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

Abstract

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 α that lies 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 compressive strength, diffraction shear moduli, and single-crystal elastic moduli from the experimental high-pressure x-ray diffraction data on bcc Fe, Au, Mo, and FeO. These data contain plastic deformation effects. The diffraction shear modulus in the limit of small deformation (elastic) is computed using rigorous formulae derived by Kröner [Z. Phys. 151, 504 (1958)] and de Wit [J. Appl. Crystallogr. 30, 510 (1997)]. The elastic moduli are derived from the computed shear moduli assuming the validity of A1. The results show that A1 with α≅0.5 is valid for small deformation in all four cases. The analysis of the experimental data suggests that A1 is valid with α<1 for solids with x>1 where x=2C44/(C11−C12); for solids with x<1, the validity of A1 requires α>1. At least for solids of the cubic system, the effect of plastic deformation appears to be fully contained in a single parameter α. In practice, deviations from A2 of varying magnitudes occur mainly because of the difficulty in avoiding diffraction from regions of stress gradient in the sample. A discussion of A3 is presented.