Deriving the Goldschmidt-like tolerance factors for solids: a simplified polyhedral approach

Abstract The approach to derive the Goldschmidt tolerance factor (GTF) for perovskite structures has been generalized and reformulated in terms of the geometry of regular polyhedra. The polyhedral approach was shown to be applicable for deriving the conceptual and functional GTF analogs for the non-perovskite structures containing at least two different and reasonably regular coordination polyhedra with the same or nearly the same edge lengths.