Mechanical and Thermal Properties of the Hf–Si System: First-Principles Calculations
Abstract
:1. Introduction
2. Computation Methods
3. Results and Discussion
3.1. Structural Properties
3.2. Elastic and Mechanical Properties
3.3. Thermal Conductivity
4. Conclusions
- (1)
- The Hf-Si system has improved plasticity and hardness as compared to Si, and reduced G/B value, which benefits in minimizing the thermal stress on the substrate, and increases their thermal shock resistance. In addition, the Young’s modulus of Hf-Si system is higher than that of Si.
- (2)
- The addition of the Hf element to Si forming silicide can increase the sound velocities and reduce the Debye temperature, and thus reduce the thermal conductivity. Compared with Si, the theoretical minimum thermal conductivity of the Hf-Si system was substantially small, which was only 0.63 W m−1 K−1 for Hf2Si with improved heat insulation ability than that of Si.
- (3)
- The calculation results show that HfSi2 in the Hf-Si system has the lowest Young’s modulus and good plasticity, making it a good candidate as a bond layer for EBCs used at a high temperature.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Materials | a () | b () | c () |
---|---|---|---|
Si | 5.450 | 5.450 | 5.450 |
Si (27-1402) | 5.431 | 5.431 | 5.431 |
HfSi2 | 3.656 | 14.640 | 3.670 |
HfSi2 (38-1373) | 3.680 | 14.556 | 3.649 |
HfSi | 6.896 | 3.788 | 5.249 |
HfSi (13-0369) | 6.885 | 3.753 | 5.191 |
Hf5Si4 | 7.067 | 7.067 | 12.877 |
Hf5Si4 (42-1166) | 7.039 | 7.039 | 12.869 |
Hf3Si2 | 7.014 | 7.014 | 3.681 |
Hf3Si2 (14-0427) | 7.000 | 7.000 | 3.671 |
Hf2Si | 6.579 | 6.579 | 5.180 |
Hf2Si (12-0467) | 6.480 | 6.480 | 5.210 |
Materials | C11 | C12 | C13 | C22 | C23 | C33 | C44 | C66 | |
---|---|---|---|---|---|---|---|---|---|
Si | 138 | 52 | 69 | ||||||
HfSi2 | 237 | 57 | 113 | 156 | 97 | 258 | 111 | 92 | 104 |
HfSi | 238 | 109 | 83 | 250 | 86 | 316 | 139 | 81 | 92 |
Hf5Si4 | 272 | 91 | 88 | 255 | 99 | 81 | |||
Hf3Si2 | 294 | 62 | 100 | 185 | 84 | 117 | |||
Hf2Si | 250 | 86 | 80 | 272 | 83 | 114 |
Materials | B (GPa) | G (GPa) | E (GPa) | μ | H (HV) | G/B |
---|---|---|---|---|---|---|
Si | 80 | 57 | 139 | 0.213 | 11 | 0.722 |
HfSi2 | 125 | 83 | 204 | 0.229 | 13 | 0.664 |
HfSi | 150 | 94 | 234 | 0.241 | 13 | 0.627 |
Hf5Si4 | 148 | 88 | 219 | 0.253 | 12 | 0.595 |
Hf3Si2 | 142 | 93 | 229 | 0.231 | 14 | 0.655 |
Hf2Si | 140 | 96 | 235 | 0.221 | 15 | 0.686 |
Materials | vL (m/s) | vT (m/s) | vm (m/s) | ΘD (K) | kmin (w/(m·k)) |
---|---|---|---|---|---|
Si | 4.42 | 2.67 | 2.94 | 488 | 1.26 |
HfSi2 | 5.42 | 3.21 | 3.56 | 418 | 0.77 |
HfSi | 5.21 | 3.05 | 3.38 | 391 | 0.71 |
Hf5Si4 | 5.02 | 2.88 | 3.20 | 366 | 0.65 |
Hf3Si2 | 4.93 | 2.91 | 3.23 | 361 | 0.65 |
Hf2Si | 4.83 | 2.89 | 3.20 | 359 | 0.63 |
Materials | Si | HfSi2 | HfSi | Hf5Si4 | Hf3Si2 | Hf2Si |
---|---|---|---|---|---|---|
kp | 1025.82 | 811.96 | 996.11 | 771.05 | 878.01 | 792.10 |
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Huang, P.; Han, G.; Liu, H.; Zhang, W.; Peng, K.; Li, J.; Wang, W.; Zhang, J. Mechanical and Thermal Properties of the Hf–Si System: First-Principles Calculations. J. Compos. Sci. 2024, 8, 129. https://doi.org/10.3390/jcs8040129
Huang P, Han G, Liu H, Zhang W, Peng K, Li J, Wang W, Zhang J. Mechanical and Thermal Properties of the Hf–Si System: First-Principles Calculations. Journal of Composites Science. 2024; 8(4):129. https://doi.org/10.3390/jcs8040129
Chicago/Turabian StyleHuang, Panxin, Guifang Han, Huan Liu, Weibin Zhang, Kexue Peng, Jianzhang Li, Weili Wang, and Jingde Zhang. 2024. "Mechanical and Thermal Properties of the Hf–Si System: First-Principles Calculations" Journal of Composites Science 8, no. 4: 129. https://doi.org/10.3390/jcs8040129