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An ultrasonic scattering theory is presented which allows one to calculate the scattering coefficients and velocities of plane longitudinal and transverse waves in polycrystals as a function of the wavenumber k times grain radius a without limitation to the Rayleigh region. The theory includes mode conversion and multiple scattering and can be used to describe ultrasonic propagation in polycrystals with randomly orientated grains as well as in those with preferred grain orientation. The calculation was done for compressional waves in polycrystals of cubic symmetry with randomly orientated grains in second-order perturbation theory using the assumption that the changes in the elastic constants and in the density of the materials from grain to grain are small. The asymptotic values at low ka (Rayleigh scattering) are exactly the same as the well-known results from Bhatia and Moore. Numerical calculations are carried out for some examples.
S. Hirsekorn (Wed,) studied this question.