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

Abstract

The elastic constants C ij of a set of synthetic single crystals belonging to the join MgAl 2 O 4 -MnAl 2 O 4 (spinel sensu stricto-galaxite) were determined by Brillouin spectroscopy at ambient conditions. The C 11 component tends to remain constant for Mg-rich compositions (X Mn < 0.5) and decreases in Mn-rich compositions, whereas C 12 increases and C 44 decreases almost linearly from MgAl 2 O 4 to MnAl 2 O 4 . The bulk modulus K S is weakly dependent upon Mg-Mn substitution within experimental uncertainties, whereas the shear modulus G decreases with increasing Mn 2+ content. For MnAl 2 O 4 , C 11 = 271.3(1.3) GPa, C 12 = 164.8(1.3) GPa, C 44 = 124.9(5) GPa, K S = 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 MgAl 2 O 4 -MnAl 2 O 4 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, Mn 2+ , and Al in tetrahedral (T) and octahedral (M) sites, which span from 153 to 270 GPa ranking as follows: K M Mn < K M Mg < K T Mg ≈ K T Mn < K M Al << K T Al . Crystal bulk modulus was perfectly reproduced within 0.1% for all Mn 2+ -bearing samples. We also found a high linear correlation between the effective polyhedral bulk modulus and the ionic potential, IP, of the coordinating cations: K j i (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 MgAl 2 O 4 -MnAl 2 O 4 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.