Vibration spectrum of silver based on metallic interaction

Abstract

A secular determinant for silver has been set up, in which the ion-ion force constants have been derived from known expressions appearing in the theory of metallic cohesion. The matrix elements have been represented as the sum of three terms. One of these arises from the Coulomb interaction of the ions and has been taken from Kellermann’s work on sodium chloride. The second mainly owes its origin to the exchange forces but includes any effect due to the non-spherical nature of the Fermi surface. It has been calculated from the experimental values of the shear constants after subtracting the electrostatic contribution. The third term is due to the volume forces and has been evaluated by means of two dispersion relations given respectively by de Launay and Bhatia. For this purpose, the bulk modulus for the volume forces has been calculated by Dayal & Tripathi’s method. Vibration frequencies and the specific heats have been calculated separately by the use of both the dispersion relations. Both the theoretical 0-T curves agree with the experimental curve at all temperatures within the accuracy of the calculations.