Complete set of elastic and piezoelectric coefficients of α-quartz at low temperatures

A complete set of low temperature elastic constants Cij and piezoelectric coefficients eij of α-quartz single crystal has been investigated by resonance ultrasound spectroscopy coupled with a laser-Doppler interferometry. Most elastic constants showed monotonic elastic stiffening, while C66 continuously softened as the temperature decreased. Two piezoelectric coefficients eij showed monotonic decreasing upon cooling, and we found a strong correlation between e11 and C66, representing that thermal contraction induced internal strain plays an important role in their temperature behaviors. Group theoretical lattice dynamics analysis revealed that the elastic softening and the correlation can be attributed to an optical-mode-phonon-type internal strain having doubly degenerated E symmetry in the point group of D3.

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