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Nuclear inelastic scattering in powders of anisotropic materials

The determination of the vibrational densities of states (DOS) in anisotropic materials from the spectra of inelastic nuclear absorption on a powder material is an inverse scattering problem, which can be solved with a certain degree of precision. To estimate this degree, we solve the direct problem, and find a difference between the powder-averaged DOS and the “apparent DOS" as is extracted from the spectra of a powder. These two quantities are fully equivalent only in single-site isotropic structures. We determine the temperature, energy and orientation dependencies of a difference between them in an anisotropic material, using the example of anisotropic DOS in iron borate. Deriving components of anisotropic DOS from multiple measurements on aligned powders is analysed vs. varying degree of alignment.