Crystal Dynamics of Copper

TLDR

Previous studies have not assigned physically realistic errors to force constants in copper; this work does so for the first time. Inelastic neutron scattering was used to measure copper’s dispersion relations and frequency distributions, which were then employed to compute thermodynamic quantities that agree well with experiment. The study determined copper’s dispersion relations and force constants, revealing dominant first‑neighbor interactions with significant longer‑range forces, found that conventional frequency errors are overestimated by a factor of two, and showed that calculated thermodynamic properties agree with experiment within a few percent, matching previous independent measurements.

Abstract

The frequency/wave-vector dispersion relation for the symmetry directions [$00\ensuremath{\zeta}$], [$0\ensuremath{\zeta}\ensuremath{\zeta}$], [$\ensuremath{\zeta}\ensuremath{\zeta}\ensuremath{\zeta}$], and [$0\ensuremath{\zeta}1$] 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.