Vibrational modes and phase transition of Si-Ge solid solution

We present the simplified treatment where the lattice vibrations of Si or Ge atoms in the Si-Ge solid solution are replaced with that of pure Si or Ge crystal at lattice constants of the alloy. Considering the volume effect on the force constants of the pure constituent, we obtain the phonon dispersion curves of the local and band modes for Si_0.91Ge_0.09 and Si_0.11Ge_0.89 systems and the concentration x-dependence of the local and band modes frequencies in the Si_1?xGe_x solid solutions. Then, from the calculation of the effective mode Grüneisen parameter γ_i for the average phonon modes in the Si_1?xGe_x systems, we obtain the predominant correlation between TA mode Grüneisen parameter γ^X_TA at the point X and the phase transition pressure P_t, and the softening of TA modes is related to the pressure-induced phase transition of the Si-Ge solid solution.