we used to calculate tolerance factor only for perovskite .
is it meaning full calculation of tolerance factor for other structures ?
[1]Goldschmidt proposed
“tolerance factor” ( t=rA +rO / √2 ( rB+rO)
where rA, rB and rO are the ionic radii of A, B and O, respectively to study the stability of perovskites.
[2] For an ideal perovskite, the ratio of D (A–O), the bond length of A–O bond, to D (B–O),the bond length of B–O bond is √2:1.Thus, if the bond length is roughly assumed to be the sum of two ionic radii,the “t” value of an ideal perovskite should be equal to 1.0.However, Goldschmidt found that, as an experimental fact, “t” values of most cubic perovskites are in the range of 0.8–0.9,and distorted perovskites occur in somewhere wider range of “t”.
[3]Goldschmidt’s tolerance factor "t " has been widely accepted as a criterion for the formation of the perovskite structure, a number of researchers have used it to discuss the perovskite stability, including oxides, fluorides, chlorides. Up to now, almost all known perovskite have “t” values in the range of 0.75–1.00.
REF:
Journal of Alloys and Compounds 372 (2004) 40–48
yes u are right..but my question is this formula can be extended for Rhombohedral structure eg.Fe2O3 .
Goldschmidt's tolerance factor is an indicator for the stability and distortion of crystal structures.[1] It was originally only used to describe perovskite structure, but now tolerance factors are also used for ilmenite
here ilmenite structure also called rhombohedral structure eg.Ti-doped Fe2O3
Tolerance factor is pure geometry. You can create some formula for any type of structure using the expected positions of ions and assumption that the ions are solid spheres touching each other. The question is whether this formula will be useful. In case of ABO3 compounds single perovskite-type tolerance factor appears to describe the whole range of the RA:RB ratios from extremely small B ions forming aragonite structure to RA:RB~1 when the ilmenite structure is formed. This is why this case became the most widely applied. Another cases often mentioned in the textbooks are AX (NaCl or CsCl structures) and AX2 (quartz, rutile or fluorite structure).
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