If the chemical element and 3D location of every atom in a material are known, then the material’s physical properties can, in principle at least, be predicted using the laws of physics. The atomic positions of crystals have long-range periodicity, which has enabled the development of powerful methods that combine diffraction experiments with the mathematics of symmetry to determine the precise atomic structure of these materials. Moreover, deviations from periodicity that create defects in crystals can be imaged with sub-ångström resolution. But these methods do not work for glasses, which lack long-range periodicity. Our knowledge of the atomic structure of glasses is therefore limited and acquired indirectly. Writing in Nature, Yang et al.1 report the experimental determination of the 3D positions of all the atoms in a nanometre-scale sample of a metallic glass.
The authors accomplished this feat using atomic-resolution electron tomography. In this method, 2D projections of the 3D atomic structure of a sample are acquired by passing a beam of electrons through the sample: a series of 2D images is produced by altering the orientation of the sample to the beam, and these images are then reconstructed into a 3D image of the whole sample. This technique has been used to determine the atomic structure of crystals for a decade2,3. However, most of the information required to construct the full 3D atomic structure of a crystal is contained in just a few of the 2D images, which are acquired when the sample is oriented in ways that cause the atoms to line up in rows, one behind the other, with empty space between them4. Unfortunately, such orientations do not exist for glasses.
Special orientations are also lacking for non-crystalline biomolecules. Electron microscopists have overcome this problem by studying millions of nearly identical copies of the same biomolecule, thereby achieving single-atom resolution in tomographic reconstructions5. By contrast, every cubic nanometre of a glass has a unique structure, which means that Yang et al. had to adopt a different strategy. They used a combination of state-of-the-art computational imaging techniques — including sophisticated methods to correct distortions and to reduce noise that obscures the image signal — to produce a series of high-quality 2D images that capture subtle variations in contrast when the glass is viewed in different orientations. They then used an original approach to reconstruct the final, atomically resolved 3D image (Fig. 1). Although the authors cannot specifically identify the element for each atom, they do assign each atom to one of three categories, each of which includes either two or four of the eight elements in the glass.
Theoretical descriptions of glass structure rely on long-standing principles that define motifs of atoms. For glasses in which the atoms are covalently bonded, such as commonplace window glass, the principle is preservation of bond lengths and angles, and the motif is a continuous random network of bonds6 (Fig. 1a). The random-network motif has been elaborated to accommodate, for example, atoms that have varying numbers of bonds7.
For glasses in which the atoms exhibit metallic bonding, the principle is to achieve dense, random packing of spherical atoms8 (Fig. 1b), and the motifs are clusters of atoms that define the vertices of various polyhedra (such as the polyhedra defined in ref. 9). The principle of dense random packing has been elaborated to include the chemical propensity of some elements to bond preferentially to other elements10. Experiments have confirmed various aspects of these descriptions of metallic-glass structure11, but only computer simulations have been able to determine the unique position and element for every atom (see ref. 12, for example). Unfortunately, simulations can model the motions of atoms only at short timescales, and therefore can’t really account for the very slow motions of atoms that occur in glasses and glass-forming liquids — thus limiting their ability to predict the atomic structure of glasses.
Yang and colleagues’ results (Fig. 1c) are a major step towards experimental confirmation of current models of metallic-glass structure. The authors’ structural analysis provides support for a model in which solute atoms (those that occur in small quantities in the glass) are found at the centres of clusters of solvent atoms (which account for the majority of the atoms). The clusters act as ‘super atoms’ that pack together densely at length scales greater than the atomic scale to form the glass structure13. Yang et al. show that, in their glass, some of these clusters are densely packed, but others are not. The observed loose packing of some clusters might be a product of the extremely rapid cooling that was used to synthesize the studied glasses, but it could also point to important gaps in current models.
The next experimental challenges are to identify the specific element for every atom, which should be possible for glasses that have a simpler composition than that of the glass in the current study, and to improve the precision of the determined atom positions. Yang et al. report a random uncertainty of 21 picometres in the atomic positions (1 pm is 10–12 metres). That is a tiny distance, but it represents about 8% of the most common interatomic distance in the glass. Shifts in position of that scale would cause significant changes in the energy of the bonds between the atoms and in the geometries of the super-atom clusters. The uncertainty might also explain why the abundances of polyhedra observed in the current study differ from those predicted by previously reported simulations12 — if the atoms in the simulations were all randomly shifted by up to 21 pm, the resulting polyhedra distributions could be more similar to those reported by Yang and co-workers. It remains to be seen whether the authors’ characterization of the structure (the specific way in which they partitioned atoms into super-atoms, and the packing of those super-atoms) is the best theoretical description of the studied system, and whether solute-centred clusters will become the most useful general description of metallic-glass structures.
Advanced electron tomography promises to substantially advance glass science. The acquisition of complete atomic-structure data for more metallic glasses could provide insights that aid the development of methods for discovering new glass-forming alloys, and could improve our understanding of unusual materials such as polyamorphous14 and structurally anisotropic15 glasses. It could also open the way to techniques for characterizing structural defects in glasses; such characterization is currently restricted to defects that have a spectroscopic signature. Technologies such as superconducting quantum bits (used in quantum computers) and the LIGO gravitational-wave observatory are limited by glass defects known as two-level systems16,17, which can be detected only by their effects, not by their structure. Having the ability to identify defect structures could be a first step towards engineering better materials for various applications. In the meantime, Yang et al. have achieved something that glass scientists have dreamt of for at least 90 years6 — measuring the positions of all the atoms in a glass.