Phase-Field Simulation of Grain Boundary Groove Formation

doi:10.11900/0412.1961.2024.00138

Acta Metall Sin

2026, Vol. 62

Issue (3): 523-531 DOI: 10.11900/0412.1961.2024.00138

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Phase-Field Simulation of Grain Boundary Groove Formation

SHEN Wenlong¹, LIAO Yuxuan¹, WU Xuezhi², JIANG Yanbo¹, LIU Wenbo¹^,³(

)

^1.School of Nuclear Science and Technology, Xi'an Jiaotong University, Xi'an 710049, China
^2.Institute of Reactor Engineering and Technology, China Institute of Atomic Energy, Beijing 102413, China
^3.Shaanxi Key Laboratory of Advanced Nuclear Energy and Technology, Xi'an Jiaotong University, Xi'an 710049, China

Cite this article:

SHEN Wenlong, LIAO Yuxuan, WU Xuezhi, JIANG Yanbo, LIU Wenbo. Phase-Field Simulation of Grain Boundary Groove Formation. Acta Metall Sin, 2026, 62(3): 523-531.

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Abstract

The grain boundary grooves formed on material surface significantly affect the mechanisms of mass transport, altering the driving force for grain boundary migration, and consequently influencing the kinetics of grain growth. Herein, a phase-field model is developed to simulate the coupled evolution of grain boundary grooving and grain growth in UO₂ ceramic fuels. The process of developing the model begins by constructing a free energy equation for a polycrystalline system, where the reduction in total free energy drives system evolution. The mobility coefficients are then adjusted to ensure that the formation of grain boundary grooves and grain growth follow different kinetic processes. Results show that groove evolution at individual grain boundary is controlled by surface diffusion, aligning closely with Mullins' classical theoretical solution. Moreover, with the movement of grain boundaries, the groove contours become decreasingly symmetric, with increased material accumulation occurring in the grain in front of the moving direction of the grain boundary. The evolution results of a 3D polycrystalline thin film structure show that all grains evolve toward a columnar crystal structure, with grooves gradually forming at the intersections of grain boundaries and the surface. Moreover, grooves generated by different grain boundaries within the same grain tend to overlap on the grain surface, altering the groove contours. With increasing groove depth, grain boundary movement becomes increasingly slow, ultimately reducing the rate of grain growth.

Key words: phase-field simulation grain boundary groove surface grain growth diffusion

Received: 07 May 2024

ZTFLH:

TG148

Fund: National Natural Science Foundation of China(12375258);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, professor, Tel: (029)82668648, E-mail: liuwenbo@xjtu.edu.cn

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https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00138 OR https://www.ams.org.cn/EN/Y2026/V62/I3/523

Fig.1 Schematic of phase field variables (ρ—concentration field variable, η₁—order parameter of grain 1, η₂—order parameter of grain 2)

Table 1 Non-dimensional parameters used in the present simulation

Fig.2 Microstructure evolution (a1-d1) and corresponding local magnifications (a2-d2) of a groove of a stationary grain boundary (The blue and yellow parts represent the vapour phase and the grains, respectively)
(a1, a2) initial microstructure (b1, b2) 25 × 10⁵ steps
(c1, c2) 50 × 10⁵ steps (d1, d2) 100 × 10⁵ steps

Fig.3 Temporal evolution of the groove depth and the fitting result (t—time)

Fig.4 Comparison of the normalized groove profile and Mullins' theory^[7]

Fig.5 Comparison of the groove profile of a migrating grain boundary and Mullins' theory^[8]

Fig.6 Microstructures (a1-c1) and grain size distributions (a2-c2) of three-dimensional polycrystalline structure for t = 0 (a1, a2), t = 400 (b1, b2), and t = 1000 (c1, c2) (The blue parts represent the surface and the grain boundaries, and the gray parts represent the grains, the same in Fig.7)

Fig.7 Temporal evolution of the film surface profile
(a) selected surface location (b) surface profile of the selected area

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