Handbook of Materials Modeling pp 149-194 | Cite as

*AB Initio* Atomistic Thermodynamics and Statistical Mechanics of Surface Properties and Functions

## Abstract

Previous and present “academic” research aiming at atomic scale understanding is mainly concerned with the study of individual molecular processes possibly underlying materials science applications. In investigations of crystal growth one would, for example, study the diffusion of adsorbed atoms at surfaces, and in the field of heterogeneous catalysis it is the reaction path of adsorbed species that is analyzed. Appealing properties of an individual process are then frequently discussed in terms of their direct importance for the envisioned material function, or reciprocally, the function of materials is often believed to be understandable by essentially one prominent elementary process only. What is often overlooked in this approach is that in macroscopic systems of technological relevance typically a large number of distinct atomic scale processes take place. Which of them are decisive for observable system properties and functions is then not only determined by the detailed individual properties of each process alone, but in many, if not most cases, also the interplay of all processes, i.e., how they act together, plays a crucial role. For a *predictive materials science modeling with microscopic understanding*, a description that treats the statistical interplay of a large number of microscopically well-described elementary processes must therefore be applied. Modern electronic structure theory methods such as density-functional theory (DFT) have become a standard tool for the accurate description of the individual atomic and molecular processes.

## Keywords

Monte Carlo Statistical Mechanic Potential Energy Surface Elementary Process Bulk Oxide## Preview

Unable to display preview. Download preview PDF.

## References

- [1]P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,”
*Phys. Rev. B*, 136, 864, 1964.CrossRefMathSciNetADSGoogle Scholar - [2]W. Kohn and L. Sham, “Self consistent equations including exchange and correlation effects,”
*Phys. Rev. A*, 140, 1133, 1965.CrossRefMathSciNetADSGoogle Scholar - [3]R.G. Parr and W. Yang,
*Density Functional Theory of Atoms and Molecules*, Oxford University Press, New York, 1989.Google Scholar - [4]R.M. Dreizler and E.K.U. Gross,
*Density Functional Theory*, Springer, Berlin, 1990.MATHGoogle Scholar - [5]M.P. Allen and D.J. Tildesley,
*Computer Simulation of Liquids*, Oxford University Press, Oxford, 1997.Google Scholar - [6]D. Frenkel and B. Smit,
*Understanding Molecular Simulation*, 2nd edn., Academic Press, San Diego, 2002.Google Scholar - [7]R. Car and M. Parrinello, “Unified approach for molecular dynamics and density-functional theory,”
*Phys. Rev. Lett.*, 55, 2471, 1985.CrossRefADSGoogle Scholar - [8]M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, and J.D. Joannopoulos, “Iterative minimization techniques for
*ab initio*total energy calculations: molecular dynamics and conjugate gradients,”*Rev. Mod. Phys.*, 64, 1045, 1992.CrossRefADSGoogle Scholar - [9]G. Galli and A. Pasquarello, “First-principle molecular dynamics,” In: M.P. Allen, and DJ. Tildesley (eds.),
*Computer Simulations in Chemical Physics*, Kluwer, Dordrecht, 1993.Google Scholar - [10]A. Gross, “Reactions at surfaces studied by
*ab initio*dynamics calculations,”*Surf. Sci. Rep.*, 32, 293, 1998.ADSGoogle Scholar - [11]G.J. Kroes, “Six-dimensional quantum dynamics of dissociative chemisorption of H
_{2}on metal surfaces,”*Prog. Surf. Sci.*, 60, 1, 1999.CrossRefADSGoogle Scholar - [12]A.F. Voter, F. Montalenti, and T.C. Germann, “Extending the time scale in atomistic simulation of materials,”
*Annu. Rev. Mater. Res.*, 32, 321, 2002.CrossRefGoogle Scholar - [13]A. Zangwill,
*Physics at Surfaces*, Cambridge University Press, Cambridge, 1988.Google Scholar - [14]R.I. Masel,
*Principles of Adsorption and Reaction on Solid Surfaces*, Wiley, New York, 1996.Google Scholar - [15]C. Stampfl, M.V. Ganduglia-Pirovano, K. Reuter, and M. Scheffler, “Catalysis and corrosion: the theoretical surface-science context,”
*Surf. Sci.*, 500, 368, 2002.CrossRefADSGoogle Scholar - [16]M. Scheffler and C. Stampfl, “Theory of adsorption on metal substrates,” In: K. Horn and M. Scheffler (eds.),
*Handbook of Surface Science*, vol. 2: Electronic Structure, Elsevier, Amsterdam, 2000.Google Scholar - [17]G.R. Darling and S. Holloway, “The dissociation of diatomic molecules at surfaces,”
*Rep. Prog. Phys.*, 58, 1595, 1995.CrossRefADSGoogle Scholar - [18]E. Kaxiras, Y. Bar-Yam, J.D. Joannopoulos, and K.C. Pandey, “
*Ab initio*theory of polar semiconductor surfaces. I. Methodology and the (22) reconstructions of GaAs(111),”*Phys. Rev. B*, 35, 9625, 1987.CrossRefADSGoogle Scholar - [19]M. Scheffler, “Thermodynamic aspects of bulk and surface defects — first-principles calculations,” In: J. Koukal (ed.),
*Physics of Solid Surfaces — 1987*, Elsevier, Amsterdam, 1988.Google Scholar - [20]M. Scheffler and J. Dabrowski, “Parameter-free calculations of total energies, inter-atomic forces, and vibrational entropies of defects in semiconductors,”
*Phil. Mag. A*, 58, 107, 1988.CrossRefADSGoogle Scholar - [21]G.-X. Qian, R.M. Martin, and D.J. Chadi, “First-principles study of the atomic reconstructions and energies of Ga-and As-stabilized GaAs(100) surfaces,”
*Phys. Rev. B*, 38, 7649, 1988.CrossRefADSGoogle Scholar - [22]X.-G. Wang, W. Weiss, Sh.K. Shaikhutdinov, M. Ritter, M. Petersen, F. Wagner, R. Schlögl, and M. Scheffler, “The hematite (alpha-Fe
_{2}O_{3})(0001) surface: evidence for domains of distinct chemistry,”*Phys. Rev. Lett.*, 81, 1038, 1998.CrossRefADSGoogle Scholar - [23]X.-G. Wang, A. Chaka, and M. Scheffler, “Effect of the environment on Al
_{2}O_{3}(0001) surface structures,”*Phys. Rev. Lett.*, 84, 3650, 2000.CrossRefADSGoogle Scholar - [24]K. Reuter and M. Scheffler, “Composition, structure, and stability of RuO
_{2}(110) as a function of oxygen pressure,”*Phys. Rev. B*, 65, 035406, 2002.CrossRefADSGoogle Scholar - [25]K. Reuter and M. Scheffler, “First-principles atomistic thermodynamics for oxidation catalysis: surface phase diagrams and catalytically interesting regions,”
*Phys. Rev. Lett.*, 90, 046103, 2003.CrossRefADSGoogle Scholar - [26]K. Reuter and M. Scheffler, “Composition and structure of the RuO
_{2}(1 10) surface in an O_{2}and CO environment: implications for the catalytic formation of CO_{2},”*Phys. Rev. B*, 68, 045407, 2003.CrossRefADSGoogle Scholar - [27]Z. Lodzianan and J.K. Nørskov, “Stability of the hydroxylated (0001) surface of Al
_{2}O_{3},”*J. Chem. Phys.*, 118, 11179, 2003.CrossRefADSGoogle Scholar - [28]K. Reuter and M. Scheffler, “Oxide formation at the surface of late 4d transition metals: insights from first-principles atomistic thermodynamics,”
*Appl. Phys. A*, 78, 793, 2004.CrossRefADSGoogle Scholar - [29]K. Reuter “Nanometer and sub-nanometer thin oxide films at surfaces of late transition metals,” In: U. Heiz, H. Hakkinen, and U. Landman (eds.),
*Nanocatalysis: Principles, Methods, Case Studies*, 2005.Google Scholar - [30]G. Ertl, H. Knözinger, and J. Weitkamp (eds.),
*Handbook of Heterogeneous Catalysis*, Wiley, New York, 1997.Google Scholar - [31]D.P. Woodruff and T.A. Delchar,
*Modern Techniques of Surface Science*, 2nd edn., Cambridge University Press, Cambridge, 1994.CrossRefGoogle Scholar - [32]W.-X. Li, C. Stampfl, and M. Scheffler, “Insights into the function of silver as an oxidation catalyst by ab initio atomistic thermodynamics,”
*Phys. Rev. B*, 68, 16541, 2003.Google Scholar - [33]W.-X. Li, C. Stampfl, and M. Scheffler, “Why is a noble metal catalytically active? the role of the O-Ag interaction in the function of silver as an oxidation catalyst,”
*Phys. Rev. Lett.*, 90, 256102, 2003.CrossRefADSGoogle Scholar - [34]D.A. Mc Quarrie,
*Statistical Mechanics*, Harper and Row, New York, 1976.Google Scholar - [35]D.R. Stull and H. Prophet,
*JANAF Thermochemical Tables*, 2nd edn., U.S. National Bureau of Standards, Washington, D.C., 1971.Google Scholar - [36]E. Lundgren, J. Gustafson, A. Mikkelsen, J.N. Andersen, A. Stierle, H. Dosch, M. Todorova, J. Rogal, K. Reuter, and M. Scheffler, “Kinetic hindrance during the initial oxidation of Pd(100) at ambient pressures,”
*Phys. Rev. Lett.*, 92, 046101, 2004.CrossRefADSGoogle Scholar - [37]M. Todorova, E. Lundgren, V. Blum, A. Mikkelsen, S. Gray, J. Gustafson, M. Borg, J. Rogal, K. Reuter, J.N. Andersen, and M. Scheffler, “The Pd(100)-(√5 x √5) R27°-O surface oxide revisited,”
*Surf. Sci.*, 541, 101, 2003.CrossRefADSGoogle Scholar - [38]E. Lundgren, G. Kresse, C. Klein, M. Borg, J.N. Andersen, M. De Santis, Y Gauthier, C. Konvicka, M. Schmid, and P. Varga, “Two-dimensional oxide on Pd(111),”
*Phys. Rev. Lett.*, 88, 246103, 2002.CrossRefADSGoogle Scholar - [39]A. Michaelides, M.L. Bocquet, P. Sautet, A. Alavi, and D.A. King, “Structures and thermodynamic phase transitions for oxygen and silver oxide phases on Ag(111),”
*Chem. Phys. Lett.*, 367, 344, 2003.CrossRefADSGoogle Scholar - [40]C.M. Weinert and M. Scheffler, In: H.J. von Bardeleben (ed.),
*Defects in Semiconductors, Mat. Sci. Forum*, 10–12, 25, 1986.Google Scholar - [41]S.-H. Lee, W. Moritz, and M. Scheffler, “GaAs(00l) under conditions of low as pressure: edvidence for a novel surface geometry,”
*Phys. Rev. Lett.*, 85, 3890, 2000.CrossRefADSGoogle Scholar - [42]C.B. Duke, “Semiconductor surface reconstruction: the structural chemistry of twodimensional surface compounds,”
*Chem. Rev.*, 96, 1237, 1996.CrossRefGoogle Scholar - [43]T. Engel and G. Ertl, “Oxidation of carbon monoxide,” In: D.A. King and D.P. Woodruff (eds.),
*The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis*, Elsevier, Amsterdam, 1982.Google Scholar - [44]B.L.M. Hendriksen, S.C. Bobaru, and J.W.M. Frenken, “Oscillatory CO oxidation on Pd(100) studied with
*in situ*scanning tunnelling microscopy,”*Surf. Sci.*, 552, 229, 2003.CrossRefADSGoogle Scholar - [45]H. Over and M. Muhler, “Catalytic CO oxidation over ruthenium — bridging the pressure gap,”
*Prog. Surf. Sci.*, 72, 3, 2003.CrossRefADSGoogle Scholar - [46]G. Ertl, “Heterogeneous catalysis on the atomic scale,”
*J. Mol. Catal. A*, 182, 5, 2002.CrossRefGoogle Scholar - [47]D.P. Landau and K. Binder,
*A Guide to Monte Carlo Simulations in Statistical Physics*, Cambridge University Press, Cambridge, 2002.Google Scholar - [48]D. de Fontaine, In: P.E.A. Turchi and A. Gonis (eds.),
*Statics and Dynamics of Alloy Phase Transformations*, NATO ASI Series, Plenum Press, New York, 1994.Google Scholar - [49]J.M. Sanchez, F. Ducastelle, and D. Gratias, “Generalized cluster description of multicomponent systems,”
*Physica A*, 128, 334, 1984.CrossRefMathSciNetADSGoogle Scholar - [50]A. Zunger, “First principles statistical mechanics of semiconductor alloys and intermetallic compounds,” In: P.E.A. Turchi and A. Gonis (eds.),
*Statics and Dynamics of Alloy Phase Transformations*, NATO ASI Series, Plenum Press, New York, 1994.Google Scholar - [51]P. Piercy, K. De’Bell, and H. Pfniir, “Phase diagram and critical behavior of the adsorption system O/Ru(001): comparison with lattice-gas models,”
*Phys. Rev. B*, 45, 1869, 1992.CrossRefADSGoogle Scholar - [52]G.M. Xiong, C. Schwennicke, H. Pfniir, and H.-U. Everts, “Phase diagram and phase transitions of the adsorbate system S/Ru(0001): a monte carlo study of a lattice gas model,”
*Z Phys. B*, 104, 529, 1997.CrossRefADSGoogle Scholar - [53]V.P. Zhdanov and B. Kasemo, “Simulation of oxygen desorption from Pt(l 11),”
*Surf. Sci.*, 415, 403, 1998.CrossRefADSGoogle Scholar - [54]S.-J. Koh and G. Ehrlich, “Pair-and many-atom interactions in the cohesion of surface clusters: Pd
_{x}and Ir_{x}on W(l 10),”*Phys. Rev. B*, 60, 5981, 1999.CrossRefADSGoogle Scholar - [55]L. Osterlund, M.Ø. Pedersen, I. Stensgaard, E. Lægsgaard, and F. Besenbacher, “Quantitative determination of adsorbate-adsorbate interactions,”
*Phys. Rev. Lett.*, 83, 4812, 1999.CrossRefADSGoogle Scholar - [56]S.H. Payne, H.J. Kreuzer, W. Frie, L. Hammer, and K. Heinz, “Adsorption and desorption of hydrogen on Rh(311) and comparison with other Rh surfaces,”
*Surf. Sci.*, 421, 279, 1999.CrossRefADSGoogle Scholar - [57]C. Stampfl, H.J. Kreuzer, S.H. Payne, H. Pfniir, and M. Scheffler, “First-principles theory of surface thermodynamics and kinetics,”
*Phys. Rev. Lett.*, 83, 2993, 1999.CrossRefADSGoogle Scholar - [58]C. Stampfl, HJ. Kreuzer, S.H. Payne, and M. Scheffler, “Challenges in predictive calculations of processes at surfaces: surface thermodynamics and catalytic reactions,”
*Appl. Phys. A*, 69, 471, 1999.CrossRefADSGoogle Scholar - [59]J. Shao, “Linear model selection by cross-validation,”
*J. Amer. Statist. Assoc.*, 88, 486, 1993.MATHCrossRefMathSciNetGoogle Scholar - [60]P. Zhang, “Model selection via multifold cross-validation,”
*Ann. statist.*, 21, 299, 1993.CrossRefMathSciNetGoogle Scholar - [61]A. van de Walle and G. Ceder, “Automating first-principles phase diagram calculations,”
*J. Phase Equilibria*, 23, 348, 2002.CrossRefGoogle Scholar - [62]N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,”
*J. Chem. Phys.*, 21, 1087, 1976.CrossRefADSGoogle Scholar - [63]J.-S. McEwen, S.H. Payne, and C. Stampfl, “Phase diagram of O/Ru(0001) from first principles,”
*Chem. Phys. Lett.*, 361, 317, 2002.CrossRefADSGoogle Scholar - [64]H.J. Kreuzer and S.H. Payne, “Theoretical approaches to the kinetics of adsorption, desorption and reactions at surfaces,” In: M. Borowko (eds.),
*Computational Methods in Surface and Colloid*, Marcel Dekker, New York, 2000.Google Scholar - [65]C. Stampfl and M. Scheffler, “Theory of alkali metal adsorption on close-packed metal surfaces,”
*Surf. Rev. Lett.*, 2, 317, 1995.CrossRefGoogle Scholar - [66]D.L. Actams, “New phenomena in the adsorption of alkali metals on A1 surfaces,”
*Appl. Phys. A*, 62, 123, 1996.CrossRefADSGoogle Scholar - [67]M. Borg, C. Stampfl, A. Mikkelsen, J. Gustafson, E. Lundgren, M. Scheffler, and J.N. Andersen, “Density of configurational states from first-principles: the phase diagram of Al-Na surface alloys,”
*Chem. Phys. Chem.*(in press), 2005.Google Scholar - [68]F. Wang and D.P. Landau, “Efficient, multiple-range random walk algorithm to calculate the density of states,”
*Phys. Rev. Lett.*, 86, 2050, 2001.CrossRefADSGoogle Scholar - [69]H.C. Kang and W.H. Weinberg, “Modeling the kinetics of heterogeneous catalysis,”
*Chem. Rev.*, 95, 667, 1995.CrossRefGoogle Scholar - [70]A.B. Bortz, M.H. Kalos, and J.L. Lebowitz, “New algorithm for Monte Carlo simulation of ising spin systems,”
*J. Comp. Phys.*, 17, 10, 1975.CrossRefADSGoogle Scholar - [71]D.T. Gillespie, “General method for numerically simulating stochastic time evolution of coupled chemical reactions,”
*J. Comp. Phys.*, 22, 403, 1976.CrossRefMathSciNetADSGoogle Scholar - [72]A.R Voter, “Classically exact overlayer dynamics: diffusion of rhodium clusters on Rh(100),”
*Phys. Rev. B*, 34, 6819, 1986.CrossRefADSGoogle Scholar - [73]H.C. Kang and W.H. Weinberg, “Dynamic Monte Carlo with a proper energy barrier: surface diffusion and two-dimensional domain ordering,”
*J. Chem. Phys.*, 90, 2824, 1989.CrossRefADSGoogle Scholar - [74]K.A. Fichthorn and W.H. Weinberg, “Theoretical foundations of dynamical Monte Carlo simulations,”
*J. Chem. Phys.*, 95, 1090, 1991.CrossRefADSGoogle Scholar - [75]P. Ruggerone, C. Ratsch, and M. Scheffler, “Density-functional theory of epitaxial growth of metals,” In: D.A. King and D.P. Woodruff (eds.),
*Growth and Properties of Ultrathin Epitaxial Layers. The Chemical Physics of Solid Surfaces*, vol. 8, Elsevier, Amsterdam, 1997.Google Scholar - [76]C. Ratsch, P. Ruggerone, and M. Scheffler, “Study of strain and temperature dependence of metal epitaxy,” In: Z. Zhang and M.G. Lagally (eds.),
*Morphological Organization in Epitaxial Growth and Removal*, World Scientific, Singapore, 1998.Google Scholar - [77]S. Glasston, K.J. Laidler, and H. Eyring,
*The Theory of Rate Processes*, McGraw-Hill, New York, 1941.Google Scholar - [78]G.H. Vineyard, “Frequency factors and isotope effects in solid state rate processes,”
*J. Phys. Chem. Solids*, 3, 121, 1957.CrossRefADSGoogle Scholar - [79]K.J. Laidler,
*Chemical Kinetics*, Harper and Row, New York, 1987.Google Scholar - [80]C. Ratsch and M. Scheffler, “Density-functional theory calculations of hopping rates of surface diffusion,”
*Phys. Rev. B*, 58, 13163, 1998.CrossRefADSGoogle Scholar - [81]G. Henkelman, G. Johannesson, and H. Jonsson, “Methods for finding saddle points and minimum energy paths,” In: S.D. Schwartz (ed.),
*Progress on Theoretical Chemistry and Physics*, Kluwer, New York, 2000.Google Scholar - [82]T. Ala-Nissila, R. Ferrando, and S.C. Ying, “Collective and single particle diffusion on surfaces,”
*Adv. Phys.*, 51, 949, 2002.CrossRefADSGoogle Scholar - [83]S. Ovesson, A. Bogicevic, and B.I. Lundqvist, “Origin of compact triangular islands in metal-on-metal growth,”
*Phys. Rev. Lett.*, 83, 2608, 1999.CrossRefADSGoogle Scholar - [84]K.A. Fichthorn and M. Scheffler, “Island nucleation in thin-film epitaxy: a first-principles investigation,”
*Phys. Rev. Lett.*, 84, 5371, 2000.CrossRefADSGoogle Scholar - [85]P. Kratzer M. Scheffler, “Surface knowledge: Toward a predictive theory of materials,”
*Comp. in Science and Engineering*, 3(6), 16, 2001.CrossRefGoogle Scholar - [86]P. Kratzer and M. Scheffler, “Reaction-limited island nucleation in molecular beam epitaxy of compound semiconductors,”
*Phys. Rev. Lett.*, 88, 036102, 2002.CrossRefADSGoogle Scholar - [87]P. Kratzer, E. Penev, and M. Scheffler, “First-principles studies of kinetics in epitaxial growth of III-V semiconductors,”
*Appl. Phys. A*, 75, 79, 2002.CrossRefADSGoogle Scholar - [88]E.W. Hansen and M. Neurock, “Modeling surface kinetics with first-principles-based molecular simulation,”
*Chem. Eng. Sci.*, 54, 3411, 1999.CrossRefGoogle Scholar - [89]E.W. Hansen and M. Neurock, “First-principles-based Monte Carlo simulation of ethylene hydrogenation kinetics on Pd,”
*J. Catal.*, 196, 241, 2000.CrossRefGoogle Scholar - [90]K. Reuter, D. Frenkel, and M. Scheffler, “The steady state of heterogeneous catalysis, studied with first-principles statistical mechanics,”
*Phys. Rev. Lett.*, 93, 116105, 2004.CrossRefADSGoogle Scholar