Acta Metallurgica Sinica (English Letters) ›› 2024, Vol. 37 ›› Issue (7): 1238-1248.DOI: 10.1007/s40195-024-01694-0
Special Issue: 2024年 高温合金专辑
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Guan-Cheng Gu1, Zhao-Jing Han1, Ze-Yu Chen1, Zhao-Xuan Li1, Sheng-Bao Xia1, Zheng-Ning Li1, Hua Jin1(
), Wei-Wei Xu1(
), Xing-Jun Liu2
Received:2023-10-18
Revised:2023-12-27
Accepted:2024-02-20
Online:2024-04-17
Published:2024-04-17
Contact:
Hua Jin, Wei-Wei Xu
Guan-Cheng Gu, Zhao-Jing Han, Ze-Yu Chen, Zhao-Xuan Li, Sheng-Bao Xia, Zheng-Ning Li, Hua Jin, Wei-Wei Xu, Xing-Jun Liu. Theoretical Exploration of Alloying Effects on Stabilities and Mechanical Properties of γʹ Phase in Novel Co-Al-Nb-Base Superalloys[J]. Acta Metallurgica Sinica (English Letters), 2024, 37(7): 1238-1248.
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| Materials | Source | Structure | State | Tc (K) | a (Å)* | c (Å)* | B (GPa)# |
|---|---|---|---|---|---|---|---|
| Al | This work | FCC | NM | 3.990 | 77.7 | ||
| Expt. [33, 34] | 3.960 | 73.6 | |||||
| Ti | This work | HCP | NM | 2.997 | 4.894 | 108.7 | |
| Expt. [33, 34] | 2.950 | 4.683 | 107.2 | ||||
| V | This work | BCC | NM | 2.997 | 170.2 | ||
| Expt. [33, 34] | 3.028 | 165.1 | |||||
| Cr | This work | BCC | PM | 77 | 2.863 | 198.9 | |
| Expt. [33, 34] | 2.879 | 194.0 | |||||
| Co | This work | HCP | FM | 1514 | 2.563 | 4.185 | 213.7 |
| Expt. [33, 34] | 2.500 | 4.081 | 195.2 | ||||
| Ni | This work | FCC | FM | 609 | 3.527 | 193.0 | |
| Expt. [33, 34] | 3.517 | 190.0 | |||||
| Zr | This work | HCP | NM | 3.309 | 5.404 | 87.6 | |
| Expt. [33, 34] | 3.231 | 5.148 | 85.0 | ||||
| Nb | This wok | BCC | NM | 3.308 | 159.6 | ||
| Expt. [33, 34] | 3.294 | 173.6 | |||||
| Mo | This work | BCC | NM | 3.163 | 247.7 | ||
| Expt. [33, 34] | 3.141 | 277.9 | |||||
| Ru | This work | HCP | NM | 2.779 | 4.538 | 300.2 | |
| Expt. [33, 34] | 2.700 | 4.273 | 327.1 | ||||
| Ta | This work | BCC | NM | 3.325 | 188.8 | ||
| Expt. [33, 34] | 3.291 | 204.0 | |||||
| W | This work | BCC | NM | 3.192 | 291.0 | ||
| Expt. [33, 34] | 3.159 | 329.6 | |||||
| Re | This work | HCP | NM | 2.858 | 4.667 | 350.1 | |
| Expt. [33, 34] | 2.760 | 4.458 | 379.0 | ||||
| Co3Al | This work | L12 | FM | 421 | 3.584 | 182.9 | |
| Calc. [35] | 3.574 | 188.2 | |||||
| Co3(Al, Nb) | This work | L12 | FM | 328 | 3.612 | 191.6 | |
| Expt. [14] | 3.644 |
Table 1 Structure, lattice parameters (a and c, in units of Å), Curie temperature Tc (K), and bulk modulus B (GPa) for selected elements at room temperature, together with the available data from experiments [14,33,34] and other calculations [35]
| Materials | Source | Structure | State | Tc (K) | a (Å)* | c (Å)* | B (GPa)# |
|---|---|---|---|---|---|---|---|
| Al | This work | FCC | NM | 3.990 | 77.7 | ||
| Expt. [33, 34] | 3.960 | 73.6 | |||||
| Ti | This work | HCP | NM | 2.997 | 4.894 | 108.7 | |
| Expt. [33, 34] | 2.950 | 4.683 | 107.2 | ||||
| V | This work | BCC | NM | 2.997 | 170.2 | ||
| Expt. [33, 34] | 3.028 | 165.1 | |||||
| Cr | This work | BCC | PM | 77 | 2.863 | 198.9 | |
| Expt. [33, 34] | 2.879 | 194.0 | |||||
| Co | This work | HCP | FM | 1514 | 2.563 | 4.185 | 213.7 |
| Expt. [33, 34] | 2.500 | 4.081 | 195.2 | ||||
| Ni | This work | FCC | FM | 609 | 3.527 | 193.0 | |
| Expt. [33, 34] | 3.517 | 190.0 | |||||
| Zr | This work | HCP | NM | 3.309 | 5.404 | 87.6 | |
| Expt. [33, 34] | 3.231 | 5.148 | 85.0 | ||||
| Nb | This wok | BCC | NM | 3.308 | 159.6 | ||
| Expt. [33, 34] | 3.294 | 173.6 | |||||
| Mo | This work | BCC | NM | 3.163 | 247.7 | ||
| Expt. [33, 34] | 3.141 | 277.9 | |||||
| Ru | This work | HCP | NM | 2.779 | 4.538 | 300.2 | |
| Expt. [33, 34] | 2.700 | 4.273 | 327.1 | ||||
| Ta | This work | BCC | NM | 3.325 | 188.8 | ||
| Expt. [33, 34] | 3.291 | 204.0 | |||||
| W | This work | BCC | NM | 3.192 | 291.0 | ||
| Expt. [33, 34] | 3.159 | 329.6 | |||||
| Re | This work | HCP | NM | 2.858 | 4.667 | 350.1 | |
| Expt. [33, 34] | 2.760 | 4.458 | 379.0 | ||||
| Co3Al | This work | L12 | FM | 421 | 3.584 | 182.9 | |
| Calc. [35] | 3.574 | 188.2 | |||||
| Co3(Al, Nb) | This work | L12 | FM | 328 | 3.612 | 191.6 | |
| Expt. [14] | 3.644 |
| Phase | TM | L12 structure | D019 structure | B2 structure | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Tc | a | B | Tc | a | c | B | Tc | a | B | ||
| (Co, Ni)3(Al, Nb, TM) | free | 312 | 3.541 | 191.0 | 287 | 5.118 | 4.105 | 187.4 | 397 | 2.880 | 168.2 |
| Ti | 292 | 3.546 | 202.6 | 271 | 5.122 | 4.108 | 188.6 | 384 | 2.885 | 175.5 | |
| V | 278 | 3.541 | 203.9 | 265 | 5.115 | 4.103 | 191.8 | 383 | 2.881 | 177.8 | |
| Cr | 288 | 3.538 | 203.7 | 285 | 5.111 | 4.099 | 192.7 | 394 | 2.881 | 179.0 | |
| Zr | 305 | 3.558 | 190.6 | 105 | 5.142 | 4.125 | 188.4 | 384 | 2.900 | 175.6 | |
| Mo | 262 | 3.547 | 199.6 | 246 | 5.125 | 4.110 | 193.5 | 373 | 2.888 | 180.6 | |
| Ru | 268 | 3.543 | 195.8 | 254 | 5.120 | 4.107 | 191.1 | 414 | 2.885 | 183.2 | |
| Ta | 275 | 3.553 | 198.3 | 259 | 5.133 | 4.117 | 192.8 | 376 | 2.892 | 179.2 | |
| W | 262 | 3.550 | 201.3 | 244 | 5.127 | 4.112 | 195.2 | 371 | 2.889 | 181.8 | |
| Re | 246 | 3.547 | 201.9 | 234 | 5.123 | 4.109 | 196.3 | 377 | 2.888 | 183.0 | |
Table 2 Calculated physical properties of the TM-doped (Co, Ni)3(Al, Nb) phase in L12, D019, and B2 structures, including lattice parameters (a and c) (Å), Curie temperature Tc (K), and bulk modulus B (GPa)
| Phase | TM | L12 structure | D019 structure | B2 structure | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Tc | a | B | Tc | a | c | B | Tc | a | B | ||
| (Co, Ni)3(Al, Nb, TM) | free | 312 | 3.541 | 191.0 | 287 | 5.118 | 4.105 | 187.4 | 397 | 2.880 | 168.2 |
| Ti | 292 | 3.546 | 202.6 | 271 | 5.122 | 4.108 | 188.6 | 384 | 2.885 | 175.5 | |
| V | 278 | 3.541 | 203.9 | 265 | 5.115 | 4.103 | 191.8 | 383 | 2.881 | 177.8 | |
| Cr | 288 | 3.538 | 203.7 | 285 | 5.111 | 4.099 | 192.7 | 394 | 2.881 | 179.0 | |
| Zr | 305 | 3.558 | 190.6 | 105 | 5.142 | 4.125 | 188.4 | 384 | 2.900 | 175.6 | |
| Mo | 262 | 3.547 | 199.6 | 246 | 5.125 | 4.110 | 193.5 | 373 | 2.888 | 180.6 | |
| Ru | 268 | 3.543 | 195.8 | 254 | 5.120 | 4.107 | 191.1 | 414 | 2.885 | 183.2 | |
| Ta | 275 | 3.553 | 198.3 | 259 | 5.133 | 4.117 | 192.8 | 376 | 2.892 | 179.2 | |
| W | 262 | 3.550 | 201.3 | 244 | 5.127 | 4.112 | 195.2 | 371 | 2.889 | 181.8 | |
| Re | 246 | 3.547 | 201.9 | 234 | 5.123 | 4.109 | 196.3 | 377 | 2.888 | 183.0 | |
Fig. 1 a Formation energy Hf value of γʹ phase in D019 and L12 structures before and after doping (with the energy of B2 as the reference state) and b increment ratio (δ) of ΔH values as: δ = (ΔHfree−ΔHTM)/ΔHfree where ΔHfree and ΔHTM are the energy different for doping-free and TM-doped cases
Fig. 2 a Total and b partial density of states (DOS) for doping-free and V-doped phases in D019 and L12 structures. Note that the fermi level is labeled as EF
| Phase | TM | Source | C11 | C12 | C44 | B | G | E | ν | AU | Hv |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ni3Al | - | This work | 212.7 | 163.9 | 142.6 | 180.2 | 71.9 | 190.4 | 0.32 | 4.8 | 5.3 |
| - | Expt. [39] | 224.0 | 148.0 | 125.0 | 173.3 | 77.7 | 202.9 | 0.31 | - | - | |
| - | Calc. [40] | 232.7 | 151.4 | 120.6 | 178.5 | 78.1 | 204.4 | 0.31 | - | - | |
| (Co, Ni)3(Al, Nb, TM) | free | This work | 284.7 | 144.1 | 166.8 | 191.0 | 117.9 | 293.4 | 0.24 | 1.0 | 15.5 |
| Ti | This work | 304.8 | 151.6 | 165.6 | 202.6 | 121.5 | 303.8 | 0.25 | 0.7 | 15.2 | |
| V | This work | 312.3 | 149.7 | 168.5 | 203.9 | 125.8 | 313.0 | 0.24 | 0.7 | 16.2 | |
| Cr | This work | 310.3 | 150.5 | 168.3 | 203.7 | 124.8 | 311.0 | 0.25 | 0.7 | 16.0 | |
| Zr | This work | 290.1 | 140.8 | 162.5 | 190.6 | 118.9 | 295.3 | 0.24 | 0.8 | 15.8 | |
| Mo | This work | 315.4 | 141.7 | 169.0 | 199.6 | 129.4 | 319.2 | 0.23 | 0.6 | 17.7 | |
| Ru | This work | 306.3 | 140.6 | 169.9 | 195.8 | 127.3 | 314.0 | 0.23 | 0.6 | 17.6 | |
| Ta | This work | 308.5 | 143.2 | 167.4 | 198.3 | 126.1 | 312.2 | 0.24 | 0.6 | 17.0 | |
| W | This work | 318.4 | 142.7 | 169.7 | 201.3 | 130.3 | 321.4 | 0.23 | 0.5 | 17.8 | |
| Re | This work | 322.2 | 141.7 | 171.0 | 201.9 | 132.3 | 325.7 | 0.23 | 0.5 | 18.3 |
Table 3 Calculated elastic constants Cij (i.e., C11, C12, and C44) (GPa), and the corresponding aggregate properties of bulk (B), shear (G) and Young’s (E) moduli (GPa), Poisson’s ratio (ν), AU and Hardness (Hv) for L12 (Co, Ni)3(Al, Nb, TM) phases, together with available data from experimental [39] and theoretical [40] results
| Phase | TM | Source | C11 | C12 | C44 | B | G | E | ν | AU | Hv |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ni3Al | - | This work | 212.7 | 163.9 | 142.6 | 180.2 | 71.9 | 190.4 | 0.32 | 4.8 | 5.3 |
| - | Expt. [39] | 224.0 | 148.0 | 125.0 | 173.3 | 77.7 | 202.9 | 0.31 | - | - | |
| - | Calc. [40] | 232.7 | 151.4 | 120.6 | 178.5 | 78.1 | 204.4 | 0.31 | - | - | |
| (Co, Ni)3(Al, Nb, TM) | free | This work | 284.7 | 144.1 | 166.8 | 191.0 | 117.9 | 293.4 | 0.24 | 1.0 | 15.5 |
| Ti | This work | 304.8 | 151.6 | 165.6 | 202.6 | 121.5 | 303.8 | 0.25 | 0.7 | 15.2 | |
| V | This work | 312.3 | 149.7 | 168.5 | 203.9 | 125.8 | 313.0 | 0.24 | 0.7 | 16.2 | |
| Cr | This work | 310.3 | 150.5 | 168.3 | 203.7 | 124.8 | 311.0 | 0.25 | 0.7 | 16.0 | |
| Zr | This work | 290.1 | 140.8 | 162.5 | 190.6 | 118.9 | 295.3 | 0.24 | 0.8 | 15.8 | |
| Mo | This work | 315.4 | 141.7 | 169.0 | 199.6 | 129.4 | 319.2 | 0.23 | 0.6 | 17.7 | |
| Ru | This work | 306.3 | 140.6 | 169.9 | 195.8 | 127.3 | 314.0 | 0.23 | 0.6 | 17.6 | |
| Ta | This work | 308.5 | 143.2 | 167.4 | 198.3 | 126.1 | 312.2 | 0.24 | 0.6 | 17.0 | |
| W | This work | 318.4 | 142.7 | 169.7 | 201.3 | 130.3 | 321.4 | 0.23 | 0.5 | 17.8 | |
| Re | This work | 322.2 | 141.7 | 171.0 | 201.9 | 132.3 | 325.7 | 0.23 | 0.5 | 18.3 |
Fig. 3 Increment ratio per atom (ΔX) of a elastic constants (Cij) and b aggregate properties of Bulk (B), Shear (G), and Young’s (E) moduli for the TM-doped (Co, Ni)3(Al, Nb) phase. Herein, ΔX = (XTM−Xfree)/Xfree where Xfree and XTM are the elastic properties (X: Cij, B, G, and E))
Fig. 5 Increment ratio maps of a formation energies ΔH(δ) and b-d mechanical properties of B/G ratio (ΔB/G), Young’s modulus E (ΔE), and hardness Hv (ΔHv) as a function of V and Cr contents
Fig. 6 Increment ratio maps of a formation energies ΔH(δ) and b-d mechanical properties of B/G ratio (ΔB/G), Young’s modulus E (ΔE), and hardness Hv (ΔHv) as a function of V and Ta contents
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