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.

中文翻译：

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纳米晶体形状建模的方法

与整体不同，纳米级的形状决定了性能。理解和预测纳米晶体形状的必要性导致了几十年来大量数学模型及其软件实现的发展。在这篇综述中，首先概述了用于模拟晶体形状的各种数学方法，从具有百年历史的 Wulff 结构到描述支撑孪生纳米晶体的一年（2020）方法，以及术语的讨论和消歧。然后，详细描述了这些基于 Wulff 的形状模型的大量已发布软件实现，描述了它们的技术方面、优点和局限性。最后，讨论了形状模型在预测形状或使用形状来推导热力学和/或动力学参数方面的科学应用，并得出结论。这篇综述为寻求在需要日益复杂的晶体形状和成分来实现纳米技术令人兴奋的前景的领域中模拟晶体形状的科学家提供了指导。