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Abstract

Due to the limitation of existing experimental techniques, it is difficult to observe the evolution of microstructure in the sintering process in real time, resulting in a lack of in-depth understanding of the sintering mechanism of two-phase composite fuels. Therefore, it is greatly important to carry out theoretical simulation studies in the sintering process of composite fuels. In this work, a phase-field model of the two-phase sintering process of ceramic composite fuel is established, and the sintering process of UN-U ₃Si ₂composite fuel is simulated by using this method. The simulation results show that during the formation of sintering neck, the surface deformation of the grains with higher surface energy is significant. The size of the final equilibrium dihedral angle formed by the two-phase double grains depends on the ratio of the grain boundary energy to the surface energy of the two phases. The phenomenon of large grains swallowing small grains does not occur between the two unequal double grains. Subsequently, the pore shrinkage and the properties of the trident grain boundary among the two-phase three grains are investigated in the sintering process. It is found that the angle of the trident grain boundary formed by the two-phase three grains deviates from 120°. The high-energy barrier at the grain boundary hinders the diffusion of the pore vacancies along the grain boundary, resulting in a slow shrinkage rate of the pore vacancies at the trident grain boundary. In addition, the simulation results of the microstructure evolution of two-phase polycrystalline sintered tissue with different volume fraction ratios show that the grain boundary diffusion plays a major role in the two-phase sintering process. The grain growth of the phase with a higher volume fraction is dominant, and there exists a hindrance to the migration of grain boundaries between two-phase grains. The phenomenon of grain migration exists between grains of the same phase.

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Authors and contacts

Corresponding author:Liu Wen-Bo,liuwenbo@xjtu.edu.cn

Funds:Project supported by the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (NSAF Joint Fund) (Grant No. U2130105) and the Innovative Scientific Program of China National Nuclear Corporation (CNNC).

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References

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Parameter	Value	Unit	Ref.
$ D_\alpha ^{\text{s}} $	7.5 × 10^–12	m²·s^–1	[27]
$ D_\alpha ^{{\text{gb}}} $	$ 0.01D_\alpha ^{\text{s}} $	m²·s^–1	[28]
$ \gamma _{\text{s}}^\alpha $	1.6	J·m^–2	[29]
$ \gamma _{{\text{gb}}}^\alpha $	0.8	J·m^–2	[29]
δ	6	nm	[29]

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Parameter	Value	Unit	Ref.
$ D_\beta ^{\text{s}} $	100$ D_\beta ^{{\text{gb}}} $	m²·s^–1
$ D_\beta ^{{\text{gb}}} $	6.5923 × 10^–10	m²·s^–1	[30]
$ \gamma _{\text{s}}^\beta $	2.0	J·m^–2	[31]
$ \gamma _{{\text{gb}}}^\beta $	1.3	J·m^–2	[32]
δ	6	nm	[32]
Note: $ D_\alpha ^{\text{s}} $, $ D_\beta ^{\text{s}} $— surface diffusivity; $ D_\alpha ^{{\text{gb}}} $, $ D_\beta ^{{\text{gb}}} $— grain-boundary diffusivity; $ \gamma _{\text{s}}^\alpha $, $ \gamma _{\text{s}}^\beta $— surface energy; $ \gamma _{{\text{gb}}}^\alpha $, $ \gamma _{{\text{gb}}}^\beta $— grain-boundary energy;δ— diffuse interface width.

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Parameter	Value	Parameter	Value
$ \tilde A({\varphi _\alpha } = 1, {\text{ }}{\varphi _\beta } = 0) $	17	$ {\tilde \kappa _\eta } $	6.75
$ \tilde A({\varphi _\alpha } = 0, {\text{ }}{\varphi _\beta } = 1) $	11.5	$\tilde {\boldsymbol{M}}({\varphi _\alpha } = 1, {\text{ }}{\varphi _\beta } = 0)$	6817.5
$ \tilde B $	1	$\tilde {\boldsymbol{M}}({\varphi _\alpha } = 0, {\varphi _\beta } = 1)$	6817.5
$ {\tilde \kappa _\rho }({\varphi _\alpha } = 1, {\varphi _\beta } = 0) $	20.25	$ \tilde L $	1
$ {\tilde \kappa _\rho }({\varphi _\alpha } = 0, {\text{ }}{\varphi _\beta } = 1) $	14	$ \Delta x = \Delta y $	1
$ {\tilde \kappa _\phi }({\varphi _\alpha } = 1, {\text{ }}{\varphi _\beta } = 0) $	20.25	$ \Delta t $	2 × 10^–5
$ {\tilde \kappa _\phi }({\varphi _\alpha } = 0, {\text{ }}{\varphi _\beta } = 1) $	14
Note: $\tilde A$, $\tilde B$, $ {\tilde \kappa _\rho } $, $ {\tilde \kappa _\phi } $, $ {\tilde \kappa _\eta } $— non-dimensional parameters of free energy function; $ \tilde {\boldsymbol{M}} $— non-dimensional mobility; $\tilde L$—non-dimensional Allen-Cahn mobility; ∆x, ∆y— space scale; ∆t— time scale.

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Vol. 73, Issue 21 - 2024-11-05

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