Crystal Dynamics of Potassium. II. The Anharmonic Effects

Abstract

The frequencies and the lifetimes of the normal modes of vibration of potassium have been measured at four different temperatures with neutron inelastic scattering techniques. The changes in the results with temperature were found to be in reasonable agreement with calculations of the effect of anharmonicity on the normal modes. Up to nine-tenths of the melting temperature, the temperature dependence of the frequencies and of the thermal expansion coefficient was found to be in agreement with calculations based on the neutral-pseudoatom model of a crystal. The agreement between experiment and calculation for the life-time of the normal modes was less satisfactory. The discrepancy may in part be due to the difficulty in extracting the instrumental resolution function. The neutral-pseudoatom potential used in these calculations was derived from the frequencies of the normal modes of vibration at low temperature, as described previously. It is shown that the neutral-pseudoatom model for the anharmonic effects neglects interactions between three or more ions which are present in more exact theories. The agreement obtained between experiment and theory therefore suggests that the many-body forces are smaller than the two-body forces. We also describe the effect of anharmonicity on the strength of Kohn anomalies in metals; one contribution to their strength has the same temperature dependence as the Debye-Waller factor.