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Structure determination of the (100) surface of rhodium by low energy electron diffraction
Surface Science 64 (1977) 737-750 0 North-Holland Publishing Company
STRUCTUREDETERMINATIONOFTHE( 100) SURFACEOFRHOqlUMBY LOW ENERGY ELECTRON DIFFRACTION K.A.R. MITCHELL, F.R. SHEPHERD, P.R. WATSON and D.C FROST Department of Chemistry, Universityof British Columbia, Vancouver, British Coluknbia, Canada V6T I W_5 Received 17 January 1977
Elastic lowenergy electron diffraction intensity data have been measured as a function of energy for two directions of incidence for the (100) surface of rhodium. The dynamical perturbation programs of Van Hove and Tong have been used for analysing these new experimental data, and it is concluded that the normal face-centered cubic registry is maintained to the surface layer. A preliminary comparison between measured and calculated fQ curves indicates the topmost interlayer spacing to be 1.96 t 0.10 A, and therefore possibly slightly expanded from the bulk interlayer spacing of 1.90 A.
1. Introduction Interest in the surface structures of Group VIII metals has been stimulated by the successful interpretation of low-energy electron diffraction (LEED) intensity data for surfaces of nickel [ 11, by observations that cleaned (100) surfaces of iridium [2] and platinum [3] can be rearranged, and by the catalytic properties manifested by these elements [4]. In the latter regard, rhodium often shows a high catalytic activity for hydrogenation and dehydrogenation reactions, but so far this metal has not been extensively studied by LEED. In earlier work, Tucker [5-71 reported a number of adsorbate structures on the (loo), (110) and (2 10) surfaces, although no monitor of surface composition was then available. Grant and Haas [8] used Auger electron spectroscopy in a preliminary LEED study of Rh (11 l), but no measurements of diffracted beam intensities have yet been published as a function of energy (i.e. as I(E) curves) for use in surface structure determinations. Before determining the structures of adsorbed layers on Rh surfaces, it is necessary to have a good understanding of LEED from the corresponding clean surfaces. In this paper we present new results for a cleaned Rh( 100) surface. 2. Experimental The sample used in this work was obtained from the same single crystal of rhodium used in [S]. The crystal was oriented carefully by the back-reflection Laue 737
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K.A.R. Mitchell et al. /Structure
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technique and a thin slice cut by spark erosion. The surface was polished with diamond paste and the orientation of the optical face, determined by reflection of a He-Ne laser beam, was checked to be within one degree of the (100) crystal plane as fied with the Laue photograph. The sample was then mounted on a Varian manipulator with 2’55 inch offset, and installed in a Varian vacuum chamber equipped with 4-grid LEED optics. The standard heater block was replaced by a specially constructed ceramic assembly; the crystal was spot welded to a platinum cup held just in front of a tungsten filament which was used for electron bombardment heating. Surface temperatures up to 1300 K could be achieved and they were measured with an optical pyrometer. The crystal could be moved to vary independently both the polar and azimuthal angles of incidence, the former by activating the flip mechanism and the latter with a fork separately mounted on a rotating linear drive in a way similar to that described by Burkstrand [9]. A base pressure of 1 X lo-” Torr, or better, was achieved after the standard bakeout and degassing procedures. Producing a clean well ordered Rh(100) surface proved to be quite difficult. Tucker [5] reported sharp LEED patterns on heating to 1600 K; in our work, retarding-grid Auger electron spectroscopy showed that prolonged heating at 1300 K caused appreciable amounts of Si, C and B to accumulate on the surface. The Si and B could be removed by bombarding with argon ions (500 eV, -5 I.IA cm-*) for 10 min. Annealing at 1000 K in vacuum, or slightly lower temperatures in oxygen (1 X 10s6 Torr), reduced the C Auger signal to below the detectable limit. However, depending on the precise time and temperature of annealing, Si was sometimes found to reappear on the surface. We found that a sharp (1 X 1) LEED pattern, with low background intensity and minimal contamination as indicated by Auger electron spectroscopy, could be obtained from several cycles of argon ion bombardment and heat treatment in oxygen followed by a final annealing for a few minutes at 900 K in vacuum. Heating at or below 600 K in hydrogen (1 X lo-’ Torr) was found to be useful for removing any residual oxygen during the final stages of cleaning. On several occasions during the cleaning and ordering procedures, faint fractional-order diffraction spots were found for limited energy ranges; this LEED pattern corresponded to a two-domain (3 X 1) surface structure. However, Auger electron spectroscopy indicated that this pattern was not simply due to a reconstructed’ top metal layer but rather was associated with the presence of Si impurity which had segregated to and ordered on the surface. It would be interesting to know the actual surface structure involved; a coincidence site superposition, perhaps involving a rhodium silicide layer, may seem more plausible than a l/3 monolayer coverage of atomic Si. The diffracted beam intensities were recorded by photographing the LEED screen at intervals of 2 eV in the incident beam energy, and a complete record of all intensity data to 300 eV for each direction of incidence could be obtained in about five minutes. After making suitable background corrections, integrated intensities,
K.A.R. Mitchell et al. /Structure
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139
normahsed to unit incident beam current, were determined by scanning the negative images of the patterns with a computer-controlled Vidicon camera [lo]. In the present work, the previously-described analysis was speeded up by: (i) selecting the same size annulus around each diffraction spot in the evaluation of the local background correction; (ii) automatically tracking the position of each diffracted beam from one frame of the film to the next as the energy changes. Intensities were measured for normal incidence and for 0 = 9’ 4 = 20°, where the direction of incidence is specified by the angle from the surface normal and the azimuthal angle respectively. We follow the notation of Jona [ 1 l] for designating both azimuthal angles and the diffracted beams.
3. Computational
scheme
The calculated &Y) curves for clean Rh( 100) were obtained for the directions of incidence studied experimentally using the convergent perturbation methods of Van Hove and Tong [12]. Even though the observed LEED patterns indicate the surface has the diperiodicity expected on the basis of the bulk structure, the registry and the spacing between the two topmost layers are additional variables for the calculations, particularly since (100) surfaces of some other similar facecentered cubic metals are known to rearrange. However, the general experience at present is that surface structures whose translational symmetries are related simply to those of the substrate correspond to adsorption on symmetrical sites. As a result we considered only three possibilities for the registry of the topmost layer in our calculations. The first is where atoms of the top layer are over four-fold sites of the layer below (position A in fig. 1, this corresponds to a continuation of the bulk structure); the other possibilities are where the topmost atoms are over two-fold sites (position B) or directly over atoms (position C) in the layer below. To be consistent with the experimental LEED pattern showing the four-fold symmetry of the substrate, an appropriate average of calculated intensities over the two equivalent domains is necessary for top-layer adsorption on the two-fold sites. The atomic scattering factor was expressed in terms of phase shifts obtained from a muffin-tin potential constructed from a superposition of atomic charge densities for a cube-octahedral Rhis cluster. Slater’s Xa approximation [I3 ] was used, since this is believed to provide a good model for the exchange part of the potential for LEED calculations [ 141, and the value of (Yfor Rh was taken from the tabulation of Schwarz [ 151. The phase shifts used in the LEED calculations were those for the centre atom in the Rhrs cluster; their energy dependence is shown in fig. 2. The corresponding calculation for Agrs produced phase shifts for silver which agreed closely with those used by Jepsen, Marcus and Jona [ 161. At low energies, an inner potential equal to the sum of the Fermi energy and the work function is expected [ 161. This is about 14.5 eV for rhodium [17,18] ; Demuth, Marcus and Jepsen [l] observed empirically for Ni surfaces that a suitable
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K.A.R. Mitchell et al. /Structure
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of (100) surface of Rh by LEED
gY
Y
T .
02.
22*
Tl* .
X
11. 00.
20’
7i*
.
ii*
02.
(0)
-sx
22.
(b)
Fig. 1. A schematic diagram of (b) using the notation of Jona for atoms in the second layer, registry belonging to the bulk, Other registries considered are directly over atoms in the layer
the Rh(lOO) surface (a) and of the corresponding LEED pattern [ 111. The unit mesh is marked in (a). The complete circles are and the dashed circles correspond to the topmost layer with the i.e. atoms in the top layer are above the 4-fold sites such as A. where atoms in the top layer are over the 2-fold sites (like B) or below (as for C).
inner potential is 2.5 eV less than the static value. This encouraged us to set the muffin tin potential at 12 eV below the vacuum level in these calculations. Absorption was included by an imaginary contribution (-io> to the inner potential; p was taken to be energy-dependent with the form 1.12 E113 [ 11, where both 0 and constant
2.0
I
I
I
I
I.0 D 2 i g
00
W Y B -1.0
-20
I
100
1
I
ENERGY
I
300
200
I
400
(eV)
Fig. 2. Energy dependence of the rhodium phase shifts (I = O-7).
K.A.R. Mitchell et al. f Structure determination of (100) surface of Rh by LEELI
741
E are in eV, by fitting the calculated peak widths to those in the experimental Z(E) curves. The calculations assumed isotropic vibrational amplitudes and the Debye temperature (0.) for all layers was fured at do.7 times [19] the bulk value of 480 K [20]. To provide a preliminary assessment of other values of 8o, one set of calculations (fig. 4 below) were made with Bo = 250 K. At normal incidence, the symmetry of the system was exploited to shorten computation times [21]; for example, with four-fold symmetry, groups of symmetrically equivalent plane waves within the 69 beams used (up to and including the (62) beam set) were reduced to 13 independent wave functions. Calculations made with both the renormalised forward scattering and layer doubling formalisms [21, 221, for stacking the crystal layers, produced identical Z(E) curves. The computation time on an IBM 370/168 computer was about 8 set per energy point at 180 eV and normal incidence and about 25 set at off-normal incidence; the corresponding times were shorter at lower energies.
4. Results and discussion The Z(E) curves measured for the (11) set of beams, which should be equivalent at normal incidence, are shown in the upper half of fig. 3; the same peak positions and overall intensity variation is observed for the (1 l), (11) and (11) beams. Similarly the (20) (02) and (02) beams have almost identical profiles. Small variations in the relative peak intensities for beams in the (11) set were always present in independent experiments at normal incidence, whilst the agreement between individual beams in the (20}, (22) and other beam sets was in general slightly better. Such variations have to be attributed to experimental errors (involving such factors as uneven response of the screen, imperfections in the crystal surface, and uncertainties in setting the angle of incidence), and they limit the level of agreement to be expected between calculation and experiment. Fig. 4 compares experimental Z(E) curves at normal incidence for the (11) and (20) beams with those calculated for the different registries; in these calculations the top interlayer spacings are fixed by the hard-sphere model for atomic radii determined by the bulk structure of rhodium {23]. It is concluded from fig. 4 that the theoretical curves for registries B and C do not agree as well as those for the bulk stacking sequence (registry A), although the level of agreement for the latter is by no means ideal. Considerations of other diffracted beams and other topmost interlayer spacings further preclude the registries B and C; it seems that the surface structure of Rh(100) is interpreted best by an unreconstructed packing sequence for the top layer. The calculated Z(E) curves in fig. 4 have been made with 8o = 250 K. Comparison with the later curves, where 8D has been fixed at 402 K, indicates that the calculations give a better account of the experimental data for the (20) beam with the lower value of Bo. Although further work is needed for fixing the optimal value of 8o, we find that the calculated peak positions are hardly affected
742
K.A.R. Mitchell et al. /Structure
determination
2
Rh(100)
of (I 00) surface of Rh by LEED
e-0”
(iI)
(lil
(20)
(023 (03
---Ye-k ENERGY
(eV>
Fig. 3. @5’) curves for two sets of beams which should be equivalent at normal incidence on ~h(lOO); the fourth member in each set is obscured by the sample manipulator. The intensity scale is arbitrary.
by variation in this parameter; the effect of the lower value is mainly to reduce peak intensities at the higher energies. Exper~ent~ data taken at normal incidence, which have been averaged over equivalent beams and over independent experiments, are compared with calculations for different top layer spacings in figs. 5-7 for the (1 l), (20) and (22) beams respectively; data for the (31) beam are not shown but they have been included in the analysis below. The top layer spacings in figs. 5-7 range from a 5% contraction to a 7.5% expansion about the bulk value (labelled 0%). Similar comparisons, but over a more restricted energy range, are shown in fig. 8 for eight diffracted beams for non-normal incidence (6 = 9’) @= 20”). The determination of the top interlayer spacing which gives “best agreement” between theory and experiment is difficult, and this is brought out by observations from figs. 5-7 that changing the top spacing by *2.5% may produce only subtle changes in the calculated I(E) curves. Finding the best fit “by inspection” is subjec-
K.A.R. Mitchell et al. /Structure
-
determination
143
of (100) surface of Rh by LEED
-
l-
Rh(100) 80”
Rh(100) 6=0”
(2 0) BEAM
(11) BEAM Expt.
1
Expt.
I (a)
(a)
1
i :m’, :;‘: :/ 5, ,; :: ! I ‘,,:.: ~-___;_ I Th.Aj ;
Lb)
(b)
7 )
cc)
Th.C (d)
i
I
:d)
J
t
1
280
ENERGY kV)
Fig. 4. Comparison of experimentalI curves for the (11) and (20) beams at normal incidence on Rh(lOO) with the theoretical curves for the topmost registries defined by A, B and C in fii. la. The experimental curves have been obtained by averaging over all available members of the set. The topmost interlayer spacings are 1.90,2.33 and 2.69 A for the 4-fold, 2-fold and l-fold registries respectively.
tive, and a more quantitative reliability index is needed [24]. Furthermore, we have identified several systematic sources of discrepancy between calculation and experiment in our present analysis. For example, beams converging on the centre of the LEED screen at high energies may be partly obscured by the sample manipulator. This can affect the background correction and thereby introduce errors in the intensities (e.g. the (11) beam near 280 eV in fig. 5). Also beams displayed close to the edge of the curved LEED screen present a smaller solid angle to the observer than those nearer the centre; the grid transmission is also lower at the edges [25] and the combined effect is to artifically suppress the intensity of such beams. In
744
K.A.R. Mitchell et al. /Structure determination of (I OO]surface of Rh by LEED
E N ERGY (eV )
Fig. 5. Comparison of experimental (dotted tines) and calculated (full lines) I(E) cnrws for the (11) beam diffracted from Rb(100) for normal incidence. The calculations are made for a series of topmost interlayer spacings ranging from a 5% contraction to a 7.5% expansion over the bulk spacing. The intensity scale is arbitrary but is constant for ail calculated curves; magnification factors are given for,certain regions of the curves.
this regard, we estimate that the inclusion of these effects could result in the experimental peaks for the (22) beam at about 140 eV (fig. 7) being increased by a factor of about five, thereby bringing this region of the experimental curve into closer agreement with the calculations. Strictly such effects should be accommodated in the procedures for comparing experimental and calculated intensities. In the present study we have used a semi-q~titative approach to help place
K.A.R. Mitchell et al. / Structure determination of (I 00) surface of Rh by LEED
745
I
Rh(100)
B=O”
(20) BEAM I
40
120
200
280
ENERGYteV) Fig. 6. The same comparisonas in fg. 5 but for the (20) beam.
limits on the top layer spacing. This involves evaluating the deviation in the energy of a calculated peak in a particular I(E) curve from the corresponding experimental energy, A.? = I (E=t -L&t) I; th e value for all peaks in that 1(E) curve are then averaged to yield Al?, for a particular topmost layer spacing d. A “grand average” ZT of the m for all available beams is plotted in fig. 9 as a function of the percentage expansion d% = [(d - do)/&] X 100, where do is the appropriate interlayer spacing for the bulk (1.902 A). The value of d which yields the lowest value of iS is then the “best fit” by this criterion, i.e. about +2% in fig. 9b.
146
K.A.R. Mitchell et al. /Structure
I
10
determination
120 ENERGY
of (100) surface of Rh by LEED
200
2
(eV)
Fig. 7. The same comparison as in fii. 5 but for the (22) beam.
Since the real part of the inner potential is not accurately known, we have investigated the effect of changing V,, from its initial value of 12 eV to 8 eV and 16 eV; this rigidly shifts the calculated curves to higher and lower energies respectively (compared with experimental curves) and changes the degree of correspondence between calculation and experiment. This is shown in fig. 9 where the minimum value of 2 changes from +6% to 4% as V,, changes from 8 eV to 16 eV. The energies in the measured Im curves are uncorrected; contributions from the contact
Rh(100) 9.9”
6-20’ till BEAM
(001 BEAM ::
1
.._ I
x
x
l-
40
120
ENERGY
Rh(100)
(eV1
9=9”
-
56-20’
-I-
120 ENERGY
Rh(100)
40 (eL9
0=$
(i%ll)BEAM
1$=20’ 1311BEAM
j : ::i : :: j: ::
_. 4 -_. . _.
~
1 40 NERGY (eV)
!I
1
3 ENERGY feV)
Fig. 8. Comparison of experimental (dotted lines) and cakulated (fulI lines) IQ curves for eight diffracted beams from Rh(100) for a direction of incidence defined by 8 = 9” and + = 20° [ 111. The calculations are made for a series of topmost interlayer spacings in the range from a 5% contraction to a 10% expansion compared with the bulk value.
748
K.A.R. Mitchell et al. /Structure determination of (1 OO]surface of Rh by LEED
potential difference between the sample and the filament of the electron gun are likely to be small, and they are included in an empirical deter~nation of V,, Intuitively the lowest minimum of il should indicate the best fit for d and V,,; unfortunately the amount of scatter in the plots in fig. 9 ensures a substantial uncertainty in Vor (and therefore d). A parallel analysis which considered only the ~tensities at peak energies exhibited too great a scatter to be useful. However, aside from the evidence involving peak positions, a significant contraction of the topmost spacing seems unlikely because the large peaks appearing in the calculated curves at 140 eV and 230 eV in fig. 5 and at 120 eV in fig. 6 are either absent in the experimental curves or are present as weak peaks. Conversely, in corresponding theoretical curves for a slight expansion of the surface, these peaks are much weaker. Cases where no peak was observed in the experimental curves were not included in the analysis in fig. 9, and this artificially enhances the fit for negative values of d%.
-10
-5
0 0%
l5
*IO
d,
%o
-5
0
(b)
Fig. 9. Plots of ii versus d%~(both defined in text) to assess the levels of correspondence between peak positions in experimental and calculated I(E) curves for different values of the reat part of the inner potential (VW). The vertical lines through each point on the plots are error bars corresponding to mean deviations.
K.A.R. Mitchell et al. / Structure determination of (100) surface of Rh by LEED 5.
749
Concluding remarks
The agreement reached between calculated and experimental @‘) curves in this work seems moderately successful. It is an open question as yet whether some discrepancies (e.g. no experimental peak near 220 eV in fig, 5) are associated with incomplete surface characterisation, with the scattering potential, or other factors. Nevertheless, the present analysis suggests that the clean Rh(100) surface is unreconstructed with the topmost spacing expanded by 3 + 5% from the bulk value and with the effective real part of the inner potential equal to 11 i: 2 eV. A more complete matching of Z(E) curves, which takes into account the overall variation of beam intensities, would be preferable to the approach used here, and in this regard the analysis proposed recently by Zanazzi and Jona [26] may provide a more reliable way of fxing both the structural and non-structural parameters. This is to be investigated in our further work on the surface structures of rhodium.
Acknowledgements We are grateful to the National Research Council of Canada for supporting this research. We have also received the most generous assistance from Dr. C.W. Tucker, Jr., who lent us the rhodium single crystal, Dr. M.A. Van Hove, who provided his multiple scattering computer programs, and Dr. L. Noodleman who helped with the determination of the rhodium phase shifts. One of us (P.R.W.) is grateful for a graduate fellowship awarded by the International Nickel Company of Canada.
References [ 11 J.E. Demuth, P.M. Marcus and D.W. Jepsen, Phys. Rev. Bll (1975) 1460. [2] J.T. Grant, Surface Sci. 18 (1969) 228; A. Ignatiev, A.V. Jones and T.N. Rhodin, Surface Sci. 30 (1972) 573. [ 31 H.B. Lyon and G.A. Somorjai, J. Chem. Phys. 46 (1967) 2539; H.P. Bonzel, C.R. Helms and S. Keleman, Phys. Rev. Letters 35 (1975) 1237. [4] G.C. Bond, Catalysis by Metals (Academic Press, London, 1962). (51 C.W. Tucker, Jr., J. Appl. Phys. 37 (1966) 3013. [6] C.W. Tucker, Jr., J. Appl. Phys. 37 (1966) 4147. (71 C.W. Tucker, Jr., Acta Met. 15 (1967) 1465. [8] J.T. Grant and T.W. Haas, Surface Sci. 21 (1970) 76. [9] J.M. Burkstrand, Rev. Sci. Instrum. 44 (1973) 774. [lo] D.C. Frost, K.A.R. Mitchell, F.R. Shepherd and P.R. Watson, J. Vacuum Sci.#Technol. 13 (1976) 1196. (11) F. Jona, I.B.M.J. Res. Develop. 14 (1970) 444. (121 M.A. Van Hove and S.Y. Tong, J. Vacuum Sci. Technol. 12 (1975) 230. [ 131 J.C. Slater, Advan. Quantum Chem. 6 (1972) 1. [ 141 S.Y. Tong, J.B. Pendry and L.L. Kesmodel, Surface Sci. 54 (1976) 21. [15] K. Schwarz, Theoret. Chim. Acta 34 (1974) 225.
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Mitchell et al. /Structure
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[16] D.W. Jepsen, P.M. Marcus and F. Jona, Phys. Rev. BS (1972) 3933.
[ 171 O.K. Andersen, Phys. Rev. B2 (1970) 883. [ 181 American Institute of Physics Handbook, Ed. D.E. Gray (McGraw-Hill, New York, 1972). [19] [20] [Zl] [22] [23]
M.A. Van Hove and S.Y. Tong, Surface Sci. 54 (1976) 91. K.A. Gschneider, Solid State Phys. 16 (1964) 275. M.A. Van Hove and J.B. Pendry, J. Phys. C8 (1975) 1362. S.Y. Tong,Progr. Surface Sci. 7 (1975) 1. J.D.H. Donnay, G. Domray, E.G. COX, 0. Kennard and M.V. King, Crystal Data (Am. Crystallographic Assoc., 1963). (241 F. Jona, Discussions Faraday Sot. 60 (1975) 210. [25] K.O. Legg, M. Prutton and C. Kinniburgh, J. Phys. C7 (1974) 4236. [26] E. Zanazziand F. Jona, Surface Sci. 62 (1977) 61.
STRUCTUREDETERMINATIONOFTHE( 100) SURFACEOFRHOqlUMBY LOW ENERGY ELECTRON DIFFRACTION K.A.R. MITCHELL, F.R. SHEPHERD, P.R. WATSON and D.C FROST Department of Chemistry, Universityof British Columbia, Vancouver, British Coluknbia, Canada V6T I W_5 Received 17 January 1977
Elastic lowenergy electron diffraction intensity data have been measured as a function of energy for two directions of incidence for the (100) surface of rhodium. The dynamical perturbation programs of Van Hove and Tong have been used for analysing these new experimental data, and it is concluded that the normal face-centered cubic registry is maintained to the surface layer. A preliminary comparison between measured and calculated fQ curves indicates the topmost interlayer spacing to be 1.96 t 0.10 A, and therefore possibly slightly expanded from the bulk interlayer spacing of 1.90 A.
1. Introduction Interest in the surface structures of Group VIII metals has been stimulated by the successful interpretation of low-energy electron diffraction (LEED) intensity data for surfaces of nickel [ 11, by observations that cleaned (100) surfaces of iridium [2] and platinum [3] can be rearranged, and by the catalytic properties manifested by these elements [4]. In the latter regard, rhodium often shows a high catalytic activity for hydrogenation and dehydrogenation reactions, but so far this metal has not been extensively studied by LEED. In earlier work, Tucker [5-71 reported a number of adsorbate structures on the (loo), (110) and (2 10) surfaces, although no monitor of surface composition was then available. Grant and Haas [8] used Auger electron spectroscopy in a preliminary LEED study of Rh (11 l), but no measurements of diffracted beam intensities have yet been published as a function of energy (i.e. as I(E) curves) for use in surface structure determinations. Before determining the structures of adsorbed layers on Rh surfaces, it is necessary to have a good understanding of LEED from the corresponding clean surfaces. In this paper we present new results for a cleaned Rh( 100) surface. 2. Experimental The sample used in this work was obtained from the same single crystal of rhodium used in [S]. The crystal was oriented carefully by the back-reflection Laue 737
738
K.A.R. Mitchell et al. /Structure
determination
of (I 00) surface of Rh by LEED
technique and a thin slice cut by spark erosion. The surface was polished with diamond paste and the orientation of the optical face, determined by reflection of a He-Ne laser beam, was checked to be within one degree of the (100) crystal plane as fied with the Laue photograph. The sample was then mounted on a Varian manipulator with 2’55 inch offset, and installed in a Varian vacuum chamber equipped with 4-grid LEED optics. The standard heater block was replaced by a specially constructed ceramic assembly; the crystal was spot welded to a platinum cup held just in front of a tungsten filament which was used for electron bombardment heating. Surface temperatures up to 1300 K could be achieved and they were measured with an optical pyrometer. The crystal could be moved to vary independently both the polar and azimuthal angles of incidence, the former by activating the flip mechanism and the latter with a fork separately mounted on a rotating linear drive in a way similar to that described by Burkstrand [9]. A base pressure of 1 X lo-” Torr, or better, was achieved after the standard bakeout and degassing procedures. Producing a clean well ordered Rh(100) surface proved to be quite difficult. Tucker [5] reported sharp LEED patterns on heating to 1600 K; in our work, retarding-grid Auger electron spectroscopy showed that prolonged heating at 1300 K caused appreciable amounts of Si, C and B to accumulate on the surface. The Si and B could be removed by bombarding with argon ions (500 eV, -5 I.IA cm-*) for 10 min. Annealing at 1000 K in vacuum, or slightly lower temperatures in oxygen (1 X 10s6 Torr), reduced the C Auger signal to below the detectable limit. However, depending on the precise time and temperature of annealing, Si was sometimes found to reappear on the surface. We found that a sharp (1 X 1) LEED pattern, with low background intensity and minimal contamination as indicated by Auger electron spectroscopy, could be obtained from several cycles of argon ion bombardment and heat treatment in oxygen followed by a final annealing for a few minutes at 900 K in vacuum. Heating at or below 600 K in hydrogen (1 X lo-’ Torr) was found to be useful for removing any residual oxygen during the final stages of cleaning. On several occasions during the cleaning and ordering procedures, faint fractional-order diffraction spots were found for limited energy ranges; this LEED pattern corresponded to a two-domain (3 X 1) surface structure. However, Auger electron spectroscopy indicated that this pattern was not simply due to a reconstructed’ top metal layer but rather was associated with the presence of Si impurity which had segregated to and ordered on the surface. It would be interesting to know the actual surface structure involved; a coincidence site superposition, perhaps involving a rhodium silicide layer, may seem more plausible than a l/3 monolayer coverage of atomic Si. The diffracted beam intensities were recorded by photographing the LEED screen at intervals of 2 eV in the incident beam energy, and a complete record of all intensity data to 300 eV for each direction of incidence could be obtained in about five minutes. After making suitable background corrections, integrated intensities,
K.A.R. Mitchell et al. /Structure
determination
of (100) surface of Rh by LEED
139
normahsed to unit incident beam current, were determined by scanning the negative images of the patterns with a computer-controlled Vidicon camera [lo]. In the present work, the previously-described analysis was speeded up by: (i) selecting the same size annulus around each diffraction spot in the evaluation of the local background correction; (ii) automatically tracking the position of each diffracted beam from one frame of the film to the next as the energy changes. Intensities were measured for normal incidence and for 0 = 9’ 4 = 20°, where the direction of incidence is specified by the angle from the surface normal and the azimuthal angle respectively. We follow the notation of Jona [ 1 l] for designating both azimuthal angles and the diffracted beams.
3. Computational
scheme
The calculated &Y) curves for clean Rh( 100) were obtained for the directions of incidence studied experimentally using the convergent perturbation methods of Van Hove and Tong [12]. Even though the observed LEED patterns indicate the surface has the diperiodicity expected on the basis of the bulk structure, the registry and the spacing between the two topmost layers are additional variables for the calculations, particularly since (100) surfaces of some other similar facecentered cubic metals are known to rearrange. However, the general experience at present is that surface structures whose translational symmetries are related simply to those of the substrate correspond to adsorption on symmetrical sites. As a result we considered only three possibilities for the registry of the topmost layer in our calculations. The first is where atoms of the top layer are over four-fold sites of the layer below (position A in fig. 1, this corresponds to a continuation of the bulk structure); the other possibilities are where the topmost atoms are over two-fold sites (position B) or directly over atoms (position C) in the layer below. To be consistent with the experimental LEED pattern showing the four-fold symmetry of the substrate, an appropriate average of calculated intensities over the two equivalent domains is necessary for top-layer adsorption on the two-fold sites. The atomic scattering factor was expressed in terms of phase shifts obtained from a muffin-tin potential constructed from a superposition of atomic charge densities for a cube-octahedral Rhis cluster. Slater’s Xa approximation [I3 ] was used, since this is believed to provide a good model for the exchange part of the potential for LEED calculations [ 141, and the value of (Yfor Rh was taken from the tabulation of Schwarz [ 151. The phase shifts used in the LEED calculations were those for the centre atom in the Rhrs cluster; their energy dependence is shown in fig. 2. The corresponding calculation for Agrs produced phase shifts for silver which agreed closely with those used by Jepsen, Marcus and Jona [ 161. At low energies, an inner potential equal to the sum of the Fermi energy and the work function is expected [ 161. This is about 14.5 eV for rhodium [17,18] ; Demuth, Marcus and Jepsen [l] observed empirically for Ni surfaces that a suitable
140
K.A.R. Mitchell et al. /Structure
determination
of (100) surface of Rh by LEED
gY
Y
T .
02.
22*
Tl* .
X
11. 00.
20’
7i*
.
ii*
02.
(0)
-sx
22.
(b)
Fig. 1. A schematic diagram of (b) using the notation of Jona for atoms in the second layer, registry belonging to the bulk, Other registries considered are directly over atoms in the layer
the Rh(lOO) surface (a) and of the corresponding LEED pattern [ 111. The unit mesh is marked in (a). The complete circles are and the dashed circles correspond to the topmost layer with the i.e. atoms in the top layer are above the 4-fold sites such as A. where atoms in the top layer are over the 2-fold sites (like B) or below (as for C).
inner potential is 2.5 eV less than the static value. This encouraged us to set the muffin tin potential at 12 eV below the vacuum level in these calculations. Absorption was included by an imaginary contribution (-io> to the inner potential; p was taken to be energy-dependent with the form 1.12 E113 [ 11, where both 0 and constant
2.0
I
I
I
I
I.0 D 2 i g
00
W Y B -1.0
-20
I
100
1
I
ENERGY
I
300
200
I
400
(eV)
Fig. 2. Energy dependence of the rhodium phase shifts (I = O-7).
K.A.R. Mitchell et al. f Structure determination of (100) surface of Rh by LEELI
741
E are in eV, by fitting the calculated peak widths to those in the experimental Z(E) curves. The calculations assumed isotropic vibrational amplitudes and the Debye temperature (0.) for all layers was fured at do.7 times [19] the bulk value of 480 K [20]. To provide a preliminary assessment of other values of 8o, one set of calculations (fig. 4 below) were made with Bo = 250 K. At normal incidence, the symmetry of the system was exploited to shorten computation times [21]; for example, with four-fold symmetry, groups of symmetrically equivalent plane waves within the 69 beams used (up to and including the (62) beam set) were reduced to 13 independent wave functions. Calculations made with both the renormalised forward scattering and layer doubling formalisms [21, 221, for stacking the crystal layers, produced identical Z(E) curves. The computation time on an IBM 370/168 computer was about 8 set per energy point at 180 eV and normal incidence and about 25 set at off-normal incidence; the corresponding times were shorter at lower energies.
4. Results and discussion The Z(E) curves measured for the (11) set of beams, which should be equivalent at normal incidence, are shown in the upper half of fig. 3; the same peak positions and overall intensity variation is observed for the (1 l), (11) and (11) beams. Similarly the (20) (02) and (02) beams have almost identical profiles. Small variations in the relative peak intensities for beams in the (11) set were always present in independent experiments at normal incidence, whilst the agreement between individual beams in the (20}, (22) and other beam sets was in general slightly better. Such variations have to be attributed to experimental errors (involving such factors as uneven response of the screen, imperfections in the crystal surface, and uncertainties in setting the angle of incidence), and they limit the level of agreement to be expected between calculation and experiment. Fig. 4 compares experimental Z(E) curves at normal incidence for the (11) and (20) beams with those calculated for the different registries; in these calculations the top interlayer spacings are fixed by the hard-sphere model for atomic radii determined by the bulk structure of rhodium {23]. It is concluded from fig. 4 that the theoretical curves for registries B and C do not agree as well as those for the bulk stacking sequence (registry A), although the level of agreement for the latter is by no means ideal. Considerations of other diffracted beams and other topmost interlayer spacings further preclude the registries B and C; it seems that the surface structure of Rh(100) is interpreted best by an unreconstructed packing sequence for the top layer. The calculated Z(E) curves in fig. 4 have been made with 8o = 250 K. Comparison with the later curves, where 8D has been fixed at 402 K, indicates that the calculations give a better account of the experimental data for the (20) beam with the lower value of Bo. Although further work is needed for fixing the optimal value of 8o, we find that the calculated peak positions are hardly affected
742
K.A.R. Mitchell et al. /Structure
determination
2
Rh(100)
of (I 00) surface of Rh by LEED
e-0”
(iI)
(lil
(20)
(023 (03
---Ye-k ENERGY
(eV>
Fig. 3. @5’) curves for two sets of beams which should be equivalent at normal incidence on ~h(lOO); the fourth member in each set is obscured by the sample manipulator. The intensity scale is arbitrary.
by variation in this parameter; the effect of the lower value is mainly to reduce peak intensities at the higher energies. Exper~ent~ data taken at normal incidence, which have been averaged over equivalent beams and over independent experiments, are compared with calculations for different top layer spacings in figs. 5-7 for the (1 l), (20) and (22) beams respectively; data for the (31) beam are not shown but they have been included in the analysis below. The top layer spacings in figs. 5-7 range from a 5% contraction to a 7.5% expansion about the bulk value (labelled 0%). Similar comparisons, but over a more restricted energy range, are shown in fig. 8 for eight diffracted beams for non-normal incidence (6 = 9’) @= 20”). The determination of the top interlayer spacing which gives “best agreement” between theory and experiment is difficult, and this is brought out by observations from figs. 5-7 that changing the top spacing by *2.5% may produce only subtle changes in the calculated I(E) curves. Finding the best fit “by inspection” is subjec-
K.A.R. Mitchell et al. /Structure
-
determination
143
of (100) surface of Rh by LEED
-
l-
Rh(100) 80”
Rh(100) 6=0”
(2 0) BEAM
(11) BEAM Expt.
1
Expt.
I (a)
(a)
1
i :m’, :;‘: :/ 5, ,; :: ! I ‘,,:.: ~-___;_ I Th.Aj ;
Lb)
(b)
7 )
cc)
Th.C (d)
i
I
:d)
J
t
1
280
ENERGY kV)
Fig. 4. Comparison of experimentalI curves for the (11) and (20) beams at normal incidence on Rh(lOO) with the theoretical curves for the topmost registries defined by A, B and C in fii. la. The experimental curves have been obtained by averaging over all available members of the set. The topmost interlayer spacings are 1.90,2.33 and 2.69 A for the 4-fold, 2-fold and l-fold registries respectively.
tive, and a more quantitative reliability index is needed [24]. Furthermore, we have identified several systematic sources of discrepancy between calculation and experiment in our present analysis. For example, beams converging on the centre of the LEED screen at high energies may be partly obscured by the sample manipulator. This can affect the background correction and thereby introduce errors in the intensities (e.g. the (11) beam near 280 eV in fig. 5). Also beams displayed close to the edge of the curved LEED screen present a smaller solid angle to the observer than those nearer the centre; the grid transmission is also lower at the edges [25] and the combined effect is to artifically suppress the intensity of such beams. In
744
K.A.R. Mitchell et al. /Structure determination of (I OO]surface of Rh by LEED
E N ERGY (eV )
Fig. 5. Comparison of experimental (dotted tines) and calculated (full lines) I(E) cnrws for the (11) beam diffracted from Rb(100) for normal incidence. The calculations are made for a series of topmost interlayer spacings ranging from a 5% contraction to a 7.5% expansion over the bulk spacing. The intensity scale is arbitrary but is constant for ail calculated curves; magnification factors are given for,certain regions of the curves.
this regard, we estimate that the inclusion of these effects could result in the experimental peaks for the (22) beam at about 140 eV (fig. 7) being increased by a factor of about five, thereby bringing this region of the experimental curve into closer agreement with the calculations. Strictly such effects should be accommodated in the procedures for comparing experimental and calculated intensities. In the present study we have used a semi-q~titative approach to help place
K.A.R. Mitchell et al. / Structure determination of (I 00) surface of Rh by LEED
745
I
Rh(100)
B=O”
(20) BEAM I
40
120
200
280
ENERGYteV) Fig. 6. The same comparisonas in fg. 5 but for the (20) beam.
limits on the top layer spacing. This involves evaluating the deviation in the energy of a calculated peak in a particular I(E) curve from the corresponding experimental energy, A.? = I (E=t -L&t) I; th e value for all peaks in that 1(E) curve are then averaged to yield Al?, for a particular topmost layer spacing d. A “grand average” ZT of the m for all available beams is plotted in fig. 9 as a function of the percentage expansion d% = [(d - do)/&] X 100, where do is the appropriate interlayer spacing for the bulk (1.902 A). The value of d which yields the lowest value of iS is then the “best fit” by this criterion, i.e. about +2% in fig. 9b.
146
K.A.R. Mitchell et al. /Structure
I
10
determination
120 ENERGY
of (100) surface of Rh by LEED
200
2
(eV)
Fig. 7. The same comparison as in fii. 5 but for the (22) beam.
Since the real part of the inner potential is not accurately known, we have investigated the effect of changing V,, from its initial value of 12 eV to 8 eV and 16 eV; this rigidly shifts the calculated curves to higher and lower energies respectively (compared with experimental curves) and changes the degree of correspondence between calculation and experiment. This is shown in fig. 9 where the minimum value of 2 changes from +6% to 4% as V,, changes from 8 eV to 16 eV. The energies in the measured Im curves are uncorrected; contributions from the contact
Rh(100) 9.9”
6-20’ till BEAM
(001 BEAM ::
1
.._ I
x
x
l-
40
120
ENERGY
Rh(100)
(eV1
9=9”
-
56-20’
-I-
120 ENERGY
Rh(100)
40 (eL9
0=$
(i%ll)BEAM
1$=20’ 1311BEAM
j : ::i : :: j: ::
_. 4 -_. . _.
~
1 40 NERGY (eV)
!I
1
3 ENERGY feV)
Fig. 8. Comparison of experimental (dotted lines) and cakulated (fulI lines) IQ curves for eight diffracted beams from Rh(100) for a direction of incidence defined by 8 = 9” and + = 20° [ 111. The calculations are made for a series of topmost interlayer spacings in the range from a 5% contraction to a 10% expansion compared with the bulk value.
748
K.A.R. Mitchell et al. /Structure determination of (1 OO]surface of Rh by LEED
potential difference between the sample and the filament of the electron gun are likely to be small, and they are included in an empirical deter~nation of V,, Intuitively the lowest minimum of il should indicate the best fit for d and V,,; unfortunately the amount of scatter in the plots in fig. 9 ensures a substantial uncertainty in Vor (and therefore d). A parallel analysis which considered only the ~tensities at peak energies exhibited too great a scatter to be useful. However, aside from the evidence involving peak positions, a significant contraction of the topmost spacing seems unlikely because the large peaks appearing in the calculated curves at 140 eV and 230 eV in fig. 5 and at 120 eV in fig. 6 are either absent in the experimental curves or are present as weak peaks. Conversely, in corresponding theoretical curves for a slight expansion of the surface, these peaks are much weaker. Cases where no peak was observed in the experimental curves were not included in the analysis in fig. 9, and this artificially enhances the fit for negative values of d%.
-10
-5
0 0%
l5
*IO
d,
%o
-5
0
(b)
Fig. 9. Plots of ii versus d%~(both defined in text) to assess the levels of correspondence between peak positions in experimental and calculated I(E) curves for different values of the reat part of the inner potential (VW). The vertical lines through each point on the plots are error bars corresponding to mean deviations.
K.A.R. Mitchell et al. / Structure determination of (100) surface of Rh by LEED 5.
749
Concluding remarks
The agreement reached between calculated and experimental @‘) curves in this work seems moderately successful. It is an open question as yet whether some discrepancies (e.g. no experimental peak near 220 eV in fig, 5) are associated with incomplete surface characterisation, with the scattering potential, or other factors. Nevertheless, the present analysis suggests that the clean Rh(100) surface is unreconstructed with the topmost spacing expanded by 3 + 5% from the bulk value and with the effective real part of the inner potential equal to 11 i: 2 eV. A more complete matching of Z(E) curves, which takes into account the overall variation of beam intensities, would be preferable to the approach used here, and in this regard the analysis proposed recently by Zanazzi and Jona [26] may provide a more reliable way of fxing both the structural and non-structural parameters. This is to be investigated in our further work on the surface structures of rhodium.
Acknowledgements We are grateful to the National Research Council of Canada for supporting this research. We have also received the most generous assistance from Dr. C.W. Tucker, Jr., who lent us the rhodium single crystal, Dr. M.A. Van Hove, who provided his multiple scattering computer programs, and Dr. L. Noodleman who helped with the determination of the rhodium phase shifts. One of us (P.R.W.) is grateful for a graduate fellowship awarded by the International Nickel Company of Canada.
References [ 11 J.E. Demuth, P.M. Marcus and D.W. Jepsen, Phys. Rev. Bll (1975) 1460. [2] J.T. Grant, Surface Sci. 18 (1969) 228; A. Ignatiev, A.V. Jones and T.N. Rhodin, Surface Sci. 30 (1972) 573. [ 31 H.B. Lyon and G.A. Somorjai, J. Chem. Phys. 46 (1967) 2539; H.P. Bonzel, C.R. Helms and S. Keleman, Phys. Rev. Letters 35 (1975) 1237. [4] G.C. Bond, Catalysis by Metals (Academic Press, London, 1962). (51 C.W. Tucker, Jr., J. Appl. Phys. 37 (1966) 3013. [6] C.W. Tucker, Jr., J. Appl. Phys. 37 (1966) 4147. (71 C.W. Tucker, Jr., Acta Met. 15 (1967) 1465. [8] J.T. Grant and T.W. Haas, Surface Sci. 21 (1970) 76. [9] J.M. Burkstrand, Rev. Sci. Instrum. 44 (1973) 774. [lo] D.C. Frost, K.A.R. Mitchell, F.R. Shepherd and P.R. Watson, J. Vacuum Sci.#Technol. 13 (1976) 1196. (11) F. Jona, I.B.M.J. Res. Develop. 14 (1970) 444. (121 M.A. Van Hove and S.Y. Tong, J. Vacuum Sci. Technol. 12 (1975) 230. [ 131 J.C. Slater, Advan. Quantum Chem. 6 (1972) 1. [ 141 S.Y. Tong, J.B. Pendry and L.L. Kesmodel, Surface Sci. 54 (1976) 21. [15] K. Schwarz, Theoret. Chim. Acta 34 (1974) 225.
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Mitchell et al. /Structure
determination
of (I 00) surface of Rh by LEED
[16] D.W. Jepsen, P.M. Marcus and F. Jona, Phys. Rev. BS (1972) 3933.
[ 171 O.K. Andersen, Phys. Rev. B2 (1970) 883. [ 181 American Institute of Physics Handbook, Ed. D.E. Gray (McGraw-Hill, New York, 1972). [19] [20] [Zl] [22] [23]
M.A. Van Hove and S.Y. Tong, Surface Sci. 54 (1976) 91. K.A. Gschneider, Solid State Phys. 16 (1964) 275. M.A. Van Hove and J.B. Pendry, J. Phys. C8 (1975) 1362. S.Y. Tong,Progr. Surface Sci. 7 (1975) 1. J.D.H. Donnay, G. Domray, E.G. COX, 0. Kennard and M.V. King, Crystal Data (Am. Crystallographic Assoc., 1963). (241 F. Jona, Discussions Faraday Sot. 60 (1975) 210. [25] K.O. Legg, M. Prutton and C. Kinniburgh, J. Phys. C7 (1974) 4236. [26] E. Zanazziand F. Jona, Surface Sci. 62 (1977) 61.