He scattering study of diffusion at a melting surface

Surface Science 211/212 (1989) 21--30 North-Holland, Amsterdam

He SCA’ITERING J.W.M.

FRENKEN

Max-Plan&-Institut

21

STUDY OF DIFFUSION *, B.J. HINCH

ftir Str6mungsforschung,

AT A MELTING

SURFACE

and J.P. TOENNIES Bunsenstrasse

IO, 3400 Giittingen,

Fed. Rep. of Germany

Received

14 August

1988; accepted

for publication

7 September

1988

A new application of He atom scattering is introduced. It is shown that the quasielastic scattering of low-energy He atoms can be used to study two-dimensional diffusion at surfaces on an atomic scale. Measurements are presented for the self-diffusion along the [liO] azimuth at the Pb(ll0) surface at a temperature of 521 K. Other experiments have shown the Pb(ll0) surface to be partially disordered at this temperature, as a result of the onset of a surface melting transition. From the dependence of the width of the quasielastic energy distribution, of scattered He atoms, on the initial and final angles, both the diffusion mechanism and the diffusion coefficient are derived. The results show that the diffusion coefficient at the surface along [liO], at 521 K, exceeds the value for bulk-liquid Pb at the bulk melting point, Tzb = 600.7 K. The diffusive motion can be described in terms of jumps with a continuous distribution of jump lengths and an average jump length of - 4.4 Ai.

1. Introduction The scattering of atom beams from crystal surfaces is a well-established experimental technique in modem surface science, dating back to the classic diffraction experiment by Estermann and Stern in 1930 [l]. Measurements of diffraction intensities can be used to study the geometrical structure of clean and adsorbate-covered crystal surfaces [2]. The diffuse elastic intensity, between diffraction directions, contains information on the shape of the surface corrugation profile of individual surface “defects”, such as steps [3] or adsorbed molecules [4]. The narrow energy distribution, which can be obtained in nozzle beams of He atoms, is exploited in high-resolution inelastic atom-scattering measurements of surface phonons [5], and vibrational frequencies of adsorbed atoms or molecules [6]. In this paper we demonstrate that, when the diffuse scattering signal, arising from individual surface defects, is measured with sufficiently high energy resolution, atomic-scale information can be extracted on the diffusive * Present address: FOM-Institute Amsterdam. The Netherlands.

for Atomic

and Molecular

0039-6028/89/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

Physics,

B.V.

Kruislaan

407, 1098 SJ

22

a[liol = 3.L9 A

Fig. 1. Perspective

view of the Pb(l10)

surface

motion of these defects. The “quasielastic” He atom-scattering technique is applied here to the self-diffusion at a melting surface. Surface melting is a continuous order-disorder phase transition, which can take place at crystal surfaces at temperatures below the bulk melting point T,, [7,8]. This surface phase transition is of particular interest, since it is thought to play an important role in nucleating bulk melting, thereby preventing superheating of solids above T,, under normal conditions. Although the possibility of surface melting has been conjectured long ago [9,10], the first unambiguous experimental demonstrations of this phenomenon have been made only quite recently [llL16]. At present, the most extensive experimental information on surface melting is available for surfaces of Pb crystals [11,12,15,16]. For this material it has been shown that the occurrence of surface melting depends critically on the crystal face; the most densely packed faces remain stable up to r., while the most open surfaces exhibit the strongest surface-melting effect [12]. In order to determine whether or not a “melting surface” features liquid-like atomic mobilities, we have performed quasielastic He atom scattering measurements on the (110) surface of Pb (fig. 1). In an earlier report of the first quasielastic scattering experiments with low-energy He atoms, we have shown that the Pb adatom diffusivities become noticeably large above - 450 K, in both the [liO] and the [OOl] surface direction [16]. Here, we demonstrate that quasielastic He atom scattering can be used to determine the actual mechanism of diffusion on an atomic scale. For the Pb(ll0) surface. ion-scattering measurements have shown that the disordering starts at - 450 K and proceeds layer builds up, of about ten in two stages. Up to - 580 K, a transition monolayers thickness, over which the order is gradually lost with distance from the underlying crystal to the surface. Above this temperature, this region of transition moves into the bulk, leaving a surface which in ion-scattering measurements looks completely disordered. The quasielastic scattering measurements described in this paper have been performed for the [liO] azimuth

J. W.M. Frenken et al. / He scattering study

of a melting

surface

23

at a fixed crystal temperature of 521 K. The selected temperature lies within the temperature range where partial lattice order is still observed at the surface. Nevertheless, the diffusion motion found here along the [liO] azimuth (fig. l), does not show clear signs of crystalline order. The diffusion constant derived from our data for the [liO] direction at this temperature, exceeds the bulk-liquid value by almost a factor two.

2. Principal of quasielastic atom scattering The quasielastic scattering of low-energy atoms from a surface with laterally diffusing adatoms has been treated theoretically by Levi et al. [17]. Analogously to the case of thermal-energy neutron scattering [18], the energy distribution of He atoms, which are diffusely scattered from the moving particles, is weakly inelastic. The small energy transfers, responsible for the quasielastic broadening of the reflected energy distribution, with respect to the incident energy distribution, have an origin analogous to Doppler broadening. For the diffusion mechanisms, considered in this work, the quasielastic energy profile S(K, w) has a Lorentzian shape:

S(K, 0) -

f(K) w2+f2(K)

(1)

Here, AK is the component of the momentum transfer parallel to the surface (in the following we will simply call K the parallel momentum transfer, and K its magnitude 1K I), and ttw is the energy transfer in the scattering process. Departing from the convention of earlier work of our group, we denote the parallel momentum transfer by K instead of AK, since the symbol “A” will be used to designated a width instead of a transfer. The function f(K) explicitly depends on the assumed model for the lateral diffusion [19,20]. The full-widthat-half-maximum (FWHM) of this energy distribution amounts to

AE(K)=2tf(K).

(2)

Table 1 lists AE(K) relations for four simple diffusion models. In case of random continuous diffusion, model I, the mean-square diffusion distance is proportional to the time. This results in a parabolic dependence of AE on K [17-201. For the jump-diffusion models II, III and IV BE(K) was derived with use of the theoretical work by Chudley and Elliott [20]. The discreteness of the jump lengths in models II and III leads to a periodicity of the quasi-elastic energy width in reciprocal space. The continuous distribution of jump lengths up to some maximum value in model IV, gives rise to a damped oscillation in AE versus K. Note, that for all four diffusion models in table 1, AE( K = 0)= 0 (specular scattering is always purely elastic), and AE(smal1 K) = 2ADK 2. This simply

Table

1

Relation

between the quasielastic

four one-dimensional

diffusion

energy width

.!E

and the parallel

Model

Description

I

Continuous

II

Jumps ocw i II. with a\eragr time 7

A E( K

T

Jumps over i (1. k70.

with average

Continuous

distribution

)

for

t, 27

co.\h'u+cos 2Ku

2

of jump lengtha,

Xc,'

)

47. 0 111,1,

with 3 maximum length u,,,,~~ and

67

average time 7 between successiveJumps K is aligned with the direction

K

I)

( I ~ co\ Ktr)

-+

time 7 betweenJumpx IV

transfer

2 hDK'

random dlffuawn

hetueen succe5ai\~eJumps III

momentum

models

of the diffusion.

The diffuion

coefficient

the mean-square travelled distance per umt of time, n = X’,Or. and the average time between successive jumps.

fI, dcfincd ;15 0.5 tlmcs

is expressed in the jump

length

for models II to IV.

means, that on a sufficiently large length scale, corresponding to small enough values of K. the diffusion always can be adequately described as a continuous process (model I). The diffuse, elastically scattered intensity arises from the presence of defects on the surface. He atom scattering is sensitive to defects such as adatoms, vacancies and step edges. The latter is not expected to be as mobile as the other type of defects [3]. Assuming that adatoms have a much higher cross section for diffuse scattering than vacancies [21], we can determine, from our low-energy He atom-scattering measurements, the diffusion coefficients and diffusion mechanisms for Pb adatoms on the Pb(ll0) surface.

3. Crystal preparation and experimental

set-up

The Pb(ll0) specimen was spark-cut from a single-crystal ingot of 99.999 purity. Smooth. clean and well-ordered surfaces were obtained by a standard procedure [ll], which involves a chemical etch-polish treatment, followed by cycles of sputtering and annealing in ultrahigh vacuum (UHV). The crystal was clamped in a MO container, which could be heated radiatively from its reverse side. The crystal temperature was monitored with a Pt resistance thermometer and an infrared pyrometer, calibrated against the bulk-melting point (600.7 K). Cleanliness and surface crystalline order were checked with Auger electron spectroscopy and He diffraction. Fig. 2 schematically shows the experimental set-up used for the quasielastic He-scattering measurements. A supersonic He beam. with a central energy of

J. W.M. Frenken et 01. / He scuttering studs

HE

of o melting

surface

25

GAS NOZZLE SKIMMER

ION OPTICS MULTIPLIER Fig. 2. Schematic

representation

of the atom scattering

apparatus

- 5 meV, was produced by expansion of He gas from a cooled (10 pm diameter) nozzle, through a skimmer and a set of diaphragms into the UHV scattering chamber. Scattered He atoms were detected at a fixed scattering beam, as indicated in fig. 2. angle of 90” with respect to the incident Time-of-flight (TOF) analysis between chopper 1 and the detector was used to obtain energy distributions of scattered He atoms. The energy resolution of the complete system, including the energy width of the incident He beam and the time resolution of the TOF measurement, amount to - 150 to - 170 PeV at the beam energy of 5 meV. This was determined both from measurements with the crystal at room temperature, and measurements of the (purely elastic) specular beam. In order to raise the low signal-to-background ratio in these measurements, a second chopper was introduced, between the crystal and the detector, which runs in phase with chopper 1 [22]. Chopper 2 only lets through a narrow time window of the TOF spectrum, which was centered, in the present experiments. around the time of arrival of the quasielastic peak. Since only the time interval of interest in the TOF distribution is transmitted to the detector. the frequency, with which this selected time interval is scanned, may be raised without signal overlap. For our set-up, this has increased the signal by a factor 6.

4. Results Fig. 3 shows a measured energy spectrum of He atoms scattered from Pb(ll0) at a crystal temperature of 521 K. with a beam energy of 5.3 meV and

26

r;

r 5.3~-~~ meV

9 z Q

~ [1101 AZIMUTH, -_ ~~~~~

He-Pb~llOl.

0, = 36".

T=

521K I

i ~,

-LOO

-200 ENERGY

0 TRANSFER

200

LOO

(peV1

Fig. 3. Energy distribution of He atoms scattered from a Pb(ll0) surface. at a crystal temperature of 521 K, for K = 0.70 k’ along the [ITO] surface azimuth. The most probable beam energy is 5.3 meV. The dashed curve shows the experimental resolution of 172 PeV. The full curve serves to guide the eye.

an incident

angle of 36’ with respect to the surface normal, corresponding to along the [liO] azimuth. The spectrum has been corrected by the subtraction of a smoothly varying inelastic background. The dashed Gauss curve illustrates the instrumental resolution of 172 PeV, measured at the same temperature at K = 0.In fact, each measured quasielastic peak is the sum of many (typically 20) shorter measurements, which have been interrupted by reference measurements at K = 0.The sum of these reference measurements was used to determine the actual instrumental energy resolution during a quasielastic scattering measurement. This procedure eliminates the effects of possible slow variations in beam energy and beam quality. The quasielastic energy broadening, for K = 0.70 A-’ at 521 K. is clearly visible in fig. 3. Correcting the FWHM of the measured energy distribution in fig. 3 for the Gaussian instrumental response function, we find for the width of the Lorentzian quasielastic energy profile, A E = 38 PeV. In order to obtain an atomic-scale picture of the self-diffusion on Pb(ll0). we have measured the angular dependence of the quasielastic energy width AE, along the [liO] surface direction, at one fixed temperature of 521 K. Fig. 4 displays the results, with the incident and final angles converted to parallel momentum transfer K. Several diffusion models can be ruled out immediately, from a visual inspection of fig. 4. First. the energy width is not proportional to K2 over the

K = 0.70 A-’

J. W.M. Frenken et al. / He scattering study

PARALLEL

MOMENTUM

ofa melting

TRANSFER

surface

21

K (A-‘,

Fig. 4. Dependence of the energy width A E of the quasielastic peak on the parallel momentum transfer K, along the (liO] direction. at a crystal temperature of 521 K. The different symbols are discussed in the text. The dashed vertical line indicates the reciprocal lattice point at K =1.80 A ‘. Calculated curves are shown for the four diffusion models of table 1: (I) continuous random diffusion (dotted curve): (II) jump diffusion over single lattice spacings (dashed curve); (III) jump diffusion over single and double lattice spacings (dash-dotted cur/e); (IV) jump diffusion with a continuous distribution of jump lengths (full-curve). Details of the calculations are given in the text.

entire K range. This shows that, at this temperature, the self-diffusion on Pb(ll0) along [liO] cannot be described as continuous, random diffusion (model I, dotted curve). Second, the data in fig. 4 are not periodic in K. The minimum in A E around K = 0 is much broader than the narrow minimum in A E around K= 2r/'al,i,l- 1.80A-‘. From this we conclude that the meaa surements cannot be simply described in terms of jump diffusion with instantaneous jumps of length a[lIo) or integer multiples thereof. This is illustrated by the curves for models II (jumps over k a[iiol, dashed curve) and III (equally curve) in fig. 4. probable jumps over f aniol and k 2allIol, dash-dotted The scattering intensities suggest that the measurements around K = 1.80 k' are dominated by a purely elastic diffraction contribution from the Pb(ll0) substrate. The surface is not yet completely disordered at 521 K. The high intensities near K = 1.80k' do not originate from defects. We are thus forced to ignore the few datapoints (open symbols in fig. 4) around 1.80 k’. We then see that the quasielastic signal for this azimuth, from individual diffusing atoms on the surface, does not exhibit any significant minimum in energy width except at K = 0. The dash-dotted curve, for the single-and-double jump model (model III), was obtained assuming and average time between successive jumps of r = 4.3 x lo-” s, corresponding to a diffusion coefficient of DfIio] = 3.5 X lop5 cm2 this curve does not fit the experimental AE values for K > 1.5 S -‘. Although

A -‘, it does describe the data quite well up to 1.5 A ‘. including the local ” minimum in AE for K = 0.90 A-‘. This indicates that both the diffusion coefficient, the average jump length and the average time between successive jumps are already approximately described byJ model III. The simplest alternative model, which does not lead to a distinct periodicity of AE in reciprocal space, allows a continuous distribution of equally probable jump lengths between zero and a maximum jump length u,,,,, (model IV). From the average jump length for the single-and-double jump model of l.Scttiiol. we could estimate the nlaximum jump length to be unlen = 3ctii~ol = 10 A. The fitting of the continuous-distribution model to the data instead leads to s. This corresponds to D~i~lo]= 3.8 X lo-' u mi,x= 8.7 A and r = 3.4 X IO-” cm’ s ‘. This best fit is shown by the full curve in fig. 4.

5. Discussion In summary, the K-dependence of the quasielastic energy widths in fig. 4 shows, that at 521 K the self-diffusion at the Pb(ll0) surface along the [liO] surface rows, can be described in terms of jumps, with a continuous distribution of jump lengths from 0 to - 8.7 A. The average time between successive jumps of 3.4X 10-i’ s is much larger than the typical vibrational period, which is for Pb in the order of 1 X 10 ” s 1231. The surface diffusion coefficient along [l?O] at this temperature exceeds the value for bulk-solid Pb of 4.5 x lop" cm2 SC’ [24] by five orders of magnitude. It exceeds the bulk-liquid value of 2.2 x lo-'cm2 s-i [25] by more than 50%. This finding is in agreement with the result of molecular dynamics calculations for LennardJones systems at high temperatures [26,27]. These show that close to melting, lateral surface atomic mobilities exceed the diffusion coefficient for the three-dimensional liquid. It is interesting to compare the results, obtained here for the surface of a three-dimensional solid, with recent quasielastic neutron-scattering results by Bienfait et al. for thin adsorbed methane films on MgO powder [28,29]. The MgO particles expose mainly (001) surfaces. on which the methane overlayers grow epitaxially. As for the Pb(ll0) surface, surface self-diffusion coefficients were found for the methane films which exceed the bulk-liquid value. Although the (001) surfaces were of course randomly oriented in the neutronscattering experiments, the hE( K) data, which were measured at temperatures where the surface layers of the thin methane films were “molten”, provided evidence for jump diffusion of the methane molecules over single lattice spacings of the square (001) lattice. The present results for diffusion along [1iO]on Pb(ll0) cannot be described by such a simple diffusion model. A possible cause for this difference, between the melting surfaces of Pb and adsorbed methane films, could be the difference in substrate order. The

J. W. M. Frenkrn et al. / He sruttenng

.srudy of a meltrng surface

29

influence of the MgO(001) substrate with fully preserved lattice order, is of course absent for the Pb(ll0) surface. At first sight it is surprising that the diffusion along [liO] does not exhibit a recognizable signature of the the lattice periodicity at 521 K, whereas ion scattering [ll], LEED [15] and He atom diffraction [30] show residual lattice order at the surface, at this temperature. One might imagine that fluctuations make the surface inhomogeneously disordered, and the diffusion mainly takes place on the more disordered patches of the surface. The more ordered regions would then be responsible for the diffraction signal, while the energy-broadened, diffusely scattered signal would arise from the disordered regions. In order to explain the high-temperature behavior of the mass-transport diffusion coefficients, found on various metal surfaces, Bonzel has proposed that a non-localized diffusion process dominates at high temperatures [31]. In this process the adatoms could diffuse by a two-dimensional gas-like flight. The expected A,!?(K) relation for a gas is linear [19]. Clearly, the data in fig. 4 are also in conflict with this behavior. The maximum (average) jump length, along [liO] at 521 K, of 8.7 (4.4) A would make such a description of the diffusive motion, in terms of gas-like flight, rather inappropriate.

6. Conclusion Quasielastic He atom scattering measurements can be used to study lateral diffusion processes at surfaces. Not only macroscopic diffusion parameters. such as diffusion coefficients, can be determined, but also information on an atomic scale. The microscopic diffusion mechanism can be obtained from A E( K ) measurements. The present results, for self-diffusion at the Pb(ll0) surface at high temperature, add to our current understanding of the phenomena involved in surface melting. Preliminary results for diffusion on Pb(ll0) along surface directions other than the [liO] direction, show that both the diffusion coefficient and the diffusion mechanism exhibit a marked azimuthal anisotropy at 521 K [32]. This is suggestive of special behavior of the quasiliquid surface layer, which combines liquid-like and lattice-like properties. With still higher energy resolution, quasielastic He atom scattering will open the way to other analogous studies. In the future the technique will be available for the measurement of self-diffusion at relatively lower temperatures and might be applied also to studies of surface diffusion of adsorbates.

Acknowledgements

We thank A.J. Riemersma and A.C. Moleman, of the University of Amsterdam, and B. Pluis, of the FOM-Institute for Atomic and Molecular

30

J. W. M. Frenken

et al. / He scutrrnng

rrud, of u nwltrng surfuc~r

Physics in Amsterdam, for the preparation of our Pb specimen. authors (J.W.M.F. and B.H.) thank the Alexander-von-Humboldt for fellowships.

Two of the Foundation

References [I] I. Estermann and 0. Stern. J. Phys. 61 (1930) 95. (21 T. Engel and K.H. Rieder. in: Structural Studies of Surfaces. Vol. 91 of Springer Tracts in Modern Physics (Springer, Berlin, 1982). [3] A.M. Lahee, J.R. Manson. J.P. Toennies and Ch. WBII. Phys. Rev. Letters 57 (1986) 471. [4] A.M. Lahee, J.R. Mattson, J.P. Toennies and Ch. Wiill, J. Chem. Phya. X6 (1987) 7194. [5] J.P. Toennies. J. Vacuum Sci. Technol. A 5 (1987) 440. [6] A.M. Lahee. J.P. Toennies and Ch. Wall. Surface Sci. 117 (1986) 371. [7] J.F. van der Veen, B. Pluis and A.W. Denier van der Gon. in: Chemistry and Physics of Solid Surfaces. Vol. II (Springer, Berlin, 1988) and references thercin. in press. [8] J.F. van der Veen and J.W.M. Frenken, Surface Sci. 17X (1986) 382. [9] M. Faraday. Proc. Roy. Sot. (London) 10 (1860) 440. [lo] G. Tammann. 2. Phys. Chem. 68 (1910) 205. [11] J.W.M. Frenken, P.M.J. Marie and J.F. van der Veen. Phys. Rev. B 34 (1986) 7506. [12] B. Pluis. A.W. Denier van der Gon, J.W.M. Frenken and J.F. van der Veen, Phy$. Rev. Letters 59 (1987) 267X. [13] D.-M. Zhu and J.G. Dash. Phys. Rev. Letters 57 (19X6) 2959. [14] J. Krim. J.P. Coulomb and J. Bouzidi. Phys. Rev. Letters 5X (1987) 583. [15] K.C. Prince, U. Breuer and H.P. Bonzel, Phys. Rev. Letters 60 (1988) 1146. [16] J.W.M. Frenken. J.P. Toennies and Ch. Wall, Phys. Rev. Letters 60 (198X) 1727. [17] A.C. Levi, R. Spadacini and G.E. Tommei. Surface Sci. 121 (1982) 504. [I 81 I_. Van Hove, Phys. Rev. 95 (1954) 249. [19] G.H. Vineyard. Phys. Rev. 110 (1958) 999. 1201 C.T. Chudley and R.J. Elliott. Proc. Phys. Sot. (London) 77 (1961) 353. [21] E. Zaremba, Surface Sci. 151 (1985) 91. [22] H.H. Sawin. D.D. Wilkinson, W.M. Chan. S. Smiriga and R.P. Merrill, J. Vacuum Sci. Technol. 14 (1977) 1205. [23] The estimate of the vibrational period of Pb atoms of 1 x 10 ” s is based on the typical phonon energies of Pb. which are of the order of several meV. [24] N.H. Nachtrieb. Ber. Bunsenges. 80 (1976) 678. 1251 J.W. Miller. Phys. Rev. 181 (1969) 1095. [26] V. Rosato. G. Cicotti and V. Pontikis. Phys. Rev. B 33 (1986) 1860. [27] J.Q. Broughton and G.H. Gilmer, J. Chem. Phys. 79 (1983) 5119. [28] M. Bienfait. Europhys. Letters 4 (1987) 79. [29] M. Bienfait, J.P. Coulomb and J.P. Palmari. Surface Sci. 182 (1987) 557. 1301 J.W.M. Frenken. B.J. Hinch. J.P Toennies and Ch. Wiill. to be published. [31] H.P. Bonzel, in: Surface Mobilities on Solid Materials. Ed. Vu Thien Binh (Plenum Press, New York. 1983) p. 195. and references therein. [32] J.W.M. Frenken. B.J. Hinch. J.P. Toennies and Ch. Wiill. to be published.