High-pressure elasticity of a natural magnetite crystal

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): c₁₁ = 260.5(1.0), c₁₂ = 148.3(3.0), and c₄₄ = 63.3(1.5). While c₁₁ and c₁₂ have similar positive pressure derivatives of 5.14(13) and 5.39(10), respectively, the c₄₄ elastic constant exhibits mode-softening over this pressure range, with dc₄₄/dP = -0.13(4), calculated from the pressure dependence of the [100] shear velocity. The adiabatic bulk modulus (K_os) is 185.7(3.0) GPa, with K_s = 5.1(1), and the shear modulus (G_o) 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_OT = 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.