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(A_1-i)^M(A_iB_2-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 – MnAl₂O_4. 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 C_ij 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 K_S 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 [1] we have inferred the effectve polyhedral bulk moduli of Mg, Mn and Al in T and M sites. We observe that K_Mn^M < K_Mg^M < K_Mg^T  ≈ K_Mn^T < K_Al^M << K_Al^T. The relationship between polyhedral moduli and ionic potential IP [2] can be expressed as K_i ^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 [3] 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: [1] Hazen, R. M. (1988) Am. J. Sci., 288-A, 242; [2] Bosi, F., et al. (2011) Am. Mineral., 96, 594; [3] Shannon, R.D. (1976) Acta Crystall., A32, 751.