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- Title
The elasticity of MgAl<sub>2</sub>O<sub>4</sub>-MnAl<sub>2</sub>O<sub>4</sub> spinels by Brillouin scattering and an empirical approach for bulk modulus prediction.
- Authors
BRUSCHINI, ENRICO; SPEZIALE, SERGIO; ANDREOZZI, GIOVANNI B.; BOSI, FERDINANDO; HALENIUS, ULF
- Abstract
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: Bi KMnM < KMgM < KMgT ≈ KMnT < KAlM < KAlT. 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 andj 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.
- Subjects
MAGNESIUM compounds; MAGNESIUM crystals; SINGLE crystals spectra; BRILLOUIN scattering; BULK modulus
- Publication
American Mineralogist, 2015, Vol 100, Issue 2/3, p644
- ISSN
0003-004X
- Publication type
Article
- DOI
10.2138/am-2015-4993