Publishing type：Research paper (scientific journal)  

Sintering is a fundamental technology for powder metallurgy, the ceramics industry, and additive manufacturing processes such as three-dimensional printing. Improvement of the properties of sintered materials requires prediction of their microstructure using numerical simulations. However, the physical values and material parameters used for such predictions are generally unknown. Data assimilation (DA) enables the estimation of unobserved states and unknown material parameters by integrating simulation results and observational data. In this paper, we develop a new model that couples an ensemble-based four-dimensional variational (En4DVar) DA with a phase-field model of solid-state sintering (En4DVar-PF model) to estimate the state of the sintered material and multiple unknown material parameters. The developed En4DVar-PF model is validated by numerical experiments called twin experiments, in which a priori assumed-true initial state and multiple material parameters are estimated. The results of the twin experiments demonstrate that, using only three-dimensional morphological data of the sintered microstructure, our developed En4DVar-PF model can simultaneously and accurately estimate the particle shape, distribution of grain boundaries, and material parameters, including diffusion coefficients and mobilities related to grain boundary migration. Furthermore, our work identifies criteria for determining appropriate DA conditions such as the observational time interval required to accurately estimate the material parameters using our developed model. The developed En4DVar-PF model provides a promising framework to obtain unobservable states and difficult-to-measure material parameters in sintering, which is crucial for the accurate prediction of sintering processes and for the development of superior materials.

DOI： 10.1088/1361-651X/ac13cd

Publishing type：Research paper (scientific journal)  

Three-dimensional grain growth behaviors under anisotropic (misorientation-dependent) grain boundary energy and mobility are investigated via phase-field simulations. Based on a multi-phase-field model and parallel graphics-processing unit computing on a supercomputer, very large-scale simulations with more than three million grains are achieved, enabling reliable statistical evaluation of anisotropic grain growth. The anisotropic boundary properties are introduced by the classical Read-Shockley and sigmoidal models; the threshold misorientation angle, Delta theta(h), included in these models is used as a quantity to determine the anisotropy strength of the system. Systematic simulations are performed for different Delta theta(h) values, through which the correlations between the anisotropy strength and grain growth characteristics such as grain size and misorientation distributions are examined. The obtained results show that anisotropic grain growth reaches the steady-state regime irrespective of the Delta theta(h) value. However, the kinetics and microstructural morphology during the steady-state growth are largely dependent on Delta theta(h). Furthermore, by comparison with the simulated results, the applicability of analytical grain growth theories to anisotropic systems are tested. The tests reveal that the steady-state microstructure in anisotropic growth cannot be well captured by the existing theories, which is likely because the basic assumptions of the theories do not hold for anisotropic systems.

DOI： 10.1016/j.commatsci.2020.109992

Publishing type：Research paper (scientific journal)  

<p>The phase-field method has been widely employed recently for simulating grain growth. Phase-field grain growth models are classified into two types according to their conservation constraints for phase-field variables: the multi-phase-field model and the continuum-field model. In addition, within the multi-phase-field model framework, three models with different formulations exist. These models are reported to accurately simulate grain growth under conditions of isotropic or weakly anisotropic grain boundary energy and mobility. However, for cases of strongly anisotropic grain boundary properties, the accuracy of these models has not yet been examined in detail. In this study, using the continuum-field model and three different multi-phase-field models, systematic grain growth simulations with anisotropic grain boundary energies and mobilities are performed. Through the detailed investigation of the accuracy of the simulated results, the suitability of each model for anisotropic grain growth simulations is revealed. Furthermore, based on the higher-order terms, accuracy improvement of the phase-field models is attempted.</p>

DOI： 10.2355/isijinternational.isijint-2019-305

CiNii Article

Publishing type：Research paper (scientific journal)  

The micrometer-scale polycrystalline microstructure is directly obtained from a 10 billion atom molecular dynamics (MD) simulation of the nucleation and growth of crystals from an undercooled melt, which is performed on a graphics processing unit-rich supercomputer. The grain size distribution in the as-grown microstructure obtained from the MD simulation largely deviates from that resulting from steady-state growth in ideal grain growth, whereas the distribution of the disorientation angle between grains in contact with each other basically agrees with a random distribution. The atomistic configuration of the polycrystalline microstructure is then converted into a phase-field profile (diffuse interface description) of a phase-field model (PFM) and the subsequent grain growth is examined by multi-phase-field (MPF) simulation. A significant achievement in this study is direct mapping of the atomistic configuration into the phase-field profile used in the MPF simulation since only representative parameters for larger-scale model (e.g. interatomic potentials for MD and interfacial parameters for PFM) are extracted from a smaller-scale simulation in conventional multi-scale modeling. Our new achievement supported by high-performance supercomputing can be regarded as an evolution of multi-scale modeling, which we call inter-scale modeling to differentiate it from conventional multi-scale modeling.

DOI： 10.1088/1361-651X/ab1d28

Publishing type：Research paper (scientific journal)  

In this study, assuming an ideal system free from thermal grooving and anisotropy in grain boundary properties, we analyze thin-film grain growth via three-dimensional (3D) phase-field simulations with approximately one million initial grains. The large-scale simulations accelerated by multiple graphics processing units allow for the reliable statistical investigation of grain growth behaviors in films with various thickness. Over the transition from 3D to two-dimensional (2D) growth modes, variations in the averages and distributions of grain sizes are quantified and compared for different regions of the films. Furthermore, we propose a comprehensive scaling law of thin-film grain growth, by which the 3D-2D transition behaviors and grain growth kinetics can be described in a unified manner independent of film thickness.

DOI： 10.1088/1361-651X/ab1e8b

Publishing type：Research paper (scientific journal)  

Grain growth is one of the most fundamental phenomena affecting the microstructure of polycrystalline materials. In experimental studies, three-dimensional (3D) grain growth is usually investigated by examining two-dimensional (2D) cross sections. However, the extent to which the 3D microstructural characteristics can be obtained from cross-sectional observations remains unclear. Additionally, there is some disagreement as to whether a cross-sectional view of 3D grain growth can be fully approximated by 2D growth. In this study, by employing the multi-phase-field method and parallel graphics processing unit computing on a supercomputer, we perform large-scale simulations of 3D and 2D ideal grain growth with approximately three million initial grains. This computational scale supports the detailed comparison of 3D, cross-sectional, and 2D grain structures with good statistical reliability. Our simulations reveal that grain growth behavior in a cross section is very different from those in 3D and fully 2D spaces, in terms of the average and distribution of the grain sizes, as well as the growth kinetics of individual grains. On the other hand, we find that the average grain size in 3D can be estimated as being around 1.2 times that observed in a cross section, which is in good agreement with classical theory in the stereology. Furthermore, based on the Saltykov-Schwartz method, we propose a predictive model that can estimate the 3D grain size distribution from the cross-sectional size distribution.

DOI： 10.1007/s10853-018-2680-y

Publishing type：Research paper (scientific journal)  

To achieve a highly accurate and efficient prediction of polycrystalline grain growth, we propose a method to bridge atomistic and continuum-based simulations by converting molecular dynamics-generated atomic configurations into interfacial profiles of the phase-field model. This method enables us to perform phase-field grain growth simulations in succession to molecular dynamics nucleation simulation. Using the present method, molecular dynamics and phase-field grain growth simulations from the same initial structure are carried out and directly compared. The results of each simulation exhibit a similar tendency in terms of grain morphology and grain growth kinetics, but only after an initial short duration.

DOI： 10.1016/j.commatsci.2018.05.046

Publishing type：Research paper (scientific journal)  

Grain growth kinetics under the anisotropic grain boundary properties is investigated by large-scale and long-time molecular dynamics (MD) simulations of contentious processes of nucleation, solidification and grain growth in a submicrometer-scale system. Microstructures obtained via homogeneous nucleation from undercooled melt iron consists of approximately 1500 grains and the number of grains decreases to one tenth of the number via the grain growth process. The grain growth exponent obtained from the MD simulation deviates from the ideal value since anisotropic effects in the grain boundary properties are inherently included in MD simulations. It is confirmed that the decrease of the reduced mobility (i.e., the product of the intrinsic grain boundary mobility and the grain boundary energy) is a dominant factor for the deviation from the ideal grain growth. The deviation from the Mackenzie function for the distribution of the disorientation angle between neighboring grains implies that the preferential selection of grain boundaries with small grain boundary energies occurs during the grain growth. This enhances the anisotropy in grain boundary properties and therefore decreases the reduced mobility of the grain boundary. Moreover, a multi-phase-field simulation starting from a MD configuration results in an ideal grain growth when a constant value of the reduced mobility is employed, which validates the discussion on the reduced mobility. The new insight in this study is achieved for the first time owing to a multi-graphics processing unit (GPU) parallel computation over 50 days for one case using 128 GPUs on the GPU-rich supercomputer. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.actamat.2018.04.060

Publishing type：Research paper (scientific journal)  

Numerical studies of the effects of anisotropic (misorientation-dependent) grain-boundary energy and mobility on polycrystalline grain growth have been carried out for decades. However, conclusive knowledge has yet to be obtained even for the simplest two-dimensional case, which is mainly due to limitations in the computational accuracy of the grain-growth models and computer resources that have been employed to date. Our study attempts to address these problems by utilizing a higher-order multi-phase-field (MPF) model, which was developed to accurately simulate grain growth with anisotropic grain-boundary properties. In addition, we also employ general-purpose computing on graphics processing units to accelerate MPF grain-growth simulations. Through a series of simulations of anisotropic grain growth, we succeeded in confirming that both the anisotropies in grain-boundary energy and mobility affect the morphology formed during grain growth. On the other hand, we found the grain growth kinetics in anisotropic systems to follow parabolic law similar to isotropic growth, but only after an initial transient period.

DOI： 10.1016/j.jcrysgro.2016.11.097

Publishing type：Research paper (scientific journal)  

Grain growth, a competitive growth of crystal grains accompanied by curvature-driven boundary migration, is one of the most fundamental phenomena in the context of metallurgy and other scientific disciplines. However, the true picture of grain growth is still controversial, even for the simplest (or 'ideal') case. This problem can be addressed only by large-scale numerical simulation. Here, we analyze ideal grain growth via ultra-large-scale phase-field simulations on a supercomputer for elucidating the corresponding authentic statistical behaviors. The performed simulations are more than ten times larger in time and space than the ones previously considered as the largest; this computational scale gives a strong indication of the achievement of true steady-state growth with statistically sufficient number of grains. Moreover, we provide a comprehensive theoretical description of ideal grain growth behaviors correctly quantified by the present simulations. Our findings provide conclusive knowledge on ideal grain growth, establishing a platform for studying more realistic growth processes.

DOI： 10.1038/s41524-017-0029-8

Publishing type：Research paper (scientific journal)  

Can completely homogeneous nucleation occur? Large scale molecular dynamics simulations performed on a graphics-processing-unit rich supercomputer can shed light on this long-standing issue. Here, a billion-atom molecular dynamics simulation of homogeneous nucleation from an undercooled iron melt reveals that some satellite-like small grains surrounding previously formed large grains exist in the middle of the nucleation process, which are not distributed uniformly. At the same time, grains with a twin boundary are formed by heterogeneous nucleation from the surface of the previously formed grains. The local heterogeneity in the distribution of grains is caused by the local accumulation of the icosahedral structure in the undercooled melt near the previously formed grains. This insight is mainly attributable to the multi-graphics processing unit parallel computation combined with the rapid progress in high-performance computational environments.

DOI： 10.1038/s41467-017-00017-5

Publishing type：Research paper (scientific journal)  

Based on the multi-phase-field (MPF) model reported by Steinbach et al., we constructed a higher-order MPF model in a previous study that contains a higher-order term and an additional kinetic parameter to represent the properties of triple junctions (TJs); this model was observed to be suitable for the simulation of 2D grain growth with anisotropic grain-boundary (GB) energy and mobility, which are strongly dependent on the misorientation angle (Delta theta). In the current study, we attempt to improve the accuracy of 3D MPF simulations of anisotropic grain growth by extending this higher-order MPF model such that it accounts for the properties of quadruple junctions as well as those of TJs. In addition, using the extended higher-order MPF model, a series of grain-growth simulations are performed for a 3D columnar structure while considering the anisotropic GB properties, through which the accuracy of the model is examined in detail. The results confirm that the extended higher-order MPF model enables the anisotropic GB properties to be handled accurately for wider-ranging Delta theta than in previous models. (C) 2016 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.commatsci.2016.04.014

Publishing type：Research paper (scientific journal)  

The multi-phase-field (MPF) model proposed by Steinbach et al. has several advantages when it comes to numerically simulating the grain growth, recrystallization, and multiple phase transitions. In this study, in order to improve the accuracy of MPF simulations using the anisotropic grain-boundary energy and mobility, which depend strongly on the misorientation angles, we account for the triple-junction properties in the MPF model. Further, two-dimensional simulations of grain-boundary migrations in three-grain systems as well as simulations of abnormal grain growth in a polycrystalline system are performed using the proposed model, in order to confirm its validity. The results show that the proposed model allows for the introduction of the anisotropic energy and mobility with high accuracy for a wider range of misorientations, in contrast to the conventional model. (C) 2015 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.commatsci.2015.10.010

Presentation type：Oral presentation (general)  

Venue：Frankfurt am Main, Germany  

Presentation type：Oral presentation (general)  

Venue：Frankfurt am Main, Germany  

Presentation type：Oral presentation (invited, special)  

Venue：Seoul, Korea  

Presentation type：Oral presentation (general)  

Presentation type：Oral presentation (general)  

Presentation type：Oral presentation (general)