Approaches to modelling the shape of nanocrystals

Unlike in the bulk, at the nanoscale shape dictates properties. The imperative to understand and predict nanocrystal shape led to the development, over several decades, of a large number of mathematical models and, later, their software implementations. In this review, the various mathematical approaches used to model crystal shapes are first overviewed, from the century-old Wulff construction to the year-old (2020) approach to describe supported twinned nanocrystals, together with a discussion and disambiguation of the terminology. Then, the multitude of published software implementations of these Wulff-based shape models are described in detail, describing their technical aspects, advantages and limitations. Finally, a discussion of the scientific applications of shape models to either predict shape or use shape to deduce thermodynamic and/or kinetic parameters is offered, followed by a conclusion. This review provides a guide for scientists looking to model crystal shape in a field where ever-increasingly complex crystal shapes and compositions are required to fulfil the exciting promises of nanotechnology.