Acta Metallurgica Sinica (English Letters) ›› 2019, Vol. 32 ›› Issue (12): 1511-1520.DOI: 10.1007/s40195-019-00925-z
• Orginal Article • Previous Articles Next Articles
Wei Diao1,2, Li-Hua Ye1, Zong-Wei Ji1,3, Rui Yang1, Qing-Miao Hu1()
Received:
2019-04-01
Revised:
2019-04-24
Online:
2019-12-10
Published:
2019-11-25
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[J]. Acta Metallurgica Sinica (English Letters), 2019, 32(12): 1511-1520.
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References | a (?) | c/a | Hf (eV/?) | B (GPa) |
---|---|---|---|---|
This work | 3.993 | 1.020 | -?0.405 | 114.5 |
DFT | ||||
Tang et al. [ | 3.981 | 1.024 | -?0.403 | 114.2 |
Ghosh et al. [ | 3.989 | 1.020 | -?0.406 | 113.7 |
Ghosh and Asta [ | 3.981 | 1.025 | -?0.412 | 112.1 |
Zou and Fu [ | 3.953 | 1.010 | -?0.420 | |
Asta et al. [ | 3.992 | 1.012 | -?0.437 | 128.0 |
Yu et al. [ | 3.995 | 1.020 | -?0.408 | |
Fu et al. [ | 4.001 | 1.012 | ||
Music and Schneider [ | 4.003 | 1.014 | -?0.401 | 112.0 |
Shu et al. [ | 4.006 | 1.012 | 111.0 | |
EXP | ||||
Duwez and Taylor [ | 3.997 | 1.018 | ||
Sridharan et al. [ | 4.001 | 1.017 | ||
He et al. [ | -?0.435 | 109.8 | ||
Tanaka [ | 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
References | a (?) | c/a | Hf (eV/?) | B (GPa) |
---|---|---|---|---|
This work | 3.993 | 1.020 | -?0.405 | 114.5 |
DFT | ||||
Tang et al. [ | 3.981 | 1.024 | -?0.403 | 114.2 |
Ghosh et al. [ | 3.989 | 1.020 | -?0.406 | 113.7 |
Ghosh and Asta [ | 3.981 | 1.025 | -?0.412 | 112.1 |
Zou and Fu [ | 3.953 | 1.010 | -?0.420 | |
Asta et al. [ | 3.992 | 1.012 | -?0.437 | 128.0 |
Yu et al. [ | 3.995 | 1.020 | -?0.408 | |
Fu et al. [ | 4.001 | 1.012 | ||
Music and Schneider [ | 4.003 | 1.014 | -?0.401 | 112.0 |
Shu et al. [ | 4.006 | 1.012 | 111.0 | |
EXP | ||||
Duwez and Taylor [ | 3.997 | 1.018 | ||
Sridharan et al. [ | 4.001 | 1.017 | ||
He et al. [ | -?0.435 | 109.8 | ||
Tanaka [ | 3.975 | 1.023 | 110.0 |
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
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 |
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
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 |
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
References | Method | Composition | Heat treatment | Site |
---|---|---|---|---|
Konitzer et al. [ | ALCHEMI | Ti-47.0Al-5.0Nb, Ti-52.0Al-5.0Nb | Homogenized at 1000 °C, slow cooling to room temperature | Ti |
Mohandas and Beaven [ | ALCHEMI | Ti-54.0Al-2.0Nb | Homogenized at 1200 °C, equilibrated at 1300 °C, water quenched | 0.89Ti, 0.11Al |
Hao et al. [ | 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. [ | ALCHEMI | Ti-47.5Al-1.0Nb | Homogenized at 1300 °C | Ti |
Doi et al. [ | X-ray scattering | Ti-48.5Al-2.19Nb, Ti-47.69Al-5.52Nb | Homogenized at 1000 °C, water quenched | Ti |
Kassab et al. [ | FIM | Ti-48Al-5Nb | Levitation-melting in high vacuum | Ti |
Wesemann et al. [ | APFIM | Ti-45Al-5Nb | Homogenized at 1000 °C, cooled in air | Ti |
Table 4 Site occupancy of Nb in γ-TiAl from experimental measurements
References | Method | Composition | Heat treatment | Site |
---|---|---|---|---|
Konitzer et al. [ | ALCHEMI | Ti-47.0Al-5.0Nb, Ti-52.0Al-5.0Nb | Homogenized at 1000 °C, slow cooling to room temperature | Ti |
Mohandas and Beaven [ | ALCHEMI | Ti-54.0Al-2.0Nb | Homogenized at 1200 °C, equilibrated at 1300 °C, water quenched | 0.89Ti, 0.11Al |
Hao et al. [ | 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. [ | ALCHEMI | Ti-47.5Al-1.0Nb | Homogenized at 1300 °C | Ti |
Doi et al. [ | X-ray scattering | Ti-48.5Al-2.19Nb, Ti-47.69Al-5.52Nb | Homogenized at 1000 °C, water quenched | Ti |
Kassab et al. [ | FIM | Ti-48Al-5Nb | Levitation-melting in high vacuum | Ti |
Wesemann et al. [ | APFIM | Ti-45Al-5Nb | Homogenized at 1000 °C, cooled in air | Ti |
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