Corresponding authors:LIU Wenbo, professor, Tel:(029)82668648, E-mail:liuwenbo@xjtu.edu.cn
Received:2024-05-07Revised:2024-06-26
Fund supported:
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
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.
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)
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)
The grain boundary (GB) and average grain size considerably affect the properties of materials, such as the fracture strength, dielectric constant, and thermal conductivity. For instance, when subjected to irradiation at 1750 ℃, the swelling of the UO2 pellets and the release of fission gas from them decrease significantly with the increasing average grain size. However, several second-phase particles, such as pores, are inevitably introduced into a material during the solid-phase sintering or neutron radiation processes. Therefore, studying the interaction between the pores and GBs is considerably important. In this study, a phase-field model of the interaction between the pores and GBs is developed. Subsequently, the free-energy density function was modified, where the diffusion coefficient was incorporated in the tensor form. In addition, the selection of the phenomenological parameters, such as the coefficient in the free-energy density function of the phase-field model, was analyzed, and the influencing factors of interface energy and interface width were discussed. The phase-field model simulation results of the interaction between the pores and GBs show that the curvature of GB was the major driving force associated with the movement of GB and that pores resisted the movement of GB. Accordingly, the pores moved together with the GBs when the maximum pinning force exerted by the pores was larger than the driving force produced by the curvature of GB; however, the pores and GBs separated in the opposite case, during which the GB moved much faster than pores. The results of the phase-field simulation of the grain growth of the pore-containing UO2 show that the grain growth speed decreases with the increasing porosity. The average grain size of UO2 is a power function of time, the exponent of which increases with the increasing porosity.
A theory is presented which describes the development of surface grooves at the grain boundaries of a heated polycrystal. The mechanisms of evaporation-condensation and surface diffusion are discussed with the use of the Gibbs-Thompson formula and the assumption that the properties of an interface do not depend on its orientation. For the idealized case in which only one of the mechanisms is operative, the groove profile is shown to have a time-independent shape whose linear dimensions are proportional to t½ for evaporation-condensation, and to t½ for surface diffusion. The proportionality constants are evaluated, and criteria are developed which permit one to estimate which process predominates in practice. Order of magnitude agreement is obtained with estimates of actual grooving speeds and profiles.
MullinsW W.
The effect of thermal grooving on grain boundary motion
The nonlinear fourth-order differential equation which determines the shape of a grain-boundary groove forming by surface diffusion is solved numerically for groove root slopes ranging from 0 to 4. The groove width is within five percent of the small-slope groove width for all groove root slopes calculated. The groove depth departs by more than ten percent from the small-slope depth for groove root slopes greater than about 0.7.
CahnJ W, HilliardJ E.
Free energy of a nonuniform system. I. Interfacial free energy
Effect of concurrent thermal grooving and grain growth on morphological and topological evolution of a polycrystalline thin film: Insights from a 3D phase-field study
Phase-field method (PFM) has become a mainstream computational method for predicting the evolution of nano and mesoscopic microstructures and properties during materials processes. The paper briefly reviews latest progresses in applying PFM to understanding the thermodynamic driving forces and mechanisms underlying microstructure evolution in metallic materials and related processes, including casting, aging, deformation, additive manufacturing, and defects, etc. Focus on designing alloys by integrating PFM with constitutive relations and machine learning. Several examples are presented to demonstrate the potential of integrated PFM in discovering new multi-scale phenomena and high-performance alloys. The article ends with prospects for promising research directions.
MukherjeeR, ChakrabartiT, AnumolE A, et al.
Thermal stability of spherical nanoporous aggregates and formation of hollow structures by sintering—A phase-field study
Nanoporous structures are widely used for many applications and hence it is important to investigate their thermal stability. We study the stability of spherical nanoporous aggregates using phase-field simulations that explore systematically the effect of grain boundary diffusion, surface diffusion, and grain boundary mobility on the pathways for microstructural evolution. Our simulations for different combinations of surface and GB diffusivity and GB mobility show four distinct microstructural pathways en route to 100% density: multiple closed pores, hollow shells, hollow shells with a core, and multiple interconnected pores. The microstructures from our simulations are consistent with experimental observations in several different systems. Our results have important implications for rational synthesis of hollow nanostructures or aggregates with open pores, and for controlling the stability of nanoporous aggregates that are widely used for many applications.
AhmedK, YablinskyC A, SchulteA, et al.
Phase field modeling of the effect of porosity on grain growth kinetics in polycrystalline ceramics
It is shown that when certain plausible assumptions are fulfilled simple scaling laws govern the times required to produce, by sintering at a given temperature, geometrically similar changes in two or more systems of solid particles which are identical geometrically except for a difference of scale. It is suggested that experimental studies of the effect of such a change of scale may prove valuable in identifying the predominant mechanism responsible for sintering under any particular set of conditions, and may also help to decide certain fundamental questions in fields such as creep and crystal growth.
WangN, WenY H, ChenL Q.
Pinning force from multiple second-phase particles in grain growth
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.
Existing hot sintering models based on molecular dynamics focus on single-crystal alloys. This work proposes a new multiparticle model based on molecular dynamics to investigate coalescence kinetics during the hot-pressed sintering of a polycrystalline Al0.3CoCrFeNi high-entropy alloy. The accuracy and effectiveness of the multiparticle model are verified by a phase-field model. Using this model, it is found that when the particle contact zones undergo pressure-induced evolution into exponential power creep zones, the occurrences of phenomena, such as necking, pore formation/filling, dislocation accumulation/decomposition, and particle rotation/rearrangement are accelerated. Based on tensile test results, Young’s modulus of the as-sintered Al0.3CoCrFeNi high-entropy alloy is calculated to be 214.11 ± 1.03 GPa, which deviates only 0.82% from the experimental value, thus further validating the feasibility and accuracy of the multiparticle model.
... [7]的对比Comparison of the normalized groove profile and Mullins' theory<sup>[<xref ref-type="bibr" rid="R7">7</xref>]</sup>Fig.4<strong>3.2</strong> 移动晶界处的沟槽
Comparison of the groove profile of a migrating grain boundary and Mullins' theory<sup>[<xref ref-type="bibr" rid="R8">8</xref>]</sup>Fig.5<strong>3.3</strong> 多晶薄膜的形貌演化
Effect of concurrent thermal grooving and grain growth on morphological and topological evolution of a polycrystalline thin film: Insights from a 3D phase-field study
