Estimation of the elastic and piezoelectric tensors of sapphire and lithium niobate from Brillouin light backscattering measurements of a single crystal sample

Brillouin light scattering is a versatile measurement technique of the dispersion of bulk acoustic phonons in amorphous and crystalline solids. It allows contactless and non-destructive characterization of the relevant material tensors of optically transparent materials, provided that the optical refraction indices, and in addition the dielectric tensor for piezoelectric materials, are known beforehand. The complete estimation of the anisotropic material tensors is often performed using many different crystal orientations, and hence different samples of the same crystal. In this paper, we consider the problem of measuring those tensors using a single sample of an anisotropic single crystal with trigonal symmetry. A complete measurement requires sufficient experimental diversity in the phonon wavevectors when sampling the phonon velocity surfaces, hence the consideration of a large number of directions away from crystallographic axes. We estimate all six independent elastic constants of non-piezoelectric sapphire (3¯ m point group) with a single X-cut wafer and the six independent elastic constants together with the four independent piezoelectric constants of piezoelectric lithium niobate (3 m point group) with a single Y-cut wafer. The estimated tensors are in close agreement with those reported in the literature based on resonant ultrasonic techniques.