Temperature dependence of specular and non-specular leed beams from Cu3 Au

Surface Science 55 f1976) 324-334 0 North-Holland Publishing Company

TEMPERATURE DEPENDENCE OF SPECULAR AND NON-SPECULAR LEED BEAMS FROM Cu, Aut V.S. SUNDAY*

and W.D. ROBERTSON

De~rt~ent ~~En~.nee~.ng and Applied Science, Yale University, New Haven, Connecticut 06520, USA Received 10 October 1975;revised manuscript received 2 December 1975

The temperature dependence of intensities of the prominent diffraction peaks in the specular (00) and one non-specular (TJ) beam from the (100) surface of CusAu have been measured in the range of 300 to 673 K. The effective Debye temperature associated with the specular beam appears to increase continuously with energy below 50 eV but varies discontinuously at high energies. For the (ii) beam, which was available only in the higher energy range of 65 to 136 eV, the effective Debye temperature varies discontinuously with energy. Parallel and normal components of the Debye temperature were deduced from the two sets of data from which it appears that the two mean square displacements are approximately equal, compared to the harmonic approximation which indicates a difference of 30 percent. The log of peak intensity versus temperature (Debye plot) deviates from the straight line at 60” below the disordering temperature for all beams and all energies.

1. Introduction

The temperature variation of LEED intensities is the subject of a large number of investigations [ 11. The generally observed exponential decrease of intensity with temperature is usually interpreted in terms of the Debye-Waher theory which, within the framework of a singie scattering model, relates LEED ~tensities to amplitudes of vibration of atoms in the first few monolayers of the solid surface. Theoreticaf calculations [2] based on a simple pair-wise interaction model predict a larger root mean square (rms) displacement of surface atoms compared to those of bulk atoms. The larger rms displacements are primarily due to the change in the number of nearest neighbors for surface atoms. This has been confirmed by many workers [l] on t investigation supported by the Office of Naval Research under Contract SAR/N00014-670097-0003. Reproduction in whole or in part of this paper is permitted for any purpose of the United States Government. * Present address: Institute de Fisica, State University of Campinas, Campinas, Sao Paulo, Brazil 13 100.

VS. Sun&ram,

W.D. RobertsonJTemperature

dependence

of LEED beams from Cuylu

325

the basis of a kinematic analysis of the Debye-Waller factors obtained from LEED experiments. The (U~),/(U~>, values obtained from such experiments range from 1.5 to 3.0. Multiple scattering theory on the other hand only confirms the inequality (U2,),/(1/:),> 1 [3]. Laramore and Duke [3] have shown that each maximum in the intensity-energy spectrum can still be characterised by an effective Debye temperature but this temperature is no longer simply related to the rms displacement of surface atoms since the value of seff 1s f a very sensitive function of the diffraction parameters. Holland [47 showed by introducing thermal vibrations in a simple way via an Einstein model, that the dynamical origin of a given peak in the intensity profile determines its temperature dependence. This implies that the experimentally determined effective Debye temperatures can be used as a diagnostic tool to identify the scattering mechanism associated with each peak. While LEED-intensity data exist for many single component systems, data for binary systems are lacking in the literature* . Our studies [5] on the surface orderdisorder transformation in the binary system Cu3 Au( 100) involved, besides other things, the temperature dependence of LEED intensities in the range 300 to 673 K. In this paper we report the measurement of temperature dependence of intensities of the prominent diffraction peaks in the specular, (00), and one non-specular, (ii), beams from the (100) surface of Cu,Au and the extraction of the effective Debye temperatures from the data.

2. Experimental

procedure

The Cu,Au crystal used in this investigation was borrowed from Professor Roy Kaplow of MIT. After polishing with abrasives (chemical polishing was not used because of the probability of preferential removal of copper from the alloy surface) and confirmation of the orientation of the surface plane as a (100) plane (*l/2”), the crystal was mounted in a three-grid LEED apparatus in contact with a pyrolytic graphite resistance heater. Temperature was monitored by a chrommel-alummel thermocouple embedded in the back side of the crystal. The initial cleaning procedure inside the LEED apparatus consisted of annealing at 1023 K for periods extending up to 45 min followed by repeated argon ion bombardment at 340 eV. This cycle of bombardment and annealing had to be repeated at least three times before a sharp LEED pattern could be observed. Evidence that the surface was free of impurities, and that the ratio of copper to gold remained constant during protracted measurements and ion bombardment (followed by annealing to equilibrium), was obtained from Auger spectra which were collected at frequent intervals from the * See, however, the recent paper by Potter and Blakely [ 171 for an extensive investigation of surface periodicity, Auger intensity, work functions and ordering kinetics for (loo), (110) and (111) planes of Cu3Au.

326 VS. Sundaram, W.D. Robertson/Temperature

dependence

of LEED beams from CuJAu

23 II 181;

aa I; 36 II 43 II 63 I( 13 II

I 20

I

I

I

I

I

60

100

140

180

200

ENERGY

(EXTERNAL),

VOLTS

Fig. 1. The logarithm of normalized intensity of specular beam from the (100) surface of &Au at 0 = 6” (angle of incidence) and I$ = 32” (azimuthal angle) as a function of external energy at various temperatures (298 to 673 K).

Cu,Au

crystal and from a pure copper reference material located beside the crystal

PI. Intensities were measured with a spot photometer (Photo Research Corporation). The acceptance angle of the photometer was 0.25’ which subtended a 1.5 mm diameter area on the fluorescent screen. Since the average size of the diffracted beam on the screen was normally less than 1 mm, the recorded data were integrated intensities. The energy of the incident beam was varied in steps of 1 or 2 V with a step voltage power supply. The measured intensities were normalized by the procedure suggested by Jona [6]. The primary voltage was corrected for 3 eV contact potential difference between the gun cathode and the sample. For room temperature measurements the residual earth’s magnetic field inside the LEED chamber was effectively cancelled with a small trimming magnet placed outside. For high temperature measurements with current flowing through the sarnple holder, it was found necessary to use 3 or 4 magnets to reduce the field effects. The positions of the magnets were adjusted until the LEED pattern showed the pertinent symmetry and the (00) beam intensities at +0 and -0 agreed within experimental errors.

V.S. Sundaram, W.D. Robertson/Temperature dependence of LEED beamsfrom Cufiu 327

20 -40 _

40

vfp44+2v

60 A2

60

100

120

Fig. 2. Position in energy of integer order peaks, 001 in loo plotted versus Zz. From the slope of the straight line we evaluate q&Au = 3.71 .4 and from they axis intercept UO (inner potential) = -14 eV.

3. Results and discussion 3.1. Specular beam The logarithm of the normalised intensity of the specular beam from the (100) surface of Cu,Au, at an angle of incidence, 8 = 6”, is shown in fig. 3 as a function of incident energy for seven different temperatures in the range 300 to 673 K. In single scattering approximations the intensity of the back scattered electron is written as [ 1 ] I=Io

emm,

(1)

where the Debye-Waller factor 2M is given as: T @ij?

(2)

where B is the angle of incidence, X is the electron wavelength inside the crystal (calculated with an inner potential of U, = -14 eV evaluated from the peak positions in the intensity-voltage profile for the specular beam fig. 2), B”Dffis the effective Debye temperature and m is the “average” atomic mass calculated from the density of Cu,Au. Thus a “Debye plot” of log I/Z0 versus temperature according to eq. (1) yields a straight line. From the slope of this straight line, ebff can be evaluated. For energies above 70 eV the measured intensities were corrected for thermal diffuse

328 VS. Sundaram, W.D. Roberrsonlremperoture

300

420

dependence

540

of LEED beams from Cu&u

660

TEMPERATURE ( K)

Fig. 3. The logarithm of intensity for peaks in the energy range 20 to 75 eV in fig. 1, as a function of temperatures.

scattering following the method suggested by Woodruff and Seah [7] . In this method the intensity of the zero phonon component is taken to be the excess intensity of a diffraction peak over the nearest “deep” valley in the intensity-energy spectrum. This is equivalent to assuming that the entire intensity in the valleys is due to multiphonon scattering. Since multiple scattering c~c~ations do show some coherently scattered intensity along the entire reciprocal rod, this procedure in fact over-corrects for background. Figs. 3 and 4 display the Debye plots for the specular beam at various electron energies. A characteristic of all these Debye plots is the deviation of the measured intensities from a straight line at temperatures above about 600 IL Debye plots are expected to show linear behavior only in the harmonic approximation and, as the temperature approaches the critical temperature for some transformation, deviations from linearity are to be expected. Maradudin and Flinn [8] have performed numerical evaluations of Debye-Waller factors including higher order terms and have shown that the effect of higher order terms is to cause the Debye plots to become concave downward as the tem~rature of a crystal approaches the melting (transfor-

KS. Sundaram, W.D. Robertson/Temperature

-

300

dependence of LEED beams from Cufiu

329

Evl20eV

420

540

660

TEMPERATURE I K) Fig- 4. The

logarithmof intensity for peaks in the energy range 80

to I60 eV in fig. 1, as a funo

tion of temperature.

mat&) point. in the case of Ct.+Au, the bulk undergoes an order-disorder transformation at 663 K. This transformation has been shown to be a first order transfer* mation [16]. However, from our earlier measurements [S] of the long-range order parameter near the (100) surface of Cu3Au, we concluded that the surface begins to disorder about 600 K (about 60 K below the critical temperature for the buIk). The anharmonic effects associated with this disordering process are reflected in the nonlinear behavior of Debye plots which occur typically around the same temperature as the surface disordering temperatures (around 600 K). Henrion and Rhead [9] observed similar non-linear effects in Debye plots in their experiments in surface melting of lead. In other words, the observed non-linear behavior of Debye plots reinforces our earher conclusions that the surface disordering starts about 60 K beIow the buik transformation temperature. The effective Debye temperatures obtained from the slopes of the lines in figs. 3 and 4 are shown as a function of energy in fig. 5. The error bars in fig. 5 are calculated on the basis of scatter of the data points in the Debye plots. Also shown in the same Agure is the bulk Debye temperature obtained by Flinn et al. [lOI from the

330 VS. Sundaram,

W.D. Robertsonf’Temperature

320 -

I

I

dependence

I

I

I

of LEED beams from Cu&

I

280

I

8,

1

BULK

240 200,g+~~

9

160l

;

00 BEAM BEAM

0 ii

12080-

20

40

60

80

I20

140

ENERGY (EXTERNAL),

Fig. 5. Variation of the effective Debye te~~rature Bragg peaks are indicated by arrows.

160

I80

200

VOLTS

as a function of energy. The positions of

measurement of elastic constants of Cu3Au. Earlier experiments on many single component systems [l 1] indicate that the effective Debye temperature rises with increasing energy. Surface ions have considerably larger mean square displa~ments than the bulk ions and the contribution of surface ions relative to the bulk falls off with increasing energy. Hence it is to be anticipated that the effective Debye temperature would rise with increasing energy approaching the bulk Debye temperature in the limit of some high energy. It is clear from fig. 5 that the effective Debye temperature is not a linear function of energy for Cu3Au(100). Reid’s [12] results for Cu(100) show that the effective Debye tem~rature is a violently fluctuating function of energy. Similar results have been reported by Tabor et al. [13] for Cr and MO. Quint0 et al. [14] argued, using the multiple scattering formalism of Duke and Laramore [3], that if the total backscattered amplitude arises predominantly from scattering paths in which the direction is reversed only once [4], or by a sequence of smaller angle scatterings, then such maxima will show an effective Debye temperature varying smoothly with energy and as~ptoti~~y approa~~g the bulk Debye temperature at some high enough energy. Using this concept, they explained the linear variation of the effective Debye temperature with energy which was observed for aluminum (100). In the light of the above observations, our results from the (100) surface of Cu,Au can be explained in the following way. It is clear from fig. 5 that below 50 eV, the observed Debye temperature varies smoothly with energy. Thus, we interpret the 27,34, and 46 eV peaks as arising predomin~~y from scattering events involving only a single reversal [ 141. The peaks at 58,73, and 120 eV are due to scattering events involving many reversals.

VS. Sundaram, W.D. RobertsonfTemperature dependence of LEED beams from Cu+Iu 331

296 K

526 K 516 K 566 II 636 I 646 K 663 K 613 I

20

60

100 140

160 20C

ENERGY (EXTERNAL), VOLTS Fig. 6. The logarithm of normalized intensity of (ii) beam from the (100) surface of CusAu at normal incidence and $J (azimuthal angle) = 32” as a function of energy at various temperatures (298 to 673 K).

3.2. Non-specular beam The normalized intensity of the (ii) beam from the (100) surface of Cu,Au for normal incidence is shown in fig. 6 as a function of incident energy for different temperatures in the range 300 to 673 K. For the non-specular reflection, (ii), the factor 2M in eq. (1) is written as cos2a -t-

(eeff)2 Dl

sin2a! (eeff)2 DII

1T,

(3)

where 0 is the angle of incidence, h is the electron wavelength inside the crystal (calculated with U. = -14 V) and (Yis the angle between the scattering vector S = k -k’ and the surface normal. @If and ebff are the perpendicular and parallel components of the effective Debye temperature. k or the specular beam, since (Y= 0 we always measured the perpendicular component. Thus, using the values of eby calculated from the studies of (00) reflections, and the sum of the two components e$ and eeff which is obtained from the intensity variation of the (ii) reflection as a funcDII tion of temperature, the parallel component of the effective Debye temperature can be evaluated. Fig. 7 displays the Debye plots for the (ii) reflection at various electron energies.

332 VS. Sundaram,

W.D. Robertson/Temperature

1$,=224

gii

dependence

.

K

. -

300

420

540

TEMPERATURE Fig. 7. The logarithm

of intensity

of LEED beams from Cu3Au

for the prominent

.

660 ( K)

peaks in fig. 6, as a function

of temperature.

The same non linear effects are observed for the (ii) beam above 600 K as were observed in the specular beam and they are presumably due to the same anharmonic effects associated with the transformation. It was found that the slope of the Debye plots obtained for Bragg reflections in the (ii) intensity profile were about equal to those for the specular beam at the corresponding electron energies within the experimental errors. This implies that the parallel and perpendicular components of Obff are about equal within the accuracy of of our measurements. In table 1 we tabulate the slopes obtained from the Debye plots for the Bragg maxima at 65 and 119 eV and for the secondary peak at 136 eV. In the same table we list the values of Obff as calculated from the slopes. These values are shown in fig. 5. The error bars for the Debye temperatures calculated from the (ii) beam are evaluated on the basis of scatter of the data points in the Debye plots. In our experiments, we are limited to values of (II [refer eq. (3)] less than about 20’. Thus the 13bff for (ii) reflections are dominated by 8~~. Therefore, the uncertainties in eD1, evaluated from such data are too large to draw any meaningful conclusions. From our Debye-Waller measurements for the (ii) reflections, we conclude that the parallel and perpendicular components of the mean square displacements of the atoms on the (100) surface of Cu3 Au are about equal to within about +25%. Calculations [ 151 within the harmonic approximation indicate that

KS. Sundaram, W.D. Robertson/Temperature dependence of LEED beams from Cu&

333

Table 1 The slopes of the Debye-plots and the effective Debye temperatures calculated for the (00) and (ii) diffracted beams at different energies Reflection

EO CeV)

00

27 34 46 58 73 89 120 161

(TT)

6.5 119 136

0

(deg)

2a (deg)

Slope 2.3 2.6 2.4 3.05 3.98 3.56 5.63 5.91

0 0 0

33 24 22.5

sgf x x x x X X X x

1O-3 1O-3 1O-4 10-s 1O-3 1O-3 1O-3 10-s

2.62 x 1O-3 3.92 x 10-s 6.8 x 10-s

(K)

164i 170* 195 f 184 f 184* 211 f 192 f 216 +

7 8 9 10 10 12 10 12

215 f 15 225 * 17 190 f 10

(UT) should be greater than (Vi> by a factor of 1.3 for fee (100) surfaces. It is not possible to detect such differences from our present measurements. Also, these calculations were made for ideally flat surfaces assuming that the interatomic coupling constants for surface atoms are the same as those for bulk atoms. The presence of steps and other imperfections on the surface will alter the number of missing bonds parallel to the surface and hence lead to a larger rms displacement paralleI to the surface.

References Ill (a) J.M. Morabito, Jr., R.F. Steiger and G.A. Somorjai, Phys. Rev. 179 (1969) 638. (b) A.U. McRae, Surface Sci. 2 (1964) 522.

121 B.C. Clark, R. Herman and R.F. Wallis, Phys. Rev. 139 (1965) A860. 131 G.E. Laramore and C.B. Duke, Phys. Rev. B2 (1970) 4765,4783. 141 B.W. Holland, Surface Sci. 28 (1971) 258. [51 (a) VS. Sundaram, B. Farrell, R.S. Alben and W.D. Robertson, Phys. Rev. Letters 31 (1973) 1136. (b) VS. Sundaram, R.S. Alben and W.D. Robertson, Surface Sci. 46 (1974) 653. 161 F. Jona, IBM J. Res. Develop. 14 (1970) 444. 171 D.P. Woodruff and M.P. Seah, Phys. Status Solidi (a) 1 (1970) 429. PI A.A. Maradudin and P.A. Flinn, Phys. Rev. 129 (1963) 2529. PI J. Henrion and G.E. Rhead, Surface Sci. 29 (1972) 20. 1101 P.A. Flinn, G.M:McManus and J.A. Rayne, J. Phys. Chem. Solids 15 (1960) 189. [Ill See, for example, E.R. Jones, J.T. McKinney and M.B. Webb, Phys. Rev. 151 (1966) 476. [I21 R.J. Reid, Surface Sci. 29 (1972) 623. P31 D. Tabor, B.M. Wilson and J.J. Baston, Surface Sci. 26 (1971) 471. 1141 D.T. Quinto, B.W. Holland and W.D. Robertson, Surface Sci. 32 (1972) 139.

334 VS. Sundaram, W.D. ~Obe~tson~Te~~e~a~re dependence of LEED beams from Cu& [ 151 R.F. Wallis, B.C. Clark and R. Herman, in: Structure and Chemistry of Surfaces, Ed. G.A. Somojai (Wiley, New York, 1969) p. 17-l. [16] R. Feder, M. Mooney and AS. Nowick, Acta Met. 6 (1958) 266. [ 171 H.C. Potter and J.M. Blakely, J. Vacuum Sci. Technol. 12 (1975) 635.