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Crystallography

Some are less equal than others

Nature volume 391, pages 334–335 (1998)Cite this article

Why is it dark at night? This is Olber's Paradox. The modern explanation for it is that the Universe is expanding; but in 1922 C. V. L. Charlier suggested another, ingenious solution: the Universe might be infinite and hierarchical, with galaxies of galaxies of galaxies. There would be no privileged centre and all viewpoints would be quasi-equivalent, yet the density of this Universe would tend to zero with increasing scale. A similar idea might apply to the microcosmos of atomic arrangements: clusters of clusters are an alternative to strict crystalline arrangements, and could form a new type of condensed matter. On page 376 of this issue1, Hubert et al. report a structure with this theme — clustered icosahedral particles of boron suboxide.

The mathematical simplicity of infinite crystal lattices has beguiled crystallographers, with its absolute identity of lattice points. The classification system of crystals is based on the 230 symmetries allowed by that assumption — that an infinite number of asymmetric units are to be arranged so that their surroundings are absolutely identical. The assumption of crystallinity is necessary for the recovery of phase information in single-crystal X-ray diffraction, which is the principal tool of crystallography, so sharp diffraction patterns can be interpreted in terms of infinite crystals. But hierarchy could offer an alternative to lattice repetition, in providing an assembly of atoms with an infinite number of almost identical, or quasi-equivalent, sites.

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Figure 1: Clusters of boron suboxide, B6O (a, photograph; b, electron micrograph) and its X-ray diffraction pattern (c.).

H. HUBERT ET AL.

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  1. the Department of Crystallography, Birkbeck College, University of London, Malet Street, WC1E 7HX, London, UK

    Alan Mackay

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  1. Alan Mackay
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Mackay, A. Some are less equal than others. Nature 391, 334–335 (1998). https://doi.org/10.1038/34787

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