Modified Goldschmidt tolerance factor calculator for ABX3 compounds

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.

Tolerance factor equation

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.

Species Ionic Radius

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.Check out for a database of ionic radii. 

t >Structure Explanation Example
>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

Other Calculators (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).