Raman-scattering study of crystallizedMF3compounds (M=Al,Cr,Ga,V,Fe,In): An approach to the short-range-order force constants

The cubic-rhombohedral structural phase transition that occurs in M${\mathrm{F}}_3$ compounds (M=Al,Cr,Ga,V,Fe,In) is studied by calorimetric measurements (differential scanning calorimetry, differential thermal analysis) and by Raman and by Raman scattering. The transition temperatures and the hysteresis are determined with precision. The Raman spectra of M${\mathrm{F}}_3$ fluorides have been collected at room temperature and high temperature. An assignment of the four Raman-active modes of the rhombohedral phase is proposed on the basis of group-theory analysis in the cubic phase. The temperature study of Raman spectra indicates the presence of two soft modes due to the condensation of the triply degenerate ${\mathit{R}}_5$ mode of the cubic phase [at the R(1/2,1/2,1/2) point of the first cubic Brillouin zone]. The Raman data are used to adjust the parameters of a rigid-ion model and to deduce short-range interaction parameters assuming constant ratio ${\mathit{A}}_{\mathit{i}}$/${\mathit{B}}_{\mathit{i}}$. The F-F short-range interactions are obtained for a wide range of interionic distances, and their behavior is physically reasonable. The calculated phonon spectra and the phonon density of states are presented. The latter exhibits an important discontinuity at the soft-mode frequencies.