Universal approach for predicting crystallography of heterogeneous epitaxial nanocrystals with multiple orientation relationships

Heteroepitaxial nanocrystals are one of the most fundamentally and technologically important classes of materials systems. The correlation between form, dictated by crystallographic features such as growth habit and direction, and function, in terms of the ultimate physio-chemical properties is well established, thus placing an onus on precise synthesis control of nanocrystal morphology. Yet, nanocrystal heteroepitaxy can be a frustrating, time-consuming iterative process, particularly during the initial stages of development. What is desired is a powerful predictive tool that is able to successfully predict not only the interface or habit plane, but also rationalize the occurrence of epitaxial growth complexities such as multiple orientation relationships (MORs) and high-index faceting planes for a diverse range of materials. Here we provide such a powerful approach that is based on an invariant deformation element (IDE) model, and fundamentally founded on the crystallography of diffusional phase transformations. We demonstrate its impact by detailed computations supported by transmission electron microscopy evidence, for an archetypical complex metal oxide nanocrystal system (that has up to five MORs for three differing growth orientations). The method is then applied to successfully explain growth for different materials ranging from metals to metal carbides to transition metal oxides, even in thin film form. Thus, this relatively simple yet powerful predictive guide significantly reduces the systemic inefficiencies of guesswork and blind growth. Ultimately it can be easily integrated with machine learning techniques toward reliable and efficient advanced nanomaterials fabrication.