Olivine [(Mg, Fe)2SiO4] and pyroxene [(Mg, Fe)Si2O6] are naturally occurring silicate phases. Both the phases crystallize with orthorhombic symmetry, displaying ordering of Mg2+ and Fe2+ in their non-equivalent octahedral lattice sites (M1, M2). We address two major issues: (1) how far an inversion of the cation ordering: type I (Mg2+ in M1; Fe2+ in M2) to type II (Mg2+ in M2; Fe2+in M1) can modify their elastic properties and (2) what are the effects of this inversion on their electronic properties? Using density functional theory, we calculate the elastic constant tensors (Cij) as a function of hydrostatic pressure for types I and II ordering. Our calculations suggest that the inversion (types I to II) in olivine significantly reduces the shear elastic constant C55 (∼25%). This has little effect on the Cij of pyroxene in ambient condition, but the effects become strong at elevated pressures (100 GPa), resulting in large variations (>40%) of all the shear elastic constants: C44, C55, and C66. We predict contrasting variations in compressional (VP) and shear (VS) wave velocities by 1% and 9% and by 2% and 11% for olivine and pyroxene, respectively, on types I to II switchover. Our Debye temperature (θD) calculations show that θD of olivine is less sensitive to ordering inversion, whereas that of pyroxene varies substantially (∼22%) under ambient condition. We evaluate the electronic DOS of pyroxene, and obtain a large difference in the magnetic moment between types I and II.

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