Metallic cohesion and vibration spectrum of copper

Abstract

A new method of setting up a secular determinant for copper has been described in which the ion-ion force constants are not based on hypothetical force models but have been derived from known expressions appearing in the theory of metallic cohesion. Numerical calculations have been made for copper. The Coulomb coupling coefficient has been taken from Kellermann's work on sodium chloride, while the contribution of the ion-ion exchange has been calculated from Fuchs' force constants. The single elastic constant due to the remaining terms of the interaction has been calculated, and has been used to find an expression for the electronic coupling coefficient on the lines of Bhatia's work. There is good agreement between the calculated frequencies for the longitudinal 110 branch and the experimental ones observed in neutron scattering. The calculated θ-T curve is found to be about 6%-7% higher than the experimental curve. This is due to the fact that the repulsive force constant of Fuchs is definitely an overestimate and gives higher value of C 44. If this constant is calculated from observed value of (C 11-C12) and C44, the calculated curve will almost coincide with the experimental one without spoiling the agreement with the results of neutron scattering.