Single-Crystal Elastic Properties of the Spinel (MgAl2O4) – Galaxite (MnAl2O4) Solid Solution Series
Abstract:Spinels are a subject of intense research in solid state physics, materials science and geosciences. Their general formula is T(A1-i)M(AiB2-i)X4 (A and B are cations, X are anions, T and M indicate tetrahedrally- and octahedrally-coordinated sites and i is the inversion degree). They are ideal materials to study the interplay between chemical substitutions, structure and the physical properties of solids. As spinel-structured ringwoodite (Mg,Fe)2SiO4 is the most abundant mineral in the lower transition zone, understanding the effect of chemical substitution on the elastic properties of spinels is of crucial for geophysics.
We have experimentally studied the variation of the elastic properties along the join MgAl2O4 – MnAl2O4. Crystals of 4 compositions along the join were synthesized at the very same experimental conditions and their crystal chemistry was fully characterized. Single-crystal elastic constants Cij of all the samples were measured by Brillouin spectroscopy at ambient conditions. For compositions with Mn/Mg < 0.5 C11 remains constant, then it decreases of ~4% for higher Mn contents. From MgAl2O4 to MnAl2O4 C12 lineraly increases ~ 5% and C44 decreases ~ 20% . The bulk modulus KS is almost constant, whereas the shear modulus G decreases ~ 18% across the join. The elastic constants of MnAl2O4 are C11 = 271.3 (± 1.3) GPa, C12 = 164.8 (± 1.3) GPa and C44 = 124.9 (5) GPa.
Using the empirical polyhedral approach  we have inferred the effectve polyhedral bulk moduli of Mg, Mn and Al in T and M sites. We observe that KMnM < KMgM < KMgT ≈ KMnT < KAlM << KAlT. The relationship between polyhedral moduli and ionic potential IP  can be expressed as Ki j (GPa) = 20 ( ± 2) × IP + 108 (± 10), where i is the cation, j is the site and IP is in units of (e/Å). Using our correlation and atomic radii from  we successfully reproduced the bulk modulus of different oxide spinels with bi- and tri-valent cations. Our preliminary results confirm that empirical correlations based on experimental data and simple models of interatomic interactions can successfully reproduce the relationship between chemical composition and elastic properties of oxide spinels.
References:  Hazen, R. M. (1988) Am. J. Sci., 288-A, 242;  Bosi, F., et al. (2011) Am. Mineral., 96, 594;  Shannon, R.D. (1976) Acta Crystall., A32, 751.