Goldschmidt tolerance factor

From Online Dictionary of Crystallography

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Facteur de tolérance de Goldschmidt (Fr); Fattore di tolleranza di Goldschmidt (It);

Goldschmidt's tolerance factor is a a dimensionless number that measures the stability and distortion of crystal structures. Originally introduced to describe perovskite structure, tolerance factors are today also used for ilmenite. It can be used to calculate the compatibility of an ion with a crystal structure.

The Goldschmidt tolerance factor (t) is calculated from the ratio of the ionic radii:

[math]t={r_A+r_0 \over \sqrt{2}(r_B+r_0)}[/math]

where rA is the radius of the A-cation, rB is the radius of the B-cation and r0 is the radius of the anion (usually oxygen).

In an ideal cubic perovskite structure the cell parameter a can be calculated from the atomic radii as follows: