Analysis of nonhydrostatic high-pressure diffraction data (cubic system): Assessment of various assumptions in the theory

The mathematical formulation commonly used to analyze the high-pressure diffraction data from the sample under nonhydrostatic compression is based on three assumptions: A1—a weighted harmonic mean of the diffraction shear moduli under Reuss and Voigt limits with a weight parameter that\udlies between 0.5 and 1 describes adequately the diffraction shear modulus; A2—a stress tensor with only the diagonal terms describes the stress state at the center of the sample under nonhydrostatic compression; and A3—the lattice-strain equations derived using only the linear elasticity theory are adequate to derive strength and elastic moduli from the diffraction data. To examine A1 we derive\udcompressive strength, diffraction shear moduli, and single-crystal elastic moduli from the\udexperimental high-pressure x-ray diffraction data on bcc Fe, Au, Mo, and FeO. These data contain\udplastic deformation effects. The diffraction shear modulus in the limit of small deformation elastic\udis computed using rigorous formulae derived by Kröner Z. Phys. 151, 504 1958 and de Wit\udJ. Appl. Crystallogr. 30, 510 1997. The elastic moduli are derived from the computed shear\udmoduli assuming the validity of A1. The results show that A1 with 0.5 is valid for small\uddeformation in all four cases. The analysis of the experimental data suggests that A1 is valid with\ud1 for solids with x1 where x=2C44 / C11−C12; for solids with x1, the validity of A1\udrequires 1. At least for solids of the cubic system, the effect of plastic deformation appears to\udbe fully contained in a single parameter. In practice, deviations from A2 of varying magnitudes\udoccur mainly because of the difficulty in avoiding diffraction from regions of stress gradient in the\udsample. A discussion of A3 is presented