OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 2 2023 Evaluation of vacancy formation energy for BCC-, FCC-, and HCP-metals using density functional theory Yulia Emurlaeva 1, a,*, Daria Lazurenko 1, b, Zinaida Bataeva 2, c, Ivan Petrov 3, d, Gleb Dovzhenko 4, e, Lubov Makogon 2, f, Maksim Khomyakov 5, g, Kemal Emurlaev 1, h, Ivan Bataev 1, i 1 Novosibirsk State Technical University, 20 Prospekt K. Marksa, Novosibirsk, 630073, Russian Federation 2 Siberian State University of water transport, 33 Schetinkina str., Novosibirsk, 630099, Russian Federation 3 Novosibirsk State University, 1 Pirogova str., Novosibirsk, 630090, Russian Federation 4 Siberian Circular Photon Source “SKlF” Boreskov Institute of Catalysis of Siberian Branch of the Russian Academy of Sciences (SRF “SKIF”), 1 Nikol’skii pr., Kol’tsovo, 630559, Russian Federation 5 Institute of Laser Physics of Siberian Branch of the Russian Academy of Sciences, 15B Prospekt Ak. Lavrentieva, Novosibirsk, 630090, Russian Federation a https://orcid.org/0000-0003-4835-4134, emurlaeva@corp.nstu.ru, b https://orcid.org/0000-0002-2866-5237, pavlyukova_87@mail.ru, c https://orcid.org/0000-0001-5027-6193, bataevazb@ngs.ru, d https://orcid.org/0000-0002-7968-1130, ivan77766600@outlook.com, e https://orcid.org/0000-0003-0615-0643, g.dovjenko@skif.ru, f https://orcid.org/0009-0006-1463-0697, ledimakagon@mail.ru, g https://orcid.org/0000-0001-8095-2092, mnkhomy@gmail.com, h https://orcid.org/0000-0002-1114-6799, emurlaev@corp.nstu.ru, i https://orcid.org/0000-0003-2871-0269, i.bataev@corp.nstu.ru Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2023 vol. 25 no. 2 pp. 104–116 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2023-25.2-104-116 ART I CLE I NFO Article history: Received: 10 April 2023 Revised: 18 April 2023 Accepted: 27 April 2023 Available online: 15 June 2023 Keywords: Metals Vacancy formation energy Diffusion Simulation Density functional theory Funding This study was funded by the Federal Task of Ministry of Education and Science of the Russian Federation (project FSUN2020- 0014 (2019-0931): “Investigations of Metastable Structures Formed on Material Surfaces and Interfaces under Extreme External Impacts”). Acknowledgements: Researches were conducted at core facility of NSTU “Structure, mechanical and physical properties of materials”. ABSTRACT Introduction. Vacancies are among the crystal lattice defects that have a significant effect on the structural transformations processes during thermal, chemical-thermal, thermomechanical, and other types of alloys treatment. The vacancy formation energy is one of the most important parameters used to describe diffusion processes. An effective approach to its definition is based on the use of the density functional theory (DFT). The main advantage of this method is to carry out computations without any parameters defined empirically. The purpose of the work is to estimate vacancy formation energy of BCC-, FCC- and HCPmetals widely used in mechanical engineering and to compare these findings obtained using various exchangecorrelation functionals (GGA and meta-GGA). Computation procedure. The computations were carried out using the projector-augmented wave method using the GPAW code and the atomic simulation environment (ASE). The Perdew-Burke-Ernzerhof, MGGAC and rMGGAC functionals were used. The wave functions were described by plane waves within simulations. Vacancies formation energy was evaluated using supercells approach with a size 3 × 3 × 3. Computations were carried out for BCC-metals (Li, Na, K, V, Cr, Fe, Rb, Nb, Mo, Cs, Ta, W), FCC-metals (Al, Ni, Cu, Rh, Pd, Ag, Ir, Pt, Au, Pb, Co) and HCP-metals (Be, Ti, Zr, Mg, Sc, Zn, Y, Ru, Cd, Hf, Os, Co, Re). Results and discussion. A comparison of the defined vacancy formation energies indicates the validity of the following ratio of values: PBE MGGAC rMGGAC f f f E E E < ≤ . The values obtained using the open source GPAW code are characterized by the same patterns as for widely spread commercially distributed program VASP. It was revealed that the use of the PBE and MGGAC functionals leads to a slight deviation relative to the experimentally determined vacancies formation energy in contrast to the computations using rMGGAC. For citation: Emurlaeva Yu.Yu., Lazurenko D.V., Bataeva Z.B., Petrov I.Yu., Dovzhenko G.D., Makogon L.D., Khomyakov M.N., Emurlaev K.I., Bataev I.A. Evaluation of vacancy formation energy for BCC-, FCC-, and HCP-metals using density functional theory. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2023, vol. 25, no. 2, pp. 104–116. DOI: 10.17212/1994-6309-2023-25.2-104-116. (In Russian). ______ * Corresponding author Emurlaeva Yu. Yu., Assistant Novosibirsk State Technical University, 20 Prospekt K. Marksa, 630073, Novosibirsk, Russian Federation Tel.: 8 (383) 346-06-12, e-mail: emurlaeva@corp.nstu.ru
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