Rayleigh waves in prestressed crystals

Rayleigh waves in anisotropic, prestressed crystals have been investigated by a combination of lattice dynamics and elastic-wave theory. We derive an exact expression for the Rayleigh velocity as the root of a cubic equation involving the elastic constants of the prestressed material and the applied stress in the direction of propagation. Numerical calculations show that surface modes are softened by uniaxial tension or compression parallel to the direction of propagation. For the two-dimensional triangular lattice which is elastically isotropic in the unstressed state, we have calculated the dispersion of the surface waves by analytic lattice dynamics. We find the remarkable result that the frequency of the surface waves, at all wavelengths, is proportional to $sin\left(\frac{2\pi d_x}{\lambda }\right)$, where $2d_x$ is the nearest-neighbor separation along the prestressed, close-packed $x$ direction. We have made an estimate of the surface entropy which is in reasonable agreement with other calculations.