Vacancy clustering behaviors and stable configurations in vanadium metal: First-principles investigations

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• We calculate energetics and configurations of vacancy clusters with the size up to 30 in vanadium. • The average formation energies of vacancy clusters decrease with the size. • We determined the relationship between energetics of vacancy clusters and Wigner-Seitz area in vanadium. • We establish a model by machine learning to predict formation energies of vacancy clusters. The clustering behaviors and stable configurations of vacancies with the size up to 30 in vanadium were studied by first-principles investigations. The average formation energies per vacancy of vacancy clusters decreases with the sizes. When V n cluster with the odd size forms V n +1 cluster, the average formation energy per vacancy has a lager reduction relative to the case of even size. The stabilities of vacancy clusters increase with the sizes in terms of the total binding energy ( n =2-30), the incremental binding energies of vacancy clusters show an increasing trend of fluctuation with the sizes, which can be explained by both the size characteristics and terrace-ledge-kink model. We also estimated the relationship between vacancy formation/incremental binding energy and Wigner-Seitz area. Finally, we established a machine learning model based on Linear-SVM to predict formation energies of larger vacancy clusters. These results deepened the understanding of the formation and evolution of nanovoids in vanadium metal under irradiation.