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Graph similarity drives zeolite diffusionless transformations and intergrowth


Predicting and directing polymorphic transformations is a critical challenge in zeolite synthesis1,2,3. Interzeolite transformations enable selective crystallization4,5,6,7, 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.

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Fig. 1: Types of zeolite transformations and classical explanations.
Fig. 2: Graph and supercell matching.
Fig. 3: Structural and graph similarities in zeolites.

Data availability

The zeolite datasets analysed during the current study are available online at the IZA Database ( and at the Predicted Crystallography Open Database ( Complete references for the literature analysed in this work, pairwise distances between known zeolites and isomorphism between hypothetical and known zeolites are available in the Supplementary Information.

Code availability

The code used to download journal articles for large-scale text mining is available at The code used to variationally compare crystal structures as supercell graphs is available from the corresponding author on request.


  1. 1.

    Davis, M. E. Ordered porous materials for emerging applications. Nature 417, 813–821 (2002).

    CAS  Article  Google Scholar 

  2. 2.

    Maldonado, M., Oleksiak, M. D., Chinta, S. & Rimer, J. D. Controlling crystal polymorphism in organic-free synthesis of Na-zeolites. J. Am. Chem. Soc. 135, 2641–2652 (2013).

    CAS  Article  Google Scholar 

  3. 3.

    Gallego, E. M. et al. ‘Ab initio’ synthesis of zeolites for preestablished catalytic reactions. Science 355, 1051–1054 (2017).

    CAS  Article  Google Scholar 

  4. 4.

    Honda, K. et al. Role of structural similarity between starting zeolite and product zeolite in the interzeolite conversion process. J. Nanosci. Nanotechnol. 13, 3020–3026 (2013).

    CAS  Article  Google Scholar 

  5. 5.

    Marler, B. & Gies, H. Hydrous layer silicates as precursors for zeolites obtained through topotactic condensation: a review. Eur. J. Mineral. 24, 405–428 (2012).

    CAS  Article  Google Scholar 

  6. 6.

    Eliášová, P. et al. The ADOR mechanism for the synthesis of new zeolites. Chem. Soc. Rev. 44, 7177–7206 (2015).

    Article  Google Scholar 

  7. 7.

    Li, C., Moliner, M. & Corma, A. Building zeolites from precrystallized units: nanoscale architecture. Angew. Chem. Int. Ed. 57, 15330–15353 (2018).

    CAS  Article  Google Scholar 

  8. 8.

    Goel, S., Zones, S. I. & Iglesia, E. Synthesis of zeolites via interzeolite transformations without organic structure-directing agents. Chem. Mater. 27, 2056–2066 (2015).

    CAS  Article  Google Scholar 

  9. 9.

    Baerlocher, C., McCusker, L. B. & Olson, D. H. Atlas of Zeolite Framework Types 6th edn (Elsevier, 2007).

  10. 10.

    Xie, B. et al. Organotemplate-free and fast route for synthesizing beta zeolite. Chem. Mater. 20, 4533–4535 (2008).

    CAS  Article  Google Scholar 

  11. 11.

    Iyoki, K., Itabashi, K. & Okubo, T. Progress in seed-assisted synthesis of zeolites without using organic structure-directing agents. Microporous Mesoporous Mater. 189, 22–30 (2014).

    CAS  Article  Google Scholar 

  12. 12.

    Itabashi, K., Kamimura, Y., Iyoki, K., Shimojima, A. & Okubo, T. A working hypothesis for broadening framework types of zeolites in seed-assisted synthesis without organic structure-directing agent. J. Am. Chem. Soc. 134, 11542–11549 (2012).

    CAS  Article  Google Scholar 

  13. 13.

    Verheyen, E. et al. Design of zeolite by inverse sigma transformation. Nat. Mater. 11, 1059–1064 (2012).

    CAS  Article  Google Scholar 

  14. 14.

    Zhao, Z. et al. Insights into the topotactic conversion process from layered silicate RUB-36 to FER-type zeolite by layer reassembly. Chem. Mater. 25, 840–847 (2013).

    CAS  Article  Google Scholar 

  15. 15.

    Van Tendeloo, L., Gobechiya, E., Breynaert, E., Martens, J. A. & Kirschhock, C. E. A. Alkaline cations directing the transformation of FAU zeolites into five different framework types. Chem. Commun. 49, 11737–11739 (2013).

    Article  Google Scholar 

  16. 16.

    O’Keeffe, M. & Hyde, S. T. The asymptotic behavior of coordination sequences for the 4-connected nets of zeolites and related structures. Z. Kristallogr. 211, 73–78 (1996).

    Google Scholar 

  17. 17.

    Foster, M. D. et al. Chemically feasible hypothetical crystalline networks. Nat. Mater. 3, 234–238 (2004).

    CAS  Article  Google Scholar 

  18. 18.

    Treacy, M., Rivin, I., Balkovsky, E., Randall, K. & Foster, M. Enumeration of periodic tetrahedral frameworks. II. Polynodal graphs. Microporous Mesoporous Mater. 74, 121–132 (2004).

    CAS  Article  Google Scholar 

  19. 19.

    Witman, M. et al. Cutting materials in half: a graph theory approach for generating crystal surfaces and its prediction of 2D zeolites. ACS Cent. Sci. 4, 235–245 (2018).

    CAS  Article  Google Scholar 

  20. 20.

    Blatov, V. A. Topological relations between three-dimensional periodic nets. I. UNINODAL nets. Acta Crystallogr. A 63, 329–343 (2007).

    CAS  Article  Google Scholar 

  21. 21.

    Porter, D. A., Easterling, K. E. & Sherif, M. Phase Transformations in Metals and Alloys. 3rd edn (CRC Press, 2009).

  22. 22.

    Alberti, A., Cruciani, G. & Martucci, A. Reconstructive phase transitions induced by temperature in gmelinite-Na zeolite. Am. Mineral. 102, 1727–1735 (2017).

    Article  Google Scholar 

  23. 23.

    Dusselier, M., Kang, J. H., Xie, D. & Davis, M. E. CIT-9: a fault-free gmelinite zeolite. Angew. Chem. Int. Ed. 56, 13475–13478 (2017).

    CAS  Article  Google Scholar 

  24. 24.

    Schieber, T. A. et al. Quantification of network structural dissimilarities. Nat. Commun. 8, 13928 (2017).

    CAS  Article  Google Scholar 

  25. 25.

    Bartók, A. P., Kondor, R. & Csányi, G. On representing chemical environments. Phys. Rev. B 87, 184115 (2013).

    Article  Google Scholar 

  26. 26.

    Jordá, J. L. et al. Synthesis of a novel zeolite through a pressure-induced reconstructive phase transition process. Angew. Chem. Int. Ed. 52, 10458–10462 (2013).

    Article  Google Scholar 

  27. 27.

    Deem, M. W., Pophale, R., Cheeseman, P. A. & Earl, D. J. Computational discovery of new zeolite-like materials. J. Phys. Chem. C 113, 21353–21360 (2009).

    CAS  Article  Google Scholar 

  28. 28.

    Keller, E. B., Meier, W. M. & Kirchner, R. M. Synthesis, structures of AlPO4-C and AlPO4-D, and their topotactic transformation. Solid State Ion. 43, 93–102 (1990).

    CAS  Article  Google Scholar 

  29. 29.

    Alberti, A. & Martucci, A. Reconstructive phase transitions in microporous materials: rules and factors affecting them. Microporous Mesoporous Mater. 141, 192–198 (2011).

    CAS  Article  Google Scholar 

  30. 30.

    Anderson, M. W. et al. Predicting crystal growth via a unified kinetic three-dimensional partition model. Nature 544, 456–459 (2017).

    CAS  Article  Google Scholar 

  31. 31.

    Kim, E. et al. Machine-learned and codified synthesis parameters of oxide materials. Sci. Data 4, 170127 (2017).

    CAS  Article  Google Scholar 

  32. 32.

    Jensen, Z. et al. A machine learning approach to zeolite synthesis enabled by automatic literature data extraction. ACS Cent. Sci. 5, 892–899 (2019).

    CAS  Google Scholar 

  33. 33.

    Baerlocher, Ch. & McCusker, L. B. Database of Zeolite Structures (Structure Commission of the International Zeolite Association, 2019);

  34. 34.

    Schröder, K. P. et al. Bridging hydrodyl groups in zeolitic catalysts: a computer simulation of their structure, vibrational properties and acidity in protonated faujasites (HY zeolites). Chem. Phys. Lett. 188, 320–325 (1992).

    Article  Google Scholar 

  35. 35.

    Pophale, R., Cheeseman, P. A. & Deem, M. W. A database of new zeolite-like materials. Phys. Chem. Chem. Phys. 13, 12407–12412 (2011).

    CAS  Article  Google Scholar 

  36. 36.

    Xie, T. & Grossman, J. C. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett. 120, 145301 (2018).

    CAS  Article  Google Scholar 

  37. 37.

    Cordella, L. P., Foggia, P., Sansone, C. & Vento, M. A. (Sub)graph isomorphism algorithm for matching large graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1367–1372 (2004).

    Article  Google Scholar 

  38. 38.

    Hagberg, A. A., Schult, D. A. & Swart, P. J. in Proc. 7th Python in Science Conference (eds Varoquaux, G., Vaught, T. & Millman, J.) 11–15 (SciPy, 2008).

  39. 39.

    Koda, D. S., Bechstedt, F., Marques, M. & Teles, L. K. Coincidence lattices of 2D crystals: heterostructure predictions and applications. J. Phys. Chem. C 120, 10895–10908 (2016).

    CAS  Article  Google Scholar 

  40. 40.

    Jäger, M. O. J., Morooka, E. V., Federici Canova, F., Himanen, L. & Foster, A. S. Machine learning hydrogen adsorption on nanoclusters through structural descriptors. npj Comput. Mater. 4, 37 (2018).

    Article  Google Scholar 

  41. 41.

    De, S., Bartók, A. P., Csányi, G. & Ceriotti, M. Comparing molecules and solids across structural and alchemical space. Phys. Chem. Chem. Phys. 18, 13754–13769 (2016).

    CAS  Article  Google Scholar 

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D.S.-K. acknowledges the MIT Nicole and Ingo Wender Fellowship, the MIT Robert Rose Presidential Fellowship and the MIT Energy Initiative (MITEI) Storage Seed Fund for financial support. R.G.-B. thanks MIT DMSE, Toyota Faculty Chair and MITEI for support. The work of E.O. and Z.J. was partially funded by National Science Foundation Award no. 1534340, DMREF, the MIT-Sensetime Alliance on Artificial Intelligence, and the Office of Naval Research (ONR) under Contract no. N00014-16-1-2432. D.S.-K. and R.G.-B. thank A. Corma, M. Moliner and Y. Román-Leshkov for fruitful discussions.

Author information




R.G.-B. conceived the project. D.S.-K. and R.G.-B. formulated the hypothesis of graph-similar transformations. D.S.-K. developed the graph and supercell matching methods, wrote the computer code and performed all the calculations. Z.J. and E.O. performed the literature mining and database query. Z.J., E.O. and D.S.-K. reviewed the extracted articles. D.S.-K. and R.G.-B. wrote the first version of the manuscript and made the figures. All the authors contributed to the final version of the manuscript.

Corresponding author

Correspondence to Rafael Gómez-Bombarelli.

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The authors declare no competing interests.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Appendices A–F, Supplementary Figs. 1–11, Tables 1–3 and refs. 1–262.

Supplementary Data 1

Normalized SOAP distance and D-measure for each of the 29,890 pairs of known zeolites. The csv file is sorted alphabetically by the zeolite IZA codes. The elements mij(A,B) (equation (D10)) of the transformation matrices M(A) and M(B) that minimize the graph distance between the frameworks (equation (D14)) are also given.

Supplementary Data 2

Hypothetical zeolites from PCOD with energy above quartz and their isomorphic IZA known zeolites. Only hypothetical zeolites with at least one isomorphic counterpart are shown in the table.

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Schwalbe-Koda, D., Jensen, Z., Olivetti, E. et al. Graph similarity drives zeolite diffusionless transformations and intergrowth. Nat. Mater. 18, 1177–1181 (2019).

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