Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T23:41:31.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Martensitic transformation from β to α′ and α″ phases in Ti–V alloys: A first-principles study

Published online by Cambridge University Press:  07 August 2017

Wei Mei ,
Jian Sun  and
Yufeng Wen
Wei Mei
Affiliation:
Shanghai Key Laboratory of Advanced High-Temperature Materials and Precision Forming, School of Materials Science and Engineering, Shanghai Jiaotong University, Shanghai 200240, People’s Republic of China
Jian Sun*
Affiliation:
Shanghai Key Laboratory of Advanced High-Temperature Materials and Precision Forming, School of Materials Science and Engineering, Shanghai Jiaotong University, Shanghai 200240, People’s Republic of China
Yufeng Wen
Affiliation:
School of Mathematical Sciences & Physics, Jinggangshan University, Jiangxi Province 343009, People’s Republic of China
*
a) Address all correspondence to this author. e-mail: jsun@sjtu.edu.cn
Get access

Abstract

The ground state properties of the α′ and α″ martensitic phases and energetic pathways of the β → α′/α″ martensitic transformations in Ti–(0–30 at.%)V alloys were investigated by first-principles method in combination with virtual crystal approximation. The results show that lattice parameters with c/a of the α′ phase and lattice parameters with b/a, c/a of the α″ phase are significantly sensitive to composition, and the atomic shuffle y of the α″ phase decreases from that of the α′ phase toward that of the β phase with increasing V content in Ti–V alloys. The compositional α′/α″ phase boundary is about 10 at.% V, from the viewpoints of energetics and mechanical stability of these phases. The principal lattice strains of the β → α′ transformation are insensitive to the V content, while those of the β → α″ transformation change significantly with increasing V content. The volume variation for β → α′ increases, whereas that for β → α″ decreases with increasing V content in Ti–V alloys. The energetic pathway results show that the relative stability of the α′ and α″ phases decrease with increasing V content and temperature and that there is no energy barriers during the β → α′/α″ martensitic transformations at temperatures from 0 to 400 K.

Keywords

elastic propertiesphase transformationTi
Type
Articles
Information
Journal of Materials Research , Volume 32 , Issue 16 , 28 August 2017 , pp. 3183 - 3190
Check for updates
Copyright
Copyright © Materials Research Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Contributing Editor: Susan B. Sinnott

References

REFERENCES

Saito, T., Furuta, T., Hwang, J.H., Kuramoto, S., Nishino, K., Suzuki, N., Chen, R., Yamada, A., Ito, K., Seno, Y., Nonaka, T., Ikehata, H., Nagasako, N., Iwamoto, C., Ikuhara, Y., and Sakuma, T.: Multifunctional alloys obtained via a dislocation-free plastic deformation mechanism. Science 300, 464–467 (2003).CrossRefGoogle Scholar
Abdel-Hady, M., Hinoshita, K., and Morinaga, M.: General approach to phase stability and elastic properties of β-type Ti-alloys using electronic parameters. Scr. Mater. 55, 477–480 (2006).Google Scholar
Kolli, R.P., Joost, W.J., and Ankem, S.: Phase stability and stress-induced transformations in beta titanium alloys. JOM 67, 8 (2015).CrossRefGoogle Scholar
Matsumoto, H., Watanabe, S., Masahashi, N., and Hanada, S.: Composition dependence of Young’s modulus in Ti–V, Ti–Nb, and Ti–V–Sn alloys. Metall. Mater. Trans. A 37, 3239–3249 (2006).Google Scholar
Kim, H.Y., Ikehara, Y., Kim, J.I., Hosoda, H., and Miyazaki, S.: Martensitic transformation, shape memory effect and superelasticity of Ti–Nb binary alloys. Acta Mater. 54, 2419–2429 (2006).CrossRefGoogle Scholar
Dobromyslov, A.V. and Elkin, V.A.: The orthorhombic α″-phase in binary titanium-base alloys with d-metals of V–VIII groups. Mater. Sci. Eng., A 438–440, 324–326 (2006).Google Scholar
Kim, H.Y. and Miyazaki, S.: Martensitic transformation and superelastic properties of Ti–Nb base alloys. Mater. Trans. 56, 625–634 (2015).CrossRefGoogle Scholar
Burgers, W.G.: On the process of transition of the cubic-body-centered modification into the hexagonal-close-packed modification of zirconium. Physica 1, 561–586 (1934).Google Scholar
Pathak, A., Banumathy, S., Sankarasubramanian, R., and Singh, A.K.: Orthorhombic martensitic phase in Ti–Nb alloys: A first principles study. Comput. Mater. Sci. 83, 222–228 (2014).CrossRefGoogle Scholar
Bönisch, M., Calin, M., Giebeler, L., Helth, A., Gebert, A., Skrotzki, W., and Eckert, J.: Composition-dependent magnitude of atomic shuffles in Ti–Nb martensites. J. Appl. Crystallogr. 47, 1374–1379 (2014).CrossRefGoogle Scholar
Bhattacharya, K.: Self-accommodation in martensite. Arch. Ration. Mech. Anal. 120, 201–244 (1992).Google Scholar
Chai, Y.W., Kim, H.Y., Hosoda, H., and Miyazaki, S.: Self-accommodation in Ti–Nb shape memory alloys. Acta Mater. 57, 4054–4064 (2009).Google Scholar
Inamura, T., Kim, J.I., Kim, H.Y., Hosoda, H., Wakashima, K., and Miyazaki, S.: Composition dependent crystallography of α″-martensite in Ti–Nb-based β-titanium alloy. Philos. Mag. 87, 3325–3350 (2007).Google Scholar
Leibovitch, C., Rabinkin, A., and Talianker, M.: Phase transformations in metastable Ti–V alloys induced by high pressure treatment. Metall. Trans. A 12, 1513–1519 (1981).Google Scholar
Ming, L.C., Manghnani, M.H., and Katahara, K.W.: Phase transformations in the Ti–V system under high pressure up to 25 GPa. Acta Metall. 29, 479–485 (1981).Google Scholar
Collings, E.W.: Magnetic studies of omega-phase precipitation and aging in titanium–vanadium alloys. J. Less-Common Met. 39, 63–90 (1975).Google Scholar
Hohenberg, P. and Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).Google Scholar
Kohn, W. and Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).CrossRefGoogle Scholar
Vanderbilt, D.: Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892–7895 (1990).Google Scholar
Clark, S.J., Segall, M.D., Pickard, C.J., Hasnip, P.J., Probert, M.J., Refson, K., and Payne, M.C.: First principles methods using CASTEP. Z. Kristallogr. 220, 567–570 (2005).Google Scholar
Perdew, J.P., Burke, K., and Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).Google Scholar
Pfrommer, B.G., Côté, M., Louie, S.G., and Cohen, M.L.: Relaxation of crystals with the quasi-Newton method. J. Comput. Phys. 131, 233–240 (1997).Google Scholar
Yu, R., Zhu, J., and Ye, H.Q.: Calculations of single-crystal elastic constants made simple. Comput. Phys. Commun. 181, 671–675 (2010).Google Scholar
Bellaiche, L. and Vanderbilt, D.: Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites. Phys. Rev. B 61, 7877–7882 (2000).Google Scholar
Söderlind, P., Eriksson, O., Wills, J.M., and Boring, A.M.: Theory of elastic constants of cubic transition metals and alloys. Phys. Rev. B 48, 5844–5851 (1993).Google Scholar
Li, T., Morris, J.W., Nagasako, N., Kuramoto, S., and Chrzan, D.C.: “Ideal” engineering alloys. Phys. Rev. Lett. 98, 105503 (2007).Google Scholar
Tegner, B.E., Zhu, L.G., and Ackland, G.J.: Relative strength of phase stabilizers in titanium alloys. Phys. Rev. B 85, 214106–214109 (2012).Google Scholar
Söderlind, P., Landa, A., Yang, L.H., and Teweldeberhan, A.M.: First-principles phase stability in the Ti–V alloy system. J. Alloys Compd. 581, 856–859 (2013).CrossRefGoogle Scholar
Yan, J.Y. and Olson, G.B.: Computational thermodynamics and kinetics of displacive transformations in titanium-based alloys. J. Alloys Compd. 673, 441–454 (2016).CrossRefGoogle Scholar
Dahmen, U.: Orientation relationships in precipitation systems. Acta Metall. 30, 63–73 (1982).Google Scholar
Hatt, B.A. and Rivlin, V.G.: Phase transformations in superconducting Ti–Nb alloys. J. Phys. D: Appl. Phys. 1, 1145–1149 (1968).CrossRefGoogle Scholar
Fisher, E.S. and Renken, C.J.: Single-crystal elastic moduli and the hcp → bcc transformation in Ti, Zr, and Hf. Phys. Rev. 135, A482–A494 (1964).Google Scholar
Wang, Y., Curtarolo, S., Jiang, C., Arroyave, R., Wang, T., Ceder, G., Chen, L.Q., and Liu, Z.K.: Ab initio lattice stability in comparison with CALPHAD lattice stability. Calphad 28, 79–90 (2004).Google Scholar
Aurelio, G., Guillermet, A.F., Cuello, G., and Campo, J.: Metastable phases in the Ti–V system: Part I. Neutron diffraction study and assessment of structural properties. Metall. Mater. Trans. A 33, 1307–1317 (2002).CrossRefGoogle Scholar
Li, C-X., Luo, H-B., Hu, Q-M., Yang, R., Yin, F-X., Umezawa, O., and Vitos, L.: Lattice parameters and relative stability of α″ phase in binary titanium alloys from first-principles calculations. Solid State Commun. 159, 70–75 (2013).CrossRefGoogle Scholar
Chakraborty, T., Rogal, J., and Drautz, R.: Martensitic transformation between competing phases in Ti–Ta alloys: A solid-state nudged elastic band study. J. Phys.: Condens. Matter 27, 115401–115408 (2015).Google ScholarPubMed
Mei, W. and Sun, J.: Energy landscape of displacive phase transition of β to ω in Ti–V alloys. MRS Adv., 2, 1449–1454 (2017).Google Scholar
Bonisch, M., Waltz, T., Calin, M., Skrotzki, W., and Eckert, J.: Tailoring the Bain strain of martensitic transformations in Ti–Nb alloys by controlling the Nb content. Int. J. Plast. 85, 190–202 (2016).Google Scholar
Morris, J.W.: The Khachaturyan theory of elastic inclusions: Recollections and results. Philos. Mag. 90, 3–35 (2010).CrossRefGoogle Scholar
Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. A 241, 376–396 (1957).Google Scholar
Hao, Y.J., Zhu, J., Zhang, L., Qu, J.Y., and Ren, H.S.: First-principles study of high pressure structure phase transition and elastic properties of titanium. Solid State Sci. 12, 1473–1479 (2010).Google Scholar
Simmons, G. and Wang, H.: Single Crystal Elastic Constants and Calculated Aggregate Properties. A Handbook, 2nd ed. (The MIT Press, Cambridge, Massachusetts, 1971).Google Scholar
Born, M. and Huang, K.: Dynamical Theory of Crystal Lattices (Oxford University Press, Oxford, England, 1954); p. 141.Google Scholar
Boettger, J.C. and Wallace, D.C.: Metastability and dynamics of the shock-induced phase transition in iron. Phys. Rev. B 55, 2840–2849 (1997).Google Scholar
Moruzzi, V.L., Janak, J.F., and Schwarz, K.: Calculated thermal properties of metals. Phys. Rev. B 37, 790–799 (1988).CrossRefGoogle ScholarPubMed