Graph similarity drives zeolite diffusionless transformations and intergrowth

Predicting and directing polymorphic transformations is a critical challenge in zeolite synthesis^1-3. Interzeolite transformations enable selective crystallization^4-7, but are often too complex to be designed by comparing crystal structures. Here, computational and theoretical tools are combined to both exhaustively data mine polymorphic transformations reported in the literature and analyse and explain interzeolite relations. It was found that crystallographic building units are weak predictors of topology interconversion and insufficient to explain intergrowth. By introducing a supercell-invariant metric that compares crystal structures using graph theory, we show that diffusionless (topotactic and reconstructive) transformations occur only between graph-similar pairs. Furthermore, all the known instances of intergrowth occur between either structurally similar or graph similar frameworks. We identify promising pairs to realize diffusionless transformations and intergrowth, with hundreds of low-distance pairs identified among known zeolites, and thousands of hypothetical frameworks connected to known zeolite counterparts. The theory may enable the understanding and control of zeolite polymorphism.