Geometric Refinement of the Crystal Structure of β-Mg2SiO4

Abstract

THE prediction of the details of a complicated inorganic crystal structure by calculation from first principles is not yet possible. Various attempts have been made to use electrostatic energy calculations of the Born-type for the prediction of the crystal structure of simple compounds, but these have met with limited success1,2. One aspect which has not been explored systematically is the influence of purely geometrical factors on interatomic distances and bond angles. When we consider the case of a crystal structure based on anion closest-packing and composed of octahedral and tetrahedral coordinations it is obvious that it could be undistorted only if, first, the tetrahedral cation–anion distances are 0.612 and the octahedral cation–anion distances are 0.707 (both relative to an anion–anion distance of 1.00), and, second, the individual cation–anion distances within each coordination polyhedron all have the same values. Usually, neither of these conditions is satisfied in actual crystal structures; therefore the coordination polyhedra are deformed in such a way as is geometrically necessary to make them fit each other within the structure.