Theory of Surface Effects on the Thermal Diffuse Scattering of X Rays or Electrons from Crystal Lattices

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Abstract
A theory has been developed for the effect of a free surface on the thermal diffuse scattering of x rays or electrons from a crystal lattice. The harmonic approximation is employed. It is assumed that the scattering is entirely from the surface layer. The results are presented both in terms of the eigenvalues and eigenvectors of the dynamical matrix and in terms of a function of the dynamical matrix itself. An alternative treatment based on thermodynamic Green's functions has also been developed and applied to the monatomic simple lattice with nearest- and next-nearest-neighbor central interactions. Explicit formulas are obtained for the isotropic case in the high-temperature limit when the difference between the outgoing and incoming wave vectors of the radiation is near a reciprocal lattice rod. A comparison between the surface and bulk cases is given.