Low Temperature Elastic Constants and Piezoelectric Coefficients of LiNbO₃ and LiTaO₃: Resonant Ultrasound Spectroscopy Measurement and Lattice Dynamics Analysis

The complete sets of elastic constants C_ij and piezoelectric coefficients e_ij for LiNbO₃ and LiTaO₃ single crystals have been determined by resonant ultrasound spectroscopy (RUS) from ambient temperature to 6 K. Both C_ij(T) and e_ij(T) of the two crystals monotonically increased as the temperature decreased. The Einstein temperature estimated from Varshni's equation revealed that e₁₅ and e₂₂ of LiNbO₃ have remarkably low values compared with the acoustic Debye temperature. In addition, the lattice anharmonicity of these piezoelectric coefficients was also extraordinarily low. An analysis based on the group theory and lattice dynamics revealed that both LiNbO₃ and LiTaO₃ crystals have three types of internal displacement modes: A₁, A₂, and E, and only the E mode affects e₁₅ and e₂₂. Therefore, it is reasonable to suppose that the E mode internal displacement is responsible for the unusual behaviors of the tow piezoelectric coefficients.