Complete determination of the elastic moduli of α-quartz under hydrostatic pressure up to 1 GPa:: an ultrasonic study

Using the ultrasonic pulse-echo technique and a newly developed method to treat the data, all the elastic compliances of alpha-quartz have been obtained as a function of hydrostatic pressure up to 1 GPa with great accuracy. Fifteen independent measurements were performed in five directions of high symmetry (X, Y, Z, Y ' and Z '). The pressure dependence of the six second-order elastic and two piezoelectric constants were deduced. The pressure derivatives of c(14) and c(44) are positive, whereas that of c(66) is negative, in contradiction to previously published results. Under ambient conditions, the linear and bulk moduli B-a0 = 103.4(0.5) GPa, B-c0 = 137.0(0.5) GPa and B-0 = 37.5(0.2) GPa calculated from our determination of the elastic tensor are in good agreement with the published values. However, we find a clear discrepancy with published values for the pressure derivative of the bulk modulus B ' = 4.7( 0.5). From these results, the Born stability criteria have been calculated as a function of pressure and compared with previous results. Their behavior can help to explain the structural instability of alpha-quartz at around 18 GPa.