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Expansion of the surface layers of a facetted hemispherical nanocrystal of Pb is reported at a temperature just below the melting point. Inversion of the coherent x-ray diffraction pattern yields quantitative threedimensional maps of the deformation of the crystal from its equilibrium lattice spacing. Most of the surface of the crystal has a clear outward displacement, which decays exponentially into the bulk. This is suppressed on the ͑111͒ facet itself and is stronger on the spherical regions, suggesting that it arises from the orientational variation of the underlying surface stress.

We present here an overview of Coherent X-ray Diffraction Imaging (CXDI) with its application to nanostructures. This imaging approach has become especially important recently due to advent of X-ray Free-Electron Lasers (XFEL) and its applications to the fast developing technique of serial X-ray crystallography. We start with the basic description of coherent scattering on the finite size crystals. The difference between conventional crystallography applied to large samples and coherent scattering on the finite size samples is outlined. The formalism of coherent scattering from a finite size crystal with a strain field is considered. Partially coherent illumination of a crystalline sample is developed. Recent experimental examples demonstrating applications of CXDI to the study of crystalline structures on the nanoscale, including experiments at FELs, are also presented.

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