modified Goldschmidt Tolerance Factor Calculator for ABX3 compounds
Created by Stephen A. Filippone, Jan. 2016
Note: the modified-tolerance factor, t', has been shown to be of use for oxides and sulfides1 but no evidence for any other species.
with rA,rB and rX being the ionic radii of A and B cations and X anions respectively. Δχ(X-A) is the electronegativity difference between X and A, and Δχ(O-A) is the electronegativity differences between O and A.
modified Goldschmidt Tolerance Factor:
Goldschmidt Tolerance Factor:
Here you can manually enter either the ionic radii of individual species or A-X and B-X bond lengths.
|>1||Hexagonal||A ion too big or B ion too small||BaNiO3|
|0.9-1||Cubic||A and B ions have ideal size||SrTiO3, BaTiO3|
|0.71-0.9||Orthorhombic/Rhombohedral||A ions too small to fit into B ion interstices||GdFeO3, CaTiO3|
|<0.71||Different Structures||A ions and B have similar ionic radii||FeTiO3|
http://www.me.utexas.edu/~benedekgroup/ToleranceFactorCalculator/#home (only for oxides and flourides)
References and Reading:
1. Brehm, J. A., Bennett, J. W., Schoenberg, M. R., Grinberg, I. & Rappe, A. M. The structural diversity of ABS3 compounds with d0 electronic configuration for the B-cation. The Journal of Chemical Physics 140, 224703 (2014).