OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 2 2023 Conclusions The analysis of VFE in BCC-, FCC- and HCP-metals was carried out using DFT simulation. Based on the conducted study, the following conclusions can be made. 1. The use of DFT is an effective approach to evaluate the formation energy of point defects. The VFE obtained via open source GPAW code are characterized by the same trends as the widely spread commercial software package VASP. It is reasonable to compare the application efficiency of both programs in terms of calculation accuracy and rate in further studies. 2. In most cases, the use of the PBE and MGGAC functionals provides a slighter deviation relative to the experimentally defined VFE in comparison with the calculation via rMGGAC. 3. A comparison of the computed VFE indicates the validity of the following ratio: PBE MGGAC rMGGAC f f f E E E < ≤ . 4. Despite common patterns, the calculated VFE may differ significantly from the experimental data. Thus, the VFE evaluated at T = 0 K can be used only in comparative studies. To increase the accuracy, the calculated VFE should be subject to additional correction. References 1. Gorelik S.S., Dobatkin S.V., Kaputkina L.M. Rekristallizatsiya metallov i splavov [Recrystallization of metals and alloys]. Moscow, MISiS Publ., 2005. 432 p.ISBN: 5-87623-103-7. 2. Humphreys F.J., Hatherly M. Hatherly recrystallization and related annealing phenomena. 2nd ed. Elsevier, 2004. 605 p. DOI: 10.1016/B978-0-08-044164-1.X5000-2. 3. Siegel R.W. Vacancy concentrations in metals. Journal of Nuclear Materials, 1978, vol. 69–70, pp. 117–146. DOI: 10.1016/0022-3115(78)90240-4. 4. Mehrer H. Diffusion in solids: fundamentals, methods, materials, diffusion-controlled processes. Springer, 2007. 673 p. DOI: 10.1007/978-3-540-71488-0. 5. Smigelskas A.D., Kirkendall E.O. Zinc diffusion in alpha brass. Transactions of AIME, 1947, vol. 171, pp. 130–142. 6. Paul A., Laurila T., Vuorinen V., Divinski S. Thermodynamics, diffusion and the Kirkendall effect in solids. Springer, 2014. 530 p. DOI: 10.1007/978-3-319-07461-0. 7. Kraftmakher Y. Equilibrium vacancies and thermophysical properties of metals. Physics Reports, 1998, vol. 299, iss. 2–3, pp. 79–188. DOI: 10.1016/s0370-1573(97)00082-3. 8. Medasani B., Haranczyk M., Canning A., Asta M. Vacancy formation energies in metals: A comparison of MetaGGA with LDA and GGA exchange–correlation functionals. Computational Materials Science, 2015, vol. 101, pp. 96–107. DOI: 10.1016/j.commatsci.2015.01.018. 9. Gong Y., Grabowski B., Glensk A., Körmann F., Neugebauer J., Reed R.C. Temperature dependence of the Gibbs energy of vacancy formation of fcc Ni. Physical Review B, 2018, vol. 97, p. 214106. DOI: 10.1103/ physrevb.97.214106. 10. Lazurenko D.V., Dovzhenko G.D., Lozanov V.V., Petrov I.Y., Ogneva T.S., Emurlaev K.I., Bataev I.A. Stabilization of Ti5Al11 at room temperature in ternary Ti-Al-Me (Me = Au, Pd, Mn, Pt) systems. Journal of Alloys and Compounds, 2023, vol. 944, p. 169244. DOI: 10.1016/j.jallcom.2023.169244. 11. Freysoldt C., Grabowski B., Hickel T., Neugebauer J., Kresse G., Janotti A., Van deWalle C.G. First-principles calculations for point defects in solids. Reviews of Modern Physics, 2014, vol. 86, iss. 1, pp. 253–305. DOI: 10.1103/ revmodphys.86.253. 12. Zhang X., Grabowski B., Hickel T., Neugebauer J. Calculating free energies of point defects from ab initio. Computational Materials Science, 2018, vol. 148, pp. 249–259. DOI: 10.1016/j.commatsci.2018. 13. Giustino F. Materials modelling using density functional theory: properties and predictions. Oxford University Press, 2014. 286 p. 14. Kohn W., Sham L.J. Self-consistent equations including exchange and correlation effects. Physical Review, 1965, vol. 140, iss. 4A, pp. A1133–A1138. DOI: 10.1103/PhysRev.140.A1133. 15. Perdew J.P., Chevary J.A., Vosko S.H., Jackson K.A., Pederson M., Singh D.J., Fiolhais C. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Physical Review B, 1992, vol. 46, iss. 11, pp. 6671–6687. DOI: 10.1103/PhysRevB.46.6671.
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