A general expression for the anharmonic temperature factor in the isolated-atom-potential approach

Abstract

An explicit expression is given for the anharmonic temperature factor that is gained from an isolatedatom potential in the classical regime. Since the Boltzmann function is not generally suited to form a probability density function (p.d.f.) and its Fourier transform is generally unknown, a meaningful p.d.f. can be obtained by expanding the anharmonic terms into a series. The Fourier transform of this series, i.e.

The structure factor

“…The Fourier transform of the OPP distribution, in a general coordinate system, is (Johnson, 1970a;Scheringer, 1985a) where T 0 is the harmonic temperature factor and G represents the Hermite polynomials in reciprocal space. If the OPP temperature factor is expanded in the coordinate system which diagonalizes jk , simpler expressions are obtained in which the Hermite polynomials are replaced by products of the displacement coordinates u j Coppens, 1980;Tanaka & Marumo, 1983).…”