MgSiO₃ is of interest to geologists because it is abundant in the Earth’s mantle. Silicon is normally tetrahedrally coordinated by oxygen, but, at the high pressures found in the mantle, silicon becomes octahedrally coordinated and a perovskite structure is formed.

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(a) Given bond-valence parameters Rg-o = 1.693 and Ri-o- 1.624 , calculate the expected Mg-O and Si-O distances for a cubic perovskite. (b) Use the distances calculated in part (a) to estimate the tolerance factor 1 (Section 1.5.3), and state whether you would expect MgSiO3 to form as a cubic or a distorted perovskite. (c) Experiments identify MgSiO3 as a distorted perovskite. The Si-O distances are 1.78 (x2), 1.79 (x2), and 1.80 (x2). How do those compare to your estimate of the Si-O distance in part (a)? (d) The Mg-O distances are 2.00 , 2.06 (x2), 2.29 (x2), 2.41 (x2), 2.85 , 2.96 , and 3.11 (x2). Calculate the bond-valence sum for Mg+ as a qualitative estimate of whether this is a reasonable coordination environment for Mg+