OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 2 2023 other words, the energy of the system increases proportionally to the number of atoms contained therein. A supercell containing a monovacancy obviously has one atom less than a perfect one. Thus, its energy (excluding the vacancy effect) will be lower compared to the energy of a perfect supercell. Therefore, to distinguish the vacancy contribution one needs to add the chemical potential of the removed atom to the resulting energy difference according to the equation (2). It should be noted that the issue of point defect energy formation definition is more complex for semiconductors and ionic crystals in contrast to metals [11]. Results and Discussion It is known, that the VFE in metals is well described through the following relationship: f m E AkT ≈ , (3) where Tm is a melting temperature (К); k is the Boltzmann constant; A is a proportionality constant close to 10 [27]. Hayashiuchi et al. believed that a relationship between the VFE and the melting point is caused by the similarity between processes of atomic movement during vacancy formation and also its movement at the “solid – liquid” boundary during melting. According to this theory A ≈ 9.7. Fig. 1 shows the research findings in the coordinates “Ef – Tm”. It can be noted that the trend of ViFE growth with the melting temperature of the material is confirmed by data obtained using various methods. The trends defined in this work have a similar character with the DFT computations carried out by Medasani et al. using the VASP computer program [8]. This fact testifies about the appropriateness of using of open source GPAW code as to alternative to widely used commercial software package VASP. The computational results carried out within this work and those obtained by other authors (including the experimental findings) are summarized in Appendix B. The proportionality constant А, evaluated based on the results obtained using PAS, is close to ~12.1. It is slightly above the А = 10 proposed in [27–29]. The proportionality constant was found to be approxiFig. 1. Vacancy formation energy in various metals according to its melting point
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