We report a theoretical investigation, free of any adjustable parameters, on the vacancy-type defects in metals. The approach is based on the surface thermodynamics, atomic bond energy and melting point, the approach can better reflect the essence of the vacancy formation energy and size effects. To improve the analysis of single vacancies of grain boundaries and interphases, a convenient atomic bond energy strain parameter (zeta) is defined. According to the atomic bond energy and melting point, the model is validated. The results of our work agree well with thermodynamics, molecular dynamics simulations, and experimental results. (C) 2014 Elsevier B.V. All rights reserved.