Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Determination of 4-connected framework crystal structures by simulated annealing


THE initial derivation of atomic-scale models of the 4-connected framework crystal structures of zeolites and related materials is generally difficult. Interpretation of powder X-ray diffraction data to yield a unit cell and some symmetry information is often straightforward. Chemical analyses and sorption experiments indicate the number of framework tetrahedra, nT, present in the unit cell (T represents the framework tetrahedral species, such as Si or Al) and the approximate pore dimensions. However, because synthetic zeolites are almost invariably microcrystalline, the possibilities for structure solution by conventional diffraction methods are limited, and framework structure determinations have traditionally relied heavily on the building of physical models. We describe here an alternative approach, in which approximate T-atom coordinates are derived from the unit-cell size and symmetry, and the value of nT from computer modelling. An initially arbitrary T-atom configuration is optimized with respect to a 'cost function' based on the T–T distances, T–T–T angles and number of first-neighbour T-atoms, by simulated annealing using Monte Carlo methods. The potential of the method for structural determinations in both two dimensions (for structural projections) and three dimensions are illustrated by results obtained for a hexagonal cell of space group P6/mmm and dimensions a = 18.4 Å and c = 7.5 Å, and by determination of the previously unknown structure of lithium gallosilicate.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout


  1. Meier, W. M. & Olson, D. H. Atlas of Zeolite Structure Types (Butterworths, Surrey, 1987).

    Google Scholar 

  2. LaPierre, R. B. et al. Zeolites 5, 346–348 (1985).

    Article  CAS  Google Scholar 

  3. Bennett, J. M., Richardson, J. W., Pluth, J. J. & Smith, J. V. Zeolites 7, 160–162 (1987).

    Article  CAS  Google Scholar 

  4. Treacy, M. M. J. & Newsam, J. M. Nature 332, 249–251 (1988).

    Article  ADS  CAS  Google Scholar 

  5. Newsam, J. M., Treacy, M. M. J., Koetsier, W. T. & deGruyter, C. B. Proc. R. Soc. Lond. A420, 375–405 (1988).

    Article  ADS  CAS  Google Scholar 

  6. Meier, W. M. & Villiger, H. Z. Kristallogr. 129, 411–423 (1969).

    Article  CAS  Google Scholar 

  7. Baerlocher, Ch., Hepp, A. & Meier, W. M. DLS-76 Manual (ETH, Zurich, 1977).

  8. K. Binder (ed.) Applications of the Monte Carlo Method in Statistical Physics 2nd edn (Springer, Berlin, 1987).

  9. Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. Science 220, 671–680 (1983).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  10. Smith, J. V. in Zeolites: Facts, Figures, Future (eds van Santen, R. A. & Jacobs, P. A.) 29–47 (Elsevier, Amsterdam, 1989).

    Google Scholar 

  11. Smith, J. V. & Dytrych, W. J. Z. Kristallogr. 175, 31–36 (1986).

    CAS  Google Scholar 

  12. Smith, J. V. & Dytrych, W. J. Nature 309, 607–608 (1984).

    Article  ADS  CAS  Google Scholar 

  13. Richardson, J. W., Smith, J. V. & Pluth, J. J. J. phys. Chem. (in the press).

  14. Davis, M. E., Saldarriaga, C., Montes, C., Garces, J. & Crowder, C. Nature 331, 698–699 (1988).

    Article  ADS  CAS  Google Scholar 

  15. Smith, J. V. & Bennett, J. M. Am. Miner. 66, 777–788 (1981).

    CAS  Google Scholar 

  16. Barrer, R. M. & Villiger, H. J. chem. Soc. chem. Commun., 659–660 (1969).

  17. Barri, S. A. I., Smith, G. W., White, D. & Young, D. Nature 312, 533–534 (1984).

    Article  ADS  CAS  Google Scholar 

  18. Newsam, J. M. J. phys. Chem. 92, 445–452 (1987).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

Deem, M., Newsam, J. Determination of 4-connected framework crystal structures by simulated annealing. Nature 342, 260–262 (1989).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing