Elastic, anelastic, and piezoelectric coefficients of Langasite: Resonance ultrasound spectroscopy with laser-doppler interferometry

This paper presents advanced techniques to determine all independent elastic-stiffness coefficients C_ij, the associated internal friction Q_ij^-1, and piezoelectric coefficients e_ij of monocrystal langasite (La₃Ga₅SiO₁₄) using a single rectangular parallelepiped specimen. Langasite's crystal structure belongs to the trigonal system with point group 32, thus six independent C_ij, two e_ij, and two dielectric coefficients ε_ij. All of the elastic and piezoelectric coefficients affect the mechanical resonance frequencies of the solid specimen, and measuring them very accurately permits one to determine the C_ij and e_ij with known density, dimensions, and ε_ij. We developed a piezoelectric tripod to support the specimen upward and measured the free-vibration resonance frequencies with minimum load from its own weight. This weak and stable acoustic coupling ensures high accuracy of the frequency measurement better than 10^-5, being enough to determine the reliable coefficients. Our C_ij fall in the range of results measured with previous (conventional) methods. Our e₁₁ is smaller than the reported values by 1.2-13%, and e₁₄ is larger than those by 44-97%. For the internal friction measurement, we used a solenoid coil to vibrate the specimen without any contact. The longitudinal-wave internal friction considerably exceeds the shear-wave internal friction, which can be interpreted as phonon-phonon interactions.