The hydrostatic pressure derivatives of the elastic constants of the scheelites LiYF₄and LiY_0.5Tb_0.5F₄

Abstract

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 the scheelite structure fluorides LiYF4 and LiY0.5Tb0.5F4. It is shown that the acoustic symmetry axes do not shift appreciably with pressure in either material. Hence the pressure derivatives delta CIJ/ delta P, like the elastic constants CIJ themselves, can be transformed (with usual simplification) to reference bases comprised of acoustic symmetry axes (( kappa and kappa + pi /2) or ( gamma and gamma + pi /2)) and the Z axis. A method of calculation of the acoustic model Gruneisen gammas in the long-wavelength limit, based on the transformation of the elastic constants and their pressure derivatives to the acoustic symmetry axis reference frame, is developed for TII Laue group crystals and results are given for LiYF4 and LiY0.5Tb0.5F4. Shear acoustic mode softening under pressure along the kappa and kappa + pi /2 acoustic symmetry axes has been observed in both these scheelites.