Statistical approaches for the treatment of anharmonic motion in crystals. II. Anharmonic thermal vibrations and effective atomic potentials in the fast ionic conductor lithium nitride (Li₃N)

Results of X-ray diffraction experiments on lithium nitride (Li₃N) in the temperature range between 294 and 888 K show strong anharmonic effects. The deviations from harmonicity cannot be interpreted by interstitial sites or split positions. The application of an anharmonic temperature factor which is based on the Gram-Charlier expansion leads to an excellent fit of the data, whereas an anharmonic temperature factor, based on the Edgeworth series expansion, cannot fit the measurements in a satisfactory way. The corresponding anharmonic probability densities and the effective one-particle potentials are presented. The activation energy of the ionic conduction in Li₃N perpendicular to the c axis and the thermal expansion of the lattice constant are derived from the potentials. These results agree well with results obtained by other experimental techniques. Therefore it is concluded that the potentials derived from elastic scattering experiments are physically meaningful.