1. Solid State Division, Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, Tennessee 37831, USA
2. Metals & Ceramics Division, Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, Tennessee 37831, USA

Correspondence to: B. C. Larson¹ Correspondence and requests for materials should be addressed to B.C.L. (e-mail: Email: bcl@ornl.gov).

Advanced materials and processing techniques are based largely on the generation and control of non-homogeneous microstructures, such as precipitates and grain boundaries. X-ray tomography can provide three-dimensional density and chemical distributions of such structures with submicrometre resolution¹; structural methods exist that give submicrometre resolution in two dimensions^{2, 3, 4, 5, 6, 7, 8}; and techniques are available for obtaining grain-centroid positions and grain-average strains in three dimensions^{7, 9}. But non-destructive point-to-point three-dimensional structural probes have not hitherto been available for investigations at the critical mesoscopic length scales (tenths to hundreds of micrometres). As a result, investigations of three-dimensional mesoscale phenomena—such as grain growth^{10, 11}, deformation^{12, 13, 14, 15, 16}, crumpling^{17, 18, 19} and strain-gradient effects²⁰—rely increasingly on computation and modelling without direct experimental input. Here we describe a three-dimensional X-ray microscopy technique that uses polychromatic synchrotron X-ray microbeams to probe local crystal structure, orientation and strain tensors with submicrometre spatial resolution. We demonstrate the utility of this approach with micrometre-resolution three-dimensional measurements of grain orientations and sizes in polycrystalline aluminium, and with micrometre depth-resolved measurements of elastic strain tensors in cylindrically bent silicon. This technique is applicable to single-crystal, polycrystalline, composite and functionally graded materials.