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 Cij, two eij, and two dielectric coefficients epsilon(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 Cij and eij with known density, dimensions, and epsilon(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 Cij fall in the range of results measured with previous (conventional) methods. Our ell is smaller than the reported values by 1.2-13%, and e(14) 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.