Equation of state of brucite; single-crystal Brillouin spectroscopy study and polycrystalline pressure-volume-temperature measurement

Acoustic velocities of brucite were measured at room pressure in over 48 directions from Brillouin spectroscopy using a natural sample. These data are supplemented with volume measurements as a function of pressure and temperature that range from ambient conditions to 11 GPa and 873 K using synchrotron X-ray radiation at the National Syn-chrotron Light Source (NSLS) in a cubic-anvil apparatus (SAM-85) with a synthetic po-lycrystalline sample. The diffraction patterns are collected during cooling cycles to mini-mize the effect of deviatoric stress on the measurements. These data yield internally consistent thermoelastic parameters defining the equation of state of brucite along with the single-crystal elastic moduli. The Brillouin spectroscopy measurements are best fit with the following elastic model: C11 5 156.7(8), C33 5 46.3(8), C44 5 21.7(5), C12 5 44.4(10), C13 5 12.0(15), and C14 5 0.2(8) GPa. The resultant linear compressibilities of the a and c axes are 3.8(1) 3 1023 and 19.6(6) 3 1023 (GPa21), respectively, with the Reuss bound for the bulk modulus, KR 5 36.7(10) GPa and the Hill average, KH 5 46(1) GPa. The unit-cell parameters (a, c, and volume) determined from the diffraction measurements were fit with a Birch-Murnaghan equation of state, yielding K0 5 39.6(14) Gpa, K9 5 6.7(7), (]KT/]T)P 5 20.0114(16) GPa/K, and a 5 5.0(7) 3 1025/K. The bulk modulus and linear compressibilities from X-ray diffraction are in agreement with those from Brillouin spec-troscopy. The ratio of linear compressibility of the a to c axes is about five times at ambient conditions and reduces to almost unity by 10 GPa. The axial thermal expansions reflect a similar pressure dependence. The ambient shear anisotropy (C44/C66) is about 2.5.