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Large variation of vacancy formation energies in the surface of crystalline ice


Resolving the atomic structure of the surface of ice particles within clouds, over the temperature range encountered in the atmosphere and relevant to understanding heterogeneous catalysis on ice, remains an experimental challenge. By using first-principles calculations, we show that the surface of crystalline ice exhibits a remarkable variance in vacancy formation energies, akin to an amorphous material. We find vacancy formation energies as low as ~0.1–0.2 eV, which leads to a higher than expected vacancy concentration. Because a vacancy’s reactivity correlates with its formation energy, ice particles may be more reactive than previously thought. We also show that vacancies significantly reduce the formation energy of neighbouring vacancies, thus facilitating pitting and contributing to pre-melting and quasi-liquid layer formation. These surface properties arise from proton disorder and the relaxation of geometric constraints, which suggests that other frustrated materials may possess unusual surface characteristics.

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Figure 1: The ice Ih {0001} surface.
Figure 2: Distribution of vacancy formation energies in an ice slab.
Figure 3: Dipole-moment distribution in ice slabs.
Figure 4: Correlation between vacancy formation energies and dipole moments.
Figure 5: Spatial variation of dipole magnitude.
Figure 6: Reactivity of various gases at surface vacancies.


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We thank EPSRC for funding M.W. through the grant A Quickstep Forward: Development of the CP2K/Quickstep Code and Application to Ice Transport Processes EP/F011652/1. B.S. wishes to thank R. Martonak for supplying coordinates of amorphous ice phases and S. Bramwell for useful discussions. D.P. and E.G.W. are supported by NSFC. D.P. is grateful to the Thomas Young Centre ( for a Junior Research Fellowship. A.M. is also supported by the EURYI scheme (, the EPSRC, and the European Research Council. Computational resources from the London Centre for Nanotechnology and UCL Research Computing are warmly acknowledged. Also via our membership of the UK’s HPC Materials Chemistry Consortium, which is funded by EPSRC (EP/F067496), this work made use of the facilities of HECToR, the UK’s national high-performance computing service. J.V.V. acknowledges computer resources from the Swiss National Supercomputing Centre (CSCS).

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B.S., M.W. and J.V.V. designed the research. Most of the calculations were performed by M.W. with contributions from all authors. All authors contributed to the analysis and discussion of the data and the writing of the manuscript.

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Correspondence to B. Slater.

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Watkins, M., Pan, D., Wang, E. et al. Large variation of vacancy formation energies in the surface of crystalline ice. Nature Mater 10, 794–798 (2011).

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