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Three-dimensional growth morphologies of equiaxed dendrites growing under forced convection, with their preferred growth direction inclined from the flow direction, were investigated by performing large-scale phase-field lattice Boltzmann simulations on a graphical-processing-unit supercomputer. The tip velocities of the dendrite arms with their preferred growth directions inclined toward the upstream and downstream directions increased and decreased, respectively, as a result of forced convection. In addition, the tip velocities decreased monotonically as the angle between the preferred growth direction and the upstream direction increased. Here, the degree of acceleration of the upstream tips was larger than the degree of deceleration of the downstream tips. The angles between the actual tip growth directions and the preferred growth direction of the dendrite arms exhibited a characteristic change with two local maxima and two local minima.

Continuous processes of homogeneous nucleation, solidification and grain growth are spontaneously achieved from an undercooled iron melt without any phenomenological parameter in the molecular dynamics (MD) simulation with 12 million atoms. The nucleation rate at the critical temperature is directly estimated from the atomistic configuration by cluster analysis to be of the order of 10 34 m −3 s −1 . Moreover, time evolution of grain size distribution during grain growth is obtained by the combination of Voronoi and cluster analyses. The grain growth exponent is estimated to be around 0.3 from the geometric average of the grain size distribution. Comprehensive understanding of kinetic properties during continuous processes is achieved in the large-scale MD simulation by utilizing the high parallel efficiency of a graphics processing unit (GPU), which is shedding light on the fundamental aspects of production processes of materials from the atomistic viewpoint.

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.

Melt flow drastically changes dendrite morphology during the solidification of pure metals and alloys. Numerical simulation of dendrite growth in the presence of the melt flow is crucial for the accurate prediction and control of the solidification microstructure. However, accurate simulations are difficult because of the large computational costs required. In this study, we develop a parallel computational scheme using multiple graphics processing units (GPUs) for a very large-scale three-dimensional phase-field-lattice Boltzmann simulation. In the model, a quantitative phase field model, which can accurately simulate the dendrite growth of a dilute binary alloy, and a lattice Boltzmann model to simulate the melt flow are coupled to simulate the dendrite growth in the melt flow. By performing very large-scale simulations using the developed scheme, we demonstrate the applicability of multi-GPUs parallel computation to the systematical large-scale-simulations of dendrite growth with the melt flow.

Simulating dendritic growth with natural convection is challenging because of the size of the computational domain required when compared to the dendrite scale. In this study, a phase-field-lattice Boltzmann model was used to simulate dendritic growth in the presence of natural convection due to a difference in solute concentration. To facilitate and accelerate the large-scale simulation, a parallel computing code with multiple graphics processing units was developed. The effects of the computational domain size as well as those of gravity on the dendritic morphologies were examined by performing two-dimensional free dendritic growth simulations with natural convection. The effects of the gravity direction on the dendrite spacing and morphology were also investigated by simulating unidirectional solidification from multiple seeds.

The steady-state value of primary dendrite arm spacing (PDAS) in the columnar dendrites growing between the converging and diverging grain boundaries is investigated by means of quantitative phase-field simulations. The simulations show that there is a unique value of PDAS under a given solidification condition in the system with grain boundaries. This is in contrast to existence of allowable range of PDAS under a given solidification in a system without the grain boundaries, i.e., an infinitely large columnar grain investigated in many early works. Such a unique value of PDAS depends on the pulling speed and inclination angle of the crystal, but not on the initial condition; that is, it is independent of the history of solidification condition. The dependences of the unique value on the pulling speed and inclination angle qualitatively agree with the theoretical models.

Selections of growing crystals during directional solidification of a polycrystalline binary alloy were numerically investigated using two-dimensional phase-field simulations. To accelerate the simulations, parallel graphics processing unit (GPU) simulations were performed using the GPU-rich supercomputer TSUBAME2.5 at the Tokyo Institute of Technology. Twenty simulations with a combination of five sets of different seed orientation distributions and four different temperature gradients covering dendritic and cellular growth regions were performed. The unusual grain selection phenomenon, in which the unfavorably oriented grains preferentially grow instead of the favorably oriented grains, was observed frequently. The unusual selection was more remarkable in the cellular structure than in the dendritic structure.

Dendrites are typical growth morphologies in alloy solidification. However, the ways in which dendrites grow and form solidification microstructures remain poorly understood. Here we show unexpected findings that reveal the survival of unfavorably oriented dendrites and highly complicated dendrite–dendrite interactions in three-dimensional space during the directional solidification of a binary alloy. These results are observed for the first time through very-large-scale phase-field computations performed by a graphics processing unit (GPU) supercomputer and a high-performance algorithm developed for parallel computing.

Stresses in dendrites caused by gravity that acts perpendicular to the dendrite growth direction were numerically investigated. Here, we used a phase-field method to simulate the dendritic morphology and the finite element method to evaluate the stresses in the dendrites caused by gravity. By performing two-dimensional simulations, the effects of the anisotropy strength of interface energy, the dendrite secondary arm, and the amount of undercooling on the maximum stress that occurs at the dendrite neck were investigated. Furthermore, the maximum stress calculated by the finite element method was compared with those determined using the simple cantilever model.

The phase-field simulation for dendritic solidification of a binary alloy has been accelerated by using a graphic processing unit (GPU). To perform the phase-field simulation of the alloy solidification on GPU, a program code was developed with computer unified device architecture (CUDA). In this paper, the implementation technique of the phase-field model on GPU is presented. Also, we evaluated the acceleration performance of the three-dimensional solidification simulation by using a single NVIDIA TESLA C1060 GPU and the developed program code. The results showed that the GPU calculation for 5763 computational grids achieved the performance of 170 GFLOPS by utilizing the shared memory as a software-managed cache. Furthermore, it can be demonstrated that the computation with the GPU is 100 times faster than that with a single CPU core. From the obtained results, we confirmed the feasibility of realizing a real-time full three-dimensional phase-field simulation of microstructure evolution on a personal desktop computer.

The growth kinetics and final morphology of ferrite ( α ) grains are characterized by interfacial energy and boundary mobility, which strongly correlate to constituent phase, misorientation angle and the specific orientation relationship at the α / γ interface, such as the Kurdjumov–Sachs (KS) orientation relationship. In a previous phase-field simulation of the α grain growth, interfacial energy and mobility is assumed to be constant. Therefore, the simulated morphology of α grains is equiaxed. In this study, the multi-phase-field (MPF) simulation of α grain growth during γ → α transformation is performed to study the effects of phase- and misorientation-dependent interfacial energy and boundary mobility on the growth kinetics of α grains. The phase and misorientation dependence of interfacial energy is simply described by the Read–Shockley equation. Our results indicate that the phase- and misorientation-dependent interfacial energy induces α grain growth along the γ grain boundary so as to reduce the total interfacial energy of the system. Furthermore, by considering both the phase- and misorientation-dependent interfacial energy and boundary mobility, the plausible growth kinetics of α grains can be reproduced and the morphology of α grains can be quite similar to the α grain morphology determined by the KS orientation relationship.

A multi phase-field model is developed to investigate the effect of interface energy between a film and substrate on the morphological evolution of the film during self-assembled quantum dot (QD) growth in the deposition process. The single- and multi-island growth simulations for the SiGe/Si system are carried out in two-dimensional space with various interface energies. From the numerical results, it is clarified that the island shape and the island morphological transition points dramatic change depending on the magnitude of the interface energy. Here, the transition points, such as that from a pyramid to a dome, occurred in an earlier growth stage with higher interface energy. It is also observed that high interface energy results in large island size fluctuation.

The morphological evolution of a strained heteroepitaxial thin film of Si 1− x Ge x /Si during deposition has been investigated by two-dimensional (2D) phase-field simulations. The phase-field model developed can form facet morphologies that are modeled using the generalized gradient correction coefficient for a crystal with a high anisotropy of surface energy, and can simulate the sequential shape transitions well known in the Si 1− x Ge x /Si(0 0 1) system: a 2D wetting layer, faceted three-dimensional pyramids, and multifaceted domes. The effects of Ge composition and mobility on island formation and island evolution have also been studied. Some typical and important phenomena observed in previous experimental studies during Si 1− x Ge x /Si(0 0 1) heteroepitaxy have been simulated using the phase-field model.

We have performed phase-field simulations during directional solidification of a binary alloy. Adaptive mesh refinement techniques, in which the degrees of freedom of additional hanging nodes which occur when a quadrilateral element is refined are eliminated by matrix operations, are introduced to the finite element analysis in order to conduct the phase-field simulations efficiently. The validity of the numerical techniques presented here is ascertained by comparing the numerical results of the absolute stability limit and the onset of instability with those calculated from the Mullins–Sekerka theory and from the good linear relationship between log(V) and log(λ), in which the simulations under the constant concentration and temperature gradient are conducted by varying the pulling velocity. Furthermore, we examine the morphology change from cellular to dendritic structure and the relationship between log(λ) and log(G) for varying the temperature gradient.