Vibrational anharmonicity of oxide and fluoride scheelites

Abstract

Lattice parameter measurements of LiYF4 and LiY0.5Tb0.5F4 made between -100 degrees C and +550 degrees C show that the anisotropy of the thermal expansion ( alpha 11> alpha 33) of these scheelite structure fluorides has the opposite sense to oxide scheelites ( alpha 33> alpha 11). This, together with corresponding differences found between the anisotropy of linear compressibility and elastic stiffness constants, can be understood if the oxides, but not the fluorides, are considered to show a tendency towards layer-like behaviour. Pulse echo overlap measurements of ultrasonic wave velocities have been used to obtain the hydrostatic pressure derivatives delta CIJ/ delta P of the elastic constants of CaWO4. Since the acoustic symmetry axes do not shift appreciably with pressure, the pressure derivatives delta CIJ/ delta P, like the elastic constants CIJ themselves, can be transformed (with useful simplification) to reference bases comprised of acoustic symmetry axes (( kappa and kappa + pi /2) or ( gamma and gamma + pi /2)) and the Z axis. The acoustic mode Gruneisen gammas in the long-wavelength limit obtained for CaWO4 show that shear acoustic mode softening occurs under pressure along the gamma and gamma + pi /2 acoustic symmetry axes, in contrast to that for LiYF4 and LiY0.5Tb0.5F4 which takes place along the other type ( kappa and kappa + pi /2) of acoustic symmetry axes in the (001) plane.