Atomistic simulation model on a diffusive timescale based on the extension of the cluster-activation method to continuous space.

Recently the phase-field crystal method has attracted considerable attention because it can simulate the atomic behavior of a system on a diffusive timescale. In this study an atomistic simulation model is proposed, which is an extension of the cluster-activation method (CAM) from discrete to continuous space. This approach, called the continuous CAM, can simulate various physical phenomena of atomistic systems on diffusive timescales and employs well-defined atomistic properties, such as interatomic interaction energies, as the main input parameters. The versatility of the continuous CAM was investigated by performing simulations of crystal growth in an undercooled melt, homogeneous nucleation during solidification, and formation of grain boundaries in pure metal.

Bayesian Data Assimilation of Temperature Dependence of Solid-Liquid Interfacial Properties of Nickel.

Temperature dependence of solid-liquid interfacial properties during crystal growth in nickel was investigated by ensemble Kalman filter (EnKF)-based data assimilation, in which the phase-field simulation was combined with atomic configurations of molecular dynamics (MD) simulation. Negative temperature dependence was found in the solid-liquid interfacial energy, the kinetic coefficient, and their anisotropy parameters from simultaneous estimation of four parameters. On the other hand, it is difficult to obtain a concrete value for the anisotropy parameter of solid-liquid interfacial energy since this factor is less influential for the MD simulation of crystal growth at high undercooling temperatures. The present study is significant in shedding light on the high potential of Bayesian data assimilation as a novel methodology of parameter estimation of practical materials an out of equilibrium condition.

Bayesian inference of solid-liquid interfacial properties out of equilibrium.

Solid-liquid interfacial properties out of equilibrium provide the essential information required for understanding and controlling solidification microstructures in metallic materials. However, few studies have attempted to reveal all interfacial properties out of equilibrium in detail. The present study proposes an approach for simultaneously estimating all interfacial properties in a pure metal below the melting point on the basis of the Bayesian inference theory. The solid-liquid interfacial energy, interfacial mobility, and anisotropy parameters in pure Fe are estimated by combining molecular dynamics simulation with phase-field simulation using an ensemble Kalman filter, which is a data assimilation technique. Furthermore, the temperature dependences of all interfacial parameters are computed and discussed. In summary, the proposed multiscale approach integrates atomistic and microstructural simulations within the framework of data science and it has considerable potential for a wide variety of applications in materials engineering.

Heterogeneity in homogeneous nucleation from billion-atom molecular dynamics simulation of solidification of pure metal.

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.Nucleation is a fundamental physical process, however it is a long-standing issue whether completely homogeneous nucleation can occur. Here the authors reveal, via a billion-atom molecular dynamics simulation, that local heterogeneity exists during homogeneous nucleation in an undercooled iron melt.

Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy.

A variational formulation of a quantitative phase-field model is presented for nonisothermal solidification in a multicomponent alloy with two-sided asymmetric diffusion. The essential ingredient of this formulation is that the diffusion fluxes for conserved variables in both the liquid and solid are separately derived from functional derivatives of the total entropy and then these fluxes are related to each other on the basis of the local equilibrium conditions. In the present formulation, the cross-coupling terms between the phase-field and conserved variables naturally arise in the phase-field equation and diffusion equations, one of which corresponds to the antitrapping current, the phenomenological correction term in early nonvariational models. In addition, this formulation results in diffusivities of tensor form inside the interface. Asymptotic analysis demonstrates that this model can exactly reproduce the free-boundary problem in the thin-interface limit. The present model is widely applicable because approximations and simplifications are not formally introduced into the bulk's free energy densities and because off-diagonal elements of the diffusivity matrix are explicitly taken into account. Furthermore, we propose a nonvariational form of the present model to achieve high numerical performance. A numerical test of the nonvariational model is carried out for nonisothermal solidification in a binary alloy. It shows fast convergence of the results with decreasing interface thickness.

Wafer-scale fabrication and growth dynamics of suspended graphene nanoribbon arrays.

Adding a mechanical degree of freedom to the electrical and optical properties of atomically thin materials can provide an excellent platform to investigate various optoelectrical physics and devices with mechanical motion interaction. The large scale fabrication of such atomically thin materials with suspended structures remains a challenge. Here we demonstrate the wafer-scale bottom-up synthesis of suspended graphene nanoribbon arrays (over 1,000,000 graphene nanoribbons in 2 × 2 cm(2) substrate) with a very high yield (over 98%). Polarized Raman measurements reveal graphene nanoribbons in the array can have relatively uniform-edge structures with near zigzag orientation dominant. A promising growth model of suspended graphene nanoribbons is also established through a comprehensive study that combined experiments, molecular dynamics simulations and theoretical calculations with a phase-diagram analysis. We believe that our results can contribute to pushing the study of graphene nanoribbons into a new stage related to the optoelectrical physics and industrial applications.

Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion.

We present the variational formulation of a quantitative phase-field model for isothermal low-speed solidification in a binary dilute alloy with diffusion in the solid. In the present formulation, cross-coupling terms between the phase field and composition field, including the so-called antitrapping current, naturally arise in the time evolution equations. One of the essential ingredients in the present formulation is the utilization of tensor diffusivity instead of scalar diffusivity. In an asymptotic analysis, it is shown that the correct mapping between the present variational model and a free-boundary problem for alloy solidification with an arbitrary value of solid diffusivity is successfully achieved in the thin-interface limit due to the cross-coupling terms and tensor diffusivity. Furthermore, we investigate the numerical performance of the variational model and also its nonvariational versions by carrying out two-dimensional simulations of free dendritic growth. The nonvariational model with tensor diffusivity shows excellent convergence of results with respect to the interface thickness.

Homogeneous nucleation and microstructure evolution in million-atom molecular dynamics simulation.

Homogeneous nucleation from an undercooled iron melt is investigated by the statistical sampling of million-atom molecular dynamics (MD) simulations performed on a graphics processing unit (GPU). Fifty independent instances of isothermal MD calculations with one million atoms in a quasi-two-dimensional cell over a nanosecond reveal that the nucleation rate and the incubation time of nucleation as functions of temperature have characteristic shapes with a nose at the critical temperature. This indicates that thermally activated homogeneous nucleation occurs spontaneously in MD simulations without any inducing factor, whereas most previous studies have employed factors such as pressure, surface effect, and continuous cooling to induce nucleation. Moreover, further calculations over ten nanoseconds capture the microstructure evolution on the order of tens of nanometers from the atomistic viewpoint and the grain growth exponent is directly estimated. Our novel approach based on the concept of "melting pots in a supercomputer" is opening a new phase in computational metallurgy with the aid of rapid advances in computational environments.

Misorientation/local plastic strain manifestations in chemical etching color.

Cold plastic deformation produces misorientations inside the crystal grains, and the distribution of the misorientation is quite crucial to understand the deformation behavior of the metals or alloys. The misorientation manifestations in chemical etching contrast are investigated in this study in the case of cold-deformed iron. The chemical etching is performed by using nital, while the crystal orientation is determined by electron backscatter diffraction (EBSD). The correlation between the chemical etching contrast and crystal orientation have been studied in both cold-deformed and undeformed iron. The results clearly show that the chemical etching contrast strongly reflects the crystallographic orientation. The gradual change in chemical etching contrast inside the individual deformed grains gives information of both the misorientation and local plastic strain within the grains. This method can provide an easy and alternative way to qualitatively understand the misorientation and local plastic strain distributions in the microstructures.

Quantitative phase-field modeling of nonisothermal solidification in dilute multicomponent alloys with arbitrary diffusivities.

A quantitative phase-field model is developed for simulating microstructural pattern formation in nonisothermal solidification in dilute multicomponent alloys with arbitrary thermal and solutal diffusivities. By performing the matched asymptotic analysis, it is shown that the present model with antitrapping current terms reproduces the free-boundary problem of interest in the thin-interface limit. Convergence of the simulation outcome with decreasing the interface thickness is demonstrated for nonisothermal free dendritic growth in binary alloys and isothermal and nonisothermal free dendritic growth in a ternary alloy.

Quantitative phase-field modeling for dilute alloy solidification involving diffusion in the solid.

An antitrapping current scheme for quantitative phase-field model [A. Karma, Phys. Rev. Lett. 87, 115701 (2001)] is extended to solidification process in a dilute binary alloy system involving diffusion in the solid. It is demonstrated in an asymptotic analysis that in the case of an arbitrary value of the solid diffusivity, five types of constraints exist between interpolating functions used in the phase-field model, which need to be satisfied simultaneously to eliminate all anomalous interface effects. Then, the authors present an appropriate form of the antitrapping current term for the two-sided case to remove all the spurious effects. The convergence test of the output with respect to the interface thickness was carried out for the isothermal dendrite growth process, which demonstrates an excellent performance of the present model.