Elastic behaviour of YAG under pressure

Abstract

Measurements of the effects of hydrostatic and uniaxial pressures on ultrasonic wave velocities are used to obtain the six third-order elastic constants of yttrium aluminium garnet (YAG). Results are used to investigate whether the shear isotropy and the conformity with the Cauchy relation (indicative of central forces), which hold for the second-order elastic constants of YAG, extend into the region of finite strain which determines higher-order elasticity. The compression has been extrapolated up to 150*108 Pa using the Murnaghan equation of state. The vibrational anharmonicity of YAG and yttrium iron garnet (YIG) are compared through the acoustic-mode Gruneisen gammas computed from the pressure dependences of the elastic constants. The attenuation of transverse microwave ultrasonic waves propagated along the (001) direction (the mode used in acoustic devices) due to anharmonic interactions with thermal phonons, calculated at the limits omega tau >>1 and omega tau <1, is shown to be in good agreement with previous experimental attenuation measurements for this mode.