Shape Diagram of Body-Centered Cubic Crystals

Nanocrystal research has accelerated in recent years because their properties differ markedly from those of bulk materials, finding applications in electronics, medicine, catalysis, photonics, and others. The nanocrystal shape plays a pivotal role in properties. Traditionally studied by empirical methods, shape formation mechanisms yet require a systematic analysis based on a theoretical approach. To address this, we use kinetic Monte Carlo simulations to predict body-centered cubic (BCC) nanocrystal shapes.

The simulations consider atom-by-atom growth, enabling energy tracking and shape transformation. This far exceeds the spatial and temporal resolution of traditional measurement techniques, such as microscopy and tomography. Simulations reveal nanocrystal shape control by altering relative growth rates between facets with different crystallographic directions. Experimentally, these rates are modulated by the addition of ligands and ions that adsorb to specific surface sites. This study pinpoints the surface sites (adatoms) that play a major role on shape transformations from rhombic dodecahedron (equilibrium shape of BCC) to cubes (metastable).

By defining the coordination number of BCC as the number of first and second neighbor atoms, which present minimal separation 1.16, we find that the surface sites controlling shape transformation occur at coordination numbers 4 and 5 (see graphical abstract). Future directions of this study will tackle transformations to octahedra, with the aim of predicting the full shape diagram of symmetry-preserving polyhedral shapes of BCC nanocrystals bound by low Miller index facets. The establishment of shape diagrams will transfer the scientific knowledge to engineering of nanomaterials in a similar fashion phase diagrams made for classic materials.