surface at three energies, corresponding to collisions with Al, Mn and Pd surface atoms. The Al signal peaks at a higher a than does the Pd signal, indicating that Pd atoms are beneath Al atoms. The angle a is measured with respect to the surface normal. Reprinted from Ref. [20], Copyright (2002), with permission from Elsevier.
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appropriate interatomic potential, such as the ZBL screened Coulomb potential. When this was done, the surface composition was found to be Al86 Pd13 Mn0:8 with the oxygen concentration estimated to be <1%. Compared to its average bulk composition of Al71 Pd20 Mn9 as determined by inductively coupled-plasma atomicemission spectroscopy, the surface of the i-Al–Pd–Mn sample was substantially enriched in Al. In addition to top layer analysis, which is conducted with the incident ion beam striking the sample at an oblique incidence angle, it is possible to probe exposed subsurface layers by directing the beam onto the sample at more normal incidence. The manipulator we use for LEIS measurements allows the sample to be rotated to give beam angles of incidence, a, from 0° to 90°. Monitoring scattered ion intensities from each alloy species as a function of a, provides a means to determine the relative heights of the exposed atoms. Fig. 7 illustrates such a measurement on the i-Al–Pd– Mn surface. At the more glancing angles of incidence, the Al signal dominates. However, at steeper angles of incidence the Pd signal increases and peaks near a ¼ 50°. It should be mentioned that the scattering cross section of Pd is about three times greater than that of Al under these conditions, so that the raw signal intensities do not correspond to atomic concentrations. Nevertheless, the Pd signal dependence on a indicates that exposed Pd atoms are located below the Al atoms. The Mn signal dependence suggests in a similar manner that the majority of exposed Mn atoms reside below the topmost Al layer. 4.2. Surface structure and comparison to STM and bulk models Perhaps the most intriguing LEIS data on i-Al–Pd–Mn were obtained when the sample was azimuthally rotated while probing the surface at an oblique angle of
Fig. 8. Azimuthal (/) dependence of Heþ signal intensity scattered from an i-Al–Pd–Mn fivefold surface at energies corresponding to collisions with Al, Mn and Pd surface atoms. A 72° periodic variation (marked by arrows) in the signal strength is clearly seen for Heþ scattered by Al surface atoms. The Pd atom signal also appears to exhibit fivefold symmetry. Reprinted from Ref. [20], Copyright (2002), with permission from Elsevier.
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incidence. The results are shown in Fig. 8. For a properly prepared surface, we found that the scattering signals from Al and Pd surface atoms exhibited maxima every 72° for a ¼ 67:5°. This is direct evidence that the exposed surface atoms in i-Al–Pd–Mn can reside in locales with fivefold symmetry. Examination of the model of Boudard and de Boissieu and the LEED-IV findings suggests that 10-fold symmetry, rather than fivefold symmetry, should be observed. However, given that the second layer is in close proximity to the first, the effect of this layer must be considered. It turns out that the Pd atoms in the second layer all reside below and in the center of Al pentagons in the first layer and those pentagons are all oriented in the same direction as shown in Fig. 9. At a sufficiently oblique angle of incidence, the shadow cones of the Pd atoms intersect the Al atoms in the first layer. Thus the fivefold symmetry observed is actually induced by the second layer arrangement of atoms relative to the first layer! What about atom separations? As mentioned using LEIS scattered ion intensities from each alloy species can be monitored as a function of a. Such studies yield results pertaining to distances between surface atoms by looking for an inflection in the
Fig. 9. Favored termination of the bulk model of Boudard and de Boissieu based on LEED-IV calcu below the first. Solid black circles represent lation. Two layers are shown. The second layer is only 0.38 A Al in the first layer, the open circles represent Al in the second layer, the solid grey circles represent Pd in the second layer and the circles with x in the middle represent Mn in the first layer. This figure illustrates the important relationship between Pd atom positions in the second layer and Al atoms in the first layer.
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signal as one goes from a ¼ 90° to a ¼ 0°. This inflection point represents the angle at which a shadow cone from one atom skims a neighboring atom, at which point the atom is no longer being shadowed. As noted in Fig. 2, ions are focused along the edge of this shadow cone. Thus additional signal arises because of this as soon as the cone is no longer shadowing a particular atom. From these results, LEIS reveal a 0.5 A. We also find an A1–A1 separation of 3.0 predominant separation of 7.6 A A 0.2 A. These separations show up prominently in both the model of Boudard and de Boissieu and that of Katz, Gratias and Elser, and STM data. Ledieu and coworkers have published some stunning STM images of i-Al–Pd–Mn [15,16]. Analysis of a high resolution STM image shows maxima in the radial distribution function calculated from the autocorrelation function of the STM image, at 7.3, below 15 A,
Fig. 10. Top: radial distribution function calculated from the autocorrelation of a high resolution STM image. Reprinted from Ref. [15]. Copyright (2002) by the American Physical Society. Middle: histogram of atomic separations for a favored termination of a bulk model of i-Al–Pd–Mn by Boudard and de Boissieu. Bottom: histogram of atomic separations for a favored termination of a bulk model of i-Al–Pd–Mn by Katz, Gratias and Elser.
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[15]. Using the raw data for both the bulk model of Katz and co-workers and 12.1 A [17,18] and the bulk model Boudard and co-workers [3,4] we can calculate distances between all atoms of preferred terminations. Fig. 10 shows the resulting histograms in comparison to the radial distribution function calculated by Ledieu and co workers [15]. The Katz, Gratias and Elser model has atoms separated (below 15 A) most commonly by 3.0, 4.8, 7.8, 12.0, and 12.6 A. Similarly the Boudard and de The distriBoissieu model has atomic separations of 3.0, 4.8, 7.8,10.3, and 12.6 A. bution of the separations in Fig. 10 are not the same for the models as for the STM data but this is not unexpected given that STM does not image atoms per se. However, the separations found for both models and the STM results are consistent and are also consistent with our results. Thus, LEIS provides additional evidence that the surface is essentially bulk terminated.
5. Future prospects The potential for using LEIS to study the surfaces of quasicrystals has only just begun to be explored. We discussed here only results for i-Al–Pd–Mn. Taking into account the mass resolution of LEIS, the availability of single grain samples, and their UHV compatibility, some potential candidates for further LEIS investigations are Al–Pd–Mn–Ga, Al–Cu–Ru and Al–Li–Cu. In addition to examining other compositions and orientations, molecular adsorption sites can be explored using LEIS. Looking at i-Al–Pd–Mn should prove interesting. For example, while molecular hydrogen does not dissociate on the surface of i-Al–Pd–Mn [6], H atoms should adsorb. Data about H adsorption on i-Al–Pd–Mn can then be compared to H atom adsorption on pure Al(1 1 1) [19]. Metal overlayer formation studies are another potential focus area. Much work on this is being done by STM, but additional elemental information may be obtainable by LEIS about the sites where metal atoms tend to deposit, which would help to better understand the chemical properties of such systems.
Acknowledgements This manuscript has been authored by Iowa State University of Science and Technology under Contract No. W-7405-ENG-82 with the US Department of Energy and by Sandia National Laboratories under Contract No. DE-AC0494AL85000 also with the US Department of Energy.
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