Abstract
A theoretical study was conducted to analyze electronic, elastic, and thermodynamic properties and the structural stability of the intermetallic materials Al3Ti1−xZrx for tetragonal-D022 and cubic-L12 structures carried out based on DFT. The findings indicate that the D022 phase has demonstrated more stability than the L12 phase and the possibility of a structural phase transition under pressure effect for concentrations x = 0.25 and x = 0.5. With increasing x concentration, the resulting lattice parameters drop. The density of states at the Fermi level, determines the electronic stability exhibited by these compounds. A pseudo-gap in proximity to the Fermi level implies the establishment of directional covalent bonding. The electronic structures support the phase stability results and show that the bonding in these compounds is more directed. Measurement techniques are employed to determine the number of bonding electrons per atom and the coefficient of electronic-specific heat. Both the mechanical as well as elastic properties of the considered alloys are examined. The findings demonstrate that all explored alloys are brittle, and D022 phase is stiffer than the L12 phase. The thermal characteristics are predicted via the quasi-harmonic Debye model.
Graphical abstract
Similar content being viewed by others
Data availability statements
Data sharing does not apply to this article.
References
Y.V. Milman, D.B. Miracle, S.I. Chugunova, I.V. Voskoboinik, N.P. Korzhova, T.N. Legkaya, Y.N. Podrezov, Intermetallics 9, 839 (2001)
Sauthoff G. In: Westbrook JH, Fleischer RL, editors. Intermetallic compounds, vol. 1 (Wiley, New York, 1994) p.991.
R.W. Cahn, Intermetallics 6, 563 (1998)
T.B. Massalski, H. Okamoto, P.R. Subramanian, L. Kacprzak (Eds.), Binary alloy phase diagrams, 2nd edition, ASM International, Materials Park (1990)
P. Villars, Pearson’s handbook of crystallographic data for intermetallic phases (American Society for Metals, Materials Park, 1997)
R.B. Schwarz, P.B. Desch, S. Srinivasan, P. Nash, Nanostruct. Mater. 1, 37 (1992)
C.L. Fu, J. Mater. Res. 5, 971 (1990)
M. Krajčí, J. Hafner, J. Phys, Condens. Matter 14, 1865 (2002)
M. Jahnátek, M. Krajčí, J. Hafner, Phys. Rev. B 71, 024101 (2005)
S. Saha, T.Z. Todorova, J.W. Zwanziger, Acta Mater. 89, 109 (2015)
C.J. Hsu, C.Y. Chang, P.W. Kao, N.J. Ho, C.P. Chang, Acta Mater. 54, 5241 (2006)
J. Li, M. Zhang, X. Luo, J. Alloys Compd. 556, 214 (2013)
S.S. Nayak, S.K. Pabi, B.S. Murty, Intermetallics 15, 26 (2007)
R.N. Wang, L. Ma, R.K. Pan, T.P. Luoa, S.C. Zhou, B.Y. Tang, Comput. Mat. Sci. 79, 136 (2013)
Z. Chen, H. Zou, F. Yu, J. Zou, J. Phys. Chem. Solids 71, 946–951 (2010)
G. Zhang, F. Sun, H. Liu, X. Ren, H. Xu, M. Wang, Y. Fu, Materials 14(9), 2206 (2021)
B.T. Tan, J. Zhang, K.V. Sopiha, P. Wu, Met. Mat. Int. 25(4), 869 (2019)
C.M. Fang, Z. Fan, Comp. Mat. Sci. 153, 309 (2018)
X. Pang, X. Chen, J. Yang, M. Pang, W. Yang, Y. Zhan, J. Phys. Chem. Solids 131, 243 (2019)
H. Hu, X. Wu, R. Wang, Z. Jia, W. Li, Q. Liu, J. Alloys Compd. 666, 185 (2016)
Y.H. Duan, Y. Sun, M.J. Peng, S.G. Zhou, J. Phys. Chem. Solids 75, 535–542 (2014)
C. Colinet, A. Pasturel, J. Alloys Compd. 319, 154 (2001)
C.S. Lue, B.X. Xie, S.N. Horng, J.H. Su, J.Y. Lin, Phys. Rev. B 71, 195104 (2005)
M. Yamaguchi, H. Inui, in Intermetallic Compounds, Al3Ti and its L12 variations, edited by J. Westbrook and R. Fleischer (John Wiley & Sons, New York, 1994), pp. –172.
M. Yamaguchi, H. Ini, Al3Ti and its L12 variations, in Intermetallic compounds, vol. 2, ed. by J.H. Westbrook, R.L. Fleischer (Wiley, New York, 1994), pp.147–172
S.S. Nayak, B.S. Murty, Mater. Sci. Eng. A 12, 367 (2004)
O. Andersen, Phys. Rev. B 12, 3060 (1975)
P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, an augmented plane wave plus local orbitals program for calculating crystal properties. Vienna University of Technology, Vienna, Austria (2001)
J.P. Perdew, S. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
P. Hohenberg, W. Kohn, Phys. Rev. B 136, 864 (1964)
M.A. Blanco, E. Francisco, V. Luaña, Comput. Phys. Commun. 158, 57–72 (2004)
R.A. Swalin, Thermodynamics of Solids (John Wiley, New York, 1961)
L.G. Ferreira, S.H. Wei, J.E. Bernard, A. Zunger, Phys. Rev. B 40, 3197 (1989)
L.K. Teles, J. Furthmüller, L.M.R. Scolfaro, J.R. Leite, F. Bechstedt, Phys. Rev. B 62, 2475 (2000)
F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30, 244 (1944)
R. Boulechfar, S. Ghemid, H. Meradji, B. Bouhafs, Physica B 405, 4045 (2010)
G. Ghosh, M. Asta, Acta Mater. 53, 3225 (2005)
G. Ghosh, S. Vaynman, M. Asta, M.E. Fine, Intermetallics 15, 44 (2007)
T. Hong, T.J. Watson-Yang, A.J. Freeman, T. Oguchi, J.H. Xu, Phys. Rev. B 41, 12462 (1990)
M. Asta, D.D. de Fontaine, M. van Schilfgaarde, J. Mater. Res. 8, 2554 (1993)
C. Amador, J.J. Hoyt, B.C. Chakoumakos, D. de Fontaine, Phys. Rev. Lett. 74, 4955 (1998)
C. Li, N. Cheng, Z. Chen, Z. Xie, L. Hui, Materials 11(4), 636 (2018)
Y. Cao, C. Zhang, S. Zhou, Y. Xu, B. Peng, Z. Jiao, K. Luo, C. Tian, Physica B 594, 412294 (2020)
P. Norby, N. Christensen, Acta Chem. Scand. A 40, 157 (1986)
S. Srinivasan, P.B. Desch, R.B. Schwartz, Scr. Metall. Mater. 25, 2513 (1991)
M. Nassik, F.Z. Chrifi-Alaoui, K. Mahdouk, J.C. Gachon, J. Alloy. Compd. 350, 151 (2003)
J.H. Xu, A.J. Freeman, Phys. Rev. B 41, 12553 (1990)
E. Clouet, J.M. Sanchez, C. Sigli, Phys. Rev. B 65, 094105 (2002)
S.S. Nayaka, S.K. Pabia, B.S. Murty, Intermetallics 15, 26 (2007)
P.B. Desch, R.B. Schwarz, P. Nash, J. Less-Common Met. 168, 69 (1991)
J. Murray, A. Peruzzi, J.P. Abriata, J. Phase Equilib. 13, 277–291 (1992)
D.W. Zhou, J.S. Liu, S.H. Xu, P. Peng, Comput. Mater. Sci. 51, 409 (2012)
D.W. Zhou, J.S. Liu, S.H. Xu, P. Peng, Comput. Mater. Sci. 86, 24 (2014)
B.R. Sahu, Mater. Sci. Eng. B 49, 74 (1997)
L. Vegard, Z. Phys. 5, 17 (1921)
R. Boulechfar, H. Meradji, S. Ghemid, S. Drablia, B. Bouhafs, Solid State Sci. 16, 1 (2013)
Y. Khenioui, R. Boulechfar, N. Maazi, S. Ghemid, Int. J. Mod. Phys. B 32(14), 1850167 (2018)
D. Chen, C. Xia, X. Liu, Y. Wu, M. Wang, Materials 12(9), 1539 (2019)
J. Xu, T. Oguchi, A. Freeman, Phys. Rev. B 36, 4186 (1987)
P. Ravindran, R. Asokamani, Phys. Rev. B 50, 668 (1994)
M. Jahnátek, M. Krajčí, J. Hafner, Philos. Mag. 87, 1769 (2007)
K. Nakamura, J. Kimura, Mater. Sci. 26, 2208 (1991)
M. Born, K. Huang, Dynamical theory of crystal lattices (Clarendon, Oxford, 1956)
J. Wang, S. Yip, Phys. Rev. Lett. 71, 4182 (1993)
R. Hill, Proc. Phys. Soc. Lond. 65, 349 (1952)
W. Voigt, Lehrbush der Kristallphysik (Taubner, Leipzig, 1928)
A. Reuss, Z. Angew, Math. Phys. 9, 49 (1929)
C.H. Jenkins, S.K. Khanna, Mech. Mater. 62 (2005)
S.F. Pugh, Philos. Mag. 45, 823 (1957)
J.J. Lewandowski, W.H. Wang, A.L. Greer, Philos. Mag. Lett. 85, 77 (2005)
H. Fu, D. Li, F. Peng, T. Gao, X. Cheng, Comput. Mater. Sci. 44, 774–777 (2008)
X.Q. Chen, H.Y. Niu, D.Z. Li, Y.Y. Li, Intermetallics 19, 1275 (2011)
A.T. Petit, L.P. Dulong, Ann. Chim. Phys. 10(1819), 395–2475 (2000)
G. Abadias, M.B. Kanoun, S. Goumri-Said, L. Koutsokeras, S.N. Dub, Ph. Djemia, Phys. Rev. B 90, 144107 (2014)
M.B. Kanoun, S. Goumri-Said, Surf. Coat. Technol. 255, 140–145 (2014)
Acknowledgements
Researchers Supporting Project number (RSP2023R82), King Saud University, Riyadh, Saudi Arabia. Authors thanks Prof. Waleed K. Ahmed from College of Engineering, United Arab Emirates for his carful reading of the manuscript.
Author information
Authors and Affiliations
Contributions
Each author played a significant role in the research and contributed equally to the overall development and completion of the paper.
Corresponding authors
Ethics declarations
Conflict of interest
The authors state that the research was conducted without any potential conflict of interest arising from commercial or financial relationships.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Boulechfar, R., Sayad, D., Khenioui, Y. et al. Theoretical investigations of Zr-concentration influence on the thermodynamic, elastic, electronic, and structural stability of D022/L12-Al3Ti. Eur. Phys. J. B 97, 1 (2024). https://doi.org/10.1140/epjb/s10051-023-00643-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjb/s10051-023-00643-7