Flexibility mechanisms in ideal zeolite frameworks

Michael Treacy, C. J. Dawson, V. Kapko, I. Rivin

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Zeolites are microporous crystalline aluminosilicate materials whose atomic structures can be usefully modelled in purely mechanical terms as stressfree periodic trusses constructed from rigid cornerconnected SiO4 and AlO4 tetrahedra. When modelled this way, all of the known synthesized zeolite frameworks exhibit a range of densities, known as the flexibility window, over which they satisfy the framework mechanical constraints. Within the flexibility window internal stresses are accommodated by force-free coordinated rotations of the tetrahedra about their apices (oxygen atoms). We use rigidity theory to explore the folding mechanisms within the flexibility window, and derive an expression for the configurational entropic density throughout the flexibility window. By comparison with the structures of pure silica zeolite materials, we conclude that configurational entropy associated with the flexibility modes is not a dominant thermodynamic term in most bulk zeolite crystals. Nevertheless, the presence of a flexibility window in an idealized hypothetical tetrahedral framework may be thermodynamically important at the nucleation stage of zeolite formation, suggesting that flexibility is a strong indicator that the topology is realizable as a zeolite. Only a small fraction of the vast number of hypothetical zeolites that are known exhibit flexibility. The absence of a flexibility window may explain why so few hypothetical frameworks are realized in nature.

Original languageEnglish (US)
Article number20120036
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2008
StatePublished - Feb 13 2014


  • Configurational entropy
  • Flexibility mechanism
  • Flexibility window
  • Zeolite framework

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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