Non-monotonic compositional dependence of isothermal bulk modulus of the (Mg 1–x Mn x )Cr 2 O 4 spinel solid solutions, and its origin and implication

Abstract The compressibility of the spinel solid solutions, (Mg 1− x Mn x )Cr 2 O 4 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 P V data, yielding the following values for the isothermal bulk moduli ( K T ), 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 ( K T ′ fixed as 4). The K T value of the MgCr 2 O 4 spinel is in good agreement with existing experimental determinations and theoretical calculations. The correlation between the K T and x is not monotonic, with the K T values similar at both ends of the binary MgCr 2 O 4 MnCr 2 O 4 , but decreasing towards the middle. This non-monotonic correlation can be described by two equations, K T  = −49.2 (11) x  + 198.0 (4) ( x  ≤ ∼0.6) and K T  = 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 K T and composition of a solid solution series may be complicated, and great care should be paid while estimating the K T of some intermediate compositions from the K T of the end-members.