Non-monotonic compositional dependence of isothermal bulk modulus of the (Mg1–xMnx)Cr2O4 spinel solid solutions, and its origin and implication

Abstract

The compressibility of the spinel solid solutions, (Mg1−xMnx)Cr2O4 with x = 0.00 (0), 0.20 (0), 0.44 (2), 0.61 (2), 0.77 (2) and 1.00 (0), has been investigated by using a diamond-anvil cell coupled with synchrotron X-ray radiation up to ∼10 GPa (ambient T). The second-order Birch–Murnaghan equation of state was used to fit the PV data, yielding the following values for the isothermal bulk moduli (KT), 198.2 (36), 187.8 (87), 176.1 (32), 168.7 (52), 192.9 (61) and 199.2 (61) GPa, for the spinel solid solutions with x = 0.00 (0), 0.20 (0), 0.44 (2), 0.61 (2), 0.77 (2) and 1.00 (0), respectively (KT′ fixed as 4). The KT value of the MgCr2O4 spinel is in good agreement with existing experimental determinations and theoretical calculations. The correlation between the KT and x is not monotonic, with the KT values similar at both ends of the binary MgCr2O4MnCr2O4, but decreasing towards the middle. This non-monotonic correlation can be described by two equations, KT = −49.2 (11)x + 198.0 (4) (x ≤ ∼0.6) and KT = 92 (41)x + 115 (30) (x ≥ ∼0.6), and can be explained by the evolution of the average bond lengths of the tetrahedra and octahedra of the spinel solid solutions. Additionally, the relationship between the thermal expansion coefficient and composition is correspondingly reinterpreted, the continuous deformation of the oxygen array is demonstrated, and the evolution of the component polyhedra is discussed for this series of spinel solid solutions. Our results suggest that the correlation between the KT and composition of a solid solution series may be complicated, and great care should be paid while estimating the KT of some intermediate compositions from the KT of the end-members.