Tolerance factor and phase stability of the garnet structure.

We introduce a structural descriptor, the tolerance factor, for the prediction and systematic description of the phase stability with the garnet structure. Like the tolerance factor widely adopted for the perovskite structure, it is a compositional parameter derived from the geometrical relationship between multi-type polyhedra in the garnet structure, and the calculation only needs the information of the ionic radius. A survey of the tolerance factor over 130 garnet-type compounds reveals that the data points are scattered in a narrow range. The tolerance factor is helpful in understanding the crystal chemistry of some garnet-type compounds and could serve as a guide for predicting the stability of the garnet phase. The correlation between the tolerance factor and the garnet-phase stability could be utilized by machine learning or high-throughput screening methods in material design and discovery.