Measurement of single-crystal elastic constants by neutron diffraction from polycrystals

The relationships of diffraction averaged elastic compliances for an ideally random polycrystal to the single-crystal elastic compliances are given, within the Reuss approximation, for crystal systems with orthorhombic and higher symmetry. For anisotropic materials, these diffraction elastic compliances are dependent on the reflection index hkl. Expressions for the conventional elastic constants (Young's modulus, Poisson's ratio) are also given. A connection is made to the 'X-ray elastic constants' used for diffraction-based measurements of residual stress. The relationships are used to calculate diffraction averaged constants for comparison with neutron diffraction data recorded from samples under applied uniaxial stress. The Reuss approximation works well for materials with the capacity for plastic deformation, such as metals and transformation toughening ceramics, whereas for other materials the Voigt-Reuss-Hill approximation gives better results. Based on the given relationships and experimental determinations of the diffraction elastic compliances for polycrystalline materials, a method is developed for determining the single-crystal elastic constants. The method for estimating single-crystal compliances is demonstrated here by application to extant data on Ni-Cr-Fe and Ti-6 wt% Al-4 wt% V alloys, and new measurements on cubic zirconia. It has been applied very recently [Kisi & Howard (1998). J. Am. Ceram. Soc. 81, 1682-1684] to determine the previously unknown elastic constants for a tetragonal zirconia.