Single crystal x-ray diffraction studies of materials at high temperature

The thermal motion of the atoms influences the intensities of the Bragg reflections. This influence is expressed by a temperature factor. Static disorder generates similar effects, which may be expressed by a pseudo temperature factor. The displacements of the atoms from their mean positions can be described by a probability density function (pdf). The temperature factors and the probability density functions are connected with each other by a Fourier transformation. An effective one particle potential can be calculated from the pdf. The so-called anisotropic temperature factors, frequently calculated in standard structure determinations, assumes a harmonic (parabolic) potential. A more general temperature factor formalism has to take into account anharmonic potentials and the corresponding anharmonic temperature factors. This article describes the mathematical basis of a general temperature factor formalism and an application of this formalism.