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/sub ij/, the associated internal friction Q/sub ij//sup -1/, and piezoelectric coefficients e/sub ij/ of monocrystal langasite (La/sub 3/Ga/sub 5/SiO/sub 14/) using a single rectangular parallelepiped specimen. Langasite´s crystal structure belongs to the trigonal system with point group 32, and thus possesses six independent C/sub ij/, two e/sub ij/, and two dielectric coefficients /spl epsiv//sub 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/sub ij/ and e/sub ij/ with known density, dimensions, and e/sub 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 accuracy of the frequency measurement better than 10/sup -5/, enough to determine the coefficients reliably. Our C/sub ij/ fall in the range of results measured with previous (conventional) methods. Our e/sub 11/ is smaller than the reported values by 1.2-13%, and e/sub 14/ is larger 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 explained by phonon-phonon interactions.