An example of crystal boundary (a) and crystal composition (b).  Copyright IUCr 2014
An example of crystal boundary (a) and crystal composition (b). Copyright IUCr 2014

A theoretical approach to determining the structure of solid materials side-steps a fundamental problem in crystallography allowing even the smallest crystals just a few billionths of a nanometer across to be examined and a chemical structure extracted.

If they bathe a large enough crystal with X-rays, scientists can record a snapshot of the diffracted pattern of waves scattered by a crystal. They then use sophisticated mathematics to work out the type and position of atoms within the material from that pattern. However, while this process has been yielding powerful results for a century revealing the structures of everything from sugar crystals to insulin and beyond, there is a limitation. This is the so-called phase problem which arises because trapping the data from the three-dimensional crystal on a two-dimensional photographic plate loses information.

Just as a map cannot tell you about the true curved surface of the Earth without additional information so an X-ray diffraction pattern does not confer all of the information within the crystal. The magnitudes of the diffracted waves are recorded but not the "phase" information that tells you where the atoms from which those waves were diffracted sit precisely in the crystal. It is a complicated task to convert a map into a globe as a scale model of the earth so too extracting atomic information is complicated. If crystallographers could harness the phase information as well as the magnitude this would greatly simplify the mathematics and allow them to work with lower resolution data and much smaller crystals.

Writing in the IUCrJ [2014, 1, 19-27; DOI:10.1107/S2052252513025530], John Spence and colleagues at Arizona State University, Tempe, explain that they have built on an idea by David Sayre proposed in 1952. While the Braggs' pioneering work a century ago focused on the diffraction peaks, Sayre suggested that 3D information is also locked into the measurements that might be taken between the peaks. It is as if the flat pattern has the analogue of a map's contour lines. Small nanocrystals scatter X-rays in directions between the main Bragg peaks.

The team has now demonstrated how a numerical simulation allows them to extract 3D data by combining diffraction patterns from dozens of nanocrystals for a given compound. This allows them to obtain the between-the-peaks data even if the fundamental building blocks, the unit cells, are incomplete in many of the nanocrystals.

Given that many compounds of interest, in particular proteins are reluctant to form large crystals but can form nanocrystals this work offers a powerful approach to crystal structures with potential in biomedical and pharmaceutical science as well as other areas focused on hard to crystallize materials.