X-ray diffraction under non-hydrostatic conditions in experiments with diamond anvil cell: wüstite (FeO) as an example

Abstract

The stress state in a solid specimen compressed between two flat and parallel anvil faces (in a diamond anvil cell, for example) is non-hydrostatic. The resulting lattice strains, measured by X-ray diffraction, exhibit certain features, which are absent if truly hydrostatic conditions prevail. We describe the method of analysis of lattice strain in non-hydrostatic stress states. This is based on the transformation of stress axis into crystal axis and further on the calculations of the strain in a given direction by taking into account the pressure dependence of elastic moduli. Application of the theory is demonstrated with an example of a study of wüstite (FeO) at pressures up to 18 GPa. We found that the pressure of phase transition is proportional to the uniaxial stress component, which rises from 10.1 GPa for compression without pressure medium to 15.4 GPa in Ar pressure medium. Extrapolation to zero stress conditions gives the value 16.8 GPa, which is in good agreement with the data of Fei (Y. Fei, in: M.D. Dyar, C. MacComman, M.W. Schaefer (Eds.), Mineral Spectroscopy, Geochemical Society, 1996 pp. 243–254) (powder diffraction data, compression in He pressure medium, P tr=17(1) GPa) and Shu (J. Shu, Eos Trans. Am. Geophys. Union 75 (1998) 203) (single crystal diffraction data, compression in He pressure medium, P tr=18(1) GPa).