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Challenges of structure determination of compound surfaces
Progress in Surface Science 64 (2000) 157±162 www.elsevier.com/locate/progsurf
Challenges of structure determination of compound surfaces M.A. Van Hove* Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA and Department of Physics, University of California at Davis, Davis, CA 95616, USA
Abstract Attention is drawn to challenges facing the structure determination of compound surfaces of growing complexity. Besides the questions of large unit cells and disorder, and of many independent atoms in the unit cells, one must address the determination of composition, compositional disorder and simultaneously coexisting structures. Of special concern is the issue of stability of complex and compound surfaces, and the resulting concerns about experimental surface preparation and reproducibility. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Surface structure; Surface structure determination; Compounds; Complex structures; Disorder; Polar ionic surfaces; Coexistence of structures; Low-energy electron diraction; X-ray diraction; Photoelectron diraction
1. Introduction
As surface science continues to move from ideal model surfaces to more practical and technologically relevant surfaces, it is increasingly faced with more complex materials. Compound materials vastly outnumber elemental materials in practical situations. The surface structure of such materials remains indispensable * Tel.: +1-510-486-6160; fax: +1-510-486-4995. E-mail address: [email protected] (M.A. Van Hove). 0079-6816/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 7 9 - 6 8 1 6 ( 0 0 ) 0 0 0 1 0 - 1
158
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
knowledge, but of course also becomes more dicult to determine, both from experiment and from theory. There is growing evidence that a particularly important class of compound materials, namely the polar faces of ionic materials, presents challenges that foreshadow mounting diculties as even more complex materials are studied in the future, for instance, environmental and biological materials. The underlying diculties seem to be due to the relative instability and variability of such surfaces, which diminishes surface reproducibility in the experiment, and also can cause the coexistence of dierent structures on the same surface. The evidence is now fragmentary and poorly documented: therefore, these comments are still somewhat speculative. The evidence stems mainly from observed diculties in preparing and reproducing surfaces, and is more often told orally than published in writing; it is also transparent in a few studies close to the author, such as the cases of Fe3O4(111) and Al2O3(0001). For example, the polar Fe3O4(111) surface is at present proposed to have three dierent structures, which are three dierent terminations of the bulk lattice: low-energy electron diraction (LEED) studies concluded that a termination in a single Fe layer ®ts the LEED data better [1,2]; a scanning tunneling microscope (STM) study with visual interpretation favors termination in a double Fe layer [3,4]; a photoelectron diraction (PD) analysis preferred termination in an oxygen layer [5]; a more recent reanalysis by LEED con®rmed the earlier LEED result [6]; lastly, theory favors the STM interpretation, while suggesting a possible role of hydrogen contamination [7]. With Al2O3(0001) recent LEED studies considered the coexistence of Al and O terminations [8,9]. A much earlier study by LEED of the surface SrTiO3(100) also found two coexisting bulklike terminations [10]: a termination in a mixed Sr±O plane and a termination in a mixed O±Ti±O plane. And in the case of alloys, at least one coexistence result was obtained even earlier for NiAl(111): a LEED study yielded equal amounts of Niand Al-terminated structures [11]. 2. Techniques Surface science in its ®rst decades focused on materials that generally possessed robust and unique surface structures [12]. This was highly desirable at the time when the techniques were being developed to study surfaces. Now that techniques are available in a form that gives reliable results for simple and somewhat less simple surfaces [13,14], the challenge is to apply them to the multitude of more complex materials that have not yet been studied in much detail. Currently, the most productive techniques for surface structure determination are LEED [15], PD [16] and x-ray diraction (XRD) [17], which in 1997 contributed, respectively, 71, 18 and 6% of detailed surface structure determinations [12]. For compounds, PD has the advantage of the capability to focus on the structure around a particular chemical element, or even around an atom with particular chemical shifts of its electronic levels. By contrast, LEED and XRD are relatively
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
159
less sensitive to chemical elements and quite insensitive to an atom's chemical state, or even to its ionic state. Nonetheless, it has been possible to evaluate layer-by-layer chemical composition with LEED when the elements involved have strongly diering scattering properties (i.e., when they have much dierent atomic numbers): this has been exhibited particularly for metallic alloys. The technique of chemical tensor LEED also gives access to such chemical information [18,19]. PD is also relatively more tolerant of disorder, due to the highly localized nature of the core levels frequently used as sources of photoelectrons. However, very few structure determinations have so far been performed with PD for disordered surfaces. The plane-wave diraction techniques (LEED, XRD) are sensitive to disorder, but cause scattering into diuse directions such that the diraction intensities are weak and dicult to measure; these intensities are also mixed up with scattering from undesired surface defects. Nonetheless, with XRD it is possible to obtain fractional site occupations, giving access to at least one type of disorder, random vacancies. 3. Solving complex structures Compounds frequently present complex surface structures to solve. The large two-dimensional unit cells oer a variety of atomic positions; and the number of symmetry-inequivalent atoms within the unit cell can also be large. This allows relatively many plausible structural models, each of which typically has many unknown structural parameters that need to be ®t to experiment. Thus, correspondingly larger experimental data sets are required to dierentiate between models and to determine the many parameters. So-called direct methods, which need no trial-and-error searches, have been explored for a number of years, but have not yet produced routine methods for solving complex structures. Electron-based holography, while exhibiting some successes, fails all too often; in any event, holography can only produce approximate structural information, which must be subsequently re®ned by trialand-error methods [16]. With XRD, the Patterson function and direct methods have long been used to solve bulk structures. Recently, such methods have started to be applied to surfaces as well, also in the context of transmission electron diraction [20,21]. The main advantage of these methods is the inherent kinematic or single-scattering nature of XRD, which is also paired with relatively minimal phase-shift eects: this allows higher accuracy and reliability. On the other hand, to make such methods work well requires a rather large experimental data set, and this is a challenge even with synchrotron radiation: measuring times can be days. So, even though these methods can in principle be applied to relatively complex structures, the experimental requirement is now the limiting factor. Trial-and-error methods remain dominant at present in surface structure determination. For instance, in the case of LEED most structures are now solved with the tensor LEED method, which can be eciently coupled with a steepestdescent local-optimization scheme to obtain detailed atomic coordinates [22,23].
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M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
Global search algorithms are also available or under development, such as simulated annealing and genetic algorithms [24], but are not yet routinely applied. While local optimization in LEED can be done well on workstations and PCs, the global search algorithms require supercomputers to explore many plausible models for complex structures. A particular challenge for all techniques is the case of coexisting surface structures. Clearly, any help is most welcome from other techniques (especially STM) that can identify the presence and relative sizes of dierent coexisting structures. If coexisting structures have distinct two-dimensional unit cells (i.e., dierent superlattices), then the situation is less problematic for plane-wave diraction techniques (LEED, XRD): the dierent structures produce dierent sets of diraction spots (re¯ections), which can be measured and analyzed independently. However, there always remains the possibility that coexisting structures have the same unit cell, in which case it is hard to extricate the individual contributions. One could imagine solving this extrication problem by varying the relative sizes of the dierent structures, but this appears not to have been done yet at surfaces. For point-source techniques (PD) the diraction patterns of coexisting structures overlap and are dicult to disentangle, unless it is possible to energetically separate the signals due to dierent core-level shifts. In any event, the mixing of intensities from coexisting structures reduces the ability of both direct and trial-and-error methods to eectively solve structures. The direct methods rely on treating intensities according to an idealized model (namely, single or kinematic scattering from an ideal single structural domain), which breaks down and produces arti®cial interference eects between inequivalent structures. Trial-and-error methods are faced with the task of optimizing the independent coexisting structures simultaneously. This means ®rst testing a variety of combinations of coexisting structures, which is a problem of rapidly growing proportions. A second issue is the growth in number of adjustable parameters. Every additional free parameter that becomes available necessarily improves the ®t to experiment, without necessarily implying a better structural solution. This requires a criterion to assess whether the additional parameters give rise only to arti®cial improvements in the ®t to experiment or to real improvements in the structural solution. Such a criterion has been developed for XRD in the form of the Hamilton test ratio [25]: it evaluates numerically whether the improved ®t (e.g., as measured by R-factors) appreciably exceeds that expected statistically from the increase in number of adjustable parameters. However, another test remains essential: the resulting structures must be physically meaningful, i.e., must exhibit reasonable bond lengths, etc. 4. Surface stability, preparation and reproducibility Surfaces of complex materials inherently have more structural options than simple surfaces, for the same reasons that the phase diagrams of complex
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
161
materials are more complicated than those of simple materials. An obvious source of variability is chemical composition, which is well known to vary at the surfaces of some materials through surface segregation, particularly for metallic alloys. This means in particular that there may exist several structures with total energies that are relatively close together. From the point of view of the experiment, there is under these conditions a higher likelihood that dierent structures will be produced with slightly dierent surface preparations, and that dierent structures can coexist for thermal and kinetic reasons. And from the point of view of structure determination, more plausible structures must be explored, including coexisting structures. The case of polar ionic materials is of special interest in this regard. Many such surfaces are intrinsically unstable: those which terminate in an alternation of bulk atomic layers with positive and negative charges and net dipole moment can be shown to lead to an energetic divergence [2,26], which can be resolved through surface vacancies or adatoms or more severe reconstructions. These eects, together with the possibility of variations in stoichiometry at the surface (and contamination with ubiquitous atoms like O and H), enrich the possibilities for surface structures and thus further complicate structure determination. This also puts a larger burden on the experimental surface preparation and characterization.
5. Conclusions The evidence is growing that complex compound surfaces present additional diculties that have to be overcome to solve their structures. Experimental preparation and reproducibility are a major concern, because structures can coexist for thermal or kinetic reasons. For the structure analysis, besides the additional number of plausible structural models to be tested and the greater number of parameters to be determined, it is often necessary to investigate surface segregation and the possible coexistence of dierent surface structures.
Acknowledgements This work was supported in part by the Director, Oce of Energy Research, Oce of Basic Energy Sciences, Materials Sciences Division of the US Department of Energy under Contract No. DE-AC03-76SF00098.
References [1] W. Weiss, A. Barbieri, M.A. Van Hove, G.A. Somorjai, Phys. Rev. Lett. 71 (1993) 1848. [2] A. Barbieri, W. Weiss, M.A. Van Hove, G.A. Somorjai, Surf. Sci. 302 (1994) 259. [3] N.G. Condon, P.W. Murray, F.M. Leibsle, G. Thornton, A.R. Lennie, D.G. Vaughn, Surf. Sci. 310 (1994) L609.
162
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
[4] N.G. Condon, F.M. Leibsle, T. Parker, A.R. Lennie, D.G. Vaughn, G. Thornton, Phys. Rev. B 55 (1997) 15,885. [5] Y.J. Kim, C. Westphal, R.X. Ynzunza, Z. Wang, H.C. Galloway, M. Salmeron, M.A. Van Hove, C.S. Fadley, Surf. Sci. 416 (1998) 68. [6] M. Ritter, W. Weiss, Surf. Sci. 432 (1999) 81. [7] J. Ahdjoudj, C. Martinsky, C. Minot, M.A. Van Hove, Surf. Sci. 443 (1999) 133. [8] J. Toofan, P.R. Watson, Surf. Sci. 401 (1998) 162. [9] C. Walters, K. McCarty, E. Soares, M.A. Van Hove, to be published. [10] N. Bickel, G. Schmidt, K. Heinz, K. MuÈller, Phys. Rev. Lett. 62 (1989) 2009. [11] J.R. Noonan, H.L. Davis, Phys. Rev. Lett. 59 (1987) 1714. [12] P.R. Watson, M.A. Van Hove, K. Hermann, NIST Surface Structure Database Ver. 3.0, NIST Standard Reference Data Program, Gaithersburg, MD, 1999. [13] M.A. Van Hove, Surface Structural Determination: Diraction Methods, in: J.H. Moore, N.D. Spencer (Eds.), Encyclopedia of Chemical Physics and Physical Chemistry, IOP Publishing, London, to appear 1999. [14] M.A. Van Hove, Surf. Interface Anal. 28 (1999) 36. [15] M.A. Van Hove, W.H. Weinberg, C.-M. Chan, in: Low-Energy Electron Diraction: Experiment, Theory and Structural Determination, Springer Series in Surface Sciences, Vol. 6, SpringerVerlag, Berlin, 1986. [16] C.S. Fadley, M.A. Van Hove, Z. Hussain, A.P. Kaduwela, R.E. Couch, Y.J. Kim, P.M. Len, J. Palomares, S. Ryce, S. Ruebush, E.D. Tober, Z. Wang, R.X. Ynzunza, H. Daimon, H. Galloway, M.B. Salmeron, W. Schattke, Surf. Rev. Lett. 4 (1997) 421. [17] R. Feidenhans'l, Surf. Sci. Rep. 10 (1989) 105. [18] K. Heinz, Rep. Prog. Phys. 58 (1995) 637. [19] K. Heinz, R. DoÈll, M. Kottcke, Surf. Rev. Lett. 3 (1996) 1651. [20] L.D. Marks, E. Landree, Acta Crys. A54 (1998) 296. [21] W. Sinkler, E. Bengu, L.D. Marks, Acta Crys. A54 (1998) 591. [22] M.A. Van Hove, W. Moritz, H. Over, P.J. Rous, A. Wander, A. Barbieri, N. Materer, U. Starke, G.A. Somorjai, Surf. Sci. Rep. 19 (1993) 191. [23] M.A. Van Hove, Surf. Rev. Lett. 4 (1997) 479. [24] R. DoÈll, M.A. Van Hove, Surf. Sci. 355 (1996) L393. [25] W.C. Hamilton, Acta Crys. 18 (1965) 502. [26] P.W. Tasker, J. Phys. C 12 (1979) 4977.
Challenges of structure determination of compound surfaces M.A. Van Hove* Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA and Department of Physics, University of California at Davis, Davis, CA 95616, USA
Abstract Attention is drawn to challenges facing the structure determination of compound surfaces of growing complexity. Besides the questions of large unit cells and disorder, and of many independent atoms in the unit cells, one must address the determination of composition, compositional disorder and simultaneously coexisting structures. Of special concern is the issue of stability of complex and compound surfaces, and the resulting concerns about experimental surface preparation and reproducibility. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Surface structure; Surface structure determination; Compounds; Complex structures; Disorder; Polar ionic surfaces; Coexistence of structures; Low-energy electron diraction; X-ray diraction; Photoelectron diraction
1. Introduction
As surface science continues to move from ideal model surfaces to more practical and technologically relevant surfaces, it is increasingly faced with more complex materials. Compound materials vastly outnumber elemental materials in practical situations. The surface structure of such materials remains indispensable * Tel.: +1-510-486-6160; fax: +1-510-486-4995. E-mail address: [email protected] (M.A. Van Hove). 0079-6816/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 7 9 - 6 8 1 6 ( 0 0 ) 0 0 0 1 0 - 1
158
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
knowledge, but of course also becomes more dicult to determine, both from experiment and from theory. There is growing evidence that a particularly important class of compound materials, namely the polar faces of ionic materials, presents challenges that foreshadow mounting diculties as even more complex materials are studied in the future, for instance, environmental and biological materials. The underlying diculties seem to be due to the relative instability and variability of such surfaces, which diminishes surface reproducibility in the experiment, and also can cause the coexistence of dierent structures on the same surface. The evidence is now fragmentary and poorly documented: therefore, these comments are still somewhat speculative. The evidence stems mainly from observed diculties in preparing and reproducing surfaces, and is more often told orally than published in writing; it is also transparent in a few studies close to the author, such as the cases of Fe3O4(111) and Al2O3(0001). For example, the polar Fe3O4(111) surface is at present proposed to have three dierent structures, which are three dierent terminations of the bulk lattice: low-energy electron diraction (LEED) studies concluded that a termination in a single Fe layer ®ts the LEED data better [1,2]; a scanning tunneling microscope (STM) study with visual interpretation favors termination in a double Fe layer [3,4]; a photoelectron diraction (PD) analysis preferred termination in an oxygen layer [5]; a more recent reanalysis by LEED con®rmed the earlier LEED result [6]; lastly, theory favors the STM interpretation, while suggesting a possible role of hydrogen contamination [7]. With Al2O3(0001) recent LEED studies considered the coexistence of Al and O terminations [8,9]. A much earlier study by LEED of the surface SrTiO3(100) also found two coexisting bulklike terminations [10]: a termination in a mixed Sr±O plane and a termination in a mixed O±Ti±O plane. And in the case of alloys, at least one coexistence result was obtained even earlier for NiAl(111): a LEED study yielded equal amounts of Niand Al-terminated structures [11]. 2. Techniques Surface science in its ®rst decades focused on materials that generally possessed robust and unique surface structures [12]. This was highly desirable at the time when the techniques were being developed to study surfaces. Now that techniques are available in a form that gives reliable results for simple and somewhat less simple surfaces [13,14], the challenge is to apply them to the multitude of more complex materials that have not yet been studied in much detail. Currently, the most productive techniques for surface structure determination are LEED [15], PD [16] and x-ray diraction (XRD) [17], which in 1997 contributed, respectively, 71, 18 and 6% of detailed surface structure determinations [12]. For compounds, PD has the advantage of the capability to focus on the structure around a particular chemical element, or even around an atom with particular chemical shifts of its electronic levels. By contrast, LEED and XRD are relatively
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
159
less sensitive to chemical elements and quite insensitive to an atom's chemical state, or even to its ionic state. Nonetheless, it has been possible to evaluate layer-by-layer chemical composition with LEED when the elements involved have strongly diering scattering properties (i.e., when they have much dierent atomic numbers): this has been exhibited particularly for metallic alloys. The technique of chemical tensor LEED also gives access to such chemical information [18,19]. PD is also relatively more tolerant of disorder, due to the highly localized nature of the core levels frequently used as sources of photoelectrons. However, very few structure determinations have so far been performed with PD for disordered surfaces. The plane-wave diraction techniques (LEED, XRD) are sensitive to disorder, but cause scattering into diuse directions such that the diraction intensities are weak and dicult to measure; these intensities are also mixed up with scattering from undesired surface defects. Nonetheless, with XRD it is possible to obtain fractional site occupations, giving access to at least one type of disorder, random vacancies. 3. Solving complex structures Compounds frequently present complex surface structures to solve. The large two-dimensional unit cells oer a variety of atomic positions; and the number of symmetry-inequivalent atoms within the unit cell can also be large. This allows relatively many plausible structural models, each of which typically has many unknown structural parameters that need to be ®t to experiment. Thus, correspondingly larger experimental data sets are required to dierentiate between models and to determine the many parameters. So-called direct methods, which need no trial-and-error searches, have been explored for a number of years, but have not yet produced routine methods for solving complex structures. Electron-based holography, while exhibiting some successes, fails all too often; in any event, holography can only produce approximate structural information, which must be subsequently re®ned by trialand-error methods [16]. With XRD, the Patterson function and direct methods have long been used to solve bulk structures. Recently, such methods have started to be applied to surfaces as well, also in the context of transmission electron diraction [20,21]. The main advantage of these methods is the inherent kinematic or single-scattering nature of XRD, which is also paired with relatively minimal phase-shift eects: this allows higher accuracy and reliability. On the other hand, to make such methods work well requires a rather large experimental data set, and this is a challenge even with synchrotron radiation: measuring times can be days. So, even though these methods can in principle be applied to relatively complex structures, the experimental requirement is now the limiting factor. Trial-and-error methods remain dominant at present in surface structure determination. For instance, in the case of LEED most structures are now solved with the tensor LEED method, which can be eciently coupled with a steepestdescent local-optimization scheme to obtain detailed atomic coordinates [22,23].
160
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
Global search algorithms are also available or under development, such as simulated annealing and genetic algorithms [24], but are not yet routinely applied. While local optimization in LEED can be done well on workstations and PCs, the global search algorithms require supercomputers to explore many plausible models for complex structures. A particular challenge for all techniques is the case of coexisting surface structures. Clearly, any help is most welcome from other techniques (especially STM) that can identify the presence and relative sizes of dierent coexisting structures. If coexisting structures have distinct two-dimensional unit cells (i.e., dierent superlattices), then the situation is less problematic for plane-wave diraction techniques (LEED, XRD): the dierent structures produce dierent sets of diraction spots (re¯ections), which can be measured and analyzed independently. However, there always remains the possibility that coexisting structures have the same unit cell, in which case it is hard to extricate the individual contributions. One could imagine solving this extrication problem by varying the relative sizes of the dierent structures, but this appears not to have been done yet at surfaces. For point-source techniques (PD) the diraction patterns of coexisting structures overlap and are dicult to disentangle, unless it is possible to energetically separate the signals due to dierent core-level shifts. In any event, the mixing of intensities from coexisting structures reduces the ability of both direct and trial-and-error methods to eectively solve structures. The direct methods rely on treating intensities according to an idealized model (namely, single or kinematic scattering from an ideal single structural domain), which breaks down and produces arti®cial interference eects between inequivalent structures. Trial-and-error methods are faced with the task of optimizing the independent coexisting structures simultaneously. This means ®rst testing a variety of combinations of coexisting structures, which is a problem of rapidly growing proportions. A second issue is the growth in number of adjustable parameters. Every additional free parameter that becomes available necessarily improves the ®t to experiment, without necessarily implying a better structural solution. This requires a criterion to assess whether the additional parameters give rise only to arti®cial improvements in the ®t to experiment or to real improvements in the structural solution. Such a criterion has been developed for XRD in the form of the Hamilton test ratio [25]: it evaluates numerically whether the improved ®t (e.g., as measured by R-factors) appreciably exceeds that expected statistically from the increase in number of adjustable parameters. However, another test remains essential: the resulting structures must be physically meaningful, i.e., must exhibit reasonable bond lengths, etc. 4. Surface stability, preparation and reproducibility Surfaces of complex materials inherently have more structural options than simple surfaces, for the same reasons that the phase diagrams of complex
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
161
materials are more complicated than those of simple materials. An obvious source of variability is chemical composition, which is well known to vary at the surfaces of some materials through surface segregation, particularly for metallic alloys. This means in particular that there may exist several structures with total energies that are relatively close together. From the point of view of the experiment, there is under these conditions a higher likelihood that dierent structures will be produced with slightly dierent surface preparations, and that dierent structures can coexist for thermal and kinetic reasons. And from the point of view of structure determination, more plausible structures must be explored, including coexisting structures. The case of polar ionic materials is of special interest in this regard. Many such surfaces are intrinsically unstable: those which terminate in an alternation of bulk atomic layers with positive and negative charges and net dipole moment can be shown to lead to an energetic divergence [2,26], which can be resolved through surface vacancies or adatoms or more severe reconstructions. These eects, together with the possibility of variations in stoichiometry at the surface (and contamination with ubiquitous atoms like O and H), enrich the possibilities for surface structures and thus further complicate structure determination. This also puts a larger burden on the experimental surface preparation and characterization.
5. Conclusions The evidence is growing that complex compound surfaces present additional diculties that have to be overcome to solve their structures. Experimental preparation and reproducibility are a major concern, because structures can coexist for thermal or kinetic reasons. For the structure analysis, besides the additional number of plausible structural models to be tested and the greater number of parameters to be determined, it is often necessary to investigate surface segregation and the possible coexistence of dierent surface structures.
Acknowledgements This work was supported in part by the Director, Oce of Energy Research, Oce of Basic Energy Sciences, Materials Sciences Division of the US Department of Energy under Contract No. DE-AC03-76SF00098.
References [1] W. Weiss, A. Barbieri, M.A. Van Hove, G.A. Somorjai, Phys. Rev. Lett. 71 (1993) 1848. [2] A. Barbieri, W. Weiss, M.A. Van Hove, G.A. Somorjai, Surf. Sci. 302 (1994) 259. [3] N.G. Condon, P.W. Murray, F.M. Leibsle, G. Thornton, A.R. Lennie, D.G. Vaughn, Surf. Sci. 310 (1994) L609.
162
M.A. Van Hove / Progress in Surface Science 64 (2000) 157±162
[4] N.G. Condon, F.M. Leibsle, T. Parker, A.R. Lennie, D.G. Vaughn, G. Thornton, Phys. Rev. B 55 (1997) 15,885. [5] Y.J. Kim, C. Westphal, R.X. Ynzunza, Z. Wang, H.C. Galloway, M. Salmeron, M.A. Van Hove, C.S. Fadley, Surf. Sci. 416 (1998) 68. [6] M. Ritter, W. Weiss, Surf. Sci. 432 (1999) 81. [7] J. Ahdjoudj, C. Martinsky, C. Minot, M.A. Van Hove, Surf. Sci. 443 (1999) 133. [8] J. Toofan, P.R. Watson, Surf. Sci. 401 (1998) 162. [9] C. Walters, K. McCarty, E. Soares, M.A. Van Hove, to be published. [10] N. Bickel, G. Schmidt, K. Heinz, K. MuÈller, Phys. Rev. Lett. 62 (1989) 2009. [11] J.R. Noonan, H.L. Davis, Phys. Rev. Lett. 59 (1987) 1714. [12] P.R. Watson, M.A. Van Hove, K. Hermann, NIST Surface Structure Database Ver. 3.0, NIST Standard Reference Data Program, Gaithersburg, MD, 1999. [13] M.A. Van Hove, Surface Structural Determination: Diraction Methods, in: J.H. Moore, N.D. Spencer (Eds.), Encyclopedia of Chemical Physics and Physical Chemistry, IOP Publishing, London, to appear 1999. [14] M.A. Van Hove, Surf. Interface Anal. 28 (1999) 36. [15] M.A. Van Hove, W.H. Weinberg, C.-M. Chan, in: Low-Energy Electron Diraction: Experiment, Theory and Structural Determination, Springer Series in Surface Sciences, Vol. 6, SpringerVerlag, Berlin, 1986. [16] C.S. Fadley, M.A. Van Hove, Z. Hussain, A.P. Kaduwela, R.E. Couch, Y.J. Kim, P.M. Len, J. Palomares, S. Ryce, S. Ruebush, E.D. Tober, Z. Wang, R.X. Ynzunza, H. Daimon, H. Galloway, M.B. Salmeron, W. Schattke, Surf. Rev. Lett. 4 (1997) 421. [17] R. Feidenhans'l, Surf. Sci. Rep. 10 (1989) 105. [18] K. Heinz, Rep. Prog. Phys. 58 (1995) 637. [19] K. Heinz, R. DoÈll, M. Kottcke, Surf. Rev. Lett. 3 (1996) 1651. [20] L.D. Marks, E. Landree, Acta Crys. A54 (1998) 296. [21] W. Sinkler, E. Bengu, L.D. Marks, Acta Crys. A54 (1998) 591. [22] M.A. Van Hove, W. Moritz, H. Over, P.J. Rous, A. Wander, A. Barbieri, N. Materer, U. Starke, G.A. Somorjai, Surf. Sci. Rep. 19 (1993) 191. [23] M.A. Van Hove, Surf. Rev. Lett. 4 (1997) 479. [24] R. DoÈll, M.A. Van Hove, Surf. Sci. 355 (1996) L393. [25] W.C. Hamilton, Acta Crys. 18 (1965) 502. [26] P.W. Tasker, J. Phys. C 12 (1979) 4977.