Interaction of the TO-phonon with the Acoustic Phonons near the Phase Transition Temperature in Pb_1-<i>x</i>Ge_<i>x</i>Te

Abstract

The phase transition in Pb 1- x Ge x Te with x =0.03 ∼0.1 was studied by Raman scattering and ultrasonic velocity measurements. Below T c the frequency of the A 1 -mode is 1.99 ×10 23 ( T c - T ) rad 2 /sec 2 and the E -mode 5.32 ×10 23 ( T c - T ) rad 2 /sec 2 for x =0.05. The ultrasonic velocity shows a step-like behaviors at T c . Just above T c the normal elastic moduli are C 11 =11.0 ×10 11 , C 12 =0.02 ×10 11 and C 44 =1.35 ×10 11 in dyn/cm 2 . The steps are Δ C 11 =1.52 ×10 11 , Δ C 12 =-0.20 ×10 11 and Δ C 44 =0.26 ×10 11 in dyn/cm 2 . The parameters of the free energy expansion were calculated by using the above results together with the data of the shear strain. The order parameter, the spontaneous strain and the TO-phonon frequency above T c which were estimated from thus obtained parameters are consistent with the results experimentally obtained satisfactorily.