Solid-state chemistry

Boron charged under pressure

Crystal-structure prediction methods and diffraction data show that a newly discovered form of boron is partially ionic. This is the first time such a structure has been observed for any elemental solid.

The concept of atomic structure — ordered arrangements of atoms, such as the arrays found in crystalline solids — is central to an understanding of the properties of matter. The most successful technique for determining crystal structures is X-ray diffraction. But this method doesn't always work, especially for unusually complex structures, or if the resolution of the technique is limited by the extreme conditions required for the crystals to exist. In these cases, an independent method for predicting plausible structures is desirable to assist the interpretation of experimental diffraction patterns. Such a method is extremely difficult to realize in practice. But reporting in this issue (page 863), Oganov et al.1 demonstrate the use of first-principles calculations, in combination with diffraction data, to determine the crystal structure of a new, stable form of boron that forms at high pressure.

The theoretical prediction of crystal structures has long been a challenging problem. Recently, there has been a resurgence of interest in applying first-principles calculations to predict structures, without having any prior information about the arrangement of atoms. These include ex nihilo approaches2 (which generate structures at random, and then use computational methods to 'relax' the structures into low-energy arrangements) and genetic algorithms3 (which start with a population of random structures, from which low-energy structures 'evolve' during subsequent rounds of changes that simulate natural selection). An exciting aspect of Oganov and colleagues' work1 is that it used the latter approach to successfully predict a thermodynamically stable structure.

The authors' method3 for predicting crystal structures builds on previous pioneering work4 that predicted the structures of clusters of atoms. The process starts with a population of randomly generated parent structures, from which offspring structures evolve in heredity and mutation operations. In heredity operations, two low-enthalpy structures are selected and sliced up, and slices from each structure are then combined to produce offspring (Fig. 1). Mutation operations create distortions to the unit cell (the fundamental repeat unit of a crystalline structure) and/or to the atomic positions of a parent structure. After several rounds of operations, the lowest-energy crystal structure should emerge.

Figure 1: Heredity operations in crystal-structure prediction.
figure1

Genetic algorithms are used to predict crystal structures of compounds. These involve heredity operations, whereby models of the unit cells of approximate, likely structures (parent structures) are cut into slices, and slices from different parents are combined to produce offspring structures. After several heredity and mutation operations (which generate distortions to unit cells), low-energy structures of the compound under investigation should emerge. Oganov et al.1 use genetic algorithms to determine the crystal structure of a newly identified form of boron.

Boron provides a tough test for the authors' predictive method because of its chemical and structural complexity. Discovered in 1808, the original samples of boron were later found to contain only 60–80% of the element, and it wasn't until 1909 that a 99% pure sample was isolated. So far, at least 16 polymorphs (structural forms) of boron are known, yet the ground-state structure of boron is still controversial. Oganov et al.1 report a new form of boron that adds to this mélange — a polymorph that is stable at high pressure (18–89 gigapascals). So what is its structure?

Working with a 'quenched' sample of the material (one that had been recovered to ambient pressure without disrupting its structure), the authors first obtained some basic information about the unit cell of the polymorph. They then applied their prediction technique to a range of possible atomic arrangements, and successfully obtained a thermodynamically stable structure that reproduced the observed diffraction pattern of the material. The structure is made up of icosahedral clusters of 12 boron atoms (B12) and of pairs of boron atoms (B2), arranged in a cubic lattice (see Fig. 1b on page 864). It is both gratifying and exciting that the correct structure was predicted, despite its complexity.

A surprising finding is that the bonding between the B12 clusters and the B2 pairs is partially ionic, as suggested by the infrared spectrum of the polymorph and supported by the theoretical calculations. It was generally believed that the effect of pressure on a covalently bonded compound was to weaken the bonds, and so enhance electron mobility. For example, it was suggested5 that a simple compound, such as solid hydrogen (an insulator consisting of H2 molecules, in which electrons are localized within covalent bonds), would transform under extreme pressure to a metal (containing mobile, delocalized electrons). More recent experimental and theoretical results6, however, suggest that spontaneous polarization of H2 bonds might occur under pressure, so that partial charges develop on the atoms of each molecule — electrons situated in the interstitial region would leave positive charge on the atoms.

Oganov et al.1 report the first observation of an elemental solid that has some ionic structure — the B12 clusters have a partial negative charge, whereas the B2 units have a partial positive charge. The build-up of negative charge on the B12 cluster is stabilized by sharing the negative charge (electron) among the molecular orbitals of the B12 units. This effect, combined with electrostatic interactions between the B2 and the B12 units, helps to stabilize the ionic complex. This picture, if correct, is different from the proposed spontaneous electronic polarization in dense hydrogen, and may be unique to boron.

Oganov and colleagues' results prove the efficiency and reliability of their prediction technique, but there is still some room for improvement. Simply mixing and matching planar slices of parent structures in the heredity operation isn't necessarily the best procedure for finding low-energy structures — slices that have periodic, wave-like geometries might be more efficient7. The mutation operation could (and should) also be improved.

Furthermore, there have been considerable successes in predictions of crystal structures that are based solely on randomly generated structures8 — the advantage of this approach being that the sampling of possible structures is completely unbiased. Such lack of bias might prevent the evolution process from predicting structures that lie in a local energy minimum of the potential energy surface that describes all the possible arrangements of atoms (rather than finding structures of the lowest possible energy).

Oganov and colleagues' paper1 describes a crucial first step towards a truly ab initio method for predicting crystal structures. Perhaps just as importantly, it broadens our knowledge of the possibilities for chemical bonding in elemental solids, and adds yet another chapter to the bizarre history of boron.

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Tse, J. Boron charged under pressure. Nature 457, 800–801 (2009). https://doi.org/10.1038/457800a

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