Phase-Field Simulation of the Densification Process During Sintering of UN Nuclear Fuel
QI Xiaoyong1,2, LIU Wenbo1,2(), HE Zongbei3, WANG Yifan3, YUN Di1,2
1.School of Nuclear Science and Technology, Xi'an Jiaotong University, Xi'an 710049, China 2.Shaanxi Key Laboratory of Advanced Nuclear Energy and Technology, Xi'an Jiaotong University, Xi'an 710049, China 3.State Key Laboratory for Nuclear Fuel and Materials, Nuclear Power Institute of China, Chengdu 610213, China
Cite this article:
QI Xiaoyong, LIU Wenbo, HE Zongbei, WANG Yifan, YUN Di. Phase-Field Simulation of the Densification Process During Sintering of UN Nuclear Fuel. Acta Metall Sin, 2023, 59(11): 1513-1522.
UN is a candidate fuel for light water reactors and fast reactors due to its high density, high thermal conductivity, and high melting point. The highly densified UN particles are desirable to strengthen the fuel structure and delay the release of fission gas. However, the mechanism of densification during sintering is still unclear from the view point of existing experimental results. Therefore, it is essential to simulate the densification process during sintering using the phase-field (PF) method. In the present work, the rigid body action of translation and rotation was introduced in the PF model. This work analyzed the effects of the advection flux of rigid body motion on the formation of the sintered neck, the equilibrium dihedral angle, and the densification during sintering. The simulation results showed that the introduction of advection flux of rigid body motion accelerated the formation of the sintering neck in the early stage of sintering, while such an effect was not obvious in the later stage. The equilibrium dihedral angle of the model with advection flux was consistent with that of the model, which only contained surface diffusion. The densification stomatal shrinkage was divided into three stages: surface diffusion dominated stage, advection flux dominated stage, and final densification progress. The increase in translational mobility accelerated the densification speed and increased the final density after densification, although this effect reached saturation after a certain threshold. Stable trigeminal grain boundaries (GBs) with 120° were formed when densification was completed. The characteristics of the sintered morphology of polycrystalline UN, such as trigeminal GBs, pore shrinkage, and densification, were consistent with the experimental results.
Fund: Joint Fund of National Natural Science Foundation of China and China Academy of Engineering Phy-sics (NSAF Joint Fund)(U2130105);China Postdoctoral Science Foundation(2019M663738);State Key Laboratory of New Ceramic and Fine Processing Tsinghua University(KF201713);Innovative Scientific Program of China National Nuclear Corporation
Corresponding Authors:
LIU Wenbo, associate professor, Tel: (029)82668948, E-mail: liuwenbo@xjtu.edu.cn
Fig.1 Schematic of vacancy diffusion simulated in sintering simulation (Arrows show the paths of vacancy diffusion along free surfaces and grain boundaries)
Parameter
Value
Unit
Ref.
Ds
7.5 × 10-12
m2·s-1
[26]
Dgb
0.01Ds
m2·s-1
γs
1.6
J·m-2
[27]
γgb
0.8
J·m-2
[27]
δ
6
nm
[27]
Table 1 Physical parameters of UN at 1823 K[26,27]
Parameter
Value
Parameter
Value
17
30-100
1
1
6.75
1
20.25
Δx = Δy
1
6750
Δt
2 × 10-5
Table 2 Non-dimensional parameters used in simulation
Fig.2 Simulated effects of advection flux on morphologies of two grains with the boundary between them by the phase-field methods of without (a-c) and with (d-f) advection flux (a, d) 2 × 104 step (b, e) 50 × 104 step (c, f) 100 × 104 step
Fig.3 Logarithmic growth curves of particle sintered neck methods for without and with advection flux (l—neck length, t'—time step)
Fig.4 Simulated equilibrium dihedral angles by two sintering models (a) without advection flux (b) with advection flux
Fig.5 Simulated evolutions of a pore in the grain boundary between two particles by the phase-field methods of without (a-c) and with (d-f) advection flux (a, d) 10 × 104 step (b, e) 20 × 104 step (c, f) 30 × 104 step
Fig.6 Simulated pore shrinkage curve of grain boundary between two particles by the advection flux model
Fig.7 Simulated evolutions of three particles by the phase-field methods of advection flux (a) 0 step (b) 2 × 104 step (c) 4 × 104 step (d) 6 × 104 step
Fig.8 Simulated evolutions of advection flux on morphologies of three particles (The blue-green part shows the effect of the advective flux, and the closer to the blue, the stronger the effect of the advective flux) (a) 0 step (b) 2 × 104 step (c) 4 × 104 step (d) 6 × 104 step
Fig.9 Simulated pore shrinkage curve of grain boundary among three particles by the advection flux model
Fig.10 Pore shrinkage curves for different translation mobilities (mt)
Fig.11 Simulated evolutions of four particles by the phase-field methods of advection flux (a) 1 × 104 step (b) 25 × 104 step (c) 50 × 104 step (d) 100 × 104 step
Fig.12 Simulated evolutions of multi-grain by the phase-field methods with unimodal particle size distribution (a) 1 × 104 step (b) 40 × 104 step (c) 80 × 104 step (d) 120 × 104 step (e) 160 × 104 step (f) 200 × 104 step
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