High-pressure elasticity of calcium oxide: A comparison between Brillouin spectroscopy and radial X-ray diffraction

摘要

Single-crystal Brillouin scattering to 25.2 GPa and powder X-ray diffraction to 65.2 GPa in a radial geometry were carried out on CaO (lime) at ambient temperature in a diamond cell. From Brillouin scattering measurements the isentropic elastic constants of CaO at ambient conditions are C 11 = 219.4 (7), C 12 = 58.1 (7), C 44 = 80.0 (2) GPa, where the numbers in parentheses are 1σ uncertainties on the last digit. The pressure derivatives of the compressional and off-diagonal constants at ambient pressure are ?C 11/?P = 9.9 (1), ?C 12/?P = 2.2 (1), respectively. The pressure derivative of the shear constant is ?C 44/?P = 0.25 (3), and it becomes negative at pressures above 5.9 GPa. Aggregate bulk and shear moduli are K S0 = 112.0 (2) and G 0 = 80.05 (9) GPa, and their pressure derivatives are 4.72 (6) and 1.69 (5), respectively. The radial X-ray diffraction data allow us to estimate the yield strength and the elastic constants of CaO using a phenomenological lattice strain model. The calculated strength of CaO increases from 0.3 to 1.9 GPa in the pressure range between 5.6 and 57.8 GPa. The estimated elastic constants are in good agreement with the extrapolation of the Brillouin data up to 36.6 GPa. At higher pressures, C 11 appears softer and C 12 appears stiffer than the extrapolation of Brillouin results. The value of C 44 from radial diffraction is in agreement with the Brillouin data through the entire experimental pressure range. The discrepancies between Brillouin and radial diffraction data for C 11 and C 12 can be reconciled if α, the parameter which describes degree of stress/strain continuity across the sample's grains boundary, is allowed to vary from 1 at 36.6 GPa to 0.82 at 65.2 GPa. The “hydrostatic” cell volumes determined by applying lattice strain theory were fitted to the third-order Birch-Murnaghan equation. The fitted bulk modulus and its pressure derivative are K T0 = 110 (5) GPa and (?K T /?P) T0 = 4.5 (4), consistent with the Brillouin results, although possible softening of the equation of state at high pressure has been identified. The general agreement between the results of the two methods indicates that radial diffraction with lattice strain theory is a valid probe of the mechanical properties of a moderately soft cubic solid as CaO at ultrahigh pressures. However, more tests are required to quantify the effect of plasticity and texturing on the results of this method.