Pressure dependence of single-crystal elastic constants and anharmonic properties of spinel

Abstract

The pressure dependence of the single-crystal elastic constants of synthetic stoichiometric spinel (MgAl2O4) has been measured by using the ultrasonic pulse superposition method. A quadratic pressure dependence of all three elastic constants was observed in the range from 0 to 10 kb. The zero-pressure values and the first pressure derivatives of the elastic constants agree remarkably closely with the data of Schreiber for a nonstoichiometric spinel MgO·2.6Al2O3). The value KT(∂2Ks/∂P2)T = −94 of the dimensionless second pressure derivative of the adiabatic bulk modulus Ks is about ten times larger than that for alkali halides and would give rise to markedly nonlinear pressure dependence of the P-wave velocities in the range up to 100 kb. The isothermal equation of state calculated from the elastic data on the basis of the first-order Birch equation of state agrees up to about 200 kb within experimental error with the X-ray data of Mao et al. for (FexMg1−x)2SiO4 spinel solid solutions. The orientation dependence of the microscopic first and second Grueneisen parameters (mode gammas) is calculated on the basis of the anisotropic elastic continuum model and is found to be almost isotropic for the first, but very anisotropic for the second mode gammas. The macroscopic first Grueneisen parameter, its first pressure derivative, and the Anderson-Grueneisen parameter calculated from the elastic data on the basis of the anisotropic continuum model do not agree with the coresponding thermal data. This fact is attributed to the neglect of optical modes and of dispersion in the anisotropic continuum model.