Vibrations at Surfaces
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In Chap. 3 we assumed that the atoms occupy static positions in the crystal lattice. However, even at zero temperature, they experience thermal vibrations around their equilibrium positions. In the presence of a surface, it is known, from the work of Lord Rayleigh in 1887 [4.1] on the elasticity theory of continuous media, that new vibration modes appear which are localized at the surface. Subsequently, there is a modification of the crystal vibrational thermodynamical properties. In this chapter, after having briefly reviewed the calculation of bulk modes (Sects. 4.1 and 4.2), we develop the theory of surface modes in semi-infinite crystals and explain how they can be observed experimentally (Sect. 4.3). The calculation of surface vibrational thermodynamical properties (Sect. 4.5) and mean square displacements (Sect. 4.6) is easily performed when the spectral densities of modes are known (Sect. 4.4). Finally, we show that the influence of atomic vibrations in diffraction, PhD or SEXAFS experiments can be expressed in the form of Debye-Waller factors which provide information about the mean square displacements of surface atoms (Sect. 4.6).
KeywordsForce Constant Rayleigh Wave Surface Mode Electron Energy Loss Spectroscopy Dynamical Matrix
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- M.G. Lagally: In Surface Physics of Materials II, ed. by J.M. Blakely (Academic, New York 1975Google Scholar
- 4.12H. Ibach, D.L. Mills: Electron Energy Loss Spectroscopy and Surface Vibrations (Academic, New York 1982)Google Scholar
- 4.14J. Szeftel: Surf. Sei. 152–153, 797 (1985)Google Scholar
- 4.24V.K. Semenchenko: In Surface Phenomena in Metals and Alloys, ed. by R. Kennedy (Pergamon, London 1961)Google Scholar
- 4.25G. Tréglia, M.C. Desjonquères: unpublished resultsGoogle Scholar
- 4.28N.W. Ashcroft, N.D. Mermin: Solid State Physics (Holt, Rinehart, Winston, Philadelphia p. 792Google Scholar
- A. Messiah: Mécanique Quantique (Dunod, Paris 1962) Vol. I, p. 382Google Scholar
- 4.29J.B. Pendry: Low Energy Electron Diffraction (Academic, London 1974)Google Scholar