Measurements made of the effects of hydrostatic pressure on ultrasonic wave velocities have been used to obtain the hydrostatic-pressure derivatives of the six independent second-order elastic constants (SOEC’s) and the bulk modulus of very-high-purity quartz crystals in the temperature range 243–393 K. The results, which quantify the nonlinear properties of quartz, show that (∂${\mathit{C}}_{\mathit{I}\mathit{J}}$/∂P${)}_{\mathit{T},}$${\mathit{P}}_{=0\mathrm{}}$ depend markedly upon temperature (contrary to their previous usage in technological applications as temperature-independent quantities), some to the extent of having a maximum or minimum in their values, in this technologically important temperature range. The compression estimated at very high pressures using the Murnaghan equation of state is in reasonable agreement with experimental data. A theoretical calculation of the six elastic-stiffness-tensor components and their hydrostatic-pressure derivatives has also been made by atomistic simulation techniques with the short-range interaction between Si and O ions represented by the Buckingham potential. A comparison between the calculated and experimental results shows good agreement for the SOEC’s themselves (the second derivatives of the potential energy with respect to the strain) and also reasonable accord for the (∂${\mathit{C}}_{\mathit{I}\mathit{J}}$/∂P${)}_{\mathit{T},}$ P=0, which are the combinations of the third derivatives of the potential energy with respect to the strain. That the hydrostatic-pressure derivatives (∂${\mathit{C}}_{14}$/∂P${)}_{\mathit{T},}$${\mathit{P}}_{=0\mathrm{}}$ and (∂${\mathit{C}}_{66}$/∂P${)}_{\mathit{T},}$${\mathit{P}}_{=0\mathrm{}}$ have negative signs has interesting ramifications concerning the nature of the α-β displacive phase transition of quartz.

A detailed description of the vibrational anharmonicity of the long-wavelength acoustic modes is given in terms of their Grüneisen parameters in the quasiharmonic approximation. Certain shear and quasishear acoustic modes have negative acoustic-mode Grüneisen parameters, thus accounting for the negative value of the thermal-expansion-tensor component ${\mathrm{\alpha }}_{33}$ at low temperatures. The mean acoustic-mode Grüneisen parameter ${\gamma }_{\mathit{H}}^{\mathrm{el}}$ in the long-wavelength limit decreases markedly in the temperature range 243–330 K due to the temperature dependences of the hydrostatic-pressure dependences (∂${\mathit{C}}_{\mathit{I}\mathit{J}}$/∂P${)}_{\mathit{T},}$${\mathit{P}}_{=0\mathrm{}}$ of the elastic-stiffness-tensor components.

• Received 24 September 1991

DOI:https://doi.org/10.1103/PhysRevB.45.10242