Thermal expansion of Mg2SiO4 ringwoodite at high pressures

Unit cell volumes of Mg₂SiO₄ ringwoodite were measured at temperatures from 300 to 2000 K and pressure from 15 to 24 GPa and at a temperature of 300 K and pressure from 0 to 21 GPa. The measurements were conducted using a Kawai-type multianvil apparatus that is equipped with an oscillation system to obtain high-quality diffraction pattern against grain growth. We obtained the following relations and parameters describing the pressure-volume-temperature relations of Mg₂SiO₄ ringwoodite. The unit cell volume of Mg₂SiO₄ ringwoodite at 0 GPa and 300 K is 524.8(1) ų (values in parentheses are errors). Fixing the isothermal bulk modulus to 182 GPa, its pressure derivative is 4.6(2). The thermal expansion coefficient at 0 GPa is α₀ = 2.57(9) × 10^-5 + 1.42(8) × 10^-8 (T - 300) K^-1, where T is absolute temperature in K, and its logarithmic volume dependence, Anderson-Grüneisen parameter, is 6.9(4). The temperature derivative of the isothermal bulk modulus is (∂K_T/∂T) = -0.029(1) GPa K^-1. The Debye temperature, Θ, is 846(26) K. The Grüneisen parameter and its logarithmic volume dependence are 1.93(3) and 3.5(3), respectively. The adiabatic temperature gradient in the mantle largely depends on temperature. That in the model Mg2SiO4 mantle increases from 0.29 to 0.40 K km^-1 when temperature increases from 1600 to 2000 K.