Vibrational modes and specific heat of A1Si and A1Ge alloy systems

Abstract

We present a simplified treatment where the lattice vibrations of Al, Si or Ge atoms in the Al-Si and Al-Ge solid solutions are replaced with that of pure Al, f.c.c. Si or f.c.c. Ge crystals with the lattice constant and electron density of the alloy. Considering the volume and electron density effect on the dynamical matrix of the pure constituent, we obtain the phonon dispersion curves of the local and band modes for Al 0.9Si 0.1 and Al 0.9Ge 0.1 and the concentration x-dependence of the local and band modes frequencies in the Al 1− x Si x and Al 1− x Ge x solid solutions. Then, we calculate the temperature-dependent specific heat at constant volume of these alloy systems. The obtained specific heat of the Al 1− x Si x and Al 1− x Ge x solid solutions is a monotonous function of the concentration x, but deviates largely from linearity at low temperatures.