First Principle Study on Mg2X (X = Si, Ge, Sn) Intermetallics by Bi Micro-Alloying
Abstract
:1. Introduction
2. Model and Calculation Method
3. Results and Discussion
3.1. Lattice Parameters
3.2. Elastic Properties
3.3. Electronic Properties
4. Conclusions
- (1)
- The lattice parameters of Mg2X are smaller than those of Bi-doped Mg2X, because the radius of doping element Bi is larger than that of alloying element X and Mg. The ΔHf of Mg64X31Bi is smaller than that of others, which indicates that the element Bi preferentially occupies the position of the X (X = Si, Ge, Sn) atom than other positions.
- (2)
- Mg2X (X = Si, Ge, Sn), Mg63X32Bi, Mg64X31Bi, Mg64Ge32Bi, and Mg64Sn32Bi are mechanically stable, while Mg64Si32Bi indicates that it cannot exist stably. The ability of Mg2Si to resist deformation after doping is enhanced, and Mg63Si32Bi has stronger deformation resistance. The doping of alloy element Bi makes the Mg2X (X = Si, Ge, Sn) alloy convert from brittle material to ductile material, and results in plasticity enhancement and stiffness reduction.
- (3)
- The pure and Bi-doped Mg2X (X = Si, Ge, Sn) exhibit elastic anisotropic properties. The anisotropy of Bi-doped the Mg2X (X = Si, Ge) phase is larger than that of Mg2X, whereas the anisotropy of Bi-doped Mg2Sn is smaller than that of Mg2Sn. Mg64Ge32Bi shows strong anisotropy among these phases.
- (4)
- In an energy range from −10 to 0 eV, there is no significant difference in the shape of TDOS between the pure and doped Mg2X phases. The contribution of Bi orbitals of Mg63X32Bi, Mg64X31Bi, and Mg63X32Bi are different, resulting in different hybridization effects in three types of Bi-doped Mg2X.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Phase | Lattice Constants a/Å | ΔHf (eV/atom) | ||
---|---|---|---|---|
This Work | Cal | Exp | ||
pure Mg2Si | 6.371 | 6.30 [10] | 6.35 [34] | –0.170 |
Mg64Si32 | 12.741 | –0.170 | ||
Mg63Si32Bi | 12.791 | - | - | −0.191 |
Mg64Si31Bi | 12.804 | - | - | −0.204 |
Mg64Si32Bi | 12.823 | - | - | −0.175 |
pure Mg2Ge | 6.355 | 6.318 [35] | 6.3849 [36] | −0.259 |
Mg64Ge32 | 12.710 | −0.259 | ||
Mg63Ge32Bi | 12.906 | - | - | −0.279 |
Mg64Ge31Bi | 12.909 | - | - | −0.290 |
Mg64Ge32Bi | 12.940 | - | - | −0.264 |
pure Mg2Sn | 6.843 | 6.829 [37] | 6.759 [38] | −0.196 |
Mg64Sn32 | 13.685 | −0.196 | ||
Mg63Sn32Bi | 13.688 | - | - | −0.228 |
Mg64Sn31Bi | 13.670 | - | - | −0.237 |
Mg64Sn32Bi | 13.711 | - | - | −0.220 |
Phase | C11 | C12 | C44 | B | G | E | G/B | ν | Az |
---|---|---|---|---|---|---|---|---|---|
Mg64Si32 | 111.97 | 21.55 | 41.74 | 51.69 | 43.10 | 101.17 | 0.834 | 0.174 | 0.923z |
Exp. [44] | 126.00 | 26.00 | 48.50 | 59.00 | - | - | - | - | - |
Cal. [11] | 121.20 | 23.70 | 49.50 | 56.20 | 49.20 | 113.50 | - | - | - |
Cal. [45] | 118.80 | 22.27 | 44.96 | - | - | - | - | - | - |
Mg63Si32Bi | 108.53 | 24.84 | 36.21 | 52.74 | 38.37 | 92.64 | 0.728 | 0.207 | 0.865 |
Mg64Si31Bi | 107.64 | 24.50 | 36.03 | 52.21 | 38.15 | 92.03 | 0.731 | 0.206 | 0.867 |
Mg64Si32Bi | 37.44 | 57.65 | 32.58 | - | - | - | - | - | - |
Mg64Ge32 | 103.88 | 19.65 | 37.97 | 49.73 | 39.57 | 93.01 | 0.829 | 0.175 | 0.902 |
Exp. [44] | 117.90 | 23.00 | 46.50 | 54.06 | - | - | - | - | - |
Cal. [11] | 118.10 | 23.60 | 48.00 | 55.10 | 47.70 | 111.10 | - | 0.164 | - |
Cal. [46] | 116.10 | 20.60 | 44.00 | 52.50 | 45.40 | 105.9 | - | 0.164 | - |
Mg63Ge32Bi | 101.58 | 23.26 | 34.24 | 49.37 | 36.13 | 87.14 | 0.732 | 0.206 | 0.874 |
Mg64Ge31Bi | 101.25 | 22.21 | 33.86 | 48.56 | 36.02 | 86.64 | 0.742 | 0.203 | 0.857 |
Mg64Ge32Bi | 52.54 | 43.72 | 28.52 | 46.66 | 13.91 | 37.96 | 0.298 | 0.364 | 6.472 |
Mg64Sn32 | 68.36 | 29.39 | 34.20 | 40.38 | 28.11 | 68.46 | 0.696 | 0.217 | 1.630 |
Exp. [47] | 82.40 | 20.80 | 36.60 | - | - | - | - | - | - |
Cal. [11] | 83.71 | 39.79 | 21.69 | 42.36 | 21.79 | 74.78 | 0.51 | 0.206 | - |
Cal. [44] | 81.10 | 20.16 | 34.85 | 43.73 | 31.70 | - | - | - | - |
Mg63Sn32Bi | 66.42 | 27.11 | 27.42 | 40.21 | 24.00 | 60.04 | 0.597 | 0.251 | 1.395 |
Mg64Sn31Bi | 67.51 | 25.96 | 28.63 | 39.81 | 25.18 | 62.38 | 0.632 | 0.239 | 1.378 |
Mg64Sn32Bi | 58.06 | 29.27 | 23.25 | 38.97 | 19.18 | 49.41 | 0.493 | 0.288 | 1.615 |
Non-Spin Polarized | Spin Polarized | |
---|---|---|
Total Energy (eV) | −64958.92186 | −64958.92179 |
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Bai, G.; Tian, J.; Guo, Q.; Li, Z.; Zhao, Y. First Principle Study on Mg2X (X = Si, Ge, Sn) Intermetallics by Bi Micro-Alloying. Crystals 2021, 11, 142. https://doi.org/10.3390/cryst11020142
Bai G, Tian J, Guo Q, Li Z, Zhao Y. First Principle Study on Mg2X (X = Si, Ge, Sn) Intermetallics by Bi Micro-Alloying. Crystals. 2021; 11(2):142. https://doi.org/10.3390/cryst11020142
Chicago/Turabian StyleBai, Guoning, Jinzhong Tian, Qingwei Guo, Zhiqiang Li, and Yuhong Zhao. 2021. "First Principle Study on Mg2X (X = Si, Ge, Sn) Intermetallics by Bi Micro-Alloying" Crystals 11, no. 2: 142. https://doi.org/10.3390/cryst11020142
APA StyleBai, G., Tian, J., Guo, Q., Li, Z., & Zhao, Y. (2021). First Principle Study on Mg2X (X = Si, Ge, Sn) Intermetallics by Bi Micro-Alloying. Crystals, 11(2), 142. https://doi.org/10.3390/cryst11020142