Extended Tolerance Factor

The extended formula for Goldschmidt's tolerance factor is: \[ \alpha = \frac{r_{A,\text{eff}} + r_{X,\text{eff}}} {\sqrt{2} \left( r_B + 0.5 h_{X,\text{eff}} \right)} \] where:

\(r_{A,\text{eff}}\): effective radius of cation A
\(r_B\): radius of cation B
\(r_{X,\text{eff}}\): effective radius of anion
\(h_{X,\text{eff}}\): cylinder length of anion

The globularity of cation A should be considered for greater accuracy.

Article: https://doi.org/10.1039/C4SC02211D

Cation A

Select A:

Cation A volume (Å³): \( V_{a} = \tfrac{4}{3} \pi r_{a}^3 ;\;\; r_{a} = \sqrt[3]{\tfrac{3·V_{a}}{4\pi}} \)

Article: https://doi.org/10.1016/j.jssc.2022.123635

Cation B

Select B:

\(r_B (Å)\):

Anion

Select X:

\(r_{X,\text{eff}} (Å):\)

\(h_{X,\text{eff}} (Å):\)