Maximum-entropy estimate of the orthorhombic texture from ultrasonic measurements

Abstract

The propagation of ultrasonic waves in a polycrystalline aggregate is considered for a bulk sample with orthorhombic symmetry made of cubic crystals. Use is made of both Jaynes' principle of maximum Shannon entropy, and the averaging procedures proposed by Voigt, Reuss and Hill, to derive information about the crystallite orientation distribution function from ultrasonic velocities (observables). The results obtained for the problems with the maximum number of the allowable observables are compared with each other to show how the averaging procedure affects the maximum-entropy distribution function of the crystallite orientation. In this way, it is confirmed that only the Voigt averaging procedure leads to such a maximum-entropy distribution function of the crystallite orientation that the medium anisotropy implied by this distribution is the same as that deduced from the observables by using the rules of macroscopic symmetry.