Response functions and thermal motions of a simple n-dimensional lattice model

• Published in: Surface science 1965-01, Vol.3 (4), p.386-414
• Main Author: Goodman, F.O.
• Format: Article
• Language: English
• ISSN: 0039-6028; 1879-2758
• DOI: 10.1016/0039-6028(65)90007-5

A simple n-dimensional lattice model is used and the atomic motion both normal and tangential to the lattice surface is discussed. Two different problems are considered and related; these are (i) the tangential and normal response functions of the lattice atoms and (ii) their tangential and normal thermal motion. The results are highly relevant to the theory of accommodation coefficients, which at present is effectively restricted, with very few exceptions, to (a) normal impact of gas atoms on a solid surface and (b) solid surfaces initially at rest (0°K classically). Other problems to which some of the results are relevant are (i) X-ray and electron scattering by crystals (including the theory of the Debye-Waller factor); this involves the mean square displacements of the lattice atoms while undergoing thermal motion and (ii) the Mossbauer effect; this involves the mean square displacements and velocities of the atoms. A simple method (summation over normal modes of the lattice) of calculating some of the relevant functions is described and applied to some special cases; this method is particularly good for the calculation of the response functions. The paper is restricted mainly to the use of classical mechanics.