Surface Reconstruction and Rate Processes in ... - ACS Publications

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Surface Reconstruction and Rate Processes in Adsorbed Overlayers† V. P. Zhdanov‡,§ and P. R. Norton*,‡ Centre for Interdisciplinary Studies in Chemical Physics, University of Western Ontario, London, Ontario, Canada N6A 3K7, and Institute of Catalysis, Novosibirsk 630090, Russia Received September 1, 1994X Spontaneous or adsorbate-induced restructuring of surfaces can significantly influence the kinetics of elementary rate processes in adsorbed overlayers. Theoretically, this effect can be studied by employing statistical models of surface reconstruction. The review presented describes the results of simulations carried out in this field of surface science. The main attention is paid to such processes as desorption and surface diffusion. The systems under considerations are as follows: H/Si(001), H/W(001), CO/Pt(110), H/Cu(110), and H/Pt(001).

1. Introduction Rate processes in adsorbed overlayers at finite coverages represent an example of a nontrivial phenomenon in manybody dynamical systems. To simulate these processes, lattice-gas models are customarily used.1 In the framework of these models, the surface lattice is usually assumed to be rigid and to possess a well-defined two-dimensional periodicity closely resembling the atomic ordering in the bulk. In many instances, however, the surface reconstructs spontaneously or as a result of adsorbate induced effects. In particular, adsorbate-induced buckling and lateral shifts of substrate atoms are now found experimentally even for close packed surfaces.2 More significant changes in the arrangement of substrate atoms can accompany adsorption on numerous more open surfaces.3-7 The influence of such changes on elementary rate processes in adsorbed overlayers is expected to be significant because typical energies involved in surface reconstruction are usually much higher than the thermal energy. Adsorbateinduced restructuring of the surface may thus play a crucial role in such interesting and important phenomena as bistability, kinetic oscillations and promotion and poisoning of surface reactions.7,8 In the present short review, we will consider a few examples illustrating the role of surface reconstruction in thermal desorption and surface diffusion. Our goal is to discuss the results of simulations based on microscopic statistical models of surface reconstruction. Such simulations are presently limited because the development of statistical models of surface reconstruction is in its infancy.1,6,7 The formulation and analysis of these models † Invited lecture presented at the symposium on Advances in the Measurement and Modeling of Surface Phenomena, San Luis, Argentina, August 24-30, 1994. ‡ University of Western Ontario. § Institute of Catalysis. X Abstract published in Advance ACS Abstracts, January 1, 1996.

(1) Zhdanov, V. P. Elementary Physicochemical Processes on Solid Surfaces; Plenum: New York, 1991. (2) Lindros, M.; Pfnur, H.; Held, G.; Menzel, D. Surf. Sci.1989, 222, 451. (3) Somorjai, G. A.; Van Hove, M. A. Prog. Surf. Sci. 1989, 30, 201. (4) Pick, S. Surf. Sci. Rep. 1990, 12, 99. (5) Lafemina, J. P. Surf. Sci. Rep. 1992, 16, 133. (6) Bernasconi, M.; Tosatti, E. Surf. Sci. Rep. 1993, 17, 363. Lapujoulade, J. Surf. Sci. Rep. 1994, 20, 191. (7) Phase Transitions and Adsorbate Restructuring at Metal Surfaces; The Chemical Physics of Solid Surfaces; King, D. A., Woodruff, D. P., Eds.; Elsevier: Amsterdam, 1994; Vol. 7. (8) Ertl, G. Adv. Catal. 1990, 37, 231. Schuth, F.; Henry, B. E.; Shmidt, L. D. Adv. Catal. 1993, 39, 51. Imbihl, R. Prog. Surf. Sci. 1993, 44, 185.

0743-7463/96/2412-0101$12.00/0

are usually rather cumbersome, and hence we consider below only the main physical ideas and approximations employed in calculations and do not provide a detailed description of the formalism. In general, the relationship between microscopic statistical models of surface reconstruction and kinetic processes is straightforward.1 As a rule, the rate constants for elementary rate processes in adsorbed overlayers can be represented via the probabilities of different arrangements of adsorbed particles and substrate atoms and the lateral interactions between them, including the interactions in the ground and activated states. Often, the latter interaction (i.e., the interaction of the activated complex with adjacent particles) is negligible. In this case, the coverage dependence of a rate constant can usually be expressed via the chemical potential of adsorbed particles. Employing a statistical model of surface reconstruction, it is then possible to calculate the desired probabilities or the chemical potential and then to obtain the rate constants for desorption, diffusion, or elementary chemical reactions. If restructuring of the surface is spontaneous and the structure formed is stable with respect to adsorption (i.e., adsorbate-induced changes in the surface are negligible), the effect of surface reconstruction on rate processes in adsorbed overlayers can often be described in the framework of the lattice-gas approximation simply by redefining a lattice structure. As an example, we will consider hydrogen adsorption on Si(001) (Section 2). We will pay most attention to examples where the surface structure changes with increasing or decreasing adsorbate coverage. In particular, we will discuss the following systems: H/W(001) (section 3), CO/Pt(110) (section 4), H/Cu(110) (section 5), and H/Pt(001) (section 6). The role of restructuring of the surface in the kinetic processes occurring in these systems is nontrivial, and the results predicted by microscopic statistical models are rather instructive even if the models employed are usually simplified and do not describe all the details observed in real systems. Surface reconstruction is known to be an important ingredient contributing to the oscillatory kinetics observed for different chemical reactions on metal surfaces under UHV conditions (e.g., CO oxidation on Pt(001) and Pt(110)). The available models describing oscillatory kinetics (see the reviews8 and a recent paper9), however, introduce surface reconstruction into the mean-field kinetic equations “by hands”, i.e., without underlying physics. Such (9) Hopkinson, A.; King, D. A. Chem. Phys. 1993, 177, 433.

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Figure 3. Schematic arrangement of hydrogen atoms (small filled circles) on the Si(001) surface at θ ) 1.

Figure 1. Schematic arrangement of Si atoms on the (100) surface: (a) the ideal truncated bulk; (b and c) the symmetric and asymmetric dimer models of the (2×1) reconstriction (adapted from ref 5).

Figure 2. Schematic arrangement of Si atoms in the case of the c(4×2) reconstruction in the framework of the asymmetric dimer model (adapted from ref 5).

models are an important tool in understanding of kinetic oscillations. Their description is however beyond the present review. 2. H/Si(001) 2.1. Structure of the Si(001) Surface. The ideal (1×1), or truncated bulk, Si(001) surface is shown in Figure 1a. Every surface atom in this case is 2-fold coordinated, bonding to two nearest neighbors below the surface, and possessing two dangling bonds. This surface, however, reconstructs resulting in a (2×1) structure. The general principles employed to understand the Si-surface relaxation and reconstruction are rather simple.5 A newly created surface relaxes to lower its energy. This typically occurs in an atomic configuration in which the danglingbond charge density is minimized by forming new bonds, either between surface atoms or between surface atoms and adsorbates. To a first approximation, the Si(001)-(2×1) structure can be represented in the framework of the symmetric dimer model (Figure 1b). The formation of dimers on the Si(001) surface is a well-established fact supported by direct scanning tunneling microscopy (STM).10 In reality, dimers seem to be slightly tilted (Figure 1c) as indicated by many studies (see the review5). The dimer-dimer lateral interaction is dependent on their mutual orientation and may result in a higher-order surface reconstruction (e.g., of the c(4×2) symmetry as shown in Figure 2). The magnitudes of these interactions are rather weak, and reconstruction of the latter type occurs only at low temperatures [T e 200 K (ref 11)]. The (2×1) T c(4×2) phase transition can be described in the framework of the Ising-like11 or more advanced models.12 In the discussion below, we ignore the asymmetry in the arrangement of (10) Hamers, R. J.; Tromp, R. M.; Demuth, J. E. Phys. Rev. B: Condens. Matter 1986, 34, 5343. (11) Zubkus, V. E.; Tornau, E. E. Surf. Sci. 1989, 216, 23. (12) Stillinger, F. H. Phys. Rev. B: Condens. Matter 1992, 46, 9590. Mele, E. Surf. Sci. 1992, 278, L135.

dimers and also the dimer-dimer lateral interaction because these factors are negligible at the relatively high temperatures corresponding to rate processes involving chemisorbed species. 2.2. Hydrogen Desorption and Diffusion. Adsorption of hydrogen on the Si(001)-(2×1) surface has been thoroughly studied.13-17 At θ e 1.0 (Figure 3), hydrogen is known to adsorb in 1-fold sites, saturating the dangling bonds by producing monohydride groups (SiH). The (2×1) symmetry of the adsorbate-substrate system in this case remains relatively intact. At higher coverages, dihydride species (SiH2) are formed on the surface (this region is not discussed below). The kinetics of associative desorption of hydrogen atoms from the Si(001) surface is unusual13-16 because it exhibits first-order behavior at 0.1 e θ e 1 (Figure 4). For lower hydrogen coverages, the desorption rate has been found to decrease more rapidly.16 The most reasonable interpretation of these features of the desorption kinetics is that it is connected to the hydrogen pairing at the Si dimers, i.e., with an attractive nearest-neighbor adsorbate-adsorbate lateral interaction at doubly occupied dimers.15,16 The assumption on such a preferential pairing is supported by direct STM observations.18 If, in a description of the desorption kinetics, one takes into account only the hydrogen-hydrogen interaction in the dimers, AA < 0, the arrangement of hydrogen atoms in different dimers is uncorrelated and accordingly the desorption rate is simply proportional to the probability that a dimer is occupied by two hydrogen atoms, i.e.

dθ/dt ) -ν exp(-Ed/T) PAA(θ)

(1)

where ν and Ea are the Arrhenius parameters. The probability PAA(θ) is given by the well-known quasichemical approximation (this approximation yields accurate results for the case of uncorrelated adsorption in dimers1). If the coverage is not too low, PAA(θ) ≈ θ, eq 1 predicts the first-order kinetics. At very low coverages, PAA(θ) ∝ exp(-AA/T)θ2 and the desorption kinetics will be second order. Employing eq 1 for simulating the transition between the two regimes (Figure 4b), Hoffer et al.16 have obtained AA ≈ -6 kcal/mol. The model described above has also been used19 for analyzing the coverage dependence of the chemical diffusion coefficients for jumps of hydrogen atoms along and perpendicular to the dimer rows on the Si(001) surface. At reasonable values of the parameters employed, both (13) Wise, M. L.; Koehler, B. G.; Gupta, P.; Coon, P. A.; George, S. M. Surf. Sci. 1991, 258, 166. (14) Shane, S. F.; Kolasinski, K. W.; Zare, R. N. J. Chem. Phys. 1992, 97, 1520. (15) D’Evelin, M. P.; Yang, Y. L.; Sutcu, L. F. J. Chem. Phys. 1992, 96, 852. (16) Hofer, U.; Li, L.; Heinz, T. F. Phys. Rev. B: Condens. Matter 1992, 45, 9485. (17) Lu, Z. H.; Griffiths, K.; Norton, P. R. Mod. Phys. Lett. 1993, 7, 155. (18) Boland, J. J. Phys. Rev. Lett. 1991, 67, 1539. (19) Zhdanov, V. P. Phys. Rev. B: Condens. Matter 1993, 48, 14325.

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a

Figure 5. Displacements of tungsten atoms on the W(001) surface resulting in formation of the c(2×2) structure: (a) diagonal ordering on a clean surface; (b) axial ordering during hydrogen adsorption (if the coverage is not too low). The scale of displacements along and perpendicular to the surface is about 0.2 Å.21

b

Figure 6. Schematic arrangement of particles on the W(001) surface. The black circles denote tungsten atoms that can be located in four equilibrium positions. The activation barrier for the transitions between these positions is about 0.05 eV.22,23 Formation of the c(2×2) structure on this surface is connected with lateral interactions between surface atoms. The diamonds denote the bridge sites for adsorption of hydrogen atoms.

Figure 4. Kinetics of associative desorption of hydrogen atoms from the Si(001) surface: (a) TPD spectra illustrating the firstorder regularities;13 (b) isothermal desorption16 at low coverages where the deviations from the first-order behavior are significant (the symbols indicate the experimental data; the solid lines are given by eq 1 with AA ) -0.26 eV).

diffusion coefficients are shown to decrease with increasing coverage. The anisotropy in the coverage dependence of diffusion is expected to be rather weak. Experimentally, diffusion of hydrogen on the Si(001) surface has not been studied so far (the relevant data have been obtained only for the Si(111)-(7×1) surface20). 3. H/W(001) 3.1. Phase Diagram. LEED data21 indicate that the clean W(001) surface has a perfect (1×1) symmetry at temperatures above 400 K and a c(2×2) symmetry (Figure 5) on cooling to about 200 K. The critical temperature for this phase transition is reported to lie in the range from 210 to 300 K. The large variation in published Tc seems to indicate a strong effect of surface defects on the ordering of the surface atoms. The driving mechanism for the phase transition on W(001) was first assumed to be connected with the Fermi (20) Rieder, G. A.; Hofer, U.; Heinz, T. F. Phys. Rev. Lett. 1991, 66, 1994. (21) King, D. A. Phys. Scripta 1983, T4, 34. Jupille, J.; King, D. A. Instabilities and Adsorbate Restructuring at W(100), in ref 7.

level instability associated with the electronic structure of the surface states (see the review in refs 4, 21, and 22). This phenomenon occurs if the two-dimensional Fermi surface has parallel sections and a reconstruction with a wave vector spanning such sections leads to a gap in the density of states and a lowering of the total electron energy (the “charge-density-wave” or “Peierls” mechanism). Later experimental studies of the Fermi surface of W(001) indicated however that the surface state coupling is a consequence of, rather than a driving force, for the transition.21 At present, the dominant opinion is that the details of the reconstruction periodicity are almost certainly dictated by a special feature of the potential energy for surface atoms, formed by their interaction with the underlying lattice (this mechanism is referred to as “strong coupling charge-density waves” or “short-range JahnTeller effect”22). In particular, the potential under consideration is assumed to provide four equilibrium positions for every surface atom (Figure 6). The simplest parametric form of the local potential for a surface atom contains the terms allowed by symmetry up to fourth order in its displacement, i.e.

V(u) ) -Au2/2 + Bu4/4 + Vu4 cos(4ϑ)/4

(2)

where A, B, and V are positive constants and ϑ is the angle between the atom displacement u and the X axis (the arrangement of atoms in the underlying layers is considered to be rigid and their coordinates are not included implicitly into the potential). The phase transi(22) Fasolino, A.; Tosatti, E. Phys. Rev. B: Condens. Matter 1987, 35, 4264.

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Figure 7. Phase diagram for the H/W(001) system (adapted from ref 34).

Figure 8. Phase diagram of the H/W(001) system calculated in the framework of the four-position lattice-gas approximation for W atoms (adapted from ref 31).

tion can be obtained if potential (2) is complemented by harmonic lateral interactions between surface atoms. The model described has been analyzed in detail by Roelofs and Wendelken23 by employing Monte Carlo simulations and, with minor modifications, by Han and Ying.24 Fasolino and Tosatti22 have considered a model which explicitly involves the surface and subsurface layers (a n-layer slab with n ) 25-75). The phase diagram of the H/W(001) system (Figure 7) has been studied experimentally by Barker and Estrup.25 Hydrogen adsorption occurring on bridge sites (Figure 6) was shown to maintain the diagonal c(2×2) order only at low coverages up to θ ≈ 0.15 (here and below θ ) 1 corresponds to saturation defined as two hydrogen atoms per tungsten atom). With increasing coverage above θ ≈ 0.15, the diagonal c(2×2) structure is replaced by the axial c(2×2) structure (Figure 5b), and then (at θ g 0.2) the overlayer is incommensurate with the bulk. The simplest model describing the phase diagram of the W(001) system at low coverages has been proposed by (23) Roelofs, L. D. Surf. Sci. 1986, 178, 396. Roelofs, L. D.; Wendelken, J. F. Phys. Rev. B: Condens. Matter 1986, 34, 3319. (24) Han, W. K.; Ying, S. C. Phys. Rev. B: Condens. Matter 1990, 41, 9163; 1992, 46, 1849. (25) Barker, R. A.; Estrup, P. J. J. Chem. Phys. 1981, 74, 1442.

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Lau and Ying26 employing a phenomenological Landau expression with a two-component order parameter for the free energy of the clean surface and a lattice-gas model (in the mean-field approximation) for hydrogen atoms and assuming the adsorbate-substrate interaction to be proportional to the average displacement of W atoms from their ideal (bulk) positions (these displacements in turn are proportional to the order parameter). This treatment gives all the essential features of the phase diagram at θ e 0.2, including an increase of Tc with increasing coverage and the switch in the distortion direction at a critical coverage. The same model (with minor modifications) has been used by Inaoka and Yoshimori27 for describing the incommensurate phase at θ g 0.2. Ying et al. have included into the H/W(001) model an implicit description of surface atoms (eq 2) and employed analytical approximations (based on the mean-field and renormalization-group ideas)28 and Monte Carlo simulations29 for constructing the phase diagram. A similar model has been studied by Yoshomori et al.30 by Monte Carlo simulations. The models presented in refs28-30 treat the coordinates of W atoms as continuous variables. The H/W(001) model with the four-position lattice-gas approximation for W atoms has recently been analyzed by Zuppa et al.31 All the statistical models of the H/W(001) system predict at low coverages an increase of Tc with increasing coverage (see, e.g., Figure 6). The physical reason of this phenomenon is as follows. The substrate at T < Tc spontaneously forms two types of sites for adsorption (inside and outside the zigzag rows). H atoms may choose sites which are energetically more favorable, and the ordering of H atoms results in an increase in the configurational free energy. However, this increase is completely compensated by the decrease of the potential energy. Thus, adsorption on bridge sites always stabilizes the c(2×2) structure (it does not matter if the adsorbate-substrate lateral interactions are attractive or repulsive). Real H-W lateral interaction is attractive and accordingly H atoms prefer to occupy the sites located inside zigzag rows (Figure 5a) or to form pairs of W atoms (Figure 5b) and to be located inside these pairs. 3.2. Hydrogen Desorption and Diffusion. Thermal desorption spectra for hydrogen adsorption on W(001) have been simulated in refs 32 and 33. Inaoka and Yoshimori32 have employed a model based on the phenomenological Ginzburg-Landau expression for the free energy of the clean surface. The approach takes into account fluctuations of the order parameter and the adsorbate-adsorbate lateral interactions were neglected for simplicity. The results of simulations32 are in good agreement with experiment34 (Figure 9). The main conclusion of ref 32 is that splitting of the TPD spectra is connected with surface reconstruction. In reality, the direct adsorbate-adsorbate lateral interactions may also contribute to the splitting. If however one takes into account only the short-range (26) Lau, K. H.; Ying, S. C. Phys. Rev. Lett. 1980, 44, 1222. (27) Inaoka, T.; Yoshimori, A. Surf. Sci. 1982, 115, 301. (28) Ying, S. C.; Roelofs, L. D. Surf. Sci. 1983, 125, 218; 1984, 147, 203. (29) Roelofs, L. D.; Chung, J. W.; Ying, S. C.; Estrup, P. Phys. Rev. B: Condens. Matter 1986, 34, 3319. (30) Sigibayashi, T.; Hara, M.; Yoshimory, A. J. Vac. Sci. Technol. 1987, A5, 771. Yoshimory, A. Prog. Theor. Phys. Suppl. 1991, 106, 433. Dynamic Processes on Solid Surfaces; Tamaru, K., Ed.; Plenum: New York, 1993. (31) Zuppa, C.; Bustos, V. A.; Zgrablich, G. Phys. Rev. B: Condens. Matter, in press. (32) Inaoka, T.; Yoshimori, A. Surf. Sci. 1985, 149, 241. (33) Bustos, V.; Zgrablich, G.; Zhdanov, V. P. Appl. Phys. 1993, A56, 73. (34) King, D. A.; Thomas, G. Surf. Sci. 1980, 92, 201.


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results of Monte Carlo simulations33). In the framework of this model, four equilibrium positions for W atoms (Figure 4) are replaced by two equilibrium positions in order to simplify calculations. The rate constant for desorption can formally be represented in the Arrhenius form

kd ) ν(θ) exp[-Ed(θ)/T]

b

Figure 9. (a) Thermal desorption spectra calculated32 for hydrogen adsorbed on the W(001) surface and (b) the peak temperature as a function of the initial hydrogen coverage: open circles, experiment;34 solid circles, theory.32 The model takes into account the adsorbate-substrate interaction in the ground state. The adsorbate-substrate interaction in the activated state and the adsorbate-adsorbate interactions are neglected.

adsorbate-adsorbate lateral interactions, the model does not correctly describe the ratio between the integrated intensities of the two peaks (for example, the nearestneighbor interactions result in the ratio 1:11). The model32 involving surface reconstruction predicts the correct ratio (≈2:1) of the integrated intensities of the low- and hightemperature peaks. In addition, the model reproduces the apparent first-order kinetics of the low-temperature peak. The observed features of TPD spectra of the H/W(001) system can also be described by employing a two-position lattice-gas model for a clean W(001) surface (see the

(3)

where ν(θ) and Ed(θ) are the apparent preexponential factor and activation energy. It is of interest that the experimentally obtained apparent Arrhenius parameters for hydrogen desorption from W(001) are strongly dependent on coverage. With increasing coverage, the decrease in the activation energy (≈15 kcal/mol) is accompanied by a decrease in the preexponential factor of the order of 10-6.35,36 Theoretical analysis33,37-39 shows that the observed compensation effect can be directly connected with adsorbate-induced changes in the W(001) surface. In particular, a model37 based on the phenomenological Landau expression for the free energy of the clean surface can easily yield a compensation effect of the same order of magnitude as that observed in the experiment. However, the phenomenological model seems to overestimate the influence of surface reconstruction on the Arrhenius parameters. More realistic approaches (the two-position lattice-gas model33,38 or the model based on the Peierls instability39) predict a smaller decrease in the preexponential factor (of the order of 10-2). Some additional contribution to the coverage dependence of the preexponential factor for desorption may in principle be connected with the coverage dependence of the sticking coefficient for adsorption (see the discussion in refs 33, 37, and 40). However, the latter effect seems to be minor for the H/W(001) system because the coverage dependence of the sticking coefficient is not strong in this case.36 Thus, restructuring of the surface appears to be the main reason of the compensation effect observed for hydrogen desorption from W(001). Quantitative description of this effect should however be based on more detailed models of surface reconstruction compared to those employed in refs 33, and 37-40. Restructuring of the W(001) surface may also be manifested in surface diffusion of hydrogen atoms. This effect has been qualitatively studied41 in the framework of the model based on the phenomenological Landau expression for the free energy of the clean surface (the same model as in ref 37). At realistic parameters, the diffusion coefficient is expected to increase with increasing coverage. In addition, diffusion along and perpendicular to zigzag rows is predicted to be strongly anisotropic. 4. CO/Pt(110) 4.1. Clean Pt(110) Surface. The (110) face of facecentered cubic (fcc) metals is well-known to have a strong tendency to form the missing-row (1×2) structure (Figure 10). This type of surface reconstruction is spontaneously realized on Pt, Au, and Ir2,6,42,43 The clean (110) surface of other fcc metals does not reconstruct. In the latter (35) Smith, A. H.; Barker, R. A.; Estrup, P. J. Surf. Sci. 1984, 136, 327. (36) Alnot, P.; Cassuto, A.; King, D. A. Surf. Sci. 1989, 215, 29. (37) Zhdanov, V. P. Surf. Sci. 1992, 277, 155. (38) Myshlyavtsev, A. V.; Zhdanov, V. P. J. Chem. Phys. 1990, 92, 3909. (39) Hellsing, B.; Zhdanov, V. P. Chem. Phys. Lett. 1990, 168, 584. (40) Zhdanov, V. P. Surf. Sci. Rep. 1991, 12, 183. (41) Zhdanov, V. P. Langmuir 1989, 5, 1044. (42) Campuzano, J. C. The Au(110) (1×2) T (2×1) Phase Transition, in ref 7. (43) Den Nijs, M. Roughening and Preroughening, and Reconstruction Transitions in Crystal Surfaces, in ref 7.

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Figure 10. Missing-row model of the fcc (110)-(1×2) structure. The open circles represent the first layer of metal atoms; the shaded circles show the second and third layers.

case, however, the missing-row structure may often be induced by chemisorbed atoms or molecules.44 The formation of the missing-row structure on the (110) surface is directly connected with strong anisotropy of lateral interaction between metal atoms located in the top layer. In particular, the simplest order-disorder model of the spontaneous (1×2) surface reconstruction takes into account attractive lateral interactions (yMM < 0) in the Y direction (along the rows) and repulsive interactions (xMM > 0) in the X direction (perpendicular to the rows); i.e., the Hamiltonian of the surface is represented as45

H)

(yMMni,jni,j+1 + xMMni,jni+1,j), ∑ i,j

(4)

where ni,j is the occupation number of site i,j. The critical temperature for this model is given by the well-known Onsager equation. The energetics of the missing-row reconstruction of the (110) surface of Ni, Pd, Pt, Cu, Au, and Al has been investigated by Chen and Voter.46 Employing the surface energies before and after reconstruction, obtained in ref 46, one can estimate the nearest-neighbor metal-metal lateral interactions. In particular, for Pt(110), we have xMM ) 1.5 and yMM ) -8.8 kcal/mol, and accordingly Tc ) 1200 K.47 The latter magnitude of the critical temperature is in good agreement with the experiment48 where Tc ) 1080 ( 50 K. The Ising-like model described above does not take into account multiatom interactions49 and a roughening of the surface (the latter phenomenon occurs at T g Tc48). Nevertheless, it may be used as the first step for simulating the rate processes on the (110) surface of fcc metals (e.g., for describing diffusion of metal atoms50 or CO desorption47). The more advanced statistical models43,51 of the (110) surface of fcc metals are cumbersome and their application for analyzing the kinetics is rather difficult. 4.2. CO Desorption. CO adsorption on Pt(110), occurring primarily on top sites, is accompanied by dramatic changes in the surface:52 the missing-row (1×2) structure is conserved only at low coverages (θ e 0.2); with increasing coverage from 0.2 up to 0.5, the overlayer (44) Barnes, C. J. Adsorbate Induced Reconstruction of fcc (110) Surfaces, in ref 7. (45) Campuzano, J. C.; Lahee, A. M.; Jennings, G. Surf. Sci. 1985, 152, 68. (46) Chen, S. P.; Voter, A. F. Surf. Sci. 1991, 244, L107. (47) Myshlyavtsev, A. V.; Zhdanov, V. P. Langmuir 1993, 9, 1290. (48) Robinson, I. K.; Vieg, E.; Kern, K. Phys. Rev. Lett. 1989, 63, 2578. (49) Roelofs, L. D.; Foiles, L. M.; Daw, M. S.; Baskes, M. J. Surf. Sci. 1990, 234, 63. (50) Myshlyavtsev, A. V.; Zhdanov, V. P. Surf. Sci. 1993, 291, 145. (51) Levi, A. C.; Touzani, M. Surf. Sci. 1989, 218, 233. Vilfan, I.; Villain, J. Surf. Sci. 1991, 257, 368. Den Nijs, M. Phys. Rev. B: Condens. Matter 1992, 46, 10386.

is in the disordered state; at coverages above 0.5, the (1×1) structure is stable. All these transitions can be described in the framework of the lattice-gas model47 taking into account Hamiltonain (4) for Pt atoms, assuming the topsite adsorption of CO molecules, and introducing a reasonable set of adsorbate-adsorbate and adsorbatesubstrate lateral interactions. The special feature of the former lateral interactions results from geometrical constraints in the arrangement of CO molecules in nearestneighboring sites in the Y direction (along the rows). The corresponding lateral interaction is strongly repulsive because the spacing between nearest-neighbor sites is less than the van der Waals diameter of CO.53 The adsorbatesubstrate lateral interaction is also expected to be repulsive, i.e., the adsorbate-substrate binding energy decreases with increasing the number of adjacent Pt atoms. With the lateral interactions described above, the behavior of the CO/Pt(110) system is qualitatively rationalized as follows. At low coverages (up to θ ) 0.25), CO molecules can be adsorbed on the topmost metal atoms of the missing-row structure so that the nearest-neighbor adsorbate-adsorbate pairs are absent. An arrangement of this kind is more stable compared to those involving adsorption on the second and third substrate layers of the missing-row structure or compared to the islands with a local recovered (1×1) structure of the substrate. Thus, destruction of the missing-row structure is not favorable at θ e 0.25. With increasing CO coverage above θ ) 0.25, adsorption of all the molecules on the metal atoms located in the topmost layer of the missing-row structure is hardly possible due to strong repulsion between nearest-neighbor molecules. In this case, it is more favorable (i) to adsorb a fraction of the CO molecules on the topmost metal atoms of the missing-row structure and other CO molecules on metal atoms located in the second and third layers of this structure or (ii) to destroy the missing-row structure and to recover the (1×1) arrangement of metal atoms on the surface. At 0.25 e θ e 0.5, both these possibilities seem to be realized simultaneously (i.e., the system is in the disordered state) because the energies of the corresponding configurations of particles are very close. At higher coverages, CO adsorption on the recovered (1×1) structure of the substrate becomes more preferred because in the latter case the arrangement of CO molecules on the second and third layers of the missing-row structure is suppressed both by lower binding energy on these sites and by repulsive adsorbate-adsorbate interactions. To analyze the lattice-gas model outlined above, one can employ the transfer-matrix technique.47,50 This technique is very effective for solving the problems with anisotropic lateral interactions resulting in formation of the missing-row structures because in this case the system is well ordered in one direction and much less so in the other direction. In agreement with the experimental data52,55 for CO desorption from Pt(110), the calculated TPD spectra50 contain two peaks (Figure 11). According to the model, the splitting of the spectra is connected first of all with the repulsive nearest-neighbor adsorbate-adsorbate interaction. The effect of adsorbate-induced changes in the surface on desorption does not appear to be important in this system. (52) Jackman, T. E.; Davies, J. A.; Jackson, D. P.; Unertl, W. N.; Norton, P. R. Surf. Sci. 1982, 120, 389. Hofman, P.; Bare, S. R.; King, D. A. Surf. Sci. 1982, 117, 245; 1984, 144, 347. (53) Persson, B. N. J. Surf. Sci. Rep. 1992, 15, 1. (54) Comrie, C. M.; Lambert, R. M. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1659. Fair, J.; Madix, R. J. J. Chem. Phys. 1980, 73, 3480. Hayden, B. E.; Robinson, A. W.; Tucker, P. M. Surf. Sci. 1987, 192, 163. (55) Hayden, B. E.; Lackey, D.; Schott, J. Surf. Sci. 1990, 239, 119.


Figure 11. Thermal desorption spectra for the CO/Pt(110) systems calculated47 with the following set of lateral interactions x y (kcal/mol): MM ) 1.5, MM ) -8.8, AM ) 2, 1AA ) 5, and 2AA ) -1 (the interaction in the activated state is neglected).

5. H/Cu(110) The clean Cu(110) surface does not reconstruct. Adsorption of hydrogen at T ) 200-300 K induces formation of the missing-row (1×2) structure (Figure 10) at all coverages up to saturation at θ ) 0.5 (see the data obtained by LEED55 and neutral impact collision ion scattering spectroscopy56). The HREELS study55 shows that hydrogen atoms are predominantly adsorbed in tilted trigonal sites of the missing-row structure. The TPD spectra measured for the H/Cu(110) system57 indicate firstorder desorption kinetics since the temperature of the maximum desorption rate is almost independent of initial coverage. Taking into account the information above, we may postulate that the special features of hydrogen desorption from Cu(110) are connected with restructuring of the surface. That this idea is reasonable, has been verified in simulations.58 The model proposed involves a Hamiltonian (4) with attractive metal-metal lateral interactions xMM ) -0.6 and yMM ) -6.5 kcal/mol, the repulsive nearest-neighbor adsorbate-substrate lateral interaction in the direction perpendicular to the rows xAM > 0 (this interaction stimulates formation of what are effectively one-dimensional metal rows), and the nearest-neighbor x y and AA . adsorbate-adsorbate lateral interactions AA With this set of interactions, the ideal missing-row (1×2) structure is formed only at high adsorbate coverages, θ ≈ 0.5. At lower coverages, the strong anisotropy of the metal-metal lateral interactions results in a dilute phase that is well ordered along the rows oriented in the Y direction but much less so in the perpendicular direction. In both cases (at low and high coverages), hydrogen atoms are predominantly adsorbed in effectively one-dimensional rows. The local hydrogen coverage in these rows is high (≈1). As we have pointed out above, the TPD spectra for the H/Cu(110) system indicate first-order desorption. Such an order of associative desorption is possible if the main contribution to the process is provided by hydrogen atoms located in one-dimensional rows. The latter is not realized (56) Spitzl, R.; Niehus, H.; Poelsema, B.; Comsa, G. Surf. Sci. 1990, 239, 243. (57) Anger, G.; Winkler, A.; Rendulic, K. D. Surf. Sci. 1989, 220, 1. Canepa, M.; Mattera, L.; Salvietti, M.; Traverso, M. Surf. Sci., in press. (58) Zhdanov, V. P. Surf. Sci. 1992, 277, 155.

Langmuir, Vol. 12, No. 1, 1996 107

Figure 12. Thermal desorption spectra for the H/Cu(110) system calculated48 taking into account formation of the adsorbate-induced missing-row structure. The model employed involves adsorbate-adsorbate and adsorbate-substrate lateral interactions in the ground state and also adsorbate-substrate lateral interaction in the activated state.

if one takes into account only the above-described lateral interactions between nonactivated particles. Indeed, if lateral interaction in the activated state is absent (i* ) 0), a substantial contribution to desorption will be given not only by hydrogen atoms located in rows forming the (1 × 2) spots but also by many other rare configurations. For example, the probability of finding a pair of hydrogen atoms in nearest-neighbor sites on unreconstructed parts of the surface is low due to the strong repulsive interaction xAM > 0. If, however, i* ) 0, this low probability will be compensated by the reduction of the activation barrier for desorption due to the interaction xAM, and the configurations under consideration will be important for desorption. In this case, the desorption kinetics will not be first order. To explain the first order of hydrogen desorption from the Cu(110) surface (Figure 12), it was necessary to introduce58 a strong repulsive adsorbatesubstrate lateral interaction in the activated state, x* AM, suppressing desorption from the unreconstructed regions of the surface (the magnitude of this interaction was assumed to be about the same as that of xAM). Note that lateral interactions in the activated state are often neglected in simulations of thermal desorption (see the examples collected in ref 1). This is justified if the bond between an activated complex and the surface is weak or, in other words, if the activation barrier for adsorption is low. In the case of the H/Cu(110) system, the activation barrier for adsorption is, however, substantial, Ea ≈ 14 kcal/mol,59 and the assumption that the adsorbate-substrate lateral interaction in the activated state is strong does not look unrealistic. 6. H/Pt(001) The ideal (1×1), or truncated bulk, Pt(001) surface is well known to be metastable.3,60 It reconstructs spontaneously at high temperature to form a “hexagonal” structure. Adsorption of hydrogen on the Pt(001)-hex (59) Harris, J. Surf. Sci. 1989, 221, 335; Langmuir 1991, 7, 2528. Campbell, J. M.; Campbell, C. T. Surf. Sci. 1991, 259, 1. (60) Behm, R. J.; Thiel, P. A.; Norton, P. R.; Ertl, G. J. Chem. Phys. 1983, 78, 7437. Woodruff, D. P. Adsorbate-Induced Restructuring of f.c.c. (100) Surfaces, in ref 7.

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surface recovers the (1×1) structure. The TPD spectra of the H/Pt(001) system are rather unusual: the peaks are very narrow and the peak maximum shifts to higher temperature with increasing initial coverage.61 A simple mean-field model treating the adsorbate-induced hex T (1×1) reconstruction of the Pt(001) surface in terms of theory of first-order phase transitions and describing the effect of this reconstruction on hydrogen desorption has been proposed in refs 61 and 62. The results obtained61,62 have already been reviewed in ref 1 (Chapters 3.5.1 and 5.2.5). 7. Conclusion We have considered a few examples illustrating the influence of surface reconstruction on thermal desorption and surface diffusion. In the case of desorption, the results available indicate that at present there are no general rules connecting the type of reconstruction with the special features of the TPD spectra. Sometimes, the effect of (61) Sobyanin, V. A.; Zhdanov, V. P. Surf. Sci. 1987, 181, L163. (62) Zhdanov, V. P. Surf. Sci. 1985, 164, L807; J. Phys. Chem. 1989, 93, 5582.

Zhdanov and Norton

surface reconstruction on desorption is well manifested. For example, formation of dimers on Si(001) or effectively one-dimensional rows on Cu(110) results in first-order kinetics of associative desorption of hydrogen from these surfaces (sections 2 and 5). Sometimes, however, adsorption is accompanied by dramatic changes in the surface, but the manifestation of these changes in the TPD spectra is hidden. For instance, during CO adsorption on Pt(110), the structure of the surface is directly governed by adsorption due to adsorbate-adsorbate and adsorbatesubstrate interactions (section 4), but the calculated TPD spectra for the CO/Pt(110) system are qualitatively the same as in the experiment even if surface reconstruction is neglected in simulations (i.e., the TPD spectra might be formally described by taking into account only adsorbate-adsorbate lateral interactions). Almost the same situation takes place for hydrogen adsorption on W(001) (section 3). The effect of surface reconstruction on surface diffusion is quite obvious: restructuring of the surface results often in anisotropy of this process. LA9407018

Surface Reconstruction and Rate Processes in ... - ACS Publications

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