najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2026-17-2-204-209najo-1762Research ArticlePHYSICSФИЗИКАElastic and mechanical properties of Ti–Nb–Zr based alloysУпругие и механические свойства сплавов на основе Ti–Nb–Zrhttps://orcid.org/0000-0001-5099-3942БакулинА. В.BakulinA. V.

Alexander V. Bakulin 

Tomsk, 634055 

bakulin@ispms.ruhttps://orcid.org/0000-0002-7155-3492КульковаС. Е.KulkovaS. E.

Svetlana E. Kulkova 

Tomsk, 634055 

kulkova@ispms.ruInstitute of Strength Physics and Materials Science, Siberian Branch of Russian Academy of SciencesRussian Federation202630042026172204209Copyright © Bakulin A.V., Kulkova S.E., 20262026Бакулин А.В., Кулькова С.Е.Bakulin A.V., Kulkova S.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1762

The elastic properties and mechanical characteristics of Ti–Nb22–Zr6 based alloys were calculated using the exact muffin-tin orbital method with the coherent potential approximation. Alloying by metals such as Hf, Mg and their combination were considered, and their concentration did not exceed 5 at.%. It was shown that addition of Hf and Mg leads to a decrease in Young’s modulus due to both size effect and electronic factor. The calculated Young’s modulus for the ternary Ti–Nb22–Zr6 alloy (70.1 GPa) is found in good agreement with experimental one (70 GPa). The smallest value of Young’s modulus was calculated for the Ti–Nb22–Zr6–Hf5–Mg2.5 alloy, achieving 57 GPa. Further increase in Mg concentration leads to a negative C′ and alloy destabilization. Additionally, alloying of the Ti–Nb22–Zr6 alloy results in a decrease in hardness, fracture toughness, but brittleness index is increased.

Упругие свойства и механические характеристики сплавов на основе Ti–Nb22–Zr6 были рассчитаны методом точных маффин-тин орбиталей в приближении когерентного потенциала. Рассматривалось легирование металлами, такими как Hf, Mg и их комбинациями, при этом их концентрация не превышала 5 ат.%. Было показано, что добавление Hf и Mg приводит к понижению модуля Юнга как из-за размерного эффекта, так и из-за электронного фактора. Рассчитанный модуль Юнга для тройного сплава Ti–Nb22–Zr6 (70.1 ГПа) хорошо согласуется с экспериментальным значением (70 ГПа). Наименьшее значение модуля Юнга было рассчитано для сплава Ti–Nb22–Zr6–Hf5–Mg2.5, достигая 57 ГПа. Дальнейшее увеличение концентрации Mg приводит к отрицательному значению C' и дестабилизации сплава. Кроме того, легирование сплава Ti–Nb22–Zr6 приводит к снижению твердости и трещиностойкости, но при этом повышается индекс хрупкости.

сплавы титанаупругие модулимеханические свойстваab-initio расчетыtitanium alloyselastic modulimechanical propertiesab-initio calculationsThe work was performed according to the Government research assignment for ISPMS SB RAS, project FWRW-2026-0008.ReferencesNiinomi M. Mechanical properties of biomedical titanium alloys. Mater. Sci. Eng. A, 1998, 243, P. 231-236.Niinomi M. Mechanical properties of biomedical titanium alloys. Mater. Sci. Eng. A, 1998, 243, P. 231-236.Long M., Rack H.J. Titanium alloys in total joint replacement – a materials science perspective. Biomater., 1998, 19, P. 1621–1639.Long M., Rack H.J. Titanium alloys in total joint replacement – a materials science perspective. Biomater., 1998, 19, P. 1621–1639.Geetha M., Singh A.K., Asokamani R., Gogia A.K. Ti based biomaterials, the ultimate choice for orthopaedic implants – A review. Prog. Mater. Sci., 2009, 54, P. 397–425.Geetha M., Singh A.K., Asokamani R., Gogia A.K. Ti based biomaterials, the ultimate choice for orthopaedic implants – A review. Prog. Mater. Sci., 2009, 54, P. 397–425.Niinomi M. Mechanical biocompatibilities of titanium alloys for biomedical applications. J. Mech. Behav. Biomed. Mater., 2008, 1, P. 30–42.Niinomi M. Mechanical biocompatibilities of titanium alloys for biomedical applications. J. Mech. Behav. Biomed. Mater., 2008, 1, P. 30–42.Yu Z. Titanium alloys for biomedical development and applications. Design, microstructure, properties, and application. Elsevier, Amsterdam, 2022, 245 p.Yu Z. Titanium alloys for biomedical development and applications. Design, microstructure, properties, and application. Elsevier, Amsterdam, 2022, 245 p.Biesiekierski A., Wang J., Gepreel M.A.H., Wen C. A new look at biomedical Ti-based shape memory alloys, Acta Biomater., 2012, 8, P. 1661– 1669.Biesiekierski A., Wang J., Gepreel M.A.H., Wen C. A new look at biomedical Ti-based shape memory alloys, Acta Biomater., 2012, 8, P. 1661– 1669.Illarionov A.G., Nezhdanov A.G., Stepanov S.I., Muller-Kamskii G., Popov A.A. Structure, phase composition, and mechanical properties of biocompatible titanium alloys of different types. Phys. Met. Metall., 2020, 121, P. 367–373.Illarionov A.G., Nezhdanov A.G., Stepanov S.I., Muller-Kamskii G., Popov A.A. Structure, phase composition, and mechanical properties of biocompatible titanium alloys of different types. Phys. Met. Metall., 2020, 121, P. 367–373.Li Y., Yang C., Zhao H., Qu S., Li X., Li Y. New developments of Ti-based alloys for biomedical applications. Materials, 2014, 7, P. 1709–1800.Li Y., Yang C., Zhao H., Qu S., Li X., Li Y. New developments of Ti-based alloys for biomedical applications. Materials, 2014, 7, P. 1709–1800.Marker C., Shang S.L., Zhao J.C., Liu Z.K. Effects of alloying elements on the elastic properties of bcc Ti-X alloys from first-principles calculations. Comput. Mater. Sci., 2018, 142, P. 215–226.Marker C., Shang S.L., Zhao J.C., Liu Z.K. Effects of alloying elements on the elastic properties of bcc Ti-X alloys from first-principles calculations. Comput. Mater. Sci., 2018, 142, P. 215–226.Yao Q., Sun J., Xing H., Guo W. Influence of Nb and Mo contents on phase stability and elastic property of β-type Ti-X alloys. Trans. Nonferrous Met. Soc. China., 2007, 17, P. 1417–1421.Yao Q., Sun J., Xing H., Guo W. Influence of Nb and Mo contents on phase stability and elastic property of β-type Ti-X alloys. Trans. Nonferrous Met. Soc. China., 2007, 17, P. 1417–1421.Zunger A., Wei S.H., Ferreira L.G., Bernard J.E. Special quasirandom structures. Phys. Rev. Lett., 1990, 65, P. 353–356.Zunger A., Wei S.H., Ferreira L.G., Bernard J.E. Special quasirandom structures. Phys. Rev. Lett., 1990, 65, P. 353–356.Vitos L. Computational quantum mechanics for materials engineers. The EMTO method and applications. Springer, London, 2007, 238 p.Vitos L. Computational quantum mechanics for materials engineers. The EMTO method and applications. Springer, London, 2007, 238 p.Dubinskiy S., Baranova A., Markova G., Prokoshkin S., Zelenina A., Kolotova L., Starikov S., Korotitskiy A., Bazlov A., Brailovski V. Atypical intrinsic elinvar behavior of beta Ti-22Nb-6Zr alloy in high and wide temperature range: atomic mechanism and control of the effect. Trans. Nonferrous Met. Soc. China, 2026, in press.Dubinskiy S., Baranova A., Markova G., Prokoshkin S., Zelenina A., Kolotova L., Starikov S., Korotitskiy A., Bazlov A., Brailovski V. Atypical intrinsic elinvar behavior of beta Ti-22Nb-6Zr alloy in high and wide temperature range: atomic mechanism and control of the effect. Trans. Nonferrous Met. Soc. China, 2026, in press.Hill R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc., Sect. A, 1952, 65, P. 349–354.Hill R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc., Sect. A, 1952, 65, P. 349–354.Jiang X., Zhao J., Wu A., Bai Y., Jiang X. Mechanical and electronic properties of B12-based ternary crystals of orthorhombic phase. J. Phys.: Condens. Matter., 2010, 22, 315503.Jiang X., Zhao J., Wu A., Bai Y., Jiang X. Mechanical and electronic properties of B12-based ternary crystals of orthorhombic phase. J. Phys.: Condens. Matter., 2010, 22, 315503.Lee C.M., Ju C.P., Chern Linn J.H. Structure-property relationship of cast Ti–Nb alloys. J. Oral Rehabil., 2002, 29, P. 314–322.Lee C.M., Ju C.P., Chern Linn J.H. Structure-property relationship of cast Ti–Nb alloys. J. Oral Rehabil., 2002, 29, P. 314–322.Fikeni L. Microstructural evolution and its influence on mechanical properties of Ti–Nb binary alloys. University of Pretoria, Pretoria, 2021, 95 p.Fikeni L. Microstructural evolution and its influence on mechanical properties of Ti–Nb binary alloys. University of Pretoria, Pretoria, 2021, 95 p.Niu H., Niu S., Oganov A.R. Simple and accurate model of fracture toughness of solids. J. Appl. Phys., 2019, 125, 065105.Niu H., Niu S., Oganov A.R. Simple and accurate model of fracture toughness of solids. J. Appl. Phys., 2019, 125, 065105.Boccaccini A.R. Machinability and brittleness of glass-ceramics. J. Mater. Process. Technol., 1997, 65, P. 302–304.Boccaccini A.R. Machinability and brittleness of glass-ceramics. J. Mater. Process. Technol., 1997, 65, P. 302–304.Lutjering G., Williams J.C. ¨ Titanium, second ed. Springer, Berlin, 2007, 442 p.Lutjering G., Williams J.C. ¨ Titanium, second ed. Springer, Berlin, 2007, 442 p.Schwarz K., Blaha P., Madsen G.K.H. Electronic structure calculations of solids using the WIEN2k package for material sciences, Comput. Phys. Commun., 2002, 147 (1–2), P. 71–76.Schwarz K., Blaha P., Madsen G.K.H. Electronic structure calculations of solids using the WIEN2k package for material sciences, Comput. Phys. Commun., 2002, 147 (1–2), P. 71–76.Raabe D., Sander B., Friak M., Ma D., Neugebauer J. Theory-guided bottom-up design of ´ β-titanium alloys as biomaterials based on first principles calculations: Theory and experiments. Acta Materialia, 2007, 55, P. 4475–4487.Raabe D., Sander B., Friak M., Ma D., Neugebauer J. Theory-guided bottom-up design of ´ β-titanium alloys as biomaterials based on first principles calculations: Theory and experiments. Acta Materialia, 2007, 55, P. 4475–4487.Boyer R.R., Welsch G., Collings E.W. Materials properties handbook: titanium alloys. ASM Int., Mater. Park, 1994, 1176 p.Boyer R.R., Welsch G., Collings E.W. Materials properties handbook: titanium alloys. ASM Int., Mater. Park, 1994, 1176 p.Kasparyan S.O., Bakulin A.V., Kulkova S.E. The influence of alloying elements on the elastic properties of β-Ti. J. Exp. Theor. Phys., 2026, 169, P. 71–81. (in Russian)Kasparyan S.O., Bakulin A.V., Kulkova S.E. The influence of alloying elements on the elastic properties of β-Ti. J. Exp. Theor. Phys., 2026, 169, P. 71–81. (in Russian)Kwasniak P., Wrobel J.S., Garbacz H. Origin of low Young modulus of multicomponent, biomedical Ti alloys – Seeking optimal elastic properties ´ through a first principles investigation. J. Mech. Behav. Biomed. Mater., 2018, 88, P. 352–361.Kwasniak P., Wrobel J.S., Garbacz H. Origin of low Young modulus of multicomponent, biomedical Ti alloys – Seeking optimal elastic properties ´ through a first principles investigation. J. Mech. Behav. Biomed. Mater., 2018, 88, P. 352–361.Hao C.P., Wang Q., Ma R.T., Wang Y.M., Qiang J.B., Dong C. Cluster-plus-glue-atom model in bcc solid solution alloys. Acta Phys. Sin., 2011, 60 (11), 116101.Hao C.P., Wang Q., Ma R.T., Wang Y.M., Qiang J.B., Dong C. Cluster-plus-glue-atom model in bcc solid solution alloys. Acta Phys. Sin., 2011, 60 (11), 116101.Kasparyan S.O., Ordabaev A.E., Bakulin A.V., Kulkova S.E. Elastic and thermal properties of some ternary β-Ti based alloys. Nanosystems Phys. Chem. Math., 2025, 16 (2), P. 225–234.Kasparyan S.O., Ordabaev A.E., Bakulin A.V., Kulkova S.E. Elastic and thermal properties of some ternary β-Ti based alloys. Nanosystems Phys. Chem. Math., 2025, 16 (2), P. 225–234.Kasparyan S.O. Electronic structure and elastic moduli of binary and ternary β-titanium alloys. Cand. Sci. (Phys.-Math.) Dissertation. Nat. Res. Tomsk State Univ., Tomsk, 2025, 154 p. (in Russian).Kasparyan S.O. Electronic structure and elastic moduli of binary and ternary β-titanium alloys. Cand. Sci. (Phys.-Math.) Dissertation. Nat. Res. Tomsk State Univ., Tomsk, 2025, 154 p. (in Russian).

The authors declare that there are no conflicts of interest present.