A new method for calculation of crystal susceptibilities for X-ray diffraction at arbitrary wavelength

Abstract

A novel method for the calculation of the X-ray susceptibility of a crystal in a wide range of radiation wavelengths is described. An analytical interpolation of one-electron wave functions is built to approximate the solution to Hartree± Fock equations for all atoms and ions of the periodic system of elements with high accuracy. These functions allow the calculation of the atomic form factors in the entire range of a transmitted momentum as well as the description of their anisotropy taking into account external and intracrystalline ®elds. Also, an analytical approximation for the force matrix of an arbitrary crystal is obtained and the microscopic calculation of the Debye±Waller factor for crystals with a complicated unit cell is presented.