Quantitative three-dimensional maps of the deformation of a crystal from its equilibrium lattice spacing have been obtained by inversion of the coherent X-ray diffraction pattern. This requires solving the crystallographic 'phase problem' which is achieved by oversampling and a support-constrained HIO algorithm. The lead crystal we investigated [1] was grown on a SiO_2 substrate and shows internal strain arising from its contact with the substrate. Closer examination of the strain distribution, after an important correction for X-ray refraction has been included, shows an expansion of the surface layers of the facetted hemispherical nanocrystal. Over most of the surface of the crystal there is a clear outward displacement, which decays exponentially into the bulk. The displacement is suppressed on the (111) facet itself and stronger on the surrounding regions, indicating an orietational variation in surface stress.

[1] M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder and I. K. Robinson, "Three-dimensional Mapping of a Deformation Field inside a Nanocrystal", Nature 442 63-66 (2006)

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1. Shape and stacking analysis of semiconductor nanowires using grazing-incidence diffraction and coherent scattering on single nanowires