Recent advances in the application of electron tomography to materials chemistry.

Nowadays, tomography plays a central role in pureand applied science, in medicine, and in many branches of engineering and technology. It entails reconstructing the three-dimensional (3D) structure of an object from a tilt series of two-dimensional (2D) images. Its origin goes back to 1917, when Radon showed mathematically how a series of 2D projection images could be converted to the 3D structural one. Tomographic X-ray and positron scanning for 3D medical imaging, with a resolution of ∼1 mm, is now ubiquitous in major hospitals. Electron tomography, a relatively new chemical tool, with a resolution of ∼1 nm, has been recently adopted by materials chemists as an invaluable aid for the 3D study of the morphologies, spatially-discriminating chemical compositions, and defect properties of nanostructured materials. In this Account, we review the advances that have been made in facilitating the recording of the required series of 2D electron microscopic images and the subsequent process of 3D reconstruction of specimens that are vulnerable, to a greater or lesser degree, to electron beam damage. We describe how high-fidelity 3D tomograms may be obtained from relatively few 2D images by incorporating prior structural knowledge into the reconstruction process. In particular, we highlight the vital role of compressed sensing, a recently developed procedure well-known to information theorists that exploits ideas of image compression and "sparsity" (that the important image information can be captured in a reduced data set). We also touch upon another promising approach, "discrete" tomography, which builds into the reconstruction process a prior assumption that the object can be described in discrete terms, such as the number of constituent materials and their expected densities. Other advances made recently that we outline, such as the availability of aberration-corrected electron microscopes, electron wavelength monochromators, and sophisticated specimen goniometers, have all contributed significantly to the further development of quantitative 3D studies of nanostructured materials, including nanoparticle-heterogeneous catalysts, fuel-cell components, and drug-delivery systems, as well as photovoltaic and plasmonic devices, and are likely to enhance our knowledge of many other facets of materials chemistry, such as organic-inorganic composites, solar-energy devices, bionanotechnology, biomineralization, and energy-storage systems composed of high-permittivity metal oxides.