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Comparison of surface phonon dispersion curves for clean and hydrogen covered Rh(111) surfaces
surface science Surface Science 323 (1995) 228-240
ELSEVIER
Comparison of surface phonon dispersion curves for clean and hydrogen covered Rh( 111 ) surfaces G. Witte, J.R Toennies, Ch. W611 .,1 Max-Planck-lnstitut fiir StrOmungsforschung, Bunsenstrasse 10, D-37073 GOttingen, Germany Received 11 April 1994; accepted for publication 13 September 1994
Abstract Surface phonon dispersion curves have been measured for the clean and hydrogen covered Rh(111) surfaces along the (1 i0) and (112) high symmetry directions of the surface Brillouin zone using high resolution He-atom scattering. Interatomic force constants and elastic constants, which are not available for this material, were obtained by a lattice-dynamical analysis. The significant changes of the dynamical properties of the surface upon hydrogen adsorption are shown to be related to hydrogen-induced changes in the surface electronic structure and are discussed within the framework of a pseudocharge model which has been developed recently. An analysis of the experimental phonon excitation probabilities for the two surfaces within the framework of the distorted wave Born approximation indicates large changes in the repulsive He-surface potentials upon hydrogen adsorption. Key words: Adatoms, Atom-solid interactions, Low index single crystal surfaces, Rhodium
1. Introduction
Rhodium is known to be an active heterogeneous catalyst for a number of chemical reactions. Mainly for this reason the Rh( 111 ) surface has been the subject of a large number of investigations in recent years, especially with regard to the adsorption of benzene, CO, oxygen and hydrogen [ I - 5 ] . To date, no information concerning the surface dynamical properties of this material is available. Unlike other metals a prediction of surface phonon dispersion relations based upon model calculations using bulk force constants is * Corresponding author. 1 Permanent address: Angewandte Physikalische Chemie, Universitiit Heidelberg, Im Neuenbeimer Feld 253, D-69120 Heidelberg, Germany.
not possible for rhodium (and iridium [6] ) due to the complete lack of experimental bulk phonon data. The latter is due to the fact that inelastic neutron scattering, the standard technique for measuring bulk phonons, cannot be applied easily to rhodium (and Ir) because of the anomalously high absorption cross section for thermal energy neutrons. Detailed information on the surface dynamics of Rh( 111 ) is also relevant with regard to the discussion about the origin of the surface longitudinal resonance (LR) observed for a number of metals, on which a general consensus has not yet been reached [7,8]. It would be particularly interesting to compare this with the results obtained for Pt( 111 ) (because of the similar electronic properties of the two materials), where the surface dynamics is complicated by the presence of a Kohn anomaly and a third surface phonon mode [9].
0039-6028/95/$09.50 @ 1995 Elsevier Science B.V. All rights reserved
SSDI 0 0 3 9 - 6 0 2 8 ( 9 4 ) 005931
G. Witte et al./Surface Science 323 (1995) 228-240
The adsorption of hydrogen on metal and semiconductor surfaces is of great interest since the chemisorbed H is presumably a key intermediate in many important catalytic reactions and because of possible storage applications in energy technology [ 10,11 ]. It is known that hydrogen is a passivation agent for amorphous silicon in electronics applications and on metal surfaces. Adsorbed hydrogen has also been observed to significantly affect the surface phonon dispersion curves of a number of systems including S i ( l l l ) / H [12], Ni(001)/H [13], P t ( l l l ) / H [9], W ( 1 0 0 ) / H [14], W ( l l 0 ) / H [15], M o ( l l 0 ) / H [16]. With the exception of W ( l l 0 ) and Mo(110) the effect of H is to suppress anomalous modes and to restore the surface dynamical properties to those expected for a nearly ideal termination of the bulk. In the present publication we report measurements of surface phonon dispersion curves and the corresponding excitation probabilities for the clean and the hydrogen covered Rh(111) + H ( 1 × 1 ) surfaces by helium atom scattering (HAS). In addition to the Rayleigh mode several features at higher energies appear in the time-of-flight spectra. The strong differences observed between the clean and the hydrogen covered surfaces suggest that the hydrogen atoms reduce the electronically induced softening of the clean surface atom core-core interaction. The experimental data were analyzed within the framework of lattice dynamical calculations using a Born-von Karman force constant model. The results of this analysis and the observed phonon excitation probabilities are related to recent results obtained from the pseudocharge model which has been employed recently to successfully calculate the inelastic HAS intensities for Cu( 111 ), Cu(001) and Ag(001 ) [7,1719]. The experimental procedure for sample preparation and the experimental setup for surface phonon measurements are outlined in Section 2. Experimental diffraction and time-of-flight results are presented in Section 3 for the clean surface and in Section 4 for the hydrogen saturated surface. In Section 5 results of the lattice dynamical calculations and calculations of the phonon excitation probabilities are presented. The paper closes with a final discussion in Section 6.
229
2. Experimental setup A detailed description of the He-atom time-of-flight apparatus used for diffraction and phonon experiments is given in Refs. [20,21]. Essentially, the apparatus consists of a He nozzle-beam source, a target chamber and a I. 124 m long time-of-flight drift tube, at the end of which the He-atoms are detected by a mass spectrometer with a magnetic mass selector. The supersonic helium atom source is operated at temperatures between 30 and 500 K and at pressures up to 300 bar. The resulting beams have kinetic energies between 7 and 120 meV with an energy spread ( A E / E ) of about 2% over the entire range of energies. The sample is mounted on a three axis manipulator. This allows alignment and rotation of the azimuth, tilt and polar angles. The sample temperature can be varied between 100 and 1300 K using a flexible copper braid connected to a liquid nitrogen cryostat for cooling and electron bombardment for heating. Angular distributions of He-atoms scattered off the surface are recorded by rotating the crystal around an axis perpendicular to the plane of the incident and final scattered beams which have a fixed angle of 90.5 ° between them. While the overall angular resolution of the instrument is about 0.2 ° , the angle of incidence can be measured with a resolution of 0.04 °. As the He-atom diffraction intensities for the clean Rh( 111 )-surface are found to be extremely weak the alignment of the azimuth was carried out for (2 x 2) adlayer structures of CO or 02, which exhibit a much stronger corrugation. After cleaning and heating of the substrate, the FWHM of the specular peak was found to be 0.35 °. The time-of-flight (TOF) technique allows the observation of discrete (one phonon) inelastic scattering processes with a resolution of typically 1.5 ~s channel width corresponding to 0.1 meV at an incident energy of 50 meV and an energy loss of about 17 meV. The kinematic scattering conditions were changed by varying either the incident energy or the angle of incidence. The target chamber is equipped with a low energy electron diffractometer (LEED), a quadrupole mass spectrometer for residual gas analysis, and a Leybold-Hereaus EA11 photoelectron spectrometer with X-ray and UV-light sources. The Rh( 111 ) single crystal sample was cleaned through a process of 6
230
G. Witte et al./Surface Science 323 (1995) 228-240
hours of argon sputtering followed by repeated cycles of 800 eV Ar + bombardment (1 h) and heating to 1300 K (2 min) using electron bombardment. After a few cleaning cycles, XPS signals indicated contamination levels of less than 1% of a monolayer for C and less than 0.3% for oxygen. The base pressure of 6 x 10 -ll mbar in the target chamber allowed measuring times of more than 7 h without any noticeable effect on the He specular beam signal from surface contamination. The adsorption of CO onto the clean surface could be monitored by HAS directly since the frustrated translation of the chemisorbed CO-molecule gives rise to distinct energy losses [22]. In a previous experiment the adsorption of benzene on this surface has been investigated with HAS using the same machine [ 23 ].
(11~->
R h 1111)
I. ~
0 ~,i t- O. Q~ ti=.i Q;
•>
O.
U 13~ 0"!
3. The clean R h ( l l l ) surface The structural quality of the surface and the alignment of the crystal were checked by recording angular distributions. Fig. la shows typical angular distributions for the (112) and (1 ]0) high symmetry azimuths. Note that since these distributions are symmetric with respect to the specular peak at Oi = 45.25 ° they have been displayed with the (112) and (li0) directions on the left and right hand sides of the specular peak, respectively. For a beam with an incident wave vector of 8.3 A-1 the first and second order diffraction peaks were measured along the (112) direction (G(ll~) = 2.70/~-1) and were found to have intensities of about 6.5 x 10 -3 and 6.5 x 10 -5 of the specular intensity, respectively. Along the (li0) azimuth (G
~(x,Y)=½(o{cos(2--~x)
+ cos ( ~ y )
the overall (peak-to-peak) corrugation amplitude was
L
-s.o
-~.o
-2.o
o
zo
4.o
6.0
AK [k~l Fig. 1. Angular distributions measured for the clean Rh( 111 ) surface (upper panel) and for the R h ( l l l ) + H(1 x 1) surface with saturation coverage of hydrogen (lower panel). Note that the left part of the angular distribution is along the (11~) direction whereas the right part is along the ( l i 0 ) direction. The incident beam wave vector for all scans was k i = 1 0 / ~ - 1 and the sample temperature was 135 K. While the clean R h ( l l l ) - s u r f a c e is very smooth hydrogen adsorption enhances the corrugation and the Rh( 111 ) + H ( 1 x 1 ) surface exhibits considerably stronger diffraction peaks.
calculated to be g'0 = 0.05 A. This value is larger than the corrugation amplitudes of 0.03 and 0.01/~ derived for Ag(111) [24] and Pt(111) [25,26]. Over 300 time-of-flight spectra were measured along both high-symmetry directions most of them for surface temperatures of 135 and 300 K. Mostly the phonons were measured in creation with positive Q because of the optimal kinematic resolution conditions [27]. Two main energy loss peaks can be identiffed in the typical TOF-spectra shown in Figs. 2 and 3. The resulting phonon dispersion curves are shown in Fig. 4. The lower energy mode is attributed to the Rayleigh mode (RW), which is a typical feature for clean metal surfaces. The second peak at higher energy is attributed to the anomalous longitudinal resonance
G. Witte et al./Surface Science 323 (1995) 228-240
Rh (111) <[170>
Rh (111) +H ( l x l )
231
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Fig. 2. Series of He-atom time-of-flight spectra converted to an energy transfer scale for the (l i0) direction of the clean Rh( 111 ) (left column) at 300 K and H(1 x 1) covered surface (right column) at 135 K. RW: Rayleigh wave, LR: longitudinal resonance, B: bulk resonance. The spectra were recorded with incident energies of 55 meV. The first spectrum for the H( i x 1 ) structure shows an energy loss at 28.5 meV ($2) which is not observed for the clean surface.
(LR), which has been observed on Pt(111) and on other noble and transition metal surfaces [9,7,28]. In the (112) direction, the M point zone boundary energies amount to 16.2 + 0.3 meV for the Rayleigh mode and approximately 22.5 -t- 1 meV for the longitudinal resonance. Due to the strong decrease of the phonon intensity along the (liO) direction, the dispersion curve could not be measured up to the zone boundary. Extrapolation with an assumed sine-curve dispersion relationship yields a K point zone boundary energy of
17.4 ± 0.7 meV for the Rayleigh mode. Table 1 lists the zone boundary Rayleigh phonon energies for the clean and H-covered surfaces and shows a comparison with other transition metals. Relative to the Rayleigh mode the excitation probability for the longitudinal mode on Rh( 111 ) increases with larger phonon wave vectors along both high-symmetry directions as already observed for C u ( l l l ) [7], Cu(001) [17,18] and Ag(001) [19]. For wave vectors at ]F-'-Ka weak third peak (B) was detected (see last TOF-spectrum
232
G. Witte et a l . / S u r f a c e Science 323 (1995) 2 2 8 - 2 4 0
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Fig, 3. Same as Fig. 2 but for the (112) direction.
in left column of Fig. 2). While for Cu(001) and Ag(001 ) [ 17,19] similar features have been observed above the longitudinal resonance, the peaks measured here are located between the Rayleigh mode and the longitudinal resonance. We attribute these loss peaks to the high density of states of the lower edge of a transversely polarized bulk phonon band since multiphonon excitation is expected to give rise to considerably broader features [29]. The dispersion curves of the Rayleigh mode for small wave vectors have been fitted by a straight line, the slope of which corresponds to the velocity
of sound. The resulting values of 3450 + 250 and 3210+250 m/s for the (110) and (112) azimuths obtained in this way appear to be the first measurements of these quantities for crystalline rhodium [ 30].
4. The hydrogen saturated R h ( l l l ) + H(1 × 1) surface Yates et al. [5] have investigated the kinetics of hydrogen adsorption on Rh( 111 ) and demonstrated, mainly by thermal desorption spectroscopy, that hy-
G. Witte et al./S~,ff, ace Science 323 (1995) 228-240
35
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Fig. 4. Dispersion curves of the clean Rh( 111 ) surface at 300 K. The Rayleigh mode (RW) and a longitudinal mode (LR) are observed for the (1 i0) and the (112) direction. Along the (1 i0) direction very weak extra peaks are observed which are attributed to a bulk resonance (B). The inset shows the reciprocal lattice with the first Brillouin zone. The dashed lines show the bulk band edges derived from a slab calculation using the force constants from model Fgh (Table 2).
drogen dissociatively chemisorbs at the surface, which appears to be a general feature for all d-electron transition metal surfaces. As the changes in the LEEDpattern upon hydrogen adsorption are small due the small scattering cross section of H for low-energy electrons the formation of well ordered hydrogen ovedayers could not be studied with this technique, and as a consequence, has not been reported previously. Our He-atom scattering angular distributions displayed in Fig. lb thus provide the first direct evidence that hyTable 1 Zone boundary Rayleigh phonon energies in meV for some clean and H( 1 × 1 ) covered transition metal surfaces Surface
Max.
Ref.
bulk
Clean M
H(I x 1) K
M
Ref.
K
phonon energy Pt(lll)
24.19
[41]
10.8
11.1
Pd(lll)
29.03
[41]
11.1
-
Rh(lll)
31.20
[59]
16.2 ~ 1 7 . 4
Ru
32.05
[41]
.
.
.
9.3
9.5
[9]
11.I
[60]
15.6 16.4
This work
.
233
drogen forms a well ordered (1 × 1) overlayer on the Rh( 111 )-surface. Hydrogen adsorption was carried out by heating the sample to 1300 K and then cooling down to 130 K with a subsequent exposure to H2 at a pressure of 10 -8 mbar. The adsorption could be monitored by recording the specular peak intensity, which shows an abrupt decrease upon hydrogen exposure followed by a gradual increase reaching a final value of 90% of the specular intensity for the clean surface. At this temperature the hydrogen structure seems to be very stable, peak shapes and intensities in the angular distributions revealed no changes even after very long measurements (8 hours). The adsorption site of the hydrogen atoms on Rh( 111 ) has not yet been determined, but from the information available for other transition metals (H/Pt( 111 ) [31,32], H / N i ( l l l ) [ 3 3 ] , H / P d ( l l l ) [34] andH/Ru(0001) [35] ) it appears likely that hydrogen on Rh( 111 ) is adsorbed in a three-fold hollow site. After preparation of the hydrogen overlayer a large increase in the diffraction intensities by a factor of 10-20 was observed (see Fig. lb) indicating a strong enhancement of the surface corrugation. From the relative diffraction intensities with respect to the specular intensity (5.75 × 10-2 and 2.97 × 10 - 4 for the first and second order peak along (112) and 2.88 x 10 -4 for the first order peak along (1 ]0), respectively) an effective hard wall corrugation amplitude of 0.15/~ was calculated using Eq. (1) in the Eikonal approximation. A similar strong enhancement of the surface corrugation amplitude from 0.01 to 0.18 A during the hydrogen adsorption was reported for Pt( 111 ) by Lee et al. [25]. In the right-hand-side columns of Figs. 2 and 3 representative time-of-flight spectra recorded along the (1 i0) and (112) directions for the Rh( 11 I) + H( 1 × 1 ) surface are displayed which can be directly compared to the corresponding data for the clean surface shown on the left-hand-side of the respective figure. After subtraction of the multiphonon background the inelastic scattering intensity of the Rayleigh mode is higher than for the clean surface for wave vectors larger than 0.5 /~-1. As a consequence, the dispersion curve of the Rayleigh mode (see Fig. 5) could be measured beyond the zone boundary. Along the (1 i0) direction it was possible to extend the measurements up to the M point (see inset in Fig. 4). The energies of the Rayleigh mode at the K and M points
234
G. Witte et al./Surface Science 323 (1995) 228-240
35
F
,
,
R ,
- . . . . . s~_-~, b
30
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..... •
•~20 ,
/
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~ ,\\, \
' 1~.0
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0
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Fig. 5. Dispersion curves for the Rh(lll) + H(I x 1) surface. The Rayleigh mode (RW) has been measured along the whole irreducible part of the Brillouin zone and shows the same behaviour as for the clean surface. Along the (112) direction the longitudinal mode (LR) disappearsalmost while in the (1 i0) direction the mode seems to shift to higher energies and a weak broad resonanceis observed (open cycles). Additionally close to the zone boundaries a high energy mode ($2) could be identified. The dashed lines show the bulk band edges derived from a slab calculation using the force constants from model Fgh (Table 2). are 16.4 + 0.3 and 15.6 + 0.3 meV, respectively, and are slightly lower than the clean surface energies (see Table 1 ). The energy loss peaks related to an excitation of the longitudinal resonance (LR) are much less intense than for the clean surface. For the H( 1 x 1 ) surface this mode can only be observed at high momentum transfers and, in addition, the mode is shifted to higher energies, the shift amounting to about 3 meV at the Brillouin-zone midpoints along both symmetry directions. A zone boundary energy of 25.5 + 0.7 meV for the longitudinal resonance could only be determined for the (1]0) direction at K. For large wave vectors some weak and broad peaks (open circles in Fig. 5, labelled Bt) have been observed. As multiphonon excitations typically seem to be even broader [29] features are tentatively assigned to surface resonances embedded in the bulk bands. In addition, a $2 surface longitudinal mode which is split off from the longitudinal bulk bands is observed close to the Brillouin zone boundary along both high-symmetry directions. This clearly resolved mode (see first TOF-spectrum
in the right column of Figs. 2 and 3) lies at energies of 28.5 + 0.5 and 29.7 -4-0.5 meV at K and M, respectively. In order to rule out the possibility of a soft hydrogen mode, we have repeated the time-of-flight measurements for a deuterium ( 1 x 1 ) overlayer. Time-of-flight spectra recorded for the deuterated surface are virtually identical to those measured for the hydrogenated surface, no isotope-shifts of surface vibrational frequencies could be observed. This result demonstrates clearly that the observed mode is a rhodium surface mode and is therefore the first observation of the $2 mode on a fcc (111 )-surface by helium atom scattering. The mass effect of the hydrogen atoms on the rhodium atom vibrational frequencies can be neglected since the hydrogen mass is less than 1% the mass of the Rh atom ( 104 amu), and therefore is expected to reduce the frequency at the zone boundary by less than 0.5 %. As the energies of the H-metal stretch vibrations are higher than the maximum bulk phonon energy the coupling to the substrate vibrations is expected to be very weak. Moreover these modes are expected to have very small excitation probabilities in HAS experiments and have not been observed so far. For H on Rh( 111 ) weak peaks in EEL-spectra were reported by Mate and Somorjal [36] with energy losses of 92, 136 and 175 meV. For other transition metals hydrogen vibrations have been observed with energies of 68 and 153 meV for H/Pt( 111 ) [31 ], 96 and 124 meV for H / P d ( I 11 ) [37], 102 and 140 meV for H/Ru(0001) [38] and 69 meV for H/Ir(111) [39]. Due to this decoupling any changes of surface phonon energies upon hydrogen adsorption as observed by HAS can be solely attributed to force constant changes at the surface which originate from changes in the surface electronic structure.
5. Lattice d y n a m i c a l a n a l y s i s
The best first step in analysing experimental surface phonon data is to compare with predictions obtained from a lattice-dynamical calculation. In this case we have employed a 35 layer slab and two simple force constant schemes, the first limiting interactions to the shell of nearest neighbours whereas the second additionally included couplings to second nearest neighbours. A detailed description of the algorithms
G. Witte et aL /Surface Science 323 (1995) 228-240
Table 2 Force constants for various models (N/m) Model
fll
F~h FRbh F~h FRah F~Rh rl° ~RRr2° ~
78.6 -- 1.4 2.6 --2.6 2.09 76.0 12.3 0.0 0.0 2.09 63.0 0.0 0.0 0.0 0.0 63.0 15.0 2.0 --2.0 1.5 F~Rh, but 10% intralayer softening for/31 FROh,but 20% intralayer softening for fll
B2
al
a2
used in our slab calculation has been published previously [40]. When analysing surface dynamical properties typically as a starting point the bulk force constants are used. As bulk data are not available for Rh [41] we have used the force constants derived by Black et al. [42] from a LEED Debye-Waller investigation on the Rh( 111 ) surface [43]. The two different forceconstant schemes of Black et al. are listed in Table 2 ( F ~ and F b ) [45]. The resulting energies of the Rayleigh mode and the longitudinal gap mode ($2) at the high symmetry points in the surface Brillouin zone are provided in Table 3. A comparison with the experimental data for the clean surface (Table 1) reveals significant lower energies with differences of about 3 meV for scheme F~h and of 1.5 meV for scheme F b . Without the possibility to refer to bulk data at this point it is virtually impossible to decide whether the deviations between experiment and calculations are due to deficiencies of Table 3 Calculated surface mode energies in meV for the H( 1 x 1) surface Model At M
Exp. F~h FRbh ~Rh Faah FROrl° ia FRa~2°
At
Average error at zone boundary (%)
RW
$2
RW
$2
LR
15.60 13.25 14.74 15.68 15.69 15.69 15.68
29.70 32.90 32.50 32.70 30.55 29.45 28.14
16.40 15.50 15.04 16.62 16.36 16.36 16.36
28.50 29.60 29.30 27.60 27.67 28.70 28.60
25.50 26.70 20 25.80 14 10 24.88 4 23.67 22.68
235
the force constant schemes or whether surface relaxation effects cause changes in surface phonon energies, as observed for other transition metal surfaces such as Pt(111) [9]. From analogy to the rather similar case of Pt( 111 ) we chose to fit the theoretical calculations to the experimental results for the hydrogen covered R h ( l l l ) + H ( 1 × 1)-surface, since it has been shown for P t ( l l l ) [9] and other metals such as W(100) [14], Ni(001) [13] and P d ( l l l ) [60] as well as for Si( 111 ) [ 12] that the hydrogen covered surfaces exhibits dynamical properties which are in very close agreement with predictions derived from a well parameterized bulk force constant scheme. On the basis of this assumption we can use the surface phonon data for R h ( l l l ) + H ( l x 1) to obtain a prediction for the bulk force constants of Rh using a fitting procedure. As shown in Table 3 for both schemes F~h and Fp~ the Rayleigh phonon energies are too low and the S2-1ongitudinal gap mode is too high in energy when compared to the experimental data for the hydrogen covered surface. In order to improve the agreement a single force constant model (model F ~ ) was fitted to the experimental data for the Rayleigh phonon energies at the high symmetry points of the Brillouin zone. As shown in Table 3 an effective radial force constant of 63 N / m gives rather good agreement with the Rayleigh mode but falls to yield the correct values for the $2 mode. It was found to be impossible to improve this agreement using a one force-constant scheme. A considerably better agreement was achieved with a 5 parameter model (model FaRh) with first and second nearest neighbour radial and tangential coupling parameters and an angular force constant. With this model we were able to reproduce the measured Rayleigh phonon and the S2gap-mode energies at the high-symmetry points with an accuracy better than 4%. Accepting the resulting force-constant scheme F ~ obtained by the fit to the data for the Rh( 111 ) + H ( 1 x l) surface as an improved bulk force constant parametrisation for Rh, the lower energies for the LRresonance mode observed for the clean surface can be reproduced by a softening of the surface intralayer force constant fll (which couples atoms in the surface plane), see Table 3. This observation is again similar to the case for Pt( 111 ) [9]. Note that with this simple
236
G. W&e et al./Surface
Table 4 Interaction
parameters
Azimuth
Rh( 111) P
(A-‘)
Science 323 (1995) 228-240
for single pbonon scattering Rh(lll)+H(I
x 1)
Qc (A-1)
Zo (A)
P (A-‘)
Qc (A-‘)
ZI (A)
(ITo)
3.02
0.823
4.46
4.46
1.19
3.15
(112)
3.15
0.820
4.68
4.46
1.19
3.15
force-constant scheme the LR-mode could only be obtained for the K-point. It was neither attempted to modify the force-constant scheme in order to obtain the LR-mode also for the a-point, nor did we try to fit the experimental dispersion curve of the LR-mode to the experimental data as the lack of a more precise bulk force constant scheme limits the scientific insight which can be gained by such an analysis. In order to derive further information about the He surface interaction we have analyzed the Rayleigh phonon intensities for the clean and hydrogen covered surface in the framework of the distorted wave Born approximation. The single quantum excitation probability for a projectile scattered from an interaction potential can be calculated using formulae presented by Manson and Celli [ 461. Since neither initial nor final states of the crystal can be determined, the transition rate is obtained by a summation over all final vibrational states and is averaged over all initial states. The actual intensity measured in an experiment is the differential reflection coefficient, or in other words, the number of scattered particles detected per unit final solid angle and per unit final energy, d3 R/ dEr d2&, which is proportional to the transition rate [ 181. The differential reflection coefficient for a crystal consisting only of like atoms of mass M can be written in the form [ 18,46,47] : d3R _kf dEr d2flf - ki,
n*VdQ)) Mb(Q)
e_2w
x
Ip2ez(Q) + Q’e:(Q)i”
X
I< kf~IaLff?ZIki,
>12.
emQziQz (2)
Here .* ( b( Q ) ) denotes the Bose factor, 2W the Debye-Wailer factor, w(Q) the phonon frequency and ~1, E, the longitudinal and z components of the phonon
polarisation vector. ki, kf and ki,, kfi are the initial and final momenta of the projectile and their z components, respectively. The fact that the He atoms interact with more than one surface atom simultaneously leads to a cut-off in the response to short wavelength phonons of parallel wavevectors Q > Qc. Assuming a Born-Mayer type potential V( z ) = A eCPZ for the z dependence of the static interaction the transition matrix element is given explicitly by the Mott-Jackson expression [ 481: (3) pq sinh(p)
’
sinh(q)
(P2- q212 [cash(p)
- cosh(q)12’
with the reduced initial and final perpendicular menta defined by p = 2rki,/P and q = 2rkf,//3. With the expressions for the Bose factor n+(fMQ>>
(4) mo-
eXP(~/kBT) = exp(tio/knT) - 1’
the Debye-Waller factor 2W = 3hk2kBT/Mw& and the polarisation vectors E derived from a slab calculation we have calculated the product of the terms on the right hand side of the first line in Eq. (2). We found that for our fixed angle scattering geometry (Or + Of = 90.5”) this product of terms shows only a weak Q dependence (less than 20%) compared to the strong (about two orders of magnitude) attenuation of the phonon intensity when moving from the Brillouin zone centre to the zone boundaries. The differential reflection coefficient is thus mainly determined by the cut-off factor and the matrix element. After subtracting a Gaussian shaped multiphonon background we have used the Rayleigh phonon intensities over the entire Brillouin zone (see Fig. 6) to derive values for the potential steepness p and the cut-off factor Qc for the clean and hydrogen covered surfaces using a least-squares fit. The phonon intensities vary over more than two orders of magnitude along the entire Brillouin zone. To consider all the experimental data with the same weight we have minimized the sum of the squared relative deviations (Ical - IeXP)2/Z~2alin the fit. The values obtained are listed in Table 4. For the hydrogen covered surface an enhancement of the
G. Witte et al./Surface Science 323 (1995) 228-240
%
'
a)
Rh'(111)'<11"~;
' 1
1 o
. b
.
F
I
.
.
i
~
I
%, ,
,
,
,
i
L
rib(m)
.~
0.00
025
0.50
0.75
1.00
125
1.50
1.75
Phonon Wave Vector [/1~-1] Fig. 6. Intensity of the Rayleigh phonon mode along the (115) and (1 i0) azimuths for the clean and H( 1 x 1) coveredRh( 111 ) surface as a function of the phonon wave vector. The intensity is derived from HAS time-of-flight spectra after subtraction of the multiphonon background. For both azimuthal directions the hydrogen coveredsurface shows a smaller decrease of the phonon intensity with increasing wave vector indicating a harder surface potential wall. The lines show the calculated phonon intensities based on a distorted wave Born approximation. potential steepness of about 44% and a larger cut-off factor were obtained. In addition from these values the classical point of deflection Zo = f l / Q 2 [49] can be calculated for both clean and hydrogen covered surfaces. Upon hydrogen adsorption, Z0 decreases from about 4.5 to 3.15/~. We note that although this estimate for Z0 is only approximate the shift of the classical turning point of the He-atoms towards the surface is also consistent with the observed increase in the corrugation for the hydrogen covered surface and the enhanced excitation probability for the $2 phonon mode (stronger coupling to atom cores).
6. Discussion It is well known that the interatomic bonding charge is modified in the first layer of metal surfaces with re-
237
spect to the bulk as a result of the Smoluchowski effect which usually leads to a small inward relaxation of the top plane [50], which in turn is expected to modify the interatomic interactions and thus the surface phonon energies. In addition it is known that in the case of hydrogen chemisorption on transition metals the differences in charge distribution between surface and bulk become smaller, which causes a lifting of the structural relaxation. For Pt( 111 ) there is even evidence for a small outward relaxation upon hydrogen adsorption [51 ]. In the case of H adsorbed on Rh(110) [52] it has been suggested that the hydrogen atoms act as electron acceptors with an approximate charge transfer of 0.4e per atom. This behaviour is confirmed by the work function increase of about 930 mV when the Rh(110) surface is exposed to hydrogen. Similar observations have been reported for other d-electron transition metals [ 53,54]. Self-consistent pseudopotential calculations by Louie for the electronic structure of the H( 1 × 1 ) on Pd( 111 ) system [ 55 ] also indicate that the hydrogen adsorption leads to a drastic reduction of the surface electronic density of states near the Fermi level. For P d ( 0 0 1 ) + H Tomanek et al. have also found that the electronic modification mainly affects the intralayer interaction in the top layer [56]. They calculated a charge transfer of 0.2 electrons toward hydrogen, stemming mainly from the Pd atoms in the top layer. This charge redistribution upon hydrogen adsorption is of course expected to affect the surface phonon dispersion curves and explains qualitatively the experimental results for clean and hydrogen saturated Rh( 111 ) which were described in the last section. The experimental observations are similar to those reported for Pt( 111 ) [9]. However, for Rh the dynamical changes induced upon hydrogen adsorption can be seen more easily than in the case of Pt. where the surface dynamics is complicated by the presence of a Kohn-anomaly in the Rayleigh mode and the existence of three different surface phonon modes [ 9 ]. As the results of the lattice-dynamical analysis presented for R h ( l l l ) and R h ( l l l ) + H(1 x 1) in the last section offer only limited insight in the physics behind the hydrogen induced changes of the Rh( 111 ) surface dynamical properties it would be highly desirable to analyze the present results within the framework of the pseudocharge model [ 7 ]. This approach has recently been shown to give a more adequate de-
238
G. Witte et al./Surface Science 323 (1995) 228-240
scription of the interplay between surface electronic charge rearrangement and the surface phonon dispersion curves, because it explicitly takes into account the electronic degrees of freedom and thus can take the changes in the electronic density of states caused by the hydrogen adsorption directly into account. Unfortunately, because of the lack of bulk phonon dispersion curves and continuum elastic constants for rhodium, a multipole expansion within the framework of the pseudocharge model would be very difficult and of limited value. The strong HAS excitation probability for the LRmode on the clean surface and its strong decrease with increasing hydrogen coverage are consistent with the idea behind the pseudocharge model [7], as will be shown in the following. The model assumes the existence of a certain amount of localization of electronic charge between the surface atoms for the clean surface. For longitudinally polarized phonon modes this electronic charge has a "breathing" amplitude normal to the surface which enhances the coupling to the He atoms [7]. The interatomic accumulation of electronic charge (the pseudocharge), which in the case of transition metals is higher at the surface than in the bulk as a consequence of the surface-induced electronic rearrangement [ 57], partially screens the direct core-core interaction; as a result the effective radial force constant can be expected to be weaker at the surface than in the bulk. A reduction of surface charge density e.g. by the adsorption of H-atoms, should in accord lead to a (at least partial) lifting of this softening, as has been observed previously in the case of hydrogen on P t ( l l l ) [9]. Indeed our lattice dynamical calculations (see previous section) give a good agreement with the experimental data for the clean surface after a 20% softening of the surface intralayer nearest neighbour radial force constants determined for the hydrogen covered surface. While the Rayleigh mode is largely unaffected by this reduction in interatomic coupling strength, the frequency of the longitudinal resonance decreases from 24.9 to 22.7 meV at the K-point, thus improving the agreement with experimental data (see Table 3). As the intralayer radial force constant is reduced in addition to this frequency shift the absolute values of the components of the polarisation vector for the LRmode of the first layer decrease while those for the sec-
ond and third layer increase, so that the surface character of the LR-mode becomes less pronounced [58] for the clean surface. In contrast, the polarisation vector for the $2 mode is only weakly affected and remains strongly localized in the first layer. The strong decrease of He-atom coupling strength to the LR-mode upon hydrogen adsorption thus appears to be a result of the surface charge density reduction which reduces the "breathing" character [ 7] of this mode and thus the coupling to the He-atoms. Obviously this effect overcompensates (according to our lattice dynamical calculations) the stronger localisation of the LR-mode in the surface layer, which by itself would give rise to an increase in excitation probability upon the hydrogen induced force-constant stiffening. Note, however, that the latter effect increases the longitudinal component of the LR-mode to which the He-atoms couple less effectively than to the transverse component related to the "breathing" character [ 7] of the LR-mode. In case of the S2-mode seen in the TOF-spectra for the Rh( 111 ) +H( 1 x 1 )-surface we attribute the fact that we are unable to observe this phonon for the clean surface mainly to the strongly different cut-off factor (see above), which close to the zone-boundary, where this mode is seen, decreases the excitation probability by more than an order of magnitude (see Fig. 3) with respect to the hydrogen covered surface. Our simple Born-von Karman force constant model which is constrained to first and second nearest neighbour radial force constants reproduces the longitudinal surface resonance only for the (1 i0) direction. However, for a refined pseudocharge model [ 7 ], this mode has been reproduced correctly for both azimuthal directions on a fcc ( 111 ) surface. It is interesting to note that for the clean Rh( 111 ) surface a considerably larger excitation probability for the longitudinal resonance than for the Rayleigh mode was observed for both high symmetry directions, whereas on C u ( l l l ) this it true only for the ( l i 0 ) direction. These differences are attributed to different multipole moments for the two surfaces resulting from the different electronic structure of the two materials. In summary our HAS-data reveal strong differences in the dynamical properties of the clean and hydrogen covered Rh( 111 ) surface. A comparison of the kvector dependent phonon excitation probabilities for the two surfaces suggest that the strong (opposite)
G. Witte et al./Surface Science 323 (1995) 228-240
differences in the excitation probabilities for the longitudinal surface phonon resonance, which is also found to shift to higher energies upon hydrogen adsorption, and the S2-phonon mode are a consequence of the decrease of the density of localized electronic charge at the surface during hydrogen adsorption, as found by photoelectron spectroscopy or in pseudopotential calculations. This charge transfer to the adsorbed hydrogen atoms not only leads to an increase of the steepness of the He-surface interaction potential (as derived from the phonon excitation probabilities) but also enhances the surface static corrugation.
Acknowledgements We wish to thank H. Range for experimental help in some measurements for the clean surface and Professor K.H. Rieder (FU Berlin) for calculations of the corrugation amplitude. The authors are also grateful to P. Ruggerone and J.R. Manson (Clemson University) for valuable discussions.
References [ 1 ] P.A. Thiel, H. Williams, J.T. Yates, Jr. and W.H. Weinberg, Surf. Sci. 84 (1979) 54. [2] H. Ohtani, R.J. Wilson, S. Chiang and CM. Mate, Phys. Rev. Lett. 60 (1988) 2398. 13] D.G. Castner, B.A. Sexton and G.A. Somorjai, Surf. Sci. 71 (1978) 519. 14] P.A. Thiel, J.T. Yates, Jr. and W.H. Weinberg, Surf. Sci. 82 (1979) 22. [5] J.T. Yates, Jr., P.A. Thiel and W.H. Weinberg, Surf. Sci. 84 (1979) 427. [6] S. Lehwald, J.G. Chen, G. Kisters, E. Preuss and H. lbach, Phys. Rev. B 43 (1991) 3920. [7] C. Kaden, P. Ruggerone, J.P. Toennies, G. Zhang and G. Benedek, Phys. Rev. B 46 (1992) 13509. [8] Y. Chen, S.Y. Tong, K.P. Bohnen, T. Rodach and K.M. Ho, Phys. Rev. Lett. 70 (1993) 603. 19] V. Bortolani, A. Franchini, G. Santoro, J.P. Toennies, Ch. W611 and G. Zhang, Phys. Rev. B 40 (1989) 3524. [ 10] G. Alefeld and J. V61kl, Eds., Hydrogen in Metals II, Topics in Applied Physics, Vol. 29 (Springer, Berlin, 1978). [11] F.A. Lewis, Int. J. Hydrogen Energy 6 (1981) 319. [12] U. Harten, J.P. Toennies, Ch. W611, L. Miglio, P. Ruggerone, L. Colombo and G. Benedek, Phys. Rev. B 38 (1988) 3305. [ 13] R. Berndt, J.P. Toennies and Ch. W~ill, J. Electron Spectrosc. Relat. Phenom. 44 (1987) 183. [ 14] H.J. Ernst, E. Hulpke, J.E Toennies and Ch. W611, Surf. Sci. 262 (1992) 159.
239
[ 15] E. Huipke and J. Ltidecke, Phys. Rev. Lett. 68 (1992) 2846; Surf. Sci. 272 (1992) 289. [ 16] E. Hulpke and J. Liidecke, Surf. Sci. 287/288 (1993) 837. [17] G. Benedek, J. Ellis, N.S. Luo, A. Reichmuth, P. Ruggerone and J.P. Toennies, Phys. Rev. B 48 (1993) 4917. [18] E Hofmann, J.R. Manson and J.P. Toennies, J. Chem. Phys. 101 (1994). [19] N. Bunjes, N.S. Luo, P. Rnggerone, J.P. Toennies and G. Witte, Phys. Rev. B 50 (1994) 8897. [20] B.J. Hinch, A. Lock, H.H. Madden, J.P. Toennies and G. WiRe, Phys. Rev. B 42 (1990) 1547. [21 ] J.P. Toennies, in: Surface Phonons, Springer Series in Surface Science, Vol. 21, Eds. W. Kress and E de Wette (Springer, Berlin, 1991) ch. 5. [221 G. Witte, H. Range, J.P. Toennies and Ch. W611, J. Electron Spectrosc. Relat. Phenom. 64/65 (1993) 715. [23] G. Witte, H. Range, J.P. Toennies and Ch. WOlI, Phys. Rev. Lett. 71 (1993) 1063. [24] H. Jonsson and J.H. Weare, Surf. Sci. 181 (1987) 495. [25] J. Lee, J.P. Cowin and L. Wharton, Surf. Sci. 130 (1983) 1. [26] Bortolani et al. I91 have derived a corrugation amplitude of 0.002 ,~ for the clean Pt( 111 ) surface, which is lower than the value obtained by Lee et al. [25]. This can be attributed to the procedure in deriving diffraction intensities from an angular distribution without background subtraction, and using another corrugation function. [271 D.M. Smilgies and J.P. Toennies, Rev. Sci. Instrum. 59 (1988) 2185. [28] R.B. Doak, U. Harten and J.P. Toennies, Phys. Rev. Lett. 51 (1983) 578; U. Harten, J.P. Toennies and Ch. W611, Faraday Disc. Chem. Soc. 80 (1985) 137. [29] V. Celli, D. Himes, P. Tran, J.P. Toennies, Ch. W611 and G. Zhang, Phys. Rev. Lett. 66 (1991) 3160. [30] Unfortunately, there are neither supersonic data nor elastic constants for rhodium available. The only value we have found in the literature is the velocity of the shear wave of 3005 m/s for polycrystaline rhodium. T.E. Owen, Prog. Appl. Mater. Res. 6 (1964) 69. [31] A.M. Baro, H. Ibach and H.D. Bruchmann, Surf. Sci. 88 (1979) 384. [32] K. Christmann, Z. Phys. Chem. 154 (1987) 145. [33] K. Christmann, R.J. Behm, G. Ertl, M.A. Van Hove and W.H. Weinberg, J. Chem. Phys. 70 (1979) 4168. [34] T.E. Felter, S.M. Foiles, M.S. Daw and R.H. Stulen, Surf. Sci. 171 (1986)L379. [35] M. Lindroos, H. PfnUr and D. Menzel, Surf. Sci. 192 (1987) 421. [36] C.M. Mate and G. Somorjai, Phys. Rev. B 34 (1986) 7417. [37] H. Conrad, M.E. Kordesch, R. Scala and W. Stenzel, J. Electron Spectrosc. Relat. Phenom. 38 (1986) 289. [38] H. Conrad, R. Scala, W. Stenzel and R. Unwin, J. Chem. Phys. 81 (1984) 6371. [39] D.V. Chakarov and T.S. Marinova, Surf. Sci. 204 (1988) 147. [40] R. Berndt, A. Lock and Ch. W611, Surf. Sci. 276 (1992) 213.
240
G. Witte et aL/Surface Science 323 (1995) 228-240
[41 ] Landolt-B6mstein, Tables of Phonon Data, Vol. 13, Metals, Eds. P.H. Dederichs, H. Schober and D.J. Sellmyer (Springer, Berlin, 1981 ). [42] J.E. Black, D.A. Campbell and R.F. Wallis, Surf. Sci. 105 (1981) 629. [43] D.G. Castner, G.A. Somorjai, J.E. Black, D. Castiel and R.E Wallis, Phys. Rev. B 24 (1981) 1616. [44] J.E. Black, F.C. Shanes and R.E Wallis, Surf. Sci. 133 (1983) 199. 145 ] We recall that our definition of the tangential ai radial fll and angular 6i force constants (the index i refers to the ith nearest neighbour) is different from that given by Black et al. [44] but can be converted to his definition: al = &l -&2, a2 =/32, /31 = ~l + t~2, f12 = ]~J and ~ = _3y, where the constants fiq, &2, /~1, /~2 and y are as described by Black et al. [44]. [46] J.R. Manson and V. Celli, Surf. Sci. 24 (1971) 495. [47] V. CeUi, G. Benedek, U. Harten, J.E Toennies, R.B. Doak and V. Bortolani, Surf. Sci. 143 (1984) L376. [48] EO. Goodman and A.Y. Wachman, in: Dynamics of GasSurface Scattering (Academic Press, New York, 1972) ch. 8. [49] V. Bortolani, A. Franchini, N. Garcia, E Nizzoli, G. Santoro, Phys. Rev. B 28 (1983) 7358.
[50] M.W. Finnis and V. Heine, J. Phys. F 4 (1974) L37. [51] J.A. Davies, D.P. Jackson, P.R. Nat'ton, D.E. Posner and W.N. Unertl, Solid State Commun. 34 (1980) 41. [52] G. Parschau, E. Kirsten and K.H. Rieder, Phys. Rev. B 43 (1991) 12216. [53] K. Christmann, Surf. Sci. Rep. 9 (1988) !. [54] From our UPS measurements we have derived a surprisingly small work function increase of 50 mV for the R h ( l l l ) surface. For ruthenium, another d-electron metal containing also valence s-electrons, a similar strong anisotropy of work function change for different surface orientations has been observed [531. [55] S.G. Louie, Phys. Rev. Left. 42 (1979) 476. [561 D. Tomanek, S.G. Louie and C.T. Chart, Phys. Rev. Lett. 57 (1986) 2594. [57] A. Euceda, D.M. Bylander and L. Kleinman, Phys. Rev. B 28 (1983) 528. [58] J.P. Toennies, in: Springer Series in Surface Science, Vol. 14, Ed. F.W. de Wette (Springer, Berlin, 1988) pp. 248-290. [59] V.N. Antonov, V.Y. Milman, V.V. Nemoshkalenko and A.V. Zhalko-Titarenko, Z. Phys. B (Condens. Matter) 79 (1990) 223. [60] C.H. Hsu, PhD Thesis, Boston University Graduate School (1992).
ELSEVIER
Comparison of surface phonon dispersion curves for clean and hydrogen covered Rh( 111 ) surfaces G. Witte, J.R Toennies, Ch. W611 .,1 Max-Planck-lnstitut fiir StrOmungsforschung, Bunsenstrasse 10, D-37073 GOttingen, Germany Received 11 April 1994; accepted for publication 13 September 1994
Abstract Surface phonon dispersion curves have been measured for the clean and hydrogen covered Rh(111) surfaces along the (1 i0) and (112) high symmetry directions of the surface Brillouin zone using high resolution He-atom scattering. Interatomic force constants and elastic constants, which are not available for this material, were obtained by a lattice-dynamical analysis. The significant changes of the dynamical properties of the surface upon hydrogen adsorption are shown to be related to hydrogen-induced changes in the surface electronic structure and are discussed within the framework of a pseudocharge model which has been developed recently. An analysis of the experimental phonon excitation probabilities for the two surfaces within the framework of the distorted wave Born approximation indicates large changes in the repulsive He-surface potentials upon hydrogen adsorption. Key words: Adatoms, Atom-solid interactions, Low index single crystal surfaces, Rhodium
1. Introduction
Rhodium is known to be an active heterogeneous catalyst for a number of chemical reactions. Mainly for this reason the Rh( 111 ) surface has been the subject of a large number of investigations in recent years, especially with regard to the adsorption of benzene, CO, oxygen and hydrogen [ I - 5 ] . To date, no information concerning the surface dynamical properties of this material is available. Unlike other metals a prediction of surface phonon dispersion relations based upon model calculations using bulk force constants is * Corresponding author. 1 Permanent address: Angewandte Physikalische Chemie, Universitiit Heidelberg, Im Neuenbeimer Feld 253, D-69120 Heidelberg, Germany.
not possible for rhodium (and iridium [6] ) due to the complete lack of experimental bulk phonon data. The latter is due to the fact that inelastic neutron scattering, the standard technique for measuring bulk phonons, cannot be applied easily to rhodium (and Ir) because of the anomalously high absorption cross section for thermal energy neutrons. Detailed information on the surface dynamics of Rh( 111 ) is also relevant with regard to the discussion about the origin of the surface longitudinal resonance (LR) observed for a number of metals, on which a general consensus has not yet been reached [7,8]. It would be particularly interesting to compare this with the results obtained for Pt( 111 ) (because of the similar electronic properties of the two materials), where the surface dynamics is complicated by the presence of a Kohn anomaly and a third surface phonon mode [9].
0039-6028/95/$09.50 @ 1995 Elsevier Science B.V. All rights reserved
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G. Witte et al./Surface Science 323 (1995) 228-240
The adsorption of hydrogen on metal and semiconductor surfaces is of great interest since the chemisorbed H is presumably a key intermediate in many important catalytic reactions and because of possible storage applications in energy technology [ 10,11 ]. It is known that hydrogen is a passivation agent for amorphous silicon in electronics applications and on metal surfaces. Adsorbed hydrogen has also been observed to significantly affect the surface phonon dispersion curves of a number of systems including S i ( l l l ) / H [12], Ni(001)/H [13], P t ( l l l ) / H [9], W ( 1 0 0 ) / H [14], W ( l l 0 ) / H [15], M o ( l l 0 ) / H [16]. With the exception of W ( l l 0 ) and Mo(110) the effect of H is to suppress anomalous modes and to restore the surface dynamical properties to those expected for a nearly ideal termination of the bulk. In the present publication we report measurements of surface phonon dispersion curves and the corresponding excitation probabilities for the clean and the hydrogen covered Rh(111) + H ( 1 × 1 ) surfaces by helium atom scattering (HAS). In addition to the Rayleigh mode several features at higher energies appear in the time-of-flight spectra. The strong differences observed between the clean and the hydrogen covered surfaces suggest that the hydrogen atoms reduce the electronically induced softening of the clean surface atom core-core interaction. The experimental data were analyzed within the framework of lattice dynamical calculations using a Born-von Karman force constant model. The results of this analysis and the observed phonon excitation probabilities are related to recent results obtained from the pseudocharge model which has been employed recently to successfully calculate the inelastic HAS intensities for Cu( 111 ), Cu(001) and Ag(001 ) [7,1719]. The experimental procedure for sample preparation and the experimental setup for surface phonon measurements are outlined in Section 2. Experimental diffraction and time-of-flight results are presented in Section 3 for the clean surface and in Section 4 for the hydrogen saturated surface. In Section 5 results of the lattice dynamical calculations and calculations of the phonon excitation probabilities are presented. The paper closes with a final discussion in Section 6.
229
2. Experimental setup A detailed description of the He-atom time-of-flight apparatus used for diffraction and phonon experiments is given in Refs. [20,21]. Essentially, the apparatus consists of a He nozzle-beam source, a target chamber and a I. 124 m long time-of-flight drift tube, at the end of which the He-atoms are detected by a mass spectrometer with a magnetic mass selector. The supersonic helium atom source is operated at temperatures between 30 and 500 K and at pressures up to 300 bar. The resulting beams have kinetic energies between 7 and 120 meV with an energy spread ( A E / E ) of about 2% over the entire range of energies. The sample is mounted on a three axis manipulator. This allows alignment and rotation of the azimuth, tilt and polar angles. The sample temperature can be varied between 100 and 1300 K using a flexible copper braid connected to a liquid nitrogen cryostat for cooling and electron bombardment for heating. Angular distributions of He-atoms scattered off the surface are recorded by rotating the crystal around an axis perpendicular to the plane of the incident and final scattered beams which have a fixed angle of 90.5 ° between them. While the overall angular resolution of the instrument is about 0.2 ° , the angle of incidence can be measured with a resolution of 0.04 °. As the He-atom diffraction intensities for the clean Rh( 111 )-surface are found to be extremely weak the alignment of the azimuth was carried out for (2 x 2) adlayer structures of CO or 02, which exhibit a much stronger corrugation. After cleaning and heating of the substrate, the FWHM of the specular peak was found to be 0.35 °. The time-of-flight (TOF) technique allows the observation of discrete (one phonon) inelastic scattering processes with a resolution of typically 1.5 ~s channel width corresponding to 0.1 meV at an incident energy of 50 meV and an energy loss of about 17 meV. The kinematic scattering conditions were changed by varying either the incident energy or the angle of incidence. The target chamber is equipped with a low energy electron diffractometer (LEED), a quadrupole mass spectrometer for residual gas analysis, and a Leybold-Hereaus EA11 photoelectron spectrometer with X-ray and UV-light sources. The Rh( 111 ) single crystal sample was cleaned through a process of 6
230
G. Witte et al./Surface Science 323 (1995) 228-240
hours of argon sputtering followed by repeated cycles of 800 eV Ar + bombardment (1 h) and heating to 1300 K (2 min) using electron bombardment. After a few cleaning cycles, XPS signals indicated contamination levels of less than 1% of a monolayer for C and less than 0.3% for oxygen. The base pressure of 6 x 10 -ll mbar in the target chamber allowed measuring times of more than 7 h without any noticeable effect on the He specular beam signal from surface contamination. The adsorption of CO onto the clean surface could be monitored by HAS directly since the frustrated translation of the chemisorbed CO-molecule gives rise to distinct energy losses [22]. In a previous experiment the adsorption of benzene on this surface has been investigated with HAS using the same machine [ 23 ].
(11~->
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I. ~
0 ~,i t- O. Q~ ti=.i Q;
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O.
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3. The clean R h ( l l l ) surface The structural quality of the surface and the alignment of the crystal were checked by recording angular distributions. Fig. la shows typical angular distributions for the (112) and (1 ]0) high symmetry azimuths. Note that since these distributions are symmetric with respect to the specular peak at Oi = 45.25 ° they have been displayed with the (112) and (li0) directions on the left and right hand sides of the specular peak, respectively. For a beam with an incident wave vector of 8.3 A-1 the first and second order diffraction peaks were measured along the (112) direction (G(ll~) = 2.70/~-1) and were found to have intensities of about 6.5 x 10 -3 and 6.5 x 10 -5 of the specular intensity, respectively. Along the (li0) azimuth (G
~(x,Y)=½(o{cos(2--~x)
+ cos ( ~ y )
the overall (peak-to-peak) corrugation amplitude was
L
-s.o
-~.o
-2.o
o
zo
4.o
6.0
AK [k~l Fig. 1. Angular distributions measured for the clean Rh( 111 ) surface (upper panel) and for the R h ( l l l ) + H(1 x 1) surface with saturation coverage of hydrogen (lower panel). Note that the left part of the angular distribution is along the (11~) direction whereas the right part is along the ( l i 0 ) direction. The incident beam wave vector for all scans was k i = 1 0 / ~ - 1 and the sample temperature was 135 K. While the clean R h ( l l l ) - s u r f a c e is very smooth hydrogen adsorption enhances the corrugation and the Rh( 111 ) + H ( 1 x 1 ) surface exhibits considerably stronger diffraction peaks.
calculated to be g'0 = 0.05 A. This value is larger than the corrugation amplitudes of 0.03 and 0.01/~ derived for Ag(111) [24] and Pt(111) [25,26]. Over 300 time-of-flight spectra were measured along both high-symmetry directions most of them for surface temperatures of 135 and 300 K. Mostly the phonons were measured in creation with positive Q because of the optimal kinematic resolution conditions [27]. Two main energy loss peaks can be identiffed in the typical TOF-spectra shown in Figs. 2 and 3. The resulting phonon dispersion curves are shown in Fig. 4. The lower energy mode is attributed to the Rayleigh mode (RW), which is a typical feature for clean metal surfaces. The second peak at higher energy is attributed to the anomalous longitudinal resonance
G. Witte et al./Surface Science 323 (1995) 228-240
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Fig. 2. Series of He-atom time-of-flight spectra converted to an energy transfer scale for the (l i0) direction of the clean Rh( 111 ) (left column) at 300 K and H(1 x 1) covered surface (right column) at 135 K. RW: Rayleigh wave, LR: longitudinal resonance, B: bulk resonance. The spectra were recorded with incident energies of 55 meV. The first spectrum for the H( i x 1 ) structure shows an energy loss at 28.5 meV ($2) which is not observed for the clean surface.
(LR), which has been observed on Pt(111) and on other noble and transition metal surfaces [9,7,28]. In the (112) direction, the M point zone boundary energies amount to 16.2 + 0.3 meV for the Rayleigh mode and approximately 22.5 -t- 1 meV for the longitudinal resonance. Due to the strong decrease of the phonon intensity along the (liO) direction, the dispersion curve could not be measured up to the zone boundary. Extrapolation with an assumed sine-curve dispersion relationship yields a K point zone boundary energy of
17.4 ± 0.7 meV for the Rayleigh mode. Table 1 lists the zone boundary Rayleigh phonon energies for the clean and H-covered surfaces and shows a comparison with other transition metals. Relative to the Rayleigh mode the excitation probability for the longitudinal mode on Rh( 111 ) increases with larger phonon wave vectors along both high-symmetry directions as already observed for C u ( l l l ) [7], Cu(001) [17,18] and Ag(001) [19]. For wave vectors at ]F-'-Ka weak third peak (B) was detected (see last TOF-spectrum
232
G. Witte et a l . / S u r f a c e Science 323 (1995) 2 2 8 - 2 4 0
<11~>
Rh {111}
Rh(111)+H(lx1) (11~>
250.0 Oi'=t'05( ) '
200£
RW~
j
150.0 100.0
x25
"
500 0.0 TRh=300K R W Ei=50meV
309 22.5
-
. =
TRh=130K Ei =55 meV
.
E)i =37"5°
15.0 >
u
7 %
/
7.5 0.0
i
RW'
®
16.0 Oi =36'5° LR~ ¢n c
12.0
0
D o
80
¢-
0~3
=36.5 °
4.0
E
.
t
(9i =35.5 ° RW
80 60
LR~~
4.12 2.[
Oi
i
i
i
i
6£ 4..=
\
3.[ 1.5 0.0
/11 "30.0
"20.0 -10.0
0.0
Energy TransferImeV]
10.0
-300
-200 -10.0
0.0
10.0
Energy Transfer lmeV]
Fig, 3. Same as Fig. 2 but for the (112) direction.
in left column of Fig. 2). While for Cu(001) and Ag(001 ) [ 17,19] similar features have been observed above the longitudinal resonance, the peaks measured here are located between the Rayleigh mode and the longitudinal resonance. We attribute these loss peaks to the high density of states of the lower edge of a transversely polarized bulk phonon band since multiphonon excitation is expected to give rise to considerably broader features [29]. The dispersion curves of the Rayleigh mode for small wave vectors have been fitted by a straight line, the slope of which corresponds to the velocity
of sound. The resulting values of 3450 + 250 and 3210+250 m/s for the (110) and (112) azimuths obtained in this way appear to be the first measurements of these quantities for crystalline rhodium [ 30].
4. The hydrogen saturated R h ( l l l ) + H(1 × 1) surface Yates et al. [5] have investigated the kinetics of hydrogen adsorption on Rh( 111 ) and demonstrated, mainly by thermal desorption spectroscopy, that hy-
G. Witte et al./S~,ff, ace Science 323 (1995) 228-240
35
F
K
M
<11"~>
r
3O >
J
2s
///
LR ilJ ¢U.I
.J"
,8
g ~s
/
I m
/ o
g
~"
•
im
t
/ m~ =
/.ip4"
n I
I
I ~L.
o'.5
...,~,,
--.
LR
~',
"1
,
/
\
\
l
"bx
~L/<~o~
RW
~'.o I I 1.56 t35 1'0 Phonon Wove Vector lJ~~1
\
m\ "~
\
, o5
Fig. 4. Dispersion curves of the clean Rh( 111 ) surface at 300 K. The Rayleigh mode (RW) and a longitudinal mode (LR) are observed for the (1 i0) and the (112) direction. Along the (1 i0) direction very weak extra peaks are observed which are attributed to a bulk resonance (B). The inset shows the reciprocal lattice with the first Brillouin zone. The dashed lines show the bulk band edges derived from a slab calculation using the force constants from model Fgh (Table 2).
drogen dissociatively chemisorbs at the surface, which appears to be a general feature for all d-electron transition metal surfaces. As the changes in the LEEDpattern upon hydrogen adsorption are small due the small scattering cross section of H for low-energy electrons the formation of well ordered hydrogen ovedayers could not be studied with this technique, and as a consequence, has not been reported previously. Our He-atom scattering angular distributions displayed in Fig. lb thus provide the first direct evidence that hyTable 1 Zone boundary Rayleigh phonon energies in meV for some clean and H( 1 × 1 ) covered transition metal surfaces Surface
Max.
Ref.
bulk
Clean M
H(I x 1) K
M
Ref.
K
phonon energy Pt(lll)
24.19
[41]
10.8
11.1
Pd(lll)
29.03
[41]
11.1
-
Rh(lll)
31.20
[59]
16.2 ~ 1 7 . 4
Ru
32.05
[41]
.
.
.
9.3
9.5
[9]
11.I
[60]
15.6 16.4
This work
.
233
drogen forms a well ordered (1 × 1) overlayer on the Rh( 111 )-surface. Hydrogen adsorption was carried out by heating the sample to 1300 K and then cooling down to 130 K with a subsequent exposure to H2 at a pressure of 10 -8 mbar. The adsorption could be monitored by recording the specular peak intensity, which shows an abrupt decrease upon hydrogen exposure followed by a gradual increase reaching a final value of 90% of the specular intensity for the clean surface. At this temperature the hydrogen structure seems to be very stable, peak shapes and intensities in the angular distributions revealed no changes even after very long measurements (8 hours). The adsorption site of the hydrogen atoms on Rh( 111 ) has not yet been determined, but from the information available for other transition metals (H/Pt( 111 ) [31,32], H / N i ( l l l ) [ 3 3 ] , H / P d ( l l l ) [34] andH/Ru(0001) [35] ) it appears likely that hydrogen on Rh( 111 ) is adsorbed in a three-fold hollow site. After preparation of the hydrogen overlayer a large increase in the diffraction intensities by a factor of 10-20 was observed (see Fig. lb) indicating a strong enhancement of the surface corrugation. From the relative diffraction intensities with respect to the specular intensity (5.75 × 10-2 and 2.97 × 10 - 4 for the first and second order peak along (112) and 2.88 x 10 -4 for the first order peak along (1 ]0), respectively) an effective hard wall corrugation amplitude of 0.15/~ was calculated using Eq. (1) in the Eikonal approximation. A similar strong enhancement of the surface corrugation amplitude from 0.01 to 0.18 A during the hydrogen adsorption was reported for Pt( 111 ) by Lee et al. [25]. In the right-hand-side columns of Figs. 2 and 3 representative time-of-flight spectra recorded along the (1 i0) and (112) directions for the Rh( 11 I) + H( 1 × 1 ) surface are displayed which can be directly compared to the corresponding data for the clean surface shown on the left-hand-side of the respective figure. After subtraction of the multiphonon background the inelastic scattering intensity of the Rayleigh mode is higher than for the clean surface for wave vectors larger than 0.5 /~-1. As a consequence, the dispersion curve of the Rayleigh mode (see Fig. 5) could be measured beyond the zone boundary. Along the (1 i0) direction it was possible to extend the measurements up to the M point (see inset in Fig. 4). The energies of the Rayleigh mode at the K and M points
234
G. Witte et al./Surface Science 323 (1995) 228-240
35
F
,
,
R ,
- . . . . . s~_-~, b
30
=,~===_,, ~ . ~ J ,
..... •
•~20 ,
/
C:
U.I C 15t
//
/
oO° I //
o~%~° °. j+ . . . . . . . . . B'-" I ,I
//./I
II ill, n" qb , ,
Rw
r,
F
0
I I 05
~ 1.0
1.56
F
,~=--
I ," b"
I
\\ \LR "~,p
j_ ~
t¢ %o -
• • 1~,
: Rh(1111
5If
•
o1~)
~.-.. s~ . . . .
/ i i ~ i : . . ~ ~\ ~\ ' . . . . . LR/~IIIk iI -. ",
25
0
~
,
\
\
'\
,' Rw"%, ',, +
Hllxl)
II
I I 1.35
~ ,\\, \
' 1~.0
0.5
0
Phonon Waw Veclor [~-i]
Fig. 5. Dispersion curves for the Rh(lll) + H(I x 1) surface. The Rayleigh mode (RW) has been measured along the whole irreducible part of the Brillouin zone and shows the same behaviour as for the clean surface. Along the (112) direction the longitudinal mode (LR) disappearsalmost while in the (1 i0) direction the mode seems to shift to higher energies and a weak broad resonanceis observed (open cycles). Additionally close to the zone boundaries a high energy mode ($2) could be identified. The dashed lines show the bulk band edges derived from a slab calculation using the force constants from model Fgh (Table 2). are 16.4 + 0.3 and 15.6 + 0.3 meV, respectively, and are slightly lower than the clean surface energies (see Table 1 ). The energy loss peaks related to an excitation of the longitudinal resonance (LR) are much less intense than for the clean surface. For the H( 1 x 1 ) surface this mode can only be observed at high momentum transfers and, in addition, the mode is shifted to higher energies, the shift amounting to about 3 meV at the Brillouin-zone midpoints along both symmetry directions. A zone boundary energy of 25.5 + 0.7 meV for the longitudinal resonance could only be determined for the (1]0) direction at K. For large wave vectors some weak and broad peaks (open circles in Fig. 5, labelled Bt) have been observed. As multiphonon excitations typically seem to be even broader [29] features are tentatively assigned to surface resonances embedded in the bulk bands. In addition, a $2 surface longitudinal mode which is split off from the longitudinal bulk bands is observed close to the Brillouin zone boundary along both high-symmetry directions. This clearly resolved mode (see first TOF-spectrum
in the right column of Figs. 2 and 3) lies at energies of 28.5 + 0.5 and 29.7 -4-0.5 meV at K and M, respectively. In order to rule out the possibility of a soft hydrogen mode, we have repeated the time-of-flight measurements for a deuterium ( 1 x 1 ) overlayer. Time-of-flight spectra recorded for the deuterated surface are virtually identical to those measured for the hydrogenated surface, no isotope-shifts of surface vibrational frequencies could be observed. This result demonstrates clearly that the observed mode is a rhodium surface mode and is therefore the first observation of the $2 mode on a fcc (111 )-surface by helium atom scattering. The mass effect of the hydrogen atoms on the rhodium atom vibrational frequencies can be neglected since the hydrogen mass is less than 1% the mass of the Rh atom ( 104 amu), and therefore is expected to reduce the frequency at the zone boundary by less than 0.5 %. As the energies of the H-metal stretch vibrations are higher than the maximum bulk phonon energy the coupling to the substrate vibrations is expected to be very weak. Moreover these modes are expected to have very small excitation probabilities in HAS experiments and have not been observed so far. For H on Rh( 111 ) weak peaks in EEL-spectra were reported by Mate and Somorjal [36] with energy losses of 92, 136 and 175 meV. For other transition metals hydrogen vibrations have been observed with energies of 68 and 153 meV for H/Pt( 111 ) [31 ], 96 and 124 meV for H / P d ( I 11 ) [37], 102 and 140 meV for H/Ru(0001) [38] and 69 meV for H/Ir(111) [39]. Due to this decoupling any changes of surface phonon energies upon hydrogen adsorption as observed by HAS can be solely attributed to force constant changes at the surface which originate from changes in the surface electronic structure.
5. Lattice d y n a m i c a l a n a l y s i s
The best first step in analysing experimental surface phonon data is to compare with predictions obtained from a lattice-dynamical calculation. In this case we have employed a 35 layer slab and two simple force constant schemes, the first limiting interactions to the shell of nearest neighbours whereas the second additionally included couplings to second nearest neighbours. A detailed description of the algorithms
G. Witte et aL /Surface Science 323 (1995) 228-240
Table 2 Force constants for various models (N/m) Model
fll
F~h FRbh F~h FRah F~Rh rl° ~RRr2° ~
78.6 -- 1.4 2.6 --2.6 2.09 76.0 12.3 0.0 0.0 2.09 63.0 0.0 0.0 0.0 0.0 63.0 15.0 2.0 --2.0 1.5 F~Rh, but 10% intralayer softening for/31 FROh,but 20% intralayer softening for fll
B2
al
a2
used in our slab calculation has been published previously [40]. When analysing surface dynamical properties typically as a starting point the bulk force constants are used. As bulk data are not available for Rh [41] we have used the force constants derived by Black et al. [42] from a LEED Debye-Waller investigation on the Rh( 111 ) surface [43]. The two different forceconstant schemes of Black et al. are listed in Table 2 ( F ~ and F b ) [45]. The resulting energies of the Rayleigh mode and the longitudinal gap mode ($2) at the high symmetry points in the surface Brillouin zone are provided in Table 3. A comparison with the experimental data for the clean surface (Table 1) reveals significant lower energies with differences of about 3 meV for scheme F~h and of 1.5 meV for scheme F b . Without the possibility to refer to bulk data at this point it is virtually impossible to decide whether the deviations between experiment and calculations are due to deficiencies of Table 3 Calculated surface mode energies in meV for the H( 1 x 1) surface Model At M
Exp. F~h FRbh ~Rh Faah FROrl° ia FRa~2°
At
Average error at zone boundary (%)
RW
$2
RW
$2
LR
15.60 13.25 14.74 15.68 15.69 15.69 15.68
29.70 32.90 32.50 32.70 30.55 29.45 28.14
16.40 15.50 15.04 16.62 16.36 16.36 16.36
28.50 29.60 29.30 27.60 27.67 28.70 28.60
25.50 26.70 20 25.80 14 10 24.88 4 23.67 22.68
235
the force constant schemes or whether surface relaxation effects cause changes in surface phonon energies, as observed for other transition metal surfaces such as Pt(111) [9]. From analogy to the rather similar case of Pt( 111 ) we chose to fit the theoretical calculations to the experimental results for the hydrogen covered R h ( l l l ) + H ( 1 × 1)-surface, since it has been shown for P t ( l l l ) [9] and other metals such as W(100) [14], Ni(001) [13] and P d ( l l l ) [60] as well as for Si( 111 ) [ 12] that the hydrogen covered surfaces exhibits dynamical properties which are in very close agreement with predictions derived from a well parameterized bulk force constant scheme. On the basis of this assumption we can use the surface phonon data for R h ( l l l ) + H ( l x 1) to obtain a prediction for the bulk force constants of Rh using a fitting procedure. As shown in Table 3 for both schemes F~h and Fp~ the Rayleigh phonon energies are too low and the S2-1ongitudinal gap mode is too high in energy when compared to the experimental data for the hydrogen covered surface. In order to improve the agreement a single force constant model (model F ~ ) was fitted to the experimental data for the Rayleigh phonon energies at the high symmetry points of the Brillouin zone. As shown in Table 3 an effective radial force constant of 63 N / m gives rather good agreement with the Rayleigh mode but falls to yield the correct values for the $2 mode. It was found to be impossible to improve this agreement using a one force-constant scheme. A considerably better agreement was achieved with a 5 parameter model (model FaRh) with first and second nearest neighbour radial and tangential coupling parameters and an angular force constant. With this model we were able to reproduce the measured Rayleigh phonon and the S2gap-mode energies at the high-symmetry points with an accuracy better than 4%. Accepting the resulting force-constant scheme F ~ obtained by the fit to the data for the Rh( 111 ) + H ( 1 x l) surface as an improved bulk force constant parametrisation for Rh, the lower energies for the LRresonance mode observed for the clean surface can be reproduced by a softening of the surface intralayer force constant fll (which couples atoms in the surface plane), see Table 3. This observation is again similar to the case for Pt( 111 ) [9]. Note that with this simple
236
G. W&e et al./Surface
Table 4 Interaction
parameters
Azimuth
Rh( 111) P
(A-‘)
Science 323 (1995) 228-240
for single pbonon scattering Rh(lll)+H(I
x 1)
Qc (A-1)
Zo (A)
P (A-‘)
Qc (A-‘)
ZI (A)
(ITo)
3.02
0.823
4.46
4.46
1.19
3.15
(112)
3.15
0.820
4.68
4.46
1.19
3.15
force-constant scheme the LR-mode could only be obtained for the K-point. It was neither attempted to modify the force-constant scheme in order to obtain the LR-mode also for the a-point, nor did we try to fit the experimental dispersion curve of the LR-mode to the experimental data as the lack of a more precise bulk force constant scheme limits the scientific insight which can be gained by such an analysis. In order to derive further information about the He surface interaction we have analyzed the Rayleigh phonon intensities for the clean and hydrogen covered surface in the framework of the distorted wave Born approximation. The single quantum excitation probability for a projectile scattered from an interaction potential can be calculated using formulae presented by Manson and Celli [ 461. Since neither initial nor final states of the crystal can be determined, the transition rate is obtained by a summation over all final vibrational states and is averaged over all initial states. The actual intensity measured in an experiment is the differential reflection coefficient, or in other words, the number of scattered particles detected per unit final solid angle and per unit final energy, d3 R/ dEr d2&, which is proportional to the transition rate [ 181. The differential reflection coefficient for a crystal consisting only of like atoms of mass M can be written in the form [ 18,46,47] : d3R _kf dEr d2flf - ki,
n*VdQ)) Mb(Q)
e_2w
x
Ip2ez(Q) + Q’e:(Q)i”
X
I< kf~IaLff?ZIki,
>12.
emQziQz (2)
Here .* ( b( Q ) ) denotes the Bose factor, 2W the Debye-Wailer factor, w(Q) the phonon frequency and ~1, E, the longitudinal and z components of the phonon
polarisation vector. ki, kf and ki,, kfi are the initial and final momenta of the projectile and their z components, respectively. The fact that the He atoms interact with more than one surface atom simultaneously leads to a cut-off in the response to short wavelength phonons of parallel wavevectors Q > Qc. Assuming a Born-Mayer type potential V( z ) = A eCPZ for the z dependence of the static interaction the transition matrix element is given explicitly by the Mott-Jackson expression [ 481: (3) pq sinh(p)
’
sinh(q)
(P2- q212 [cash(p)
- cosh(q)12’
with the reduced initial and final perpendicular menta defined by p = 2rki,/P and q = 2rkf,//3. With the expressions for the Bose factor n+(fMQ>>
(4) mo-
eXP(~/kBT) = exp(tio/knT) - 1’
the Debye-Waller factor 2W = 3hk2kBT/Mw& and the polarisation vectors E derived from a slab calculation we have calculated the product of the terms on the right hand side of the first line in Eq. (2). We found that for our fixed angle scattering geometry (Or + Of = 90.5”) this product of terms shows only a weak Q dependence (less than 20%) compared to the strong (about two orders of magnitude) attenuation of the phonon intensity when moving from the Brillouin zone centre to the zone boundaries. The differential reflection coefficient is thus mainly determined by the cut-off factor and the matrix element. After subtracting a Gaussian shaped multiphonon background we have used the Rayleigh phonon intensities over the entire Brillouin zone (see Fig. 6) to derive values for the potential steepness p and the cut-off factor Qc for the clean and hydrogen covered surfaces using a least-squares fit. The phonon intensities vary over more than two orders of magnitude along the entire Brillouin zone. To consider all the experimental data with the same weight we have minimized the sum of the squared relative deviations (Ical - IeXP)2/Z~2alin the fit. The values obtained are listed in Table 4. For the hydrogen covered surface an enhancement of the
G. Witte et al./Surface Science 323 (1995) 228-240
%
'
a)
Rh'(111)'<11"~;
' 1
1 o
. b
.
F
I
.
.
i
~
I
%, ,
,
,
,
i
L
rib(m)
.~
0.00
025
0.50
0.75
1.00
125
1.50
1.75
Phonon Wave Vector [/1~-1] Fig. 6. Intensity of the Rayleigh phonon mode along the (115) and (1 i0) azimuths for the clean and H( 1 x 1) coveredRh( 111 ) surface as a function of the phonon wave vector. The intensity is derived from HAS time-of-flight spectra after subtraction of the multiphonon background. For both azimuthal directions the hydrogen coveredsurface shows a smaller decrease of the phonon intensity with increasing wave vector indicating a harder surface potential wall. The lines show the calculated phonon intensities based on a distorted wave Born approximation. potential steepness of about 44% and a larger cut-off factor were obtained. In addition from these values the classical point of deflection Zo = f l / Q 2 [49] can be calculated for both clean and hydrogen covered surfaces. Upon hydrogen adsorption, Z0 decreases from about 4.5 to 3.15/~. We note that although this estimate for Z0 is only approximate the shift of the classical turning point of the He-atoms towards the surface is also consistent with the observed increase in the corrugation for the hydrogen covered surface and the enhanced excitation probability for the $2 phonon mode (stronger coupling to atom cores).
6. Discussion It is well known that the interatomic bonding charge is modified in the first layer of metal surfaces with re-
237
spect to the bulk as a result of the Smoluchowski effect which usually leads to a small inward relaxation of the top plane [50], which in turn is expected to modify the interatomic interactions and thus the surface phonon energies. In addition it is known that in the case of hydrogen chemisorption on transition metals the differences in charge distribution between surface and bulk become smaller, which causes a lifting of the structural relaxation. For Pt( 111 ) there is even evidence for a small outward relaxation upon hydrogen adsorption [51 ]. In the case of H adsorbed on Rh(110) [52] it has been suggested that the hydrogen atoms act as electron acceptors with an approximate charge transfer of 0.4e per atom. This behaviour is confirmed by the work function increase of about 930 mV when the Rh(110) surface is exposed to hydrogen. Similar observations have been reported for other d-electron transition metals [ 53,54]. Self-consistent pseudopotential calculations by Louie for the electronic structure of the H( 1 × 1 ) on Pd( 111 ) system [ 55 ] also indicate that the hydrogen adsorption leads to a drastic reduction of the surface electronic density of states near the Fermi level. For P d ( 0 0 1 ) + H Tomanek et al. have also found that the electronic modification mainly affects the intralayer interaction in the top layer [56]. They calculated a charge transfer of 0.2 electrons toward hydrogen, stemming mainly from the Pd atoms in the top layer. This charge redistribution upon hydrogen adsorption is of course expected to affect the surface phonon dispersion curves and explains qualitatively the experimental results for clean and hydrogen saturated Rh( 111 ) which were described in the last section. The experimental observations are similar to those reported for Pt( 111 ) [9]. However, for Rh the dynamical changes induced upon hydrogen adsorption can be seen more easily than in the case of Pt. where the surface dynamics is complicated by the presence of a Kohn-anomaly in the Rayleigh mode and the existence of three different surface phonon modes [ 9 ]. As the results of the lattice-dynamical analysis presented for R h ( l l l ) and R h ( l l l ) + H(1 x 1) in the last section offer only limited insight in the physics behind the hydrogen induced changes of the Rh( 111 ) surface dynamical properties it would be highly desirable to analyze the present results within the framework of the pseudocharge model [ 7 ]. This approach has recently been shown to give a more adequate de-
238
G. Witte et al./Surface Science 323 (1995) 228-240
scription of the interplay between surface electronic charge rearrangement and the surface phonon dispersion curves, because it explicitly takes into account the electronic degrees of freedom and thus can take the changes in the electronic density of states caused by the hydrogen adsorption directly into account. Unfortunately, because of the lack of bulk phonon dispersion curves and continuum elastic constants for rhodium, a multipole expansion within the framework of the pseudocharge model would be very difficult and of limited value. The strong HAS excitation probability for the LRmode on the clean surface and its strong decrease with increasing hydrogen coverage are consistent with the idea behind the pseudocharge model [7], as will be shown in the following. The model assumes the existence of a certain amount of localization of electronic charge between the surface atoms for the clean surface. For longitudinally polarized phonon modes this electronic charge has a "breathing" amplitude normal to the surface which enhances the coupling to the He atoms [7]. The interatomic accumulation of electronic charge (the pseudocharge), which in the case of transition metals is higher at the surface than in the bulk as a consequence of the surface-induced electronic rearrangement [ 57], partially screens the direct core-core interaction; as a result the effective radial force constant can be expected to be weaker at the surface than in the bulk. A reduction of surface charge density e.g. by the adsorption of H-atoms, should in accord lead to a (at least partial) lifting of this softening, as has been observed previously in the case of hydrogen on P t ( l l l ) [9]. Indeed our lattice dynamical calculations (see previous section) give a good agreement with the experimental data for the clean surface after a 20% softening of the surface intralayer nearest neighbour radial force constants determined for the hydrogen covered surface. While the Rayleigh mode is largely unaffected by this reduction in interatomic coupling strength, the frequency of the longitudinal resonance decreases from 24.9 to 22.7 meV at the K-point, thus improving the agreement with experimental data (see Table 3). As the intralayer radial force constant is reduced in addition to this frequency shift the absolute values of the components of the polarisation vector for the LRmode of the first layer decrease while those for the sec-
ond and third layer increase, so that the surface character of the LR-mode becomes less pronounced [58] for the clean surface. In contrast, the polarisation vector for the $2 mode is only weakly affected and remains strongly localized in the first layer. The strong decrease of He-atom coupling strength to the LR-mode upon hydrogen adsorption thus appears to be a result of the surface charge density reduction which reduces the "breathing" character [ 7] of this mode and thus the coupling to the He-atoms. Obviously this effect overcompensates (according to our lattice dynamical calculations) the stronger localisation of the LR-mode in the surface layer, which by itself would give rise to an increase in excitation probability upon the hydrogen induced force-constant stiffening. Note, however, that the latter effect increases the longitudinal component of the LR-mode to which the He-atoms couple less effectively than to the transverse component related to the "breathing" character [ 7] of the LR-mode. In case of the S2-mode seen in the TOF-spectra for the Rh( 111 ) +H( 1 x 1 )-surface we attribute the fact that we are unable to observe this phonon for the clean surface mainly to the strongly different cut-off factor (see above), which close to the zone-boundary, where this mode is seen, decreases the excitation probability by more than an order of magnitude (see Fig. 3) with respect to the hydrogen covered surface. Our simple Born-von Karman force constant model which is constrained to first and second nearest neighbour radial force constants reproduces the longitudinal surface resonance only for the (1 i0) direction. However, for a refined pseudocharge model [ 7 ], this mode has been reproduced correctly for both azimuthal directions on a fcc ( 111 ) surface. It is interesting to note that for the clean Rh( 111 ) surface a considerably larger excitation probability for the longitudinal resonance than for the Rayleigh mode was observed for both high symmetry directions, whereas on C u ( l l l ) this it true only for the ( l i 0 ) direction. These differences are attributed to different multipole moments for the two surfaces resulting from the different electronic structure of the two materials. In summary our HAS-data reveal strong differences in the dynamical properties of the clean and hydrogen covered Rh( 111 ) surface. A comparison of the kvector dependent phonon excitation probabilities for the two surfaces suggest that the strong (opposite)
G. Witte et al./Surface Science 323 (1995) 228-240
differences in the excitation probabilities for the longitudinal surface phonon resonance, which is also found to shift to higher energies upon hydrogen adsorption, and the S2-phonon mode are a consequence of the decrease of the density of localized electronic charge at the surface during hydrogen adsorption, as found by photoelectron spectroscopy or in pseudopotential calculations. This charge transfer to the adsorbed hydrogen atoms not only leads to an increase of the steepness of the He-surface interaction potential (as derived from the phonon excitation probabilities) but also enhances the surface static corrugation.
Acknowledgements We wish to thank H. Range for experimental help in some measurements for the clean surface and Professor K.H. Rieder (FU Berlin) for calculations of the corrugation amplitude. The authors are also grateful to P. Ruggerone and J.R. Manson (Clemson University) for valuable discussions.
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