X-ray crystallography has been central to the development of many fields of science over the past century. It has now matured to a point that as long as good-quality crystals are available, their atomic structure can be routinely determined in three dimensions. However, many samples in physics, chemistry, materials science, nanoscience, geology, and biology are noncrystalline, and thus their three-dimensional structures are not accessible by traditional x-ray crystallography. Overcoming this hurdle has required the development of new coherent imaging methods to harness new coherent x-ray light sources. Here we review the revolutionary advances that are transforming x-ray sources and imaging in the 21st century.

Inverse problems arise frequently in physics: The magnitude of the Fourier transform of some function is measurable, but not its phase. The “phase problem” in crystallography arises because the number of discrete measurements (Bragg peak intensities) is only half the number of unknowns (electron density points in space). Sayre first proposed that oversampling of diffraction data should allow a solution, and this has recently been demonstrated. Here we report the successful phasing of an oversampled hard x-ray diffraction pattern measured from a single nanocrystal of gold.

Distorted Nanoparticle: Nanoparticles have found many applications in modern technology; however, the full characterization of individual particles is challenging. One of the most interesting mechanical properties is the particle's response to lattice distortion. This property has been probed for ensembles of nanoparticles, but the required averaging may distort the results. Clark et al. (p. 56 , published online 23 May; see the Perspective by Hartland and Lo ) were able to image the generation and subsequent evolution of coherent acoustic phonons from an individual perturbed gold nanocrystal on the picosecond time scale.

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