Measurement of single crystal elastic constants by neutron diffraction from polycrystals: stress-strain state in two non-cubic materials

Full text: Although polycrystals are elastically isotropic on a macroscopic scale, the individual (single) crystallites are generally anisotropic. This influences properties such as crack propagation, magnetostriction, ferroelectric and piezoelectric response. A technique for determining single crystal elastic constants using diffraction measurements on polycrystalline samples under an applied stress have recently been developed. The method relies on the fact that although the sample has an enormous number of randomly oriented crystallites, those contributing to a given diffracted beam intercepted by a detector have a common scattering vector. Strains measured from the peak shifts as a function of applied stress can be used, via a tensor transformation, to calculate the single crystal elastic constants. The technique has been tested on materials with known elastic constants and has been used to determine the previously unknown constants for tetragonal zirconia. Underpinning the technique is a need to know whether the polycrystal is in a state of uniform stress (Reuss), uniform strain (Voigt) or an intermediate state (Voigt-Reuss-Hill average or Kroener's solution). The authors have hypothesised that ductile materials like metals can accommodate strain mismatch at grain boundaries by plastic deformation, thereby remaining largely in a state of uniform stress. Brittle materials such as most ceramics and geological materials exist in an intermediate state (Voigt-Reuss-Hill average or Kroener). In this presentation, an overview of the method and recent results from the very-high-resolution diffractometer HRPD at ISIS will be presented in support of the hypothesis