Mapping Comparison of Goldschmidt's Tolerance Factor with Perovskite Structural Conditions

A new model describing physical structural constraints for the formation of simple ideal cubic perovskites is introduced and compared with Goldschmidt's tolerance formalism. Through a transformation or mapping into ionic radii space, the structural planar constraints of this new model are compared with the planar constraints of Goldschmidt's formalism, a semi-empirical relationship. The new model indicates: (1) a structural volume instability arises that has consistency with Goldschmidt's tolerance formalism, 0.77 < T < 1.00, for low symmetry crystals; (2) a region of (likely) increased structural stability occurs in close proximity to Goldschmidt's tolerance plane, T = 1.00; and, (3) the possibility for formation of cubic materials far from T = 1.00 including regions outside Goldschmidt's tolerance range, 0.77 < T < 1.05.