Identification of the Miller indices of a crystallographic plane: a tutorial and a comprehensive review on fundamental theory, universal methods based on different case studies and matters needing attention

Micro-/nanostructures exposed with special crystallographic planes (surface or crystal facets) exhibit distinctive physicochemical properties because of their unique atomic arrangements, resulting in their widespread applications in the fields of catalysis, energy conversion, sensors, electrical devices and so on. Therefore, tremendous progress has been made in facet-dependent investigation of various micro-/nanocrystals over the past decades. However, a lot of beginners including undergraduate students as well as graduate students lack systematic knowledge and don't know how to identify the Miller indices of a crystallographic plane in the actual research process. So far, to the best of our knowledge, there is no specialized review article in this respect. Herein, we present a tutorial and a comprehensive review on the identification of the Miller indices of a crystallographic plane, including fundamental theory, universal methods based on different case studies, and matters needing attention. Hopefully, this tutorial review will be a beneficial theoretical and practical reference for beginners currently focusing on the controllable preparation and facet-dependent investigation of micro-/nanocrystals.