Elasticity of tephroite (α-Mn₂SiO₄) and a comparison of the elastic properties of silicate olivines

The elastic constants of pure tephroite (α-Mn₂SiO ₄) have been determined by Brillouin spectroscopy. From measurements, the average aggregate bulk and shear moduli at ambient conditions are 129.8 ± 0.5 and 53.1 ± 0.4 GPa, respectively, which also confirm the reality of the unexpected high elastic moduli in tephroite. An analysis based on the present data and those in literature has revealed the relative orders: fayalite > tephroite ≥ forsterite for bulk modulus and forsterite >> tephroite > fayalite for shear modulus. It also indicates that the propagation velocity of a sound wave inside forsterite will be considerably changed by dissolving a small amount of Mn²⁺ and/or Fe²⁺ (for shear wave) and Ni²⁺ cations (for compressional wave). The causes for the significant difference between forsterite and the 3d silicate olivines and the unexpected elastic behavior in tephroite have been explored by considering the nature of both electron orbitals and MO₆ octahedra.