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Nucleation mechanism for the direct graphite-to-diamond phase transition

Nature Materials volume 10, pages 693–697 (2011)Cite this article

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Abstract

Graphite and diamond have comparable free energies, yet forming diamond from graphite in the absence of a catalyst requires pressures that are significantly higher than those at equilibrium coexistence1,2,3,4,5,6,7. At lower temperatures, the formation of the metastable hexagonal polymorph of diamond is favoured instead of the more stable cubic diamond2,5,6,7. These phenomena cannot be explained by the concerted mechanism suggested in previous theoretical studies8,9,10,11,12. Using an ab initio quality neural-network potential13, we carried out a large-scale study of the graphite-to-diamond transition assuming that it occurs through nucleation. The nucleation mechanism accounts for the observed phenomenology and reveals its microscopic origins. We demonstrate that the large lattice distortions that accompany the formation of diamond nuclei inhibit the phase transition at low pressure, and direct it towards the hexagonal diamond phase at higher pressure. The proposed nucleation mechanism should improve our understanding of structural transformations in a wide range of carbon-based materials.

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Figure 1: Concerted transformation of graphite to diamond.
Figure 2: Pressure dependence of the shape and size of CD nuclei.
Figure 3: Pressure dependence of the nucleation barriers for the RG→CD (circles) and HG→HD (squares) transformations.
Figure 4: Comparison of the NN and DFT energetics for mixed graphite–diamond systems.

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Acknowledgements

The authors would like to thank G. Tribello for reading the manuscript and M. Ceriotti for discussions. This work was supported by the European Research Council (ERC-2009-AdG-247075). J.B. is grateful for financial support from the FCI and the Deutsche Forschungsgemeinschaft. T.D.K. acknowledges support by the Graduate School of Excellence Mainz. Our thanks are also due to the Swiss National Supercomputing Centre and High Performance Computing Group of ETH Zürich for computer time.

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Authors and Affiliations

  1. Department of Chemistry and Applied Biosciences, ETH Zürich, USI Campus, via G. Buffi 13, 6900 Lugano, Switzerland

    Rustam Z. Khaliullin, Hagai Eshet & Michele Parrinello

  2. Institute of Physical Chemistry, Johannes Gutenberg University Mainz, D-55128 Mainz, Germany

    Thomas D. Kühne

  3. Center for Computational Sciences, Johannes Gutenberg University Mainz, D-55128 Mainz, Germany

    Thomas D. Kühne

  4. Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany

    Jörg Behler

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  1. Rustam Z. Khaliullin
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  2. Hagai Eshet
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  4. Jörg Behler
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  5. Michele Parrinello
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Contributions

R.Z.K. conceived the study, implemented the NN code, designed the NN potential, carried out simulations, analysed results and wrote the manuscript; H.E. designed and implemented the NN code, carried out simulations, contributed to the development of the NN potential and analysed results; T.D.K. analysed results and supervised the simulations; J.B. contributed to the implementation of the NN code and supervised the construction of the NN potential; M.P. conceived the study, analysed results, edited the manuscript and supervised the project.

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Correspondence to Rustam Z. Khaliullin.

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The authors declare no competing financial interests.

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Khaliullin, R., Eshet, H., Kühne, T. et al. Nucleation mechanism for the direct graphite-to-diamond phase transition. Nature Mater 10, 693–697 (2011). https://doi.org/10.1038/nmat3078

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