Theoretical Prediction of Structural, Mechanical, and Thermophysical Properties of the Precipitates in 2xxx Series Aluminum Alloy
Abstract
:1. Introduction
2. Model and Computational Method
Phase | Crystal Structure | Space Group | V | Crystal Parameters | ΔH | Ecoh | DF | ||
---|---|---|---|---|---|---|---|---|---|
a | b | c | |||||||
Al2Cu | Tetragonal | I4/MCM | 179.8 (179.8 a) | 6.04 (6.039 a, 6.063 b, 5.99 c) | 6.04 (6.039 a, 6.063 b, 5.99 c) | 4.928 (4.93 a, 4.872 b, 4.81 c) | −0.151 (−0.164 a, −0.203 b, −0.203 c) | −4.0 (−3.89 a, −3.99 b, −3.99 c) | 0.19 (0.19 a) |
Al2CuMg | Orthorhombic | CMCM | 268.2 (268.1 a, 270.8 d) | 4.027 (4.026 a, 4.01 b, 3.89 c, 4.05 d, 4.01 e) | 9.319 (9.326 a, 9.25 b, 9.20 c, 9.28 d, 9.27 e) | 7.147 (7.142 a, 7.15 b, 7.16 c, 7.21 d, 7.12 e) | −0.17 (−0.186 a, −0.25 b, −0.25 c) | −3.5 (−3.35 a, −3.46 b, −3.46 c) | 0.16 (0.13 a) |
Al3Fe | Triclinic | P63/MMC | 108.2 (108.2 f) | 5.36 (5.357 f) | 5.36 (5.357 f) | 4.354 (4.354 f) | −0.16 (−0.154 f) | −5.3 | 0.33 |
Al3Fe2Si | Cubic | FD-3M | 1224.9 (1225 g) | 10.701 | 10.701 | 10.701 | −0.423 (−0.402 f) | −6.4 | 0.33 |
Al5Cu2Mg8Si6 | Monoclinic | PM | 385.8 | 10.479 (10.423 h) | 4.016 (4.033 h) | 10.529 | −0.02 (−0.12 h) | −3.5 | 0.13 |
Al7Cu2Fe | Tetragonal | P4/MNC | 590.5 | 6.324 (6.336 i, 6.338 j) | 6.324 (6.336 i, 6.338 j) | 14.763 (14.87 i, 14.83 j) | −0.266 (−0.298 j) | −4.6 | 0.14 |
Al6Mn | Orthorhombic | CMCM | 431.4 | 6.468 (6.499 k) | 7.544 (7.555 k) | 8.841 (8.872 k) | −0.195 | −4.7 | 0.14 |
Al3Zr_D023 | Tetragonal | I4/MMM | 280.1 | 4.020 (4.018 a, 4.015 b) | 4.020 (4.018 a, 4.015 b) | 17.332 (17.348 a, 17.454 b) | −0.489 (−0.517 a, −0.459 b) | −5.1 (5.14 a, 4.57 b) | 0.15 (0.15 a) |
Al3Zr_D022 | Tetragonal | I4/MMM | 141.8 | 3.963 | 3.963 | 9.032 | −0.464 (−0.463 l) | −5.1 | 0.2 |
Al3Zr_L12 | Cubic | PM-3M | 69.4 | 4.109 (4.111 m, 4.05 n, 4.09 o) | 4.109 (4.111 m) | 4.109 (4.111 m) | −0.461 (−0.463 l, −0.487 m, −0.47 p) | −5.1 | 0.18 |
Al20Cu2Mn3 | Orthorhombic | BBMM | 2337.3 | 24.089 (23.98 q) | 12.601 (12.54 q) | 7.700 (7.66 q) | −0.181 (−0.156 q) | −4.64 | 0.19 |
3. Results and Discussion
3.1. Mechanical Properties
Phase | B | B’ | G | BH/GH | E | σ | Hv | AB | AG | AU | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
BV | BR | BH | GV | GR | GH | |||||||||
Al2Cu | 90.5 (99.4 a, 87.7 b) | 90.5 (99.4 a, 87.6 b) | 90.5 (99.4 a, 87.7 b, 108.6 c) | 4.71 | 46.1 (38.3 a, 52.1 b) | 38.2 (35.9 a, 42.3 b) | 42.1 (37.1 a, 47.2 b, 39 c) | 2.1 | 109.5 (99 a, 120 b, 104.5 c) | 0.298 (0.33 a, 0.272 b, 0.34 c) | 4.3 | 0 | 0.09 | 1.03 |
Al2CuMg | 73.4 (80.9 b, 76.06 d) | 72.9 (80.7 b, 74.36 d) | 73.2 (80.8 b, 75.21 d, 79.48 e) | 4.639 | 45.6 (63.3 b, 51.02 d) | 41.1 (57.9 b, 45.13 d) | 43.3 (60.6 b, 48.08 d, 46.8 e) | 1.7 (1.564 d) | 108.5 (145.5 b, 118.9 d, 117.3 e) | 0.253 (0.2 b, 0.237 d, 0.254 e) | 6.8 | 0.003 | 0.052 | 0.554 (0.675 d, 0.349 e) |
Al3Fe | 129.6 (125 f) | 129.5 (125 f) | 129.6 (125 f) | 4.156 | 54.9 (55 f) | 52.0 (51 f) | 53.4 (53 f) | 2.4 | 140.9 | 0.319 (0.31 f) | 4.3 | 0.0003 | 0.027 | 0.281 (0.35 f) |
Al3Fe2Si | 155.9 | 155.9 | 155.9 | 4.498 | 95.6 | 95.5 | 95.6 | 1.6 | 238.1 | 0.245 | 13.3 | 0 | 0.0005 | 0.0052 |
Al5Cu2Mg8Si6 | 63.6 (70.5 g) | 63.4 (69.7 g) | 63.5 (70.1 g) | 4.439 | 5.8 (44.5 g) | 51.8 (42.8 g) | 28.8 (43.6 g) | 2.2 | 75.0 (108.4 g) | 0.303 (0.242 g) | 2.7 | / | / | / |
Al7Cu2Fe | 109.1 | 109.0 | 109.1 (107.8 h) | 4.42 | 91.3 | 90.8 | 91.0 (74.5 h) | 1.2 | 213.6 (181.7 h) | 0.173 (0.219 h) | 19.6 | 0.0005 | 0.0027 | 0.0285 |
Al6Mn | 102.1 | 101.9 | 102.0 (102.6 i) | 4.022 | 67.6 | 64.1 | 65.9 | 1.5 | 126.6 | 0.234 | 10.9 | 0.001 | 0.0266 | 0.275 |
Al3Zr_D023 | 101.6 (123.9 j) | 101.4 (117.4 j) | 101.5 (120.6 j, 100.2 k) | 3.977 | 84.1 (88.4 j) | 82.8 (85.8 j) | 83.4 (87.1 j, 77.1 k) | 1.2 | 196.5 (210.6 j, 184.1 k) | 0.177 (0.195 k) | 18.1 | 0.001 | 0.008 | 0.081 |
Al3Zr_D022 | 101.4 (101.9 l) | 101.2 (101.6 l) | 101.3 (101.8 l) | 3.11 | 87.4 (87.9 l) | 79.3 (80.6 l) | 83.3 (84.2 l) | 1.2 | 196.2 (198 l) | 0.177 (0.176 l) | 18.1 | 0.001 | 0.0486 | 0.513 |
Al3Zr_L12 | 101.5 | 101.5 | 101.5 (104.4 m, 103 n) | 4.134 | 63.1 | 62.2 | 62.7 (65.3 m, 64 n) | 1.6 | 156.0 (162.2 m, 159.1 n) | 0.244 (0.241 m, 0.243 n) | 9.8 | 0 | 0.0072 | 0.0723 |
Al20Cu2Mn3 | 101.5 | 100.8 | 101.1 | 4.741 | 42.5 | 38.2 | 40.4 | 2.5 | 106.9 | 0.324 | 3.0 | 0.0035 | 0.0533 | 0.569 |
3.2. Thermophysical Properties
4. Conclusions
- The calculated formation enthalpies are −0.151, −0.17, −0.16, −0.463, −0.02, −0.266, −0.195, −0.489, −0.464, −0.461, and −0.181 eV/atom for Al2Cu, Al2CuMg, Al3Fe, Al3Fe2Si, Al5Cu2Mg8Si6, Al7Cu2Fe, Al6Mn, Al3Zr_D023, Al3Zr_D022, Al3Zr_L12, and Al20Cu2Mn3, respectively. Al5Cu2Mg8Si6 shows thermodynamic and mechanical unstable.
- The bulk modulus of all precipitates are derived from 63.5 to 155.9 GPa, which has the trend of: Al3Fe2Si > Al3Fe > Al7Cu2Fe > Al6Mn ≈ Al3Zr ≈ Al20Cu2Mn3 > Al2Cu > Al2CuMg > Al5Cu2Mg8Si6. The results of B/G imply that Al2Cu and Al20Cu2Mn3 are ductile precipitates. The hardness of Al3Zr_ D022 and D023 phases is very high (~18 GPa); whereas Al5Cu2Mg8Si6 shows low hardness value. The common precipitates of Al2Cu and Al2CuMg show a moderate hardness of 4.3 GPa and 6.8 GPa.
- The thermal expansion characters are also calculated based on QHA; Al2CuMg shows the highest LTEC, followed by Al3Fe, Al2Cu, Al3Zr_L12 and others, while Al3Zr_D022 is the lowest one; the discrepancy between a-Al and Al2CuMg is the smallest.
- The results of compressibility indicate Al3Fe, Al3Fe2Si and Al7Cu2Fe are hard and anti-compressive, while Al2CuMg is the softest one.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Phase | C11 | C12 | C13 | C22 | C23 | C33 | C44 | C66 |
---|---|---|---|---|---|---|---|---|
Al2Cu | 150.2 (150.3 a, 179.7 b, 163.8 c) | 97.4 (86.1 a, 72.7 b, 78.2 c) | 59.1 (62.6 a, 75.7 b, 14.7 c) | - | - | 211.3 (171.7 a, 170.2 b, 246.7 c) | 34.5 (29.4 a, 28.0 b, 33.8 c) | 41.3 (45.5 a, 44.7 b, 37.3 c) |
Al2CuMg | 124.7 (156.4 c, 115.9 d, 133.6 e) | 22.5 (33.4 c, 35.3 d, 42.1 e) | 66.5 (62.6 c, 46.8 d, 49.9 e) | 150.5 (175.9 c, 174.1 d, 138.8 e) | 40.4 (17.7 c, 38.7 d, 58.0 e) | 126.6 (168.8 c, 153.1 d, 145.2 e) | 41.2 (43.7 c, 50.9 d, 39.0 e) | 32.6 (50.7 c, 26.6 d, 37.7 e) |
Al3Fe | 213.2 (211 f) | 100.0 (93 f) | 76.7 (73 f) | - | - | 228.8 (228 f) | 41.3 (39 f) | 57.4 (59 f) |
Al3Fe2Si | 288.2 | 89.8 | - | - | - | 93.2 | - | |
Al5Cu2Mg8Si6 | 126.8 (146.3 g) | 39.7 (42.8 g) | 30.8 (33.3 g) | - | - | 126.3 (123.3 g) | <0 | <0 |
Al7Cu2Fe | 225.0 (206 h) | 50.7 (50.6 h) | 52.6 (65.7 h) | - | - | 217.8 (194 h) | 99.5 (80.9 h) | 86.5 (71.1 h) |
Al6Mn | 200.3 | 36.0 | 71.3 | 229.7 | 51.6 | 171.4 | 48.1 | 67.4 |
Al3Zr_D023 | 203.4 (284.3 i, 206.7 j, 201.3 k) | 65.6 (67.8 i, 52.3 j, 70.5 k) | 43.1 (58.8 i, 50.7 j, 49.1 k) | - | - | 204.0 (175.9 i, 182.6 j, 196.7 k) | 83.0 (79.2 i, 81.4 j, 80.8 k) | 101.4 (97.2 i, 75.9 j) |
Al3Zr_D022 | 183.2 (185.96 l) | 87.4 (85.34 l) | 42.0 (43.13 l) | - | - | 203.7 (202.08 l) | 89.0 (90 l) | 126.0 (125.22 l) |
Al3Zr_L12 | 173.6 (182.8 m, 179 n) | 65.4 (65.2 m, 66 n) | - | - | - | - | 69.2 (70.1 m, 69 n) | - |
Al20Cu2Mn3 | 138.0 | 69.6 | 81.0 | 177.5 | 73.0 | 150.4 | 24.6 | 46.8 |
Phase | νl | νt | νm | ΘD |
---|---|---|---|---|
Al2Cu | 5.812 | 3.114 | 3.478 | 420 |
Al2CuMg | 6.105 | 3.512 | 3.9 | 438 |
Al3Fe | 6.992 | 3.622 | 4.055 | 484 |
Al3Fe2Si | 7.7 | 4.499 | 4.989 | 622 |
Al7Cu2Fe | 6.863 | 4.02 | 4.458 | 532 |
Al6Mn | 7.637 | 4.553 | 5.041 | 557 |
Al3Zr_D023 | 7.184 | 4.484 | 4.94 | 584 |
Al3Zr_D022 | 7.017 | 4.258 | 4.705 | 554 |
Al3Zr_L12 | 6.128 | 3.105 | 3.48 | 387 |
Al20Cu2Mn3 | 6.472 | 3.303 | 3.701 | 424 |
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Fang, X.; Li, Y.; Zheng, Q.; Guo, J.; Yang, Y.; Ding, W.; Ma, C.; He, K.; Su, N.; Jiang, J.; et al. Theoretical Prediction of Structural, Mechanical, and Thermophysical Properties of the Precipitates in 2xxx Series Aluminum Alloy. Metals 2022, 12, 2178. https://doi.org/10.3390/met12122178
Fang X, Li Y, Zheng Q, Guo J, Yang Y, Ding W, Ma C, He K, Su N, Jiang J, et al. Theoretical Prediction of Structural, Mechanical, and Thermophysical Properties of the Precipitates in 2xxx Series Aluminum Alloy. Metals. 2022; 12(12):2178. https://doi.org/10.3390/met12122178
Chicago/Turabian StyleFang, Xuewei, Yefei Li, Qiaoling Zheng, Jianye Guo, Yanmei Yang, Weiyun Ding, Chunhui Ma, Ke He, Ningning Su, Jingyi Jiang, and et al. 2022. "Theoretical Prediction of Structural, Mechanical, and Thermophysical Properties of the Precipitates in 2xxx Series Aluminum Alloy" Metals 12, no. 12: 2178. https://doi.org/10.3390/met12122178