Phase Field Study on the Spinodal Decomposition of β Phase in Zr–Nb-Ti Alloys
Abstract
1. Introduction
2. Phase Field Model
2.1. Cahn–Hilliard Equation
2.2. Simulation Conditions
3. Results and Discussion
3.1. Effects of the Concentration of Ti on the Spinodal Decomposition of Zr-Nb-Ti Alloys
3.2. Effects of Aging Temperature and Time on the Spinodal Decomposition of Zr-Nb-Ti Alloys
4. Conclusions
- (1)
- The spinodal decomposition occurred in the Zr-40Nb-20Ti, Zr-40Nb-25Ti and Zr-33Nb-29Ti alloys aged at 900 K with the formation of the Ti-rich phases and Ti-poor phases.
- (2)
- The Ti concentration has important effects on the morphology of the spinodal phases and the wavelength and the amplitude of the concentration modulation. The spinodal phases in the Zr-40Nb-20Ti, Zr-40Nb-25Ti and Zr-33Nb-29Ti alloys aged at 900 K were an interconnected non-oriented maze-like shape, a discrete droplet-like shape and a clustering sheet-like shape in the early aging period, respectively. Increasing the Ti concentration of the alloy increased the wavelength of the concentration modulation; decreasing the Ti concentration decreased the amplitude.
- (3)
- The aging temperature also has important effects on the morphology of the spinodal phases and on the wavelength and amplitude of the concentration modulation. For the Zr-40Nb-25Ti alloy, with the increase in the aging temperature, the shape of the Zr-rich phase changed from an interconnected non-oriented maze-like shape to a discrete droplet-like shape, and the wavelength of the concentration modulate increased quickly to a stable value, but the amplitude decreased in the alloy.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Values |
---|---|
(K) | 850 875 900 |
(J/mol) | −1272.064 + 134.71418 − 25.5768 ln − 0.663845 − 0.27880 + 7208 |
(J/mol) | −8519.353 + 142.045475 − 26.4711 ln + 2.03475 − 3.5012 − 93,399 |
(J/mol) | −525.539 + 124.9457 − 25.607406 ln − 3.40084 − 9.729 + 25,233 − 7.6143 |
(J/mol) | 13,045.3 |
(J/mol) | −9321 + 11.9 |
(J/mol) | 15,911 + 3.35 |
(J/mol) | −1000 |
(J/mol) | −13,000 |
(J/mol) | 16,800 |
(m3/mol) | 1.2496 |
(J/mol) | −171,237.75–115.83 |
(J/mol) | −131,670.56–133.36 |
(J/mol) | −135,119.44–148.59 |
(J/mol) | −358,612.72–84.43 |
(J/mol) | −104,624.81–163.15 |
(J/mol) | −395,598.95–82.03 |
(J/mol) | 14,510.81 |
(J/mol) | 113,467.29–32.01 T |
(J/mol) | 43,010.37 + 74.52 T |
(J/mol) | 41,384.1106–12.57 T |
(J/mol) | 12,851.76 |
(J/mol) | 83,103.91 + 50.78 T |
(nm) | 0.3315 0.357 0.331 |
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Yang, K.; Wang, Y.; Tang, J.; Wang, Z.; Zhang, D.; Dai, Y.; Lin, J. Phase Field Study on the Spinodal Decomposition of β Phase in Zr–Nb-Ti Alloys. Materials 2023, 16, 2969. https://doi.org/10.3390/ma16082969
Yang K, Wang Y, Tang J, Wang Z, Zhang D, Dai Y, Lin J. Phase Field Study on the Spinodal Decomposition of β Phase in Zr–Nb-Ti Alloys. Materials. 2023; 16(8):2969. https://doi.org/10.3390/ma16082969
Chicago/Turabian StyleYang, Kun, Yanghe Wang, Jingjing Tang, Zixuan Wang, Dechuang Zhang, Yilong Dai, and Jianguo Lin. 2023. "Phase Field Study on the Spinodal Decomposition of β Phase in Zr–Nb-Ti Alloys" Materials 16, no. 8: 2969. https://doi.org/10.3390/ma16082969
APA StyleYang, K., Wang, Y., Tang, J., Wang, Z., Zhang, D., Dai, Y., & Lin, J. (2023). Phase Field Study on the Spinodal Decomposition of β Phase in Zr–Nb-Ti Alloys. Materials, 16(8), 2969. https://doi.org/10.3390/ma16082969