Modified Goldschmidt tolerance factor calculator for ABX3 compounds

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+)Ce(3+)Fe(2+)Fe(3+)Fe(4+)Fe(6+)Gd(3+)La(3+)Mg(2+)Nd(3+)Pb(2+)Pb(4+)Pr(3+)Sr(2+)Zn(2+)	Å
-B-B(3+)Cr(3+)Fe(2+)Fe(3+)Fe(4+)Fe(6+)Hf(4+)Ni(2+)Ni(3+)Ni(4+)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.Check out http://abulafia.mt.ic.ac.uk/shannon/radius.php for a database of ionic radii. 

A ionic radii Å

B ionic radii Å

X ionic radii Å

Goldschmidt Tolerance Factor:

A-X bond length Å

B-X bond length Å

Goldschmidt Tolerance Factor:

To use the application click on the link below:

https://jaramillo.mit.edu/modified-goldschmidt-tolerance-factor-calculator-abx3-compounds