Measurement of single‐crystal elastic constants of bronzite as a function of pressure and temperature

The nine single-crystal elastic constants of orthopyroxene, Mg0.8Fe0.2SiO3, have been measured as a function of temperature from 25° to 350°C and at 25°C as a function of pressure to 10 kb by means of the ultrasonic pulse superposition technique. It was found that the shear constants exhibited a distinctly nonlinear pressure dependence in addition to the usual linear terms. Owing to the difficulty in obtaining precise data for the longitudinal modes above approximately 4.5 kb, where curvature might be observed, only a linear pressure dependence was found for the on-diagonal longitudinal constants. Because the second pressure derivatives of the on-diagonal longitudinal constants (c11, c22, and c33) enter the expressions required for the evaluation of the second pressure derivatives of the off-diagonal constants (c12, c23, and c13), the second derivatives of the off-diagonal constants are probably considerably in error. The second pressure derivatives of the on-diagonal shear constants and of the unprocessed data for the cross-coupling moduli, however, have been precisely and consistently measured and represent the first observations of curvature for noncubic oxide materials. The dimensionless quantities K(∂cμv/∂P2) (where K denotes the bulk modulus, cμv denotes the elastic constants, and P denotes the pressure) for the on-diagonal shear moduli are about ten times larger than the corresponding quantities for the eight alkali halides for which these quantities are known. The isotropic bulk and shear moduli and their pressure and temperature derivatives calculated from the single-crystal data by means of the Voigt-Reuss-Hill (VRH) approximation are KS = 1.035 Mb, G = 0.749 Mb, (∂KS/∂P)T = 9.59, (∂G/∂P)T = 2.38, (∂KS/∂T)p = −0.268 kb°C−1, and (∂G/∂T)p = −0.119 kb°C−1. Owing to the large values of the pressure derivatives of the longitudinal elastic constants c11, c22, and especially c33, the pressure derivative of the bulk modulus of orthopyroxene is approximately twice as large as that for most other materials normally considered to be of importance in the earth's mantle. The ultrasonic equation of state calculated from the first-order Birch equation agrees well with static-compression data and, below about 150 kb, with shock-wave data. The elastic Grueneisen parameter calculated from the VRH approximation is found to be 30% larger than the thermal Grueneisen parameter.

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