Normal Modes of Vibration in Nickel

Abstract

The frequency-wave-vector dispersion relation, $\ensuremath{\nu}(\mathrm{q})$, for the normal vibrations of a nickel single crystal at 296\ifmmode^\circ\else\textdegree\fi{}K has been measured for the [$00\ensuremath{\zeta}$], [$0\ensuremath{\zeta}\ensuremath{\zeta}$], [$\ensuremath{\zeta}\ensuremath{\zeta}\ensuremath{\zeta}$], and [$0\ensuremath{\zeta}1$] symmetric directions using inelastic neutron scattering. The results can be described in terms of the Born-von K\'arm\'an theory of lattice dynamics with interactions out to fourth-nearest neighbors. The shapes of the dispersion curves are very similar to those of copper, the normal mode frequencies in nickel being about 1.24 times the corresponding frequencies in copper. The fourth-neighbor model was used to calculate the frequency distribution function $g(\ensuremath{\nu})$ and related thermodynamic properties.