title: The significance of Bragg's law in electron diffraction and microscopy, and Bragg's second law.
abstract: Bragg's second law, which deserves to be more widely known, is recounted. The significance of Bragg's law in electron diffraction and microscopy is then discussed, with particular emphasis on differences between X-ray and electron diffraction. As an example of such differences, the critical voltage effect in electron diffraction is described. It is then shown that the lattice imaging of crystals in high-resolution electron microscopy directly reveals the Bragg planes used for the imaging process, exactly as visualized by Bragg in his real-space law. Finally, it is shown how in 2012, for the first time, on the centennial anniversary of Bragg's law, single atoms have been identified in an electron microscope using X-rays emitted from the specimen. Hence atomic resolution X-ray maps of a crystal in real space can be formed which give the positions and identities of the different atoms in the crystal, or of a single impurity atom in the crystal.
authors.affiliation: Department of Materials Science and Metallurgy, University of Cambridge, United Kingdom.
authors.forename: C J
authors.initials: CJ
authors.lastname: Humphreys