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Acta Metallurgica Sinica (English Letters)  2019, Vol. 32 Issue (12): 1511-1520    DOI: 10.1007/s40195-019-00925-z
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Site Occupation of Nb in γ-TiAl: Beyond the Point Defect Gas Approximation
Wei Diao1,2, Li-Hua Ye1, Zong-Wei Ji1,3, Rui Yang1, Qing-Miao Hu1()
1 Institute of Metal Research, Chinese Academy of Sciences,Wenhua Road 72, Shenyang 110016, China
2 School of Materials Science and Engineering, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, China
3 University of Chinese Academy of Sciences, Yuquan Road 19A, Beijing 100049, China
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Abstract  

Microalloying is an effective approach to improve the mechanical properties of γ-TiAl intermetallic compound. Knowledge about the site occupancy of the ternary alloying element in the crystal lattice of γ-TiAl is highly demanded in order to understand the physics underlying the alloying effect. Previous first-principle methods-based thermodynamic models for the determination of the site occupancy were based on the point defect gas approximation with the interaction between the point defects neglected. In the present work, we include the point defect interaction energy in the thermodynamic model, which allows us to predict the site occupancy of the ternary alloying element in γ-TiAl beyond the point defect gas approximation. The model is applied to the γ-TiAl-Nb alloy. We show that, at low temperature, the site occupancy of Nb atoms depends on the composition of the alloy: Nb atoms occupy the Al sublattice for the Ti-rich alloy but occupy Ti sublattice for the Al-rich alloy. The fraction of Nb atoms occupying Al sublattice in the Ti-rich alloy decreases drastically, whereas the fraction of Nb atoms on the Ti sublattice in the Al-rich alloy decreases slightly with increasing temperature. At high temperature, Nb atoms occupy dominantly the Ti sublattice for both the Ti-rich and Al-rich alloys. The interaction between the point defects makes the Ti sublattice more favorable for the Nb atoms to occupy.

Key words:  Site preference      Titanium aluminides      Special quasi-random structures      First principles method     
Received:  01 April 2019     

Cite this article: 

Wei Diao, Li-Hua Ye, Zong-Wei Ji, Rui Yang, Qing-Miao Hu. Site Occupation of Nb in γ-TiAl: Beyond the Point Defect Gas Approximation. Acta Metallurgica Sinica (English Letters), 2019, 32(12): 1511-1520.

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https://www.amse.org.cn/EN/10.1007/s40195-019-00925-z     OR     https://www.amse.org.cn/EN/Y2019/V32/I12/1511

Fig. 1  Unit cell of γ-TiAl with L10 structure
References a (?) c/a Hf (eV/?) B (GPa)
This work 3.993 1.020 -?0.405 114.5
DFT
Tang et al. [59]. 3.981 1.024 -?0.403 114.2
Ghosh et al. [60]. 3.989 1.020 -?0.406 113.7
Ghosh and Asta [61] 3.981 1.025 -?0.412 112.1
Zou and Fu [62] 3.953 1.010 -?0.420
Asta et al. [63] 3.992 1.012 -?0.437 128.0
Yu et al. [64] 3.995 1.020 -?0.408
Fu et al. [65] 4.001 1.012
Music and Schneider [66] 4.003 1.014 -?0.401 112.0
Shu et al. [67] 4.006 1.012 111.0
EXP
Duwez and Taylor [68] 3.997 1.018
Sridharan et al. [69] 4.001 1.017
He et al. [70] -?0.435 109.8
Tanaka [71] 3.975 1.023 110.0
Table 1  Lattice parameters (a and c/a), heat of formation (Hf), and bulk modulus (B) of perfect γ-TiAl in comparison with available experimental and theoretical values
n Ti-rich (Ti54Al54-nNbn) Al-rich (Ti54-nAl54Nbn)
NbAl NbTi + TiAl NbTi NbAl + AlTi
1 0.848 0.987 0.110 0.869
2 0.851 0.985 0.109 1.024
3 0.805 0.880 0.111 0.951
4 0.939 0.970 0.125 1.198
5 0.927 0.941 0.123 1.105
6 0.929 0.942 0.131 1.041
8 0.891 0.939 0.124 1.179
10 0.913 0.917 0.130 1.136
Table 2  Formation energies of point defect and point defect pair in both Ti-rich and Al-rich γ-TiAl, calculated with different number n of Nb atoms in the supercell with N?=?54
Fig. 2  Formation energies of point defect and point defect pair as functions of the number of Nb atoms n containing in the supercells with, respectively, direct and indirect site occupations of Nb in Ti-rich a, Al-rich bγ-TiAl. The solid squares and circles are, respectively, for the calculated formation energies of the point defect in the supercell with direct site occupation of Nb and point defect pair in the supercell with indirect site occupation of Nb, $E_{\text{f}} \left( n \right)$. The opened ones represent the corresponding corrected formation energies, $\tilde{E}_{\text{f}} \left( n \right)$
n Ti-rich Al-rich
Ti54Al54-nNbn (Ti54-nNbn)(Al54-nTin) (Ti54-nNbn)Al54 (Ti54-nAln)(Al54-nNbn)
1 0 0 0 0
2 0.008 -?0.005 -?0.002 0.310
3 -?0.127 -?0.320 0.002 0.244
4 0.365 -?0.070 0.059 1.314
5 0.397 -?0.232 0.066 1.180
6 0.486 -?0.271 0.122 1.033
8 0.349 -?0.383 0.106 2.478
10 0.650 -?0.699 0.193 2.665
n 0.071n?-?0.071 -?0.065n + 0.065 0.019n?-?0.019 0.303n?-?0.303
Table 3  Interaction energies between point defects in the supercells with direct and indirect site occupations of Nb for both Ti-rich and Al-rich γ-TiAl
Fig. 3  Interaction energies between the point defects as functions of the number of Nb atoms n containing in the supercells with direct and indirect site occupations of Nb in Ti-rich a Al-rich bγ-TiAl. The solid squares and circles are, respectively, for the calculated interaction energies, $\Delta E(n)$, in the supercell with direct site occupation of Nb and in the supercell with indirect site occupation of Nb. The lines are for the corresponding interaction energies, $\Delta \tilde{E}(n)$, from the linear fitting of the calculated data points
Fig. 4  Fraction (x/c) of Nb on Al sublattice in TiAl1-cNbc alloy a Nb on Ti sublattice in Ti1-cAlNbc alloy b within the framework of point defect gas model
Fig. 5  Fraction (x/c) of Nb on Al sublattice in TiAl1-cNbc alloy a Nb on Ti sublattice in Ti1-cAlNbc alloy b taking into account of the interaction between the point defects
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Mohandas and Beaven [29] ALCHEMI Ti-54.0Al-2.0Nb Homogenized at 1200 °C, equilibrated at 1300 °C, water quenched 0.89Ti, 0.11Al
Hao et al. [30] ALCHEMI Ti-xAl-yNb, 46.0?<?x?<?53.0, 1.0?<?y?<?5.0 Homogenized at 900 °C, ice water quenched Ti
Rossouw et al. [31] ALCHEMI Ti-47.5Al-1.0Nb Homogenized at 1300 °C Ti
Doi et al. [32] X-ray scattering Ti-48.5Al-2.19Nb, Ti-47.69Al-5.52Nb Homogenized at 1000 °C, water quenched Ti
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Table 4  Site occupancy of Nb in γ-TiAl from experimental measurements
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