Anisotropy in MgO Measured in the Deformation-DIA by using High-resolution Monochromatic Diffraction

Introduction Crystalline materials are generally elastically anisotropic. Even cubic materials are characterized by three elastic constants, whereas isotropic elastic material has only two. To define elastic anisotropy for the cubic materials, it is common to use the elastic anisotropy factor S = S11-S12S44/2 or A = 2(S11-S12)/S44, where Sij are elastic compliances. Materials become isotropic when S = 0 or A = 1. Recent high-pressure ultrasonic and Brillouin scattering experiments show that elastic anisotropy in MgO (fcc) remains positive, decreasing only modestly with pressure. If we extrapolate the anisotropy reported in these measurements to higher pressures, S becomes zero at a pressure of 11 GPa [1], 19 GPa [2], 21 GPa [3], and 21.5 GPa [4]. On the other hand, diffraction studies in the Drickamer cell [5] show that MgO becomes elastically isotropic at much lower pressures between 2 and 4 GPa. To address the discrepancy in the anisotropy factor between diffraction observations and ultrasonic or Brillouin scattering data, we examined nonhydrostatic strain in MgO up to 6 GPa at room temperature by using deformation-DIA (D-DIA) [6] and monochromatic diffraction with a 2-D charge-coupled device (CCD) detector. We used sintered polycrystalline cubic boron nitride (cBN) anvils that are x-ray transparent, which enabled us to collect complete Debye rings (with the entire 360° azimuth coverage) with a 2θ range up to about 12°. By using high-energy x-rays (small wavelengths), diffraction lines down to about 1 Å can be recorded within this 2θ range. The ellipticity of the Debye rings provided information on elastic lattice strains due to the differential stress. An iso-stress (Reuss) model was assumed, and anisotropy A was estimated from the lattice strains. The correlation between anisotropy and the differential stress level is discussed here.