The elasticity of MgAl2O4–MnAl2O4 spinels by Brillouin scattering and an empirical approach for bulk modulus prediction

The elastic constants Cij of a set of synthetic single crystals belonging to the join MgAl2O4–MnAl2O4 (spinel sensu stricto–galaxite) were determined by Brillouin spectroscopy at ambient conditions. The C11 component tends to remain constant for Mg-rich compositions (XMn < 0.5) and decreases in Mn-rich compositions, whereas C12 increases and C44 decreases almost linearly from MgAl2O4 to MnAl2O4. The bulk modulus KS is weakly dependent upon Mg-Mn substitution within experimental uncertainties, whereas the shear modulus G decreases with increasing Mn2+ content. For MnAl2O4, C11 = 271.3(1.3) GPa, C12 = 164.8(1.3) GPa, C44 = 124.9(5) GPa, KS = 200(1) GPa, and G = 88.7(5) GPa. Based on the “polyhedral approach,” we developed a model that describes the crystal bulk moduli of the MgAl2O4–MnAl2O4 spinels in terms of their cation distribution and the polyhedral bulk moduli of the different cations. We refined a set of values for the effective polyhedral bulk modulus of Mg, Mn2+, and Al in tetrahedral (T) and octahedral (M) sites, which span from 153 to 270 GPa ranking as follows: KMMn < KMMg < KTMg ≈ KTMn < KMAl << KTAl. Crystal bulk modulus was perfectly reproduced within 0.1% for all Mn2+-bearing samples. We also found a high linear correlation between the effective polyhedral bulk modulus and the ionic potential, IP, of the coordinating cations: Kij (GPa) = 20(2) IP + 108(10) (where i indicates the cation and j the polyhedral site). We tested this simple correlation by calculating the specific effective polyhedral bulk modulus of several cations in T and M coordination and then predicting the crystal bulk modulus for several spinel compositions. The success of our simple correlation in modeling the bulk modulus of spinels outside the MgAl2O4–MnAl2O4 system is encouraging, and suggests that the relationships between chemical composition, cation distribution and elastic properties in spinel-structured minerals and materials can indeed be expressed by relatively simple models.