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.
| Species | Ionic Radius |
| Å | |
| Å | |
| Å |
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.
| 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
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).
2. https://en.wikipedia.org/wiki/Goldschmidt_tolerance_factor
3. http://www.princeton.edu/~cavalab/tutorials/public/structures/perovskite...
4. https://github.com/materialsproject/pymatgen/blob/master/pymatgen/analys...
5. https://en.wikipedia.org/wiki/Perovskite_(structure)