Estimation of Single-Crystal Elastic Moduli from Polycrystalline X-Ray Diffraction at High Pressure: Application to FeO and Iron

Abstract

X-ray diffraction data obtained under nonhydrostatic compression of a polycrystalline sample yield an estimate of the single-crystal elasticity tensor of the material when analyzed using appropriate equations. The analysis requires as input the aggregate shear modulus from independent measurements. The high-pressure elastic moduli of face-centered-cubic FeO, body-centered-cubic iron ( $\ensuremath{\alpha}$-Fe), and the pressure-induced hexagonal close-packed iron ( $\ensuremath{\epsilon}$-Fe) are obtained. This analysis currently provides the only method of determining single-crystal elasticity tensors in the megabar pressure range and of studying elasticity of very high-pressure phases.