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Predicting crystal structure by merging data mining with quantum mechanics

Abstract

Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an algorithm to direct the search through the large space of possible structures is found. We present a new approach to the prediction of structure that rigorously mines correlations embodied within experimental data and uses them to direct quantum mechanical techniques efficiently towards the stable crystal structure of materials.

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Figure 1: The Fe3C and MgCu2 structure types.
Figure 2: Mutual information between pairs of variables.
Figure 3: Predicting the structure of AgMg3.
Figure 4: Large-scale prediction capability.

References

  1. Olson, G. Designing a new material world. Science 288, 993–998 (2000).

    Article  Google Scholar 

  2. Nye, J. F. Physical Properties of Crystals (Oxford Univ. Press, Oxford, 1985).

    Google Scholar 

  3. Wolverton, C., Yan, X.-Y., Vijayaraghavan, R. & Ozolinš, V. Incorporating first-principles energetics in computational thermodynamics approaches. Acta Mater. 50, 2187–2197 (2002).

    Article  Google Scholar 

  4. Asta, M., Ozolinš, V. & Woodward, C. A first-principles approach to modeling alloy phase equilibria. J. Mater. 53, 16–19 (2001).

    Google Scholar 

  5. Curtarolo, S., Morgan, D. & Ceder, G. Accuracy of ab initio methods in predicting the crystal structures of metals: A review of 80 binary alloys. CALPHAD 29, 163–211 (2005).

    Article  Google Scholar 

  6. Ceder, G. Predicting properties from scratch. Science 280, 1099–1100 (1998).

    Article  Google Scholar 

  7. Pettifor, D. G. The structures of binary compounds: I. Phenomenological structure maps. J. Phys. C 19, 285–313 (1986).

    Article  Google Scholar 

  8. Villars, P. A three-dimensional structural stability diagram for 998 binary AB intermetallic compounds. J. Less Common Met. 92, 215–238 (1983).

    Article  Google Scholar 

  9. Morgan, D. & Ceder, G. in Handbook of Materials Modeling Vol. 1 (eds Catlow, R., Shercliff, H. & Yip, S.) 395–421 (Kluwer Academic, Dordrecht, 2005).

    Book  Google Scholar 

  10. Morgan, D., Rodgers, J. & Ceder, G. Automatic construction, implementation and assessment of Pettifor maps. J. Phys. C 15, 4361–4369 (2003).

    Google Scholar 

  11. Russell, S. & Norvig, P. Artificial Intelligence: A Modern Approach (Prentice Hall, Upper Saddle River, 1995).

    Google Scholar 

  12. Morita, T. Cluster variation method of cooperative phenomena and its generalization I. J. Phys. Soc. Japan 12, 753–755 (1957).

    Article  Google Scholar 

  13. Villars, P. The Pauling File Inorganic Materials Database and Design System—Binaries Edition (CD-ROM) (ASM International, Ohio, 2002).

    Google Scholar 

  14. Cover, T. M. & Thomas, J. A. Elements of Information Theory (Wiley, New York, 1991).

    Book  Google Scholar 

  15. De Boer, F. R. Cohesion in Metals (North-Holland, Amsterdam, 1988).

    Google Scholar 

  16. Prokof'ev, M. V., Kolesnichenko, V. E. & Karonik, V. V. Composition and structure of alloys in the Mg-Ag system near Mg3Ag . Inorg. Mater. 21, 1168–1170 (1985).

    Google Scholar 

  17. Curtarolo, S., Morgan, D., Persson, K., Rodgers, J. & Ceder, G. Predicting crystal structures with data mining of quantum calculations. Phys. Rev. Lett. 91, 135503 (2003).

    Article  Google Scholar 

  18. Stone, M. Cross-validatory choice and assessment of statistical predictions. J. R. Stat. Soc. B 36, 111–147 (1974).

    Google Scholar 

  19. Jaynes, E. T. Probability Theory: The Logic of Science (Cambridge Univ. Press, New York, 2003).

    Book  Google Scholar 

  20. Cheeseman, P. & Stutz, J. in Advances in Knowledge Discovery and Data Mining (ed. Fayyad, U. M.et al.) 61–83 (AAAI Press, Menlo Park, California, 1996).

    Google Scholar 

  21. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).

    Article  Google Scholar 

  22. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    Article  Google Scholar 

  23. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

    Article  Google Scholar 

  24. Methfessel, M. & Paxton, A. T. High-precision sampling for Brillouin-zone integration in metals. Phys. Rev. B 40, 3616–3621 (1989).

    Article  Google Scholar 

Download references

Acknowledgements

This work was funded by NSF-ITR grant DMR-0312537, the Institute for Soldier Nanotechnologies (ISN) grant DAAD 19-02-D-0002, and the DOE, Office of Basic Energy Sciences under Contract No. DE-FG02-96ER45571. We would also like to acknowledge the National Science Foundation and the San Diego Supercomputer Center for additional computational resources.

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Correspondence to Gerbrand Ceder.

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Fischer, C., Tibbetts, K., Morgan, D. et al. Predicting crystal structure by merging data mining with quantum mechanics. Nature Mater 5, 641–646 (2006). https://doi.org/10.1038/nmat1691

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