electron crystallography 550 https://doi.org/10.1107/S2052520619007339 Acta Cryst. (2019). B75, 550–563 Received 30 January 2019 Accepted 20 May 2019 Edited by L. Palatinus, Czech Academy of Sciences, Czech Republic Keywords: crystal defects; 3D electron diffrac- tion; order–disorder structures; diffuse scat- tering; twinning; electron crystallography. Structure analysis of materials at the order–disorder borderline using three-dimensional electron diffraction Enrico Mugnaioli a * and Tatiana E. Gorelik b a Center for Nanotechnology Innovation@NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, Pisa, 56127, Italy, and b Central Facility for Electron Microscopy, Electron Microscopy Group of Materials Science (EMMS), University of Ulm, Albert Einstein Allee 11, Ulm, 89081, Germany. *Correspondence e-mail: enrico.mugnaioli@iit.it Diffuse scattering, observed as intensity distribution between the Bragg peaks, is associated with deviations from the average crystal structure, generally referred to as disorder. In many cases crystal defects are seen as unwanted perturbations of the periodic structure and therefore they are often ignored. Yet, when it comes to the structure analysis of nano-volumes, what electron crystallography is designed for, the significance of defects increases. Twinning and polytypic sequences are other perturbations from ideal crystal structure that are also commonly observed in nanocrystals. Here we present an overview of defect types and review some of the most prominent studies published on the analysis of defective nanocrystalline structures by means of three-dimensional electron diffraction. 1. Introduction The ideal perfection of crystal structures is often broken by local fluctuations, which may be associated with disorder features, change in structural stacking or twin boundaries. Indeed, one should never forget that ideally ordered crystals are just theoretical constructions, close to real objects only when the analyzed volume includes billions of equivalent unit cells and local structure unconformities are negligible. This is generally the case for high-quality crystals for single-crystal X-ray diffraction. Deviations from ideal crystals are anyway well known and widespread, even if often ignored or neglected by crystallographers. And yet, features such as vacancies, dislocations, planar defects, twinning and local modulations in structural packing may be crucial for understanding how a given material is formed and for addressing its macroscopic physical or chemical properties (Keen & Goodwin, 2015). Dealing with defective features is even more important when one has to characterize phases that appear only in form of nanocrystals, where the coherent crystalline volume is relatively small. The appearance of extra reflections and diffuse scattering (e.g. in the form of reflection streaking) proves to be rather common in nanocrystals. For certain materials, it is just impossible to sample a fully coherent domain, even at the scale of few tens of nanometres. Arguably, the main trouble in solving the atomic structure of crypto- crystalline materials is currently associated just with the difficulties of dealing with their high degree of disorder. Disorder features may be connected with the metastable nature of the nanocrystals, with the non-equilibrated condi- tions associated with their formation, with the existence of several polytypes that alternate at a very fine scale, with a ISSN 2052-5206 # 2019 International Union of Crystallography