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Sulfur chemisorption on W(100): Antiphase boundaries with point defects
L628
SURFACE
Surface Science 219 (1989) L628-L636 North-Holland, Amsterdam
SCIENCE
LETTERS
SULFUR CHEMISORI’TION ANTIPHASE BOUNDARIES
V. MAURICE,
ON W(100): WITH POINT
DEFECTS
J. OUDAR
Labormoire de Physico-Chink des Surfaces, nssocik au CNRS II rue P. & M. Curie, 75231 Paris Cedex OS, France
UA 425, ENSCP,
and M. HUBER Laboratoire de Chimie Appliquke de I’Etat Solide, asso& II rue P. & M. Curie, 75231 Paris Cedex 05, France
au CNRS
UA 302, ENSCP,
Received 13 March 1989; accepted for publication 19 May 1989
On the basis of LEED data recorded for sulfur chemisorbed on the (100) surface of tungsten in the 0.5-0.67 coverage range, partially ordered superstructures have been calculated within the kinematic approximation. They reveal c(2 X 2) domains separated by antiphase boundaries with point defects. The superstructures are modelled with statistical occupancies of the adsorption sites. Various possibilities for the registry of the adlayer in this coverage range are discussed.
Recently, we have reported briefly the results of calculations of structural models describing the transition between c(2 x 2) and c(fi x 3& + 3fi x fi)R45” ordered superstructures which occurs for sulfur chemisorption on the tungsten and molybdenum (100) surfaces [l-6]. It was shown that the splitting of the (l/2,1/2) spot of the c(2 x 2) LEED pattern when coverage increases from 0.5 up to 0.67 monolayer (ML), is to be related to the occurrence of antiphase boundaries in the c(2 x 2) superstructure [6]. On W(100) [1,2], this splitting produces two pairs of spots equivalent by a 90” rotation, and located along the diagonals of the substrate reciprocal unit cell (the (ll)* directions). As coverage increases, the spot separation widens continuously until it reaches l/3 of the substrate period [2] which corresponds to the c(fi x 3fi + 3fi X fi)R45O reciprocal superlattice. In order to describe this continuous splitting a series of intermediate superlattices can be selected; we choose the c(fi X llfi + llfi X &)R45”, c(fi X 7& + 7fi c(fi x 5a + 5fi x fi)R45” and p(& x 4fi + 4&f x fi)R45”, x &)R45” superlattices. All of them show systematic extinctions of some fractional order (FO) spots (they are incomplete). In our paper, it was shown 0 Elsevier Science Publishers B.V. Physics Publishing Division)
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Fig. 1. Schematic representation of the reciprocal superlattices which describe the transition between the c(2 x 2) and c(fi X 3fi)R45 o superstructures: (a) N2 x 2), (b) c(fi X 7&)R45 O, (c) @ x S@)R45 “1 (d) p(fi x 4fi)R45 o and (e) c(fi x 3@)R45 O. The dots and open circles represent the integer and fractional order reflections, respectively. Crosses represent the zero intensity fractional order reflections. All fractional order reflections can be indexed along the indicated reciprocal directions.
that these extinctions are related to an adatom-vacancy substitution disorder which affects mainly the configuration of the antiphase boundaries separating the c(2 x 2) domains. The results of computer simulations were presented for the p(fi x 4&)R45 o superstructure. On Mo(lOO), the splitting of the (l/2,1/2) spot produces streaks of intensity located between l/3 and 2/3 of the substrate period along (ll)* [5]. It was shown by the models resulting from computer simulations that in this case, disorder affects the periodicity of the antiphase boundaries and that the streaks of intensity can be related to a pseudo-periodicity of these boundaries. This Letter presents a statistical analysis of the point defects which affect the configuration of the antiphase boundaries on W(100). The c(\/z X 7fi + 7& x @)R45”, c(fi X 5& + 56 X &)R45” and p(& X 4fi + 4fi x &)R45 o superstructures are discussed. The analysis takes into account two possibilities for the S adlayer registry: (i) all atoms are located on hollow sites or (ii) they are located on both hollow and bridge sites, this second type of adsorption sites being necessary to explain the p(1 X 2 + 2 X 1) LEED pattern observed for the saturation coverage of one S atom per metal atom (1 ML). On fig. 1, we schematically present the series of reciprocal superlattices that we have selected. For all of them except the c(2 x 2) we present one of the two equivalent orientations at 90 O. Accordingly, we will discuss one orientation of the structural models. Equivalent configurations at 90” have to be considered for consistency with the fourfold symmetry of the diffraction data. The superstructure cells are indicated as well as the location of systematic extinctions.
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Fig. 2. Model ordered superstructures labelled (a): c(2 X 2), 0.5 ML; (b) and (b’): c(fi X 7fi)R45 O, 0.57 ML; (c) and (c’): c(fi X 5fi)R45 O, 0.6 ML; (d) and (d’): p(@ X 4&)R45 O, 0.62 ML; (e) and (e’): c(fi x 3fi)R45 O, 0.67 ML. In the left-hand column, all S atoms sit on fourfold hollow sites. In the right-hand column, S atoms sit on fourfold hollow and twofold bridge sites.
On fig. 2, we present two possible series of ordered superstructures having the proper periodicities and coverages. Primitive as well as centered cells are indicated. Both series show the occurrence of boundaries separating the c(2 x 2) domains. The c(2 X 2) domains are in antiphase with respect to each other since the translation vector from one domain to the neighbouring one is not a translation vector of the c(2 X 2) superstructure. The transition between the c(2 x 2) and the c(& x 3&)R45” superstructure can be described then by the increasing proportion of rows of S atoms along the (11) directions. These S rows form the antiphase boundaries. As coverage increases, the proportion of these rows increases which results in the increase of the area covered by the antiphase boundaries and in the decrease of that covered by the c(2 x 2) domains. The difference between the two series of models is related to the adsorption sites of the S atoms along the (11) rows forming the boundaries. For the series of superstructures represented on the left-hand column of fig. 2, we have assumed that the S atoms sit on fourfold hollow sites. The lateral
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repulsive interactions in the antiphase boundaries between first nearest neighbour S atoms (repulsive because a c(2 x 2) superstructure is developped at 0.5 ML) are compensated by adsorption on the most favorable sites. For the series represented on the right-hand column of fig. 2, we have assumed fourfold hollow and twofold bridge adsorption sites for the (11) rows of S atoms forming the antiphase boundaries. Note that for all the superstructures describing the phase transition, one shifts from one registry of the antiphase boundaries to the other one by displacing one S (11) row of each boundary from hollow sites to bridge sites and vice versa. This second registry corresponds to a case where the lateral repulsive interactions within the boundaries are relaxed by increasing the shortest S-S distance. These two different possibilities will be discussed later. However, these two series of ordered superstructures are not consistent with the diffraction data (except for the c(2 x 2) and the c(fi X 4fi)R45 “) as a kinematic calculation of the diffracted intensities does not reproduce the systematic extinctions indicated on fig. 1. Although the kinematic theory cannot be used to determine the registry of the adlayer with respect to the substrate, it is valid in first approximation to test its 2D configuration on the basis of the zero intensity FO reflections. Even in a multiple scattering process, electrons must be scattered at least once by the adlayer to yield non-zero intensity FO reflections. If no such event occurs (some FO reflections have zero intensity for all electron energies), it is then to be related to the structure of the diffracting adlayer and not to the scattering process so that this structure can be tested using a single scattering theory such as the kinematic theory. As the systematic extinctions in the c(fi X 7fi)R45”, c(fi x 5fi)R45” and p(& x 4&)R45” superlattices are not taken into account in the models of fig. 2 and cannot be related to glide symmetry planes, only the occurrence of point defects related to an adatom-vacancy substitution disorder may produce zero intensity FO reflections. Such a disorder leads us to consider partial occupations of the adsorption sites and it can be modelled properly by statistical superstructure cells. The calculation of such statistical cells is made easier in the present case by the fact that the c(@ X 7fi)R45 O, c(fi x 5fi)R45 o and p(& X ifi)R45 o patterns show only two non-zero FO reflections per coincidence unit cell and that these reflections are equivalent by symmetry. In figs. lb, lc and Id we have indicated reciprocal directions (R,, R, and Rd) along which all the FO reflections can be indexed. Each reciprocal superlattice can be described then, as made of series of reflections along these directions; the periodicity of these series being related to the periodicity of the coincidence cell. Besides, a diffraction pattern being basically a frequency spectrum of the real space, the series of reflections in the reciprocal space are associated with the series of harmonics of the periodic functions which describe the distributions of the atoms in the real space (i.e. the filling modulations of the adlayer). Periodic
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modulations are described by a Fourier series with each harmonic being related to a given spot in reciprocal space. For the FO spots series along the RtC R, and R, directions, only the first spot has a non-zero intensity. It corresponds in real space to the simplest Fourier series with one first order cosine term, the sine term being cancelled by the center of symmetry. On fig. 3, we present statistical unit cells for the c(& x 7&)R45 O, c(fi x 5fi)R45 o and p(& x 4&)R45 o superstructures. The occupation of
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Fig. 3. Model partially ordered superstructures labelled: (b) and (b’): c(fi X 7fi)R45 O, 0.57 ML; (c) and (c’): c(& x 5fi)R45O, 0.6 ML; (d) and (d’): p(fi ~4&)R45O, 0.62 ML. Each adsorption site is indexed with its occupancy probability given in percent. The same origin of the unit cells has been chosen for the sake of comparison with the ordered models on fig. 2. The cosine wave describing the filling profile of the adlayer along the R, direction is shown in (e) over a half period.
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the sites given in percent has been deduced from cosines waves representing the filling profile of the adlayer along the R,, R, and R, directions taking into account the periodicity and coverage of the coincidence cell. The models assume either hollow adsorption sites only (left-hand column) or both hollow and bridge adsorption sites (right-hand column). Kinematic calculations of the diffracted intensity for each model reproduce the zero intensity of the systematic extinctions. For the sake of comparison, the statistical cells have been represented with the same origin as for the unit cells given on fig. 2. In addition we have indicated by arrows the adsorption sites which are connected by the substitution disorder (for instance, the 28% missing atoms in the 72% filled sites of fig. 3c are all found in the neighbouring partially filled vacancy). Let us now discuss the possible registries of the adlayer. For -both the W(lOO)-S and the Mo(lOO)-S system, c(2 X 2) LEED patterns are observed at half-saturation of the adlayer. Dynamical calculations of the diffracted intensities have shown that on Mo(lOO), S atoms sit on hollow sites [3]. Still, for both systems, p(1 x 2 + 2 X 1) LEED patterns are observed at saturation of the adlayer. Allthough the structure of the saturated adlayer has not been calculated by a complete dynamical analysis of the diffracted intensities, the knowledge of the coverage and the relative simplicity of the superlattice restricts severely the configurational possibilities. Two models have been proposed: either the S atoms sit on hollow and bridge sites in equal proportions (see fig. 4a) or they sit on a single site which is a “semi-hollow-semibridge” position (see fig. 4b). Very recently, a scanning tunneling microscopy investigation of the structure of the saturated S adlayer on Mo(100) has been reported [7] which gives support to this second model. Since the Mo(lOO)-S and W(lOO-S systems are very similar, one may assume the same registries of
c
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Fig. 4. Model ordered superstructures labelled: (a) and (b): p(2 x l),1 ML; (c) and (d): ~(4 x 2), 0.75 ML; (e) and (f): c(fi x 3&)R45 O, 0.67 ML. The left-hand and right-hand columns show a “hollow and bridge” registry and a “semi-hollow-semi-bridge” registry respectively. One pri+tive cell is represented in all cases.
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the S adlayer at 0.5 and 1 ML on W(1OO) as on Mo(100). One has then to determine the superstructure of lowest coverage associated with the change of registry. Let us consider first that all S atoms are located on hollow sites for 0.67 ML. Each S atom has then two neighbours in first nearest position as shown on fig. 2e at a shortest distance of 3.15 A. This structural model implies that the sum of the repulsive interactions between first nearest neighbour S atoms is compensated by adsorption on hollow sites. We have assumed this possibility to be valid to calculate the series of models presented in the left-hand column of figs. 2 and 3. If we consider now that the adlayer has changed its registry at 0.67 ML, the shortest distance between S atoms becomes 3.52 A (assuming the same height for S atoms with respect to the topmost substrate plane). Each S atom has two neighbours located at this distance in the c@ x 3fi)R450 superstructure as shown on fig. 4e and fig. 4f. Such a model implies that the weaker repulsive interactions between S atoms separated by 3.52 A instead of 3.15 A compensate the energy loss related to the “off-hollow sites” locations of the S atoms. We have assumed this possibility to calculate the models presented in the right-hand column of figs. 2 and 3 with, in addition, a “hollow and bridge sites” registry. The registry change between 0.5 and 0.67 ML would then result from the formation of the antiphase boundaries in the ~$2 x 2) superstructure. It would be induced by the repulsive interaction between S atoms in the boundaries and would expand as these boundaries develop. At 0.67 ML, the registry change would be completed since the c(fi x 3fi)R45 * superstructure can be considered as one “single antiphase boundary” covering the entire surface. The work function variation (A#) recorded for the adsorption of H,S on W(lO0) may give support to a registry change in the O-5-0.67 ML range (see fig. 2 in ref. 111). From 0 up to 0.5 ML, a A+ increase is recorded which corresponds to the completion of the c(2 X 2) superstructure. A maximum value is reached which can be related to a maximum number of S atoms in hollow sites. Between 0.5 and 0.7 ML, a A+ decrease is recorded. If S atoms would further adsorb in hollow sites, a further A+ increase would be expected possibly attenuated by depolarization effects. On the other hand, assuming different adsorption for S atoms above 0.5 ML would give a continuous A$ decrease provided that the surface dipole for S atoms in the new sites is lower than for S atoms in hollow sites. Around 0.7 ML, the A+ minimum is reached which could correspond to the completion of the adlayer registry change. Above 0.7 ML, A+ increases again towards a plateau; this could be related to the completion of the saturated adlayer with the S atoms sitting in the same new sites as at 0.7 ML. Although there is no experimental evidence to determine whether or not the registry of the adlayer in the OS-O.67 ML range is similar to that for 1 ML (i.e. “hollow and bridge” versus “set-hollow-sea-badge”), it seems unlikely
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to be so for the following reason. If we assume the “hollow and bridge” registry to be valid in the OS-O.67 ML range, the superstructures may be described as made of (11) rows of S atoms sitting on hollow and bridge sites within proportions going from zero bridge for one hollow to one bridge for one hollow. The (11) rows with S atoms in hollow sites are residual structural elements of the c(2 x 2) superstructure. They should retain the same registry when the superstructure develops the c(2 x 2) antiphase domains and consequently prevent the whole adlayer to “shift” its registry towards a unique “semi-hollow-semi-bridge” one. However, such a registry “shift” may be expected as soon as the c(2 X 2) domains disappear, i.e. at completion of the c(fi X 3&)R45” superstructure and for the superstructures of higher coverages, c(4 x 2) and p(2 x 1) (see figs. 4b, 4d and 4f). There is a third possibility regarding the adlayer registry that we did not consider in the calculations of our models. It simply assumes that the structure of the adlayer is determined by strong repulsive interactions between neighbouring S atoms. Structural models are then obtain for any superstructures by maximising the distances between adatoms with as reference, the concentration and the periodicity of the cell. This results then in the same models as presented in figs. 2a and 4e or fig. 4f for the c(2 X 2) and c(fi X 3& R45 o superstructures respectively. However, for the transition between these two superstructures, in our opinion such models are not valid for three reasons: (i) the shortest distance between S atoms in this coverage range is larger than 3.52 A which is rather large in order to have both the 2D configuration and the registry of the adlayer determined only by repulsive interactions between nearest neighbors (the van der Waals diameter of sulfur is 3.70 A); (ii) would it be so, the structural models obtained do not reproduce the systematic extinctions of the reciprocal superlattices; (iii) in order to account for the zero intensity FO spots, one would have to introduce point defects; this would shorten the S-S distances. We conclude by pointing out that: (i) the LEED patterns recorded for the phase transition between the c(2 x 2) and c(fi X 3&)R45 o superstructures for the W(lOO)-S system, are characteristic of the occurrence of point defects in the adlayer; (ii) we have modelled this disorder using statistical superstructures within the ,kinematic approximation and assuming two possibilities for the adlayer registry; (iii) the A+ variations recorded in this coverage range give support to a change of registry of the adlayer.
References (11 A. Bhattacharya, L.J. Clarke and L. Morales de la Garza, J. Chem. Sot. Faraday Trans. I, 77 (1981) 2223. [2] C. Park, H.M. Kramer and E. Bauer, Surface Sci. 116 (1982) 467. [3] L.J. Clarke, Surface Sci. 102 (1981) 331.
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[4] M. Salmeron, G.A. Somorjai
and R.R. Chianelli, Surface Sci. 127 (1983) 526. [5] V. Maurice, L. Peralta. Y. Berthier and J. Oudar, Surface Sci. 148 (1984) 623. [6] V. Maurice, M. Huber and J. Oudar, in: The Structure of Surfaces II. Vol. 11 of Springer Series in Surface Sciences, Eds. J.F. van der Veen and M.A. Van Hove (Springer, Berlin. 1988). [7] B. Marchon, P. Bernhardt, M.E. Bussel, G.A. Somorjai. M. Salmeron and W. Sickhaus. Phys. Rev. Letters 60 (1988) 1166.
SURFACE
Surface Science 219 (1989) L628-L636 North-Holland, Amsterdam
SCIENCE
LETTERS
SULFUR CHEMISORI’TION ANTIPHASE BOUNDARIES
V. MAURICE,
ON W(100): WITH POINT
DEFECTS
J. OUDAR
Labormoire de Physico-Chink des Surfaces, nssocik au CNRS II rue P. & M. Curie, 75231 Paris Cedex OS, France
UA 425, ENSCP,
and M. HUBER Laboratoire de Chimie Appliquke de I’Etat Solide, asso& II rue P. & M. Curie, 75231 Paris Cedex 05, France
au CNRS
UA 302, ENSCP,
Received 13 March 1989; accepted for publication 19 May 1989
On the basis of LEED data recorded for sulfur chemisorbed on the (100) surface of tungsten in the 0.5-0.67 coverage range, partially ordered superstructures have been calculated within the kinematic approximation. They reveal c(2 X 2) domains separated by antiphase boundaries with point defects. The superstructures are modelled with statistical occupancies of the adsorption sites. Various possibilities for the registry of the adlayer in this coverage range are discussed.
Recently, we have reported briefly the results of calculations of structural models describing the transition between c(2 x 2) and c(fi x 3& + 3fi x fi)R45” ordered superstructures which occurs for sulfur chemisorption on the tungsten and molybdenum (100) surfaces [l-6]. It was shown that the splitting of the (l/2,1/2) spot of the c(2 x 2) LEED pattern when coverage increases from 0.5 up to 0.67 monolayer (ML), is to be related to the occurrence of antiphase boundaries in the c(2 x 2) superstructure [6]. On W(100) [1,2], this splitting produces two pairs of spots equivalent by a 90” rotation, and located along the diagonals of the substrate reciprocal unit cell (the (ll)* directions). As coverage increases, the spot separation widens continuously until it reaches l/3 of the substrate period [2] which corresponds to the c(fi x 3fi + 3fi X fi)R45O reciprocal superlattice. In order to describe this continuous splitting a series of intermediate superlattices can be selected; we choose the c(fi X llfi + llfi X &)R45”, c(fi X 7& + 7fi c(fi x 5a + 5fi x fi)R45” and p(& x 4fi + 4&f x fi)R45”, x &)R45” superlattices. All of them show systematic extinctions of some fractional order (FO) spots (they are incomplete). In our paper, it was shown 0 Elsevier Science Publishers B.V. Physics Publishing Division)
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Fig. 1. Schematic representation of the reciprocal superlattices which describe the transition between the c(2 x 2) and c(fi X 3fi)R45 o superstructures: (a) N2 x 2), (b) c(fi X 7&)R45 O, (c) @ x S@)R45 “1 (d) p(fi x 4fi)R45 o and (e) c(fi x 3@)R45 O. The dots and open circles represent the integer and fractional order reflections, respectively. Crosses represent the zero intensity fractional order reflections. All fractional order reflections can be indexed along the indicated reciprocal directions.
that these extinctions are related to an adatom-vacancy substitution disorder which affects mainly the configuration of the antiphase boundaries separating the c(2 x 2) domains. The results of computer simulations were presented for the p(fi x 4&)R45 o superstructure. On Mo(lOO), the splitting of the (l/2,1/2) spot produces streaks of intensity located between l/3 and 2/3 of the substrate period along (ll)* [5]. It was shown by the models resulting from computer simulations that in this case, disorder affects the periodicity of the antiphase boundaries and that the streaks of intensity can be related to a pseudo-periodicity of these boundaries. This Letter presents a statistical analysis of the point defects which affect the configuration of the antiphase boundaries on W(100). The c(\/z X 7fi + 7& x @)R45”, c(fi X 5& + 56 X &)R45” and p(& X 4fi + 4fi x &)R45 o superstructures are discussed. The analysis takes into account two possibilities for the S adlayer registry: (i) all atoms are located on hollow sites or (ii) they are located on both hollow and bridge sites, this second type of adsorption sites being necessary to explain the p(1 X 2 + 2 X 1) LEED pattern observed for the saturation coverage of one S atom per metal atom (1 ML). On fig. 1, we schematically present the series of reciprocal superlattices that we have selected. For all of them except the c(2 x 2) we present one of the two equivalent orientations at 90 O. Accordingly, we will discuss one orientation of the structural models. Equivalent configurations at 90” have to be considered for consistency with the fourfold symmetry of the diffraction data. The superstructure cells are indicated as well as the location of systematic extinctions.
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Fig. 2. Model ordered superstructures labelled (a): c(2 X 2), 0.5 ML; (b) and (b’): c(fi X 7fi)R45 O, 0.57 ML; (c) and (c’): c(fi X 5fi)R45 O, 0.6 ML; (d) and (d’): p(@ X 4&)R45 O, 0.62 ML; (e) and (e’): c(fi x 3fi)R45 O, 0.67 ML. In the left-hand column, all S atoms sit on fourfold hollow sites. In the right-hand column, S atoms sit on fourfold hollow and twofold bridge sites.
On fig. 2, we present two possible series of ordered superstructures having the proper periodicities and coverages. Primitive as well as centered cells are indicated. Both series show the occurrence of boundaries separating the c(2 x 2) domains. The c(2 X 2) domains are in antiphase with respect to each other since the translation vector from one domain to the neighbouring one is not a translation vector of the c(2 X 2) superstructure. The transition between the c(2 x 2) and the c(& x 3&)R45” superstructure can be described then by the increasing proportion of rows of S atoms along the (11) directions. These S rows form the antiphase boundaries. As coverage increases, the proportion of these rows increases which results in the increase of the area covered by the antiphase boundaries and in the decrease of that covered by the c(2 x 2) domains. The difference between the two series of models is related to the adsorption sites of the S atoms along the (11) rows forming the boundaries. For the series of superstructures represented on the left-hand column of fig. 2, we have assumed that the S atoms sit on fourfold hollow sites. The lateral
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repulsive interactions in the antiphase boundaries between first nearest neighbour S atoms (repulsive because a c(2 x 2) superstructure is developped at 0.5 ML) are compensated by adsorption on the most favorable sites. For the series represented on the right-hand column of fig. 2, we have assumed fourfold hollow and twofold bridge adsorption sites for the (11) rows of S atoms forming the antiphase boundaries. Note that for all the superstructures describing the phase transition, one shifts from one registry of the antiphase boundaries to the other one by displacing one S (11) row of each boundary from hollow sites to bridge sites and vice versa. This second registry corresponds to a case where the lateral repulsive interactions within the boundaries are relaxed by increasing the shortest S-S distance. These two different possibilities will be discussed later. However, these two series of ordered superstructures are not consistent with the diffraction data (except for the c(2 x 2) and the c(fi X 4fi)R45 “) as a kinematic calculation of the diffracted intensities does not reproduce the systematic extinctions indicated on fig. 1. Although the kinematic theory cannot be used to determine the registry of the adlayer with respect to the substrate, it is valid in first approximation to test its 2D configuration on the basis of the zero intensity FO reflections. Even in a multiple scattering process, electrons must be scattered at least once by the adlayer to yield non-zero intensity FO reflections. If no such event occurs (some FO reflections have zero intensity for all electron energies), it is then to be related to the structure of the diffracting adlayer and not to the scattering process so that this structure can be tested using a single scattering theory such as the kinematic theory. As the systematic extinctions in the c(fi X 7fi)R45”, c(fi x 5fi)R45” and p(& x 4&)R45” superlattices are not taken into account in the models of fig. 2 and cannot be related to glide symmetry planes, only the occurrence of point defects related to an adatom-vacancy substitution disorder may produce zero intensity FO reflections. Such a disorder leads us to consider partial occupations of the adsorption sites and it can be modelled properly by statistical superstructure cells. The calculation of such statistical cells is made easier in the present case by the fact that the c(@ X 7fi)R45 O, c(fi x 5fi)R45 o and p(& X ifi)R45 o patterns show only two non-zero FO reflections per coincidence unit cell and that these reflections are equivalent by symmetry. In figs. lb, lc and Id we have indicated reciprocal directions (R,, R, and Rd) along which all the FO reflections can be indexed. Each reciprocal superlattice can be described then, as made of series of reflections along these directions; the periodicity of these series being related to the periodicity of the coincidence cell. Besides, a diffraction pattern being basically a frequency spectrum of the real space, the series of reflections in the reciprocal space are associated with the series of harmonics of the periodic functions which describe the distributions of the atoms in the real space (i.e. the filling modulations of the adlayer). Periodic
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modulations are described by a Fourier series with each harmonic being related to a given spot in reciprocal space. For the FO spots series along the RtC R, and R, directions, only the first spot has a non-zero intensity. It corresponds in real space to the simplest Fourier series with one first order cosine term, the sine term being cancelled by the center of symmetry. On fig. 3, we present statistical unit cells for the c(& x 7&)R45 O, c(fi x 5fi)R45 o and p(& x 4&)R45 o superstructures. The occupation of
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Fig. 3. Model partially ordered superstructures labelled: (b) and (b’): c(fi X 7fi)R45 O, 0.57 ML; (c) and (c’): c(& x 5fi)R45O, 0.6 ML; (d) and (d’): p(fi ~4&)R45O, 0.62 ML. Each adsorption site is indexed with its occupancy probability given in percent. The same origin of the unit cells has been chosen for the sake of comparison with the ordered models on fig. 2. The cosine wave describing the filling profile of the adlayer along the R, direction is shown in (e) over a half period.
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the sites given in percent has been deduced from cosines waves representing the filling profile of the adlayer along the R,, R, and R, directions taking into account the periodicity and coverage of the coincidence cell. The models assume either hollow adsorption sites only (left-hand column) or both hollow and bridge adsorption sites (right-hand column). Kinematic calculations of the diffracted intensity for each model reproduce the zero intensity of the systematic extinctions. For the sake of comparison, the statistical cells have been represented with the same origin as for the unit cells given on fig. 2. In addition we have indicated by arrows the adsorption sites which are connected by the substitution disorder (for instance, the 28% missing atoms in the 72% filled sites of fig. 3c are all found in the neighbouring partially filled vacancy). Let us now discuss the possible registries of the adlayer. For -both the W(lOO)-S and the Mo(lOO)-S system, c(2 X 2) LEED patterns are observed at half-saturation of the adlayer. Dynamical calculations of the diffracted intensities have shown that on Mo(lOO), S atoms sit on hollow sites [3]. Still, for both systems, p(1 x 2 + 2 X 1) LEED patterns are observed at saturation of the adlayer. Allthough the structure of the saturated adlayer has not been calculated by a complete dynamical analysis of the diffracted intensities, the knowledge of the coverage and the relative simplicity of the superlattice restricts severely the configurational possibilities. Two models have been proposed: either the S atoms sit on hollow and bridge sites in equal proportions (see fig. 4a) or they sit on a single site which is a “semi-hollow-semibridge” position (see fig. 4b). Very recently, a scanning tunneling microscopy investigation of the structure of the saturated S adlayer on Mo(100) has been reported [7] which gives support to this second model. Since the Mo(lOO)-S and W(lOO-S systems are very similar, one may assume the same registries of
c
d
Fig. 4. Model ordered superstructures labelled: (a) and (b): p(2 x l),1 ML; (c) and (d): ~(4 x 2), 0.75 ML; (e) and (f): c(fi x 3&)R45 O, 0.67 ML. The left-hand and right-hand columns show a “hollow and bridge” registry and a “semi-hollow-semi-bridge” registry respectively. One pri+tive cell is represented in all cases.
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the S adlayer at 0.5 and 1 ML on W(1OO) as on Mo(100). One has then to determine the superstructure of lowest coverage associated with the change of registry. Let us consider first that all S atoms are located on hollow sites for 0.67 ML. Each S atom has then two neighbours in first nearest position as shown on fig. 2e at a shortest distance of 3.15 A. This structural model implies that the sum of the repulsive interactions between first nearest neighbour S atoms is compensated by adsorption on hollow sites. We have assumed this possibility to be valid to calculate the series of models presented in the left-hand column of figs. 2 and 3. If we consider now that the adlayer has changed its registry at 0.67 ML, the shortest distance between S atoms becomes 3.52 A (assuming the same height for S atoms with respect to the topmost substrate plane). Each S atom has two neighbours located at this distance in the c@ x 3fi)R450 superstructure as shown on fig. 4e and fig. 4f. Such a model implies that the weaker repulsive interactions between S atoms separated by 3.52 A instead of 3.15 A compensate the energy loss related to the “off-hollow sites” locations of the S atoms. We have assumed this possibility to calculate the models presented in the right-hand column of figs. 2 and 3 with, in addition, a “hollow and bridge sites” registry. The registry change between 0.5 and 0.67 ML would then result from the formation of the antiphase boundaries in the ~$2 x 2) superstructure. It would be induced by the repulsive interaction between S atoms in the boundaries and would expand as these boundaries develop. At 0.67 ML, the registry change would be completed since the c(fi x 3fi)R45 * superstructure can be considered as one “single antiphase boundary” covering the entire surface. The work function variation (A#) recorded for the adsorption of H,S on W(lO0) may give support to a registry change in the O-5-0.67 ML range (see fig. 2 in ref. 111). From 0 up to 0.5 ML, a A+ increase is recorded which corresponds to the completion of the c(2 X 2) superstructure. A maximum value is reached which can be related to a maximum number of S atoms in hollow sites. Between 0.5 and 0.7 ML, a A+ decrease is recorded. If S atoms would further adsorb in hollow sites, a further A+ increase would be expected possibly attenuated by depolarization effects. On the other hand, assuming different adsorption for S atoms above 0.5 ML would give a continuous A$ decrease provided that the surface dipole for S atoms in the new sites is lower than for S atoms in hollow sites. Around 0.7 ML, the A+ minimum is reached which could correspond to the completion of the adlayer registry change. Above 0.7 ML, A+ increases again towards a plateau; this could be related to the completion of the saturated adlayer with the S atoms sitting in the same new sites as at 0.7 ML. Although there is no experimental evidence to determine whether or not the registry of the adlayer in the OS-O.67 ML range is similar to that for 1 ML (i.e. “hollow and bridge” versus “set-hollow-sea-badge”), it seems unlikely
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to be so for the following reason. If we assume the “hollow and bridge” registry to be valid in the OS-O.67 ML range, the superstructures may be described as made of (11) rows of S atoms sitting on hollow and bridge sites within proportions going from zero bridge for one hollow to one bridge for one hollow. The (11) rows with S atoms in hollow sites are residual structural elements of the c(2 x 2) superstructure. They should retain the same registry when the superstructure develops the c(2 x 2) antiphase domains and consequently prevent the whole adlayer to “shift” its registry towards a unique “semi-hollow-semi-bridge” one. However, such a registry “shift” may be expected as soon as the c(2 X 2) domains disappear, i.e. at completion of the c(fi X 3&)R45” superstructure and for the superstructures of higher coverages, c(4 x 2) and p(2 x 1) (see figs. 4b, 4d and 4f). There is a third possibility regarding the adlayer registry that we did not consider in the calculations of our models. It simply assumes that the structure of the adlayer is determined by strong repulsive interactions between neighbouring S atoms. Structural models are then obtain for any superstructures by maximising the distances between adatoms with as reference, the concentration and the periodicity of the cell. This results then in the same models as presented in figs. 2a and 4e or fig. 4f for the c(2 X 2) and c(fi X 3& R45 o superstructures respectively. However, for the transition between these two superstructures, in our opinion such models are not valid for three reasons: (i) the shortest distance between S atoms in this coverage range is larger than 3.52 A which is rather large in order to have both the 2D configuration and the registry of the adlayer determined only by repulsive interactions between nearest neighbors (the van der Waals diameter of sulfur is 3.70 A); (ii) would it be so, the structural models obtained do not reproduce the systematic extinctions of the reciprocal superlattices; (iii) in order to account for the zero intensity FO spots, one would have to introduce point defects; this would shorten the S-S distances. We conclude by pointing out that: (i) the LEED patterns recorded for the phase transition between the c(2 x 2) and c(fi X 3&)R45 o superstructures for the W(lOO)-S system, are characteristic of the occurrence of point defects in the adlayer; (ii) we have modelled this disorder using statistical superstructures within the ,kinematic approximation and assuming two possibilities for the adlayer registry; (iii) the A+ variations recorded in this coverage range give support to a change of registry of the adlayer.
References (11 A. Bhattacharya, L.J. Clarke and L. Morales de la Garza, J. Chem. Sot. Faraday Trans. I, 77 (1981) 2223. [2] C. Park, H.M. Kramer and E. Bauer, Surface Sci. 116 (1982) 467. [3] L.J. Clarke, Surface Sci. 102 (1981) 331.
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[4] M. Salmeron, G.A. Somorjai
and R.R. Chianelli, Surface Sci. 127 (1983) 526. [5] V. Maurice, L. Peralta. Y. Berthier and J. Oudar, Surface Sci. 148 (1984) 623. [6] V. Maurice, M. Huber and J. Oudar, in: The Structure of Surfaces II. Vol. 11 of Springer Series in Surface Sciences, Eds. J.F. van der Veen and M.A. Van Hove (Springer, Berlin. 1988). [7] B. Marchon, P. Bernhardt, M.E. Bussel, G.A. Somorjai. M. Salmeron and W. Sickhaus. Phys. Rev. Letters 60 (1988) 1166.