Elastic behavior under hydrostatic pressure and acoustic-mode vibrational anharmonicity of single-crystal berlinite

Abstract

The set of the second-order elastic constants and their hydrostatic-pressure derivatives have been obtained for the rhombohedral single-crystal berlinite (${\mathrm{AlPO}}_4$) using the ultrasonic pulse echo overlap technique. To quantify the vibrational anharmonicity, the acoustic-mode Grüneisen parameters in the long-wavelength limit have been derived in the quasiharmonic approximation. The results extend previous observations that the elastic and physical behavior of berlinite is quite similar to that of quartz. The hydrostatic-pressure derivative ∂$C_{66}$/∂P has a negative value indicating that the corresponding transverse-acoustic mode softens under pressure; this is in accord with the anomalous positive temperature dependence of $C_{66}$. The anomalous behavior of $C_{66}$ indicates that there may be even at room-temperature influence of the zone-center optic phonon, whose softening is associated with the α-β structural transformation, on long-wavelength transverse-acoustic phonons propagating in the same crystallographic direction.