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Extraordinarily complex crystal structure with mesoscopic patterning in barium at high pressure

Nature Materials volume 11, pages 627–632 (2012)Cite this article

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Abstract

Elemental barium adopts a series of high-pressure phases with such complex crystal structures that some of them have eluded structure determination for many years. Using single-crystal synchrotron X-ray diffraction and new data analysis strategies, we have now solved the most complex of these crystal structures, that of phase Ba-IVc at 19 GPa. It is a commensurate host–guest structure with 768 atoms in the representative unit, where the relative alignment of the guest-atom chains can be represented as a two-dimensional pattern with interlocking S-shaped 12-chain motifs repeating regularly in one direction and repeating with constrained disorder in the other. The existence of such patterning on the nanometre scale points at medium-range interactions that are not fully screened by the itinerant electrons in this metal. On the basis of first-principles electronic structure calculations, pseudopotential theory and an analysis of the lattice periodicities and interatomic distances, we rationalize why the Ba phases with the common densely packed crystal structures become energetically unfavourable in comparison with the complex-structured Ba-IVc phase, and what the role of the well-known pressure-induced s–d electronic transfer is.

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Figure 1: Basic host–guest motif of the Ba-IV crystal structures.
Figure 2: Single-crystal X-ray diffraction data of Ba-IVc at 19 GPa.
Figure 3: Schematic view of the crystal structure of Ba-IVc.
Figure 4: Comparison of the experimental diffraction data mapped onto the (h k4) and reciprocal space planes (top half) and the simulated pattern for the final Ba-IVc structural model (bottom half).
Figure 5: Structural weights, μg |S(g)|2 |χ(g)|, for hcp Ba and the Ba-IVc stripes approximant at 19 GPa.

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Acknowledgements

We thank W. A. Crichton, M. Mezouar and A. R. Lennie for their help with the experiments and acknowledge helpful discussions with U. Schwarz, S. Scandolo and K. Syassen. We thank P. F. McMillan, M. E. Cates, J. P. Attfield and R. A. Cowley for their comments that helped to improve the manuscript. This work was supported by research grants and a fellowship (I.L.) from the UK Engineering and Physical Sciences Research Council, and facilities were made available by ESRF and SRS. The single-crystal X-ray diffraction experiments were performed as part of the ESRF Long Term Project HS-3090 on single-crystal diffraction at extreme conditions. This work also used resources provided by the Edinburgh Compute and Data Facility (ECDF, www.ecdf.ed.ac.uk); the ECDF is partially supported by the eDIKT initiative (www.edikt.org.uk).

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  1. SUPA, School of Physics and Astronomy, and Centre for Science at Extreme Conditions, The University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK

    I. Loa, R. J. Nelmes, L. F. Lundegaard & M. I. McMahon

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  1. I. Loa
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Contributions

M.I.M. and I.L. produced the Ba-IVc samples, and L.F.L., I.L. and M.I.M. performed the diffraction experiments. I.L. analysed the data, with help from L.F.L. and discussion with all co-authors. I.L. performed the electronic structure calculations. I.L. and R.J.N. developed and wrote the paper.

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Correspondence to I. Loa.

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Loa, I., Nelmes, R., Lundegaard, L. et al. Extraordinarily complex crystal structure with mesoscopic patterning in barium at high pressure. Nature Mater 11, 627–632 (2012). https://doi.org/10.1038/nmat3342

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