Nonlinear variation of structural, thermodynamic and elastic properties of Mg2SiO4-ringwoodite caused by cation disorder

Understanding the impacts of cation disorder (characterized by the inversion parameter x, the Mg fraction on the tetrahedral site) on the structural, and physical–chemical properties of Mg₂SiO₄-ringwoodite (Rw) is very important. In this study, first-principles method combined with quasi-harmonic approximation theory has been used to obtain the microstructures, thermodynamic properties, and elastic properties of Rw at six different cation disorder states, from normal spinel configuration (x = 0) to inverse spinel configuration (x = 1). By the cation configurations with the lowest enthalpies for the investigated x values, we have established quantitative relations between x and physical–chemical properties like zero-pressure volume (V₀), isothermal bulk modulus (K_T), the first pressure derivative of K_T (\({{K}}_{{T}}^{\prime}\)), the temperature derivative of K_T (∂K_T/∂T), thermal expansion coefficients (α), isobaric heat capacity (C_P), vibrational entropy (S), adiabatic bulk modulus (K_S), shear modulus(G), compressional wave velocity (V_P), and shear wave velocity (V_S). Our results show that all investigated physical–chemical properties of Rw are likely quadratically correlated to x, with the extremums of the quadratic functions presumably corresponding to the state of full cation disorder (x = 2/3). Therefore, any simplified linear extrapolation or interpolation of the properties of Rw with different cation disorders should be viewed with great caution.