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Goldschmidt's tolerance factor is an indicator for the stability and distortion of crystal structures. It was originally only used to describe perovskite structure, but now tolerance factors are also used for ilmenite.
Contents
Alternatively the tolerance factor can be used to calculate the compatibility of an ion with a crystal structure.
The first description of the tolerance factor for perovskite was made by Victor Moritz Goldschmidt in 1926.
Mathematical expression
The Goldschmidt tolerance factor (t) is a dimensionless number that is calculated from the ratio of the ionic radii:
In an ideal cubic perovskite structure the axis of the unit cell (a) can be described with the following equation:
Perovskite structure
The perovskite structure has the following tolerance factors (t):
References
Goldschmidt tolerance factor Wikipedia(Text) CC BY-SA