Normal Vibrations in Aluminum and Derived Thermodynamic Properties

Abstract

The experimental phonon-dispersion curves of aluminum at 80\ifmmode^\circ\else\textdegree\fi{}K and at 300\ifmmode^\circ\else\textdegree\fi{}K have been analyzed in terms of axially symmetric Born-von K\'arm\'an force-constant models, including 8 nearest neighbors. The resulting models have been used to compute a frequency distribution function $g(\ensuremath{\omega})$ at each temperature from which various thermodynamic properties have been derived. The specific-heat curve predicted by the $g(\ensuremath{\omega})$ appropriate to 80\ifmmode^\circ\else\textdegree\fi{}K fits excellently the experimental results in the temperature range 20 to 80\ifmmode^\circ\else\textdegree\fi{}K. At higher temperatures the experimental results deviate from this calculated curve and approach the curve appropriate to $g(\ensuremath{\omega})$ at 300\ifmmode^\circ\else\textdegree\fi{}K. Similar behavior is found for the experimental Debye-Waller coefficient in the range above 100\ifmmode^\circ\else\textdegree\fi{}K. It is concluded that inelastic-neutron-scattering data and thermodynamic data are compatible in the range of sufficiently low temperatures where deviations from the quasiharmonic approximation are small, provided a good force-constant model as well as a statistically adequate $g(\ensuremath{\omega})$ are available. There is evidence that the quasiharmonic approximation in aluminum is invalid at room temperature at least for the extreme low-frequency part of $g(\ensuremath{\omega})$.