Surface acoustic waves on a polycrystalline substrate

Abstract

We have calculated the dispersion relation for Rayleigh waves propagating on the stress-free, planar surface of a semi-infinite polycrystalline medium. The frequency shift Δω(q) = ω(q) - ω0(q), where ω(q) is the frequency of the Rayleigh wave on the polycrystalline substrate while ω0(q) is the frequency of the Rayleigh wave on a homogeneous, elastically isotropic, reference substrate, is complex, Δω(q) = η(q) - iγ(q). The real part of this shift describes the change in the frequency of the Rayleigh wave due to polycrystallinity while the imaginary part describes the attenuation of the wave due to its scattering into bulk waves and other Rayleigh waves caused by the spatial fluctuations of the elastic moduli resulting from the random orientations of the grains composing the medium. The forms η(q) and γ(q) take in the long wavelength limit are presented.