Zefsa II

Description of the algorithm

Zeolite Frameworks

Zeolites are a class of crystalline aluminosilicates both naturally occurring and synthesized in the laboratory.  They have found many uses in industrial processes, including catalytic cracking of alkanes, air separation, and ion exchange. AET
There are many different types of zeolites, but the common feature is a structural similarity.  Typically, a zeolite has a framework composed of tetrahedrally-coordinated atoms (T-atoms) joined by oxygens.  The T-atom is usually silicon, but substitutions with metals (Al, P,...) are common and often desired.  The main feature of zeolite frameworks is the presence of pores, as can be seen in the example.  These pores are 4-12 Angstrom in size and, due to the crystalline nature of the material, can be hundreds of Angstroms in length.  Some frameworks have one-dimensional pores, some have two or three-dimensional pores, which can join at cage-like intersections.  This makes zeolites very interesting as catalytic agents, since the bulk of the crystal is accessible to chemical species that fit into the pores.  Metal substitutions into the framework, Al for Si for example, will create areas of excess negative charge, where cations or non-framework species can bind.

Structure Solution

The derivation of an atomic-scale model of the framework crystal structure of a newly-synthesized zeolite is a non-trivial task.  The  difficulty stems primarily from the polycrystalline nature of most zeolite samples, with crystallite sizes typically below 5 um. Zeolites continue to be synthesized at a furious pace.  Crucial to the development of the field of zeolite science is the ability to determine the structure of newly-synthesized materials: Structure is sought after not only to understand the performance of newly synthesized catalysts but also to propose rational syntheses of homologous materials with tailored performance.  Roughly 125 framework structures have been reported, yet several dozen distinct synthetic zeolites remain unsolved in the patent literature.  The techniques of diversity synthesis have recently been introduced to the field, and this may soon lead to a tremendous explosion in the number of new, unsolved synthetic zeolites.


ZEFSA II is a direct, real-space method for zeolite structure solution from powder diffraction data [1,2,3].  Unit cell size, density, and symmetry are assumed to have already been determined from the powder diffraction data. The method then locates the positions of the T-atoms in the unit cell. The oxygens can subsequently be located by a Rietveld refinement. The approach employs an empirical potential of mean force for the tetrahedral atoms in a zeolite framework.  ZEFSA II is an improved method that makes use of powerful new ideas from Monte Carlo algorithm design [3]. ZEFSA II is able to solve all current publicly-known zeolites, starting from a high quality dataset.  ZEFSA II should be able to determine the  structure of any new single-phase zeolite for which a good powder diffraction pattern is available.

The key step in ZEFSA II is to define a cost function that is a function of the atomic positions within the crystalline unit cell and that is minimized by the structure corresponding to the experimental material. A combination of simulated annealing and biased Monte Carlo is able to  minimize the cost function and so to solve the structure in most cases. In the most difficult cases, the superior method of parallel tempering rather than simulated annealing is necessary.  Roughly 10% of the known zeolites require the method of parallel tempering.  The parallel tempering option is no more difficult to use than is the simulated annealing.

ZEFSA II is freely available from this web site under the GNU public license.  We ask that any publications making using of the method cite the original literature [1,2,3].

1) M. W. Deem and J. M. Newsam, Nature 342,  260-262 (1989).
2) M. W. Deem and J. M. Newsam, J. Am. Chem. Soc. 114,  7189-7198 (1992).
3) M. Falcioni and M. W. Deem. J. Chem. Phys. 110, 1754-1766 (1999) (download PDF file 383Kb).


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