Normal Vibrations in Aluminum and Derived Thermodynamic Properties

Abstract

The experimental phonon-dispersion curves of aluminum at 80°K and at 300°K have been analyzed in terms of axially symmetric Born-von Kármán force-constant models, including 8 nearest neighbors. The resulting models have been used to compute a frequency distribution function $g\left(\omega \right)$ at each temperature from which various thermodynamic properties have been derived. The specific-heat curve predicted by the $g\left(\omega \right)$ appropriate to 80°K fits excellently the experimental results in the temperature range 20 to 80°K. At higher temperatures the experimental results deviate from this calculated curve and approach the curve appropriate to $g\left(\omega \right)$ at 300°K. Similar behavior is found for the experimental Debye-Waller coefficient in the range above 100°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 $g\left(\omega \right)$ 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 $g\left(\omega \right)$.