The temperature variation of the scattering properties of crystals

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Abstract
It is shown how thermodynamic data (heat capacity, thermal expansion, etc.) may be used to estimate accurately certain scattering properties of crystals, assuming the validity of the quasi-harmonic approximation of lattice dynamics. In particular, Debye-Waller factors and incoherent neutron scattering cross sections can be readily correlated with thermodynamic data even though the form of the lattice frequency distribution of the crystal is not known. Thermodynamic data for vanadium, silicon, germanium and copper have been analysed and the results used to illustrate the accurate estimation of the following entities: Debye-Waller factor, total incoherent neutron scattering cross section, differential incoherent neutron cross section in the weak-binding approximation and in the n-phonon approximation. The application of the method to Mössbauer effect phenomena is also discussed. Definite criteria are suggested for deciding the conditions under which the substitution of the Debye distribution for the actual frequency distribution of a crystal leads to acceptable estimates of one or more properties of the lattice vibrations.