High-pressure elasticity of a natural magnetite crystal

Abstract

Variation of the sound velocities, elastic constants, and compressibility of a natural magnetite crystal were determined using gigahertz ultrasonic interferometry and single-crystal X-ray diffraction to 8.7 GPa. At ambient pressure, the elastic constants are (in GPa): c 11 = 260.5(1.0), c 12 = 148.3(3.0), and c 44 = 63.3(1.5). While c 11 and c 12 have similar positive pressure derivatives of 5.14(13) and 5.39(10), respectively, the c 44 elastic constant exhibits mode-softening over this pressure range, with d c 44 /d P = 0.13(4), calculated from the pressure dependence of the [100] shear velocity. The adiabatic bulk modulus ( K 0S ) is 185.7(3.0) GPa, with K S = 5.1(1), and the shear modulus ( G 0 ) is 60.3(3.0) GPa, with G ′ = −0.1(1). The bulk modulus and its pressure derivative obtained dynamically are consistent with the isothermal equation of state, measured on the same sample by single-crystal X-ray diffraction, yielding K 0T = 180.0(1.0) and K T ′ = 5.2(4). Pressure-induced shear-mode softening in magnetite is most likely related to magnetoelastic coupling and the first-order phase transition to an orthorhombic structure above 21 GPa.