Goldschmidt tolerance factor

Goldschmidt's tolerance factor (from the German word Toleranzfaktor) is an indicator for the stability and distortion of crystal structures.

[1] It was originally only used to describe the perovskite ABO3 structure, but now tolerance factors are also used for ilmenite.

[2] Alternatively the tolerance factor can be used to calculate the compatibility of an ion with a crystal structure.

[3] The first description of the tolerance factor for perovskite was made by Victor Moritz Goldschmidt in 1926.

) is a dimensionless number that is calculated from the ratio of the ionic radii:[1] In an ideal cubic perovskite structure, the lattice parameter (i.e., length) of the unit cell (a) can be calculated using the following equation:[1] The perovskite structure has the following tolerance factors (t):