Modified Goldschmidt tolerance factor calculator for ABX3 compounds

Created by Stephen A. Filippone, Jan. 2016

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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 r_A,r_B and r_X 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
-A-Ba(2+)Bi(3+)Bi(5+)Ca(2+)Fe(2+)Fe(3+)Fe(4+)Fe(6+)Gd(3+)Mg(2+)Pb(2+)Pb(4+)Sr(2+)Zn(2+)K(1+)	Å
-B-B(3+)Fe(2+)Fe(3+)Fe(4+)Fe(6+)Hf(4+)Ni(2+)Ni(3+)Ni(4+)Nb(5+)Sn(4+)Ti(4+)Zr(4+)	Å
-X-O(2-)S(2-)Se(2-)	Å

modified Goldschmidt Tolerance Factor:

Goldschmidt Tolerance Factor:

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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/perovskites.html

4. https://github.com/materialsproject/pymatgen/blob/master/pymatgen/analysis/defects/ionic_radii.json

5. https://en.wikipedia.org/wiki/Perovskite_(structure)