Electronic, Vibrational and Thermal Properties of α and β Titanium
УДК 546.82
Abstract
Titanium and titanium-based alloys are widely used for various technological applications in the aerospace, automotive, and shipbuilding industries because of their good strength-to-weight ratio and good combination of mechanical properties. To understand the fundamental properties of titanium, as well as phase transformations, it is necessary to study the electronic and phonon structure of its main phases. Although such studies have been intensively carried out since the middle of the last century, theoretical studies of the phonon system and properties based on it remain rare. The atomic and electronic structures of α and β titanium are calculated by the projector augmented-wave method within the electron density functional theory. The analysis of the electron energy spectrum and the densities of electronic states is carried out. Using the harmonic approximation and the finite displacement method, the phonon spectrum and a number of related thermodynamic characteristics are calculated. The features of the phonon subsystem of β-Ti, which indicate its dynamic instability, are discussed. The calculation of the vibrational entropy and enthalpy, as well as the lattice heat capacity, showed satisfactory agreement with the experiment. In general, the approach used can be applied to analyze the forming phases of doped titanium.
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Leyens C., Peters M. Titanium and titanium alloys. Fundamentals and applications. Weinheim, 2003.
Whittaker M., Titanium in the gas turbine engine. In E. Benini, Ed. Advances in Gas Turbine Technology. London, 2011. DOI: 10.5772/21524.
Хорев А.И. Комплексное легирование и термомеханическая обработка титановых сплавов. М., 1979.
Balazic M., Kopac J., Jackson M.J., Ahmed A. Review: titanium and titanium alloy applications in medicine // Int. J. Nano Biomat. 2007. Vol. 1. № 1. DOI: 10.1504/IJN-BM.2007.016517.
Ishfaq K., Rehman M., Khan A.R., Wang Y. A review on the performance characteristics, applications, challenges and possible solutions in electron beam melted Ti-based orthopaedic and orthodontic implants // Rapid Prototyping J. 2021. Vol. 28. № 3. DOI: 10.1108/RPJ-03-2021-0060.
Fisher E.S., Renken C.J. Single-crystal elastic moduli and the hcp bcc transformation in Ti, Zr, and Hf // Phys. Rev. 1964. Vol. 135. № 2A. DOI: 10.1103/physrev.135.a482.
Ando T., Nakashima K., Tsuchiyama T., Takaki S. Microstructure and mechanical properties of a high nitrogen titanium alloy // Mater. Sci. Eng. A. 2008. Vol. 486. № 1-2. DOI: 10.1016/j.msea.2007.08.074.
Kim H.Y., Miyazaki S. Martensitic transformation and superelastic properties of Ti-Nb base alloys // Mater. Trans. 2015. Vol. 56. № 5. DOI: 10.2320/matertrans.M2014454.
Dong R., Kou H., Wu L., Yang L., Zhao Y., Hou H. в to ш transformation strain associated with the precipitation of а phase in a metastable в titanium alloy // J. Mater. Sci. 2021. Vol. 56. DOI: 10.1007/s10853-020-05231-z.
Mattheiss L.F. Energy bands for the iron transition series // Phys. Rev. 1964. Vol. 134. № 4A. DOI: 10.1103/Phys-Rev.134.A970.
Hygh E.H., Welch R.M. Electronic structure of titanium // Phys. Rev. 1970. Vol. 1. № 6. DOI: 10.1103/PhysRevB.1.2424.
Jafari M., Hajiyani H. Optical properties of а, в and ш structure of titanium: Ab initio approach // Com-put. Mater. Sci. 2011. Vol. 50. № 9. DOI: 10.1016/j.com-matsci.2011.03.018.
Hu C.E., Zeng Z.Y., Zhang L., Chen X.R., Cai L.C., Alfe D. Theoretical investigation of the high pressure structure, lattice dynamics, phase transition, and thermal equation of state of titanium metal // J. Appl. Phys. 2010. Vol. 107. № 093509. DOI: 10.1063/1.3407560.
Sangiovanni D.G., Klarbring J. Smirnova D., Skrip-nyak N.V., Gambino D., Mrovec M., Simak S.I., Abrikosov I.A. Superioniclike diffusion in an elemental crystal: bcc titanium // Phys. Rev. Lett. 2019. Vol. 123. № 105501. DOI: 10.1103/ PhysRevLett.123.105501.
Blochl P.E. Projector augmented-wave method // Phys. Rev. B. 1994. Vol. 50. № 17953. DOI: 10.1103/ PhysRevB.50.17953.
Kresse G., Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method // Phys. Rev. B. 1999. Vol. 59. № 1758. DOI: 10.1103/PhysRevB.59.1758.
Perdew J.P., Burke K., Ernzerhof M. Generalized gradient approximation made simple // Phys. Rev. Lett. 1996. Vol. 77. № 3865. DOI: 10.1103/PhysRevLett.77.3865.
Gandi A.N., Zhu J. Reconstructive phase transformations in body-centered cubic titanium // Phys. Status Solidi. 2020. Vol. 257. № 2000193. DOI: 10.1002/pssb.202000193.
Wood R.M. The lattice constants of high purity alpha titanium // Proc. Phys. Soc. 1962. Vol. 80.
Senkov O.N., Chakoumakos B.C., Jonas J.J., Froes F.H. Effect of temperature and hydrogen concentration on the lattice parameter of beta titanium // Mater. Res. Bull. 2001. Vol. 36. DOI: 10.1016/S0025-5408(01)00604-3.
Togo A., Tanaka I. First principles phonon calculations in materials science // Scr. Mater. 2015. Vol. 108. DOI: 10.1016/j.scriptamat.2015.07.021.
Lekka Ch.E., Gutierrez-Moreno J.J., Calin M. Electronic origin and structural instabilities of Ti-based alloys suitable for orthopaedic implants // J. Phys. Chem. Solids. 2017. Vol. 102. DOI: 10.1016/j.jpcs.2016.10.013.
Киттель Ч. Введение в физику твердого тела. М., 1978.
Kulkova S.E., Egorushkin V.E., Kalchikhin V.V. The electron structure of NiTi martensite // Solid State Com-mun. 1991. Vol. 77. № 9. DOI: 10.1016/0038-1098(91)90766-O.
Stassis C., Arch D., Harmon B.N. Lattice dynamics of hcp Ti // Phys. Rev. 1979. Vol. 19. № 1. DOI: 10.1103/ PhysRevB.19.181.
Petry W., Heiming A., Trampenau J., Alba M., Herzig C., Schober H.R., Vogl G. Phonon dispersion of the bcc phase of group-IV metals. I. bcc titanium // Phys. Rev. 1991. Vol. 43. № 13. DOI: 10.1103/PhysRevB.43.10933.
Petry W, Heiming A., Trampenau J., Alba M., Vogl G. Strong phonon softening in the bcc phase of titanium // Physica B. 1989. Vol. 156-157. DOI: 10.1016/0921-4526(89)90585-1.
Barin I. Thermochemical data of pure substances, 3rd Ed., Weinheim, 1995.
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