A new method for pure modes of elastic waves search in crystals is presented. The method is based on the analysis of 3D-surfaces of phase velocities and differs from the known analogous methods by accounting for the piezoeffect. The piezoelectric corrections have an essential effect on the result of the search. The computer code is prepared to construct these surfaces and their sections by the base planes of a crystal. The code also permits to calculate the directions of pure longitudinal and pure transverse elastic wave propagation on these surfaces.
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