A method to characterize the texture of hexagonal polycrystalline aggregates with orthorhombic macroscopic symmetry is presented. Previous methods are extended to the analysis of waves propagating on three principal planes of the material. Five coefficients of the crystallographic orientation distribution function, W200, W220, W400, W420, and W440, are determined from angular variations of the phase velocity of the five ultrasonic modes considered: Bulk longitudinal waves, shear waves with in‐plane and plane‐normal polarizations, Rayleigh surface waves, and the fundamental symmetric plate mode (in the long‐wavelength limit). Analytical expressions for the texture coefficients are found for an arbitrary number of principal planes. Measurements are reported for a Zr–2.5% wt Nb pressure tube, an alloy used in CANDU nuclear reactors. The angular variations of the phase velocity of leaky Rayleigh waves and leaky surface skimming compressional waves are measured with a line‐focus acoustic microscope. Although these waves are not exactly those treated in the theory, they are closely related to pure Rayleigh waves and bulk longitudinal waves. The determined texture coefficients are sensitive to the input physical parameters when certain combinations of planes and acoustic waves requiring absolute velocity measurements are used. However, the coefficients are less sensitive to the input parameters when combinations requiring only relative velocity measurements are used. Results derived from relative measurements agreed with neutron scattering measurements.

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