Optimized determination of elastic constants of crystals and their uncertainties from surface Brillouin scattering

Surface Brillouin scattering of light allows the angular-dependent velocities of Rayleigh surface acoustic waves (SAW), pseudo-SAW and longitudinal lateral waves (L) on the surface of an opaque crystal to be measured, and the elastic constants thereby determined. Closed form expressions exist for the surface wave velocities in high symmetry directions on crystallographic symmetry planes, and these have been exploited in the past for obtaining the values of the elastic constants. This paper describes a procedure for obtaining an optimized set of elastic constants from SAW, pseudo-SAW and L velocities measured in arbitrary directions in the (0 0 1) and (1 1 0) surfaces of cubic crystals. It does so by affecting a linearization of the numerically determined angular-dependent SAW and pseudo-SAW velocities near the best fit, and using analytic expressions for the L velocity. The method also generates covariance ellipsoids, from which the uncertainties in the determined values of the elastic constants can be read off. The method is illustrated using surface Brillouin scattering data to obtain the room-temperature elastic constants C11, C12 and C44 of the cubic crystals VC0.75 and Rh3Nb.