Machine-Learning Approach for the Development of Structure–Energy Relationships of ZnO Nanoparticles

The structure–energy relationships for the zinc oxide morphologies were investigated using a newly developed fragment-based energy decomposition approach. In this approach, the local chemical compositions of a material are abstracted as fragment types that serve as the material's genes with respect to its thermodynamic properties. A machine learning-based fragment recognition scheme was developed to learn about the fragment-related knowledge from a relatively small training set consisting of computationally viable ultrasmall nanoparticles. The knowledge gained including the fragment geometries and fragment energy parameters can be used for the classification and energy expression of the test sets consisting of different polymorphs and morphologies of that material at various scales. The stabilities of ZnO nanoparticles with different morphologies were expressed explicitly as functions of the particle size. The size-related phase transitions among various morphologies including wurtzite prisms, wurtzite octahedrons, body-centered tetragonal particles, sodalite-like particles, single-layered cages, multilayered cages, and nonpolar hexagonal prisms were predicted. The multilayered cages with nonpolar surfaces exhibit superior stability among the low-energy morphologies, but wurtzite nanoparticles are more favorable under practical synthesis and growth conditions under the control of the kinetics. The growth mechanism for ZnO clusters, ultrasmall nanoparticles, nanocrystals, and bulk-sized particles is proposed based on the synergy between the size-related phase transitions and external factors that affect the surface energies of the particles. Our interpretation of the Wulff theorem at a fragment-sized resolution provides new chemical insight for understanding the structural phase transition and particle growth for ZnO at various scales.