Crystal Dynamics of Copper

Abstract

The frequency/wave-vector dispersion relation for the symmetry directions [$00\zeta$], [$0\zeta \zeta$], [$\zeta \zeta \zeta$], and [$0\zeta 1$] in copper at room temperature has been determined by inelastic neutron scattering. Interplanar and atomic force constants have been obtained. First-neighbor interactions are dominant, but longer range forces, extending to at least sixth-nearest neighbors, are also present. Physically realistic errors have been assigned to many of the force constants; to our knowledge this has not been done previously. The analysis of the data, and the excellent agreement between measurements carried out at the Chalk River and McMaster University reactors, indicate that, on the average, the errors conventionally assigned to frequencies in neutron-scattering studies are too large by about a factor of 2 to be standard deviations. Frequency distributions have been obtained and used to calculate various thermodynamic quantities which agree quite well with experiment. (Discrepancies of a few percent appear to be accounted for by anharmonic effects.) Our results are in rather good agreement with those of Sinha obtained by quite different experimental methods.