Goldschmidt tolerance factor, perovskite lattice

For the ideal cubic lattice of ABO3 perovskite, A is the larger cation surrounded by eight BC>6 octahedra. In order to estimate the general possibility of perovskite lattice formation from ionic radii, the Goldschmidt tolerance factor (ts) can be used [i] ... 

This type of orthorhombic perovskite structure appears, if the tolerance factor of Goldschmidt is smaller than t — 0.88. The example of the compound NaMnFs [t = 0.78), showing doubled lattice constants a and h (287), is likely to mark the lower limit of the field in which orthorhombic fluoro-perovskits of the GdFe03-t3q>e may occur. Fluoroperovskites which have a smaller tolerance factor than t = 0.78 never have been observed so far, nor do fluoride structures of the ilmenite type seem to exist, which might be expected for ya = Me, corresponding to 1=1/1/2=0.71. 

The ideal structure, however, was found to be retained in very few cases. Orthorhombic and rhombohedral distortions are commonly found along with less common distortions - tetragonal, monoclinic, and triclinic. The measure of deviation from the ideal structure can be represented by the tolerance factor (t) as introduced by Goldschmidt [29]. For an ideal perovskite structure, the t value is found to be unity. However, perovskite lattices with lower t values (0.75 < f < 1) are found to exist [2] ... 

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