Formation of Cu2O Solid Solution via High-Frequency Electromagnetic Field-Assisted Ball Milling: The Reaction Mechanism
Abstract
1. Introduction
2. Experimental
3. Results and Discussion
3.1. Phase Transformation
3.2. Product Microstructures and Morphologies
3.3. Catalytic Performance
3.4. Formation Mechanism and Reaction Kinetics
3.4.1. Solid-State Formation of Cuprous Oxide
3.4.2. Reaction Kinetics
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Model | F(a) = kt | K | R2 | Reaction Time |
---|---|---|---|---|
One-dimensional diffusion | a2 = kt | 0.04336 | 0.94 | 23.06 h |
Two-dimensional diffusion | (1 − a) × ln(1 − a) + a = kt | 0.03329 | 0.91 | 30.04 h |
Three-dimensional diffusion (Jander) | (1 − (1 − a)1/3))2 = kt | 0.01217 | 0.85 | 80.53 h |
Three-dimensional diffusion (Ginstling–Brounshtein) | 1 − 2/3 × a − (1 − a)2/3 = kt | 0.00874 | 0.89 | 38.13 h |
Phase boundary (planar) | a = kt | 0.03928 | 0.95 | 25.46 h |
Phase boundary (cylindrical) | 1 − (1 − a)1/2 = kt | 0.03037 | 0.94 | 32.89 h |
Phase boundary (spherical) | 1 − (1 − a)1/3 = kt | 0.02355 | 0.93 | 42.04 h |
Nucleation and growth (Avrami) | ((−ln(1 − a))1/2 = kt | 0.05202 | 0.94 | 71.45 h |
Nucleation and growth (Erofeev) | ((−ln(1 − a))1/3 = kt | 0.03588 | 0.94 | 66.88 h |
Nucleation and growth (Avrami–Erofeev) | [−ln(1 − a)]1/m = kt, 0.5 ≤ m ≤ 4 | 0.02842 | 0.93 | 67.84 h |
1-D nucleation and constant growth rate | ln a = kt | 0.07575 | 0.88 | −1.32 × 10−5 h |
Random nucleation and rapid growth | −ln(1 − a) = kt | 0.10478 | 0.89 | 131.85 h |
Chemical reaction (C1.5) | (1 − a)−1/2 − 1 = kt | 0.08924 | 0.81 | −11.21 h |
Chemical reaction (C2) | 1/(1 − a) − 1 = kt | 0.316 | 0.71 | 3,164,553.80 h |
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Zhang, Y.; Chen, Y.; Li, J.; Li, W.; Chen, D.; Qin, Q. Formation of Cu2O Solid Solution via High-Frequency Electromagnetic Field-Assisted Ball Milling: The Reaction Mechanism. Materials 2020, 13, 618. https://doi.org/10.3390/ma13030618
Zhang Y, Chen Y, Li J, Li W, Chen D, Qin Q. Formation of Cu2O Solid Solution via High-Frequency Electromagnetic Field-Assisted Ball Milling: The Reaction Mechanism. Materials. 2020; 13(3):618. https://doi.org/10.3390/ma13030618
Chicago/Turabian StyleZhang, Yingzhe, Yudao Chen, Juan Li, Wei Li, Ding Chen, and Qingdong Qin. 2020. "Formation of Cu2O Solid Solution via High-Frequency Electromagnetic Field-Assisted Ball Milling: The Reaction Mechanism" Materials 13, no. 3: 618. https://doi.org/10.3390/ma13030618
APA StyleZhang, Y., Chen, Y., Li, J., Li, W., Chen, D., & Qin, Q. (2020). Formation of Cu2O Solid Solution via High-Frequency Electromagnetic Field-Assisted Ball Milling: The Reaction Mechanism. Materials, 13(3), 618. https://doi.org/10.3390/ma13030618