Fundamental algorithms

Rong Fu, Zhiyuan Rui, Junping Du, Shihao Zhang, Fanshun Meng, Shigenobu Ogata,“Temperature and loading-rate dependent critical stress intensity factor of dislocation nucleation from crack tip: Atomistic insights into cracking at slant twin boundaries in Nano-twinned TiAl alloys”, Journal of Materials Science & Technology, In Press (2024) .

This paper investigates the temperature and loading rate dependencies of the critical stress intensity factor (KIC) for dislocation nucleation at crack tips. We develop a new KIC formula with a generalized form by incorporating the atomistic reaction pathway analysis into Transition State Theory (TST), which captures the KIC of the first dislocation nucleation event at crack tips and its sensitivity to temperature and loading rates. We use this formula and atomistic modeling information to specifically calculate the KIC for quasi-two-dimensional crack tips located at 3 various slant twin boundaries in nano-twinned TiAl alloys across a wide range of temperatures and strain rates. Our findings reveal that twinning dislocation nucleation at the crack tip dominates crack propagation when twin boundaries (TBs) are tilted at 15.79° and 29.5°. Conversely, when TBs tilt at 45.29°, 54.74°, and 70.53°, dislocation slip becomes the preferred mode. Additionally, at TB tilts of 29.5° and 70.53°, at higher temperatures above 800 K and typical experimental loading rates, both dislocation nucleation modes can be activated with nearly equal probability. This observation is particularly significant as it highlights scenarios that molecular dynamics simulations, due to their time scale limitations, cannot adequately explore. This insight underscores the importance of analyzing temperature and loading rate dependencies of the KIC to fully understand the competing mechanisms of dislocation nucleation and their impact on material behavior.

Fan-Shun Meng, Shuhei Shinzato, Shihao Zhang, Kazuki Matsubara, Jun-Ping Du, Peijun Yu, Wen-Tong Geng, Shigenobu Ogata,“A highly transferable and efficient machine learning interatomic potentials study of α-Fe–C binary system”, Acta Materialia, 281 (2024) 120408.

Machine learning interatomic potentials(MLIPs) for α-iron and carbon binary system have been constructed aiming for understanding the mechanical behavior of Fe–C steel and carbides. The MLIPs were trained using an extensive reference database produced by spin polarized density functional theory(DFT) calculations. The MLIPs reach the DFT accuracies in many important properties which are frequently engaged in Fe and Fe–C studies, including kinetics and thermodynamics of C in α-Fe with vacancy, grain boundary, and screw dislocation, and basic properties of cementite and cementiteferrite interfaces. In conjunction with these MLIPs, the impact of C atoms on the mobility of screw dislocation at finite temperature, and the C-decorated core configuration of screw dislocation were investigated, and a uniaxial tensile test on a model with multiple types of defects was conducted.

Shihao Zhang, Shihao Zhu, Fanshun Meng, Shigenobu Ogata,“Hydrogen and vacancy concentrations in α-iron under high hydrogen gas pressure and external stress: A first-principles neural network simulation study”, International Journal of Hydrogen Energy, 90 (2024) 246-256.

The metal-hydrogen-vacancy interaction in α-iron is crucial for understanding hydrogen embrittlement behavior and developing reliable materials for green gaseous hydrogen applications; however, it remains underexplored, particularly in contexts involving external stress and high hydrogen gas pressure. In this study, we performed quantitative analyses of metal-vacancy–hydrogen interactions in α-iron, measured by hydrogen solubility and the thermodynamics of vacancy–hydrogen complexes, under such challenging conditions using a reliable first-principles neural network potential. High hydrogen gas pressures reaching up to 2 GPa were investigated. As the atomic concentration surpasses approximately 0.01, hydrogen solubility is dominated by hydrogen-induced lattice distortion (primarily volumetric expansion) and the interactions between hydrogen atoms within the metal matrix, resulting in significant deviations from Sieverts’ law. Our results reveal a significant effect of shear stress on hydrogen solubility, deviating from previously used equations. Moreover, the influence of external stress on the thermodynamics of the vacancy–hydrogen complex, particularly vacancy formation free energy, is uniquely characterized by hydrogen solubility, regardless of the external stress magnitude. It thereby offers a rapid method to estimate the vacancy properties under external stress based on readily accessible external-stress-free data.

Akio Ishii,“Edge- and vertex-originated differences between nanoparticles and nanovoids: A density functional theory study of face-centered-cubic Al”, Computational Materials Science, 246 (2025) 113342.

The differences between nanoparticles and nanovoids cannot be clearly distinguished energetically using conventional comparisons based on the surface energies of these species. For example, nanoparticles and nanovoids with the same volume and shape are considered energetically equivalent to the conventional Wulff construction, and so the difference in their morphology cannot be evaluated. This can be attributed to fact that using such approaches, the effects of excess defects, edges, and vertices in nanoparticles and nanovoids are typically ignored. In this study, we investigated the energetic differences between face-centered-cubic (FCC) nanoparticles of Al and nanovoids in bulk FCC Al structure with conventional truncated octahedral shapes by calculating the excess energies attributed to their edges, vertices, and sizes. This was achieved using density functional theory calculations and our previously reported method for evaluating the effects of edges and vertices. The morphological differences between the nanoparticles and nanovoids were also discussed based on the obtained results.

Yangen Li, Jun-Ping Du, Shuhei Shinzato, Shigenobu Ogata,“Tunable interstitial and vacancy diffusivity by chemical ordering control in CrCoNi medium-entropy alloy”, npj Computational Materials, 10,134 (2024).

In this study, we utilized a quantitative atomistic analysis approach to investigate the impact of chemical ordering structures on the diffusion behavior of interstitials and vacancies within the CrCoNi medium entropy alloy (MEA), employing an advanced neural network interatomic potential (NNP). We discovered that the degree of chemical ordering, which can be precisely controlled through annealing at elevated temperatures, significantly influences both interstitial and vacancy diffusion. This phenomenon contributes to the notable sluggish diffusion characteristic of CrCoNi, largely attributable to the restriction of diffusion pathways in regions with lower degree of chemical ordering. We also emphasized the crucial role of operating temperature on diffusion, which should be remained well below the annealing temperature to preserve the sluggish diffusion effect. Our research sheds light on the interplay between chemical ordering and defect diffusion in MEAs, and it proposes effective strategies for tailoring the diffusivity of MEAs by altering their chemical ordering. These insights are instrumental in the development of next-generation materials, which are optimized for use in challenging environments, such as high-temperature and irradiation conditions.

Akio Ishii,“Energetical effects of the edges and vertices of face-centered-cubic Pd and Au nanoparticles: A density functional theory study”, Computational Materials Science, 243 (2024) 113122.

The properties of nanoparticles depend on their sizes, and these size effects in face-centered-cubic (FCC) nanoparticles are attributed to the edge and vertex effects. However, the effects of edges and vertices on the properties of nanoparticles have not yet been explicitly investigated. In this study, we propose a method to evaluate the edge and vertex effects in FCC nanoparticles using density functional theory atomistic simulations. Pd and Au FCC nanoparticles are modeled as conventional truncated octahedra with {111} and {100} faces. The changes in the excess energy due to the edges and vertices are separately described and are calculated with respect to the size of the nanoparticles. Through explicit calculations, we confirmed that for Pd and Au nanoparticles with several hundred atoms, the vertex effects are negligible, whereas the edge effects are still significant.

Akio Ishii, Nobutomo Nakamura,“Ab initio morphology prediction of Pd, Ag, Au, and Pt nanoparticles on (0001) sapphire substrates”, Journal of Applied Physics, 135 (2024) 094301.

We energetically predict the morphology of Pd, Ag, Au, and Pt nanoparticles on (0001) sapphire substrates, using density functional theory (DFT) simulations and the well-known Young–Dupre equation. In all cases, the contact angles exceed 90° , indicating that the nanoparticles are spherical. Notably, Au nanoparticles exhibit a higher contact angle than those of their counterparts. The validity of the proposed abinitio nanoparticle morphology prediction approach based on DFT simulations was assessed in comparison with our previous experimental findings pertaining to the time variation of the full width at half maximum (FWHM) of the resonant peak. Furthermore, the diffusivities of single Pd, Ag, Au, and Pt atoms on the substrate were evaluated by calculating the activation energy, offering insights into the underlying physics governing the timing of FWHM peaks. The analysis confirms a higher diffusivity of Au and Ag compared with Pd and Pt. According to the comparison between DFT and experiment results, although no clear relation is observed between the contact angles and timing of FWHM peaks, the diffusivity of sputtered atoms may influence the timing of FWHM peaks. Thus, timing can help to clarify the nanoparticle size, rather than shape.

Shihao Zhang, Fanshun Meng, Rong Fu, Shigenobu Ogata,“Highly efficient and transferable interatomic potentials for α-iron and α-iron/hydrogen binary systems using deep neural networks”, Computational Materials Science, 235 (2024) 112843-1-6.

Artificial neural network potentials (NNPs) have emerged as effective tools for understanding atomic interactions at the atomic scale in various phenomena. Recently, we developed highly transferable NNPs for 𝛼-iron and 𝛼-iron/hydrogen binary systems (Physical Review Materials 5 (11), 113606, 2021). These potentials allowed us to investigate deformation and fracture in 𝛼-iron under the influence of hydrogen. However, the computational cost of the NNP remains relatively high compared to empirical potentials, limiting their applicability in addressing practical issues related to hydrogen embrittlement. In this work, building upon our prior research on iron-hydrogen NNP, we developed a new NNP that not only maintains the excellent transferability but also significantly improves computational efficiency (more than 40 times faster). We applied this new NNP to study the impact of hydrogen on the cracking of iron and the deformation of polycrystalline iron. We employed large-scale through-thickness {110}⟨110⟩ crack models and large-scale polycrystalline 𝛼-iron models. The results clearly show that hydrogen atoms segregated at crack tips promote brittle-cleavage failure followed by crack growth. Additionally, hydrogen atoms at grain boundaries facilitate the nucleation of intergranular nanovoids and subsequent intergranular fracture. We anticipate that this high-efficiency NNP will serve as a valuable tool for gaining atomic-scale insights into hydrogen embrittlement.

Jin-Yu Zhang, Gaël Huynh, Fu-Zhi Dai, Tristan Albaret, Shi-Hao Zhang, Shigenobu Ogata, David Rodney ,“A deep-neural network potential to study transformation-induced plasticity in zirconia”, Journal of the European Ceramic Society, 44 (2024) 4243-4254.

Severe shear localization in metallic glasses (MGs) significantly limits their mechanical performance. Nanoglass (NG), composed of heterogeneous glassy domains created by introducing interfaces into MGs at the nanoscale, could be a promising strategy against severe shear localization, as demonstrated by numerous atomistic simulations. This study introduces a novel mesoscale kinetic Monte Carlo (kMC) model with a variable characteristic strain (VCS) to investigate the grain size effect in NGs. This model captures the complex evolution of shear bands during deformation, revealing a surprising transition from inhomogeneous to homogeneous deformation as the NG grain size decreases to approximately 10 nm. This transition is attributed to the impediment of shear band formation by the small grain size, facilitated by softer interfaces guiding early shear transformation zone (STZ) activities across the entire sample. Furthermore, a progressive reduction of elastic constants simulates the failure response observed in experiments. Our model predicts a critical grain size for the transition in agreement with molecular dynamics simulations and experiments, highlighting its potential for designing NGs with enhanced shear resistance. This mesoscale model enables the investigation of NG deformation with microstructural features on an experimentally-relevant spatial-temporal scale. This paves the way for tailoring NG microstructures to achieve enhanced mechanical performance, and opens new avenues for exploring the influence of interfaces in controlling shear localization.

Akio Ishii,“Influence of elastic anisotropy on the shapes of ellipsoidal blisters and stress field around the blisters in solid materials”, AIP advances, 13 (2023) 125024-1-11.

To address the embrittlement challenges posed by gas blisters in anisotropic materials, the stable shape of constant-pressure blisters in anisotropic materials (hexagonal, tetragonal, and rhombohedral) was energetically investigated based on continuum theory (micromechanics), considering the blister as Eshelby’s ellipsoidal inclusion. The non-negligible change in the blister shape was confirmed in terms of the anisotropic factor η ≡ C₃₃₃₃/C₁₁₁₁. Although the spherical shape of the blister is preferable for isotropic and cubic materials (η = 1), the x₃ normal penny and capsule shapes were theoretically confirmed to be the most stable ones for η > 1 and η < 1, respectively. The penny and capsule shape blisters generate larger stress fields around themselves than the sphere shape blisters, thus inducing crack formation. The embrittlement due to the gas (typically hydrogen or helium) inside the blister for the anisotropic materials was more significant than isotropic and cubic embrittlement.

Akio Ishii,“Ab initio stability prediction of β titanium and α and ω precipitates in β titanium matrix for titanium alloys using density functional theory and micromechanics”, Materials Today Communications, 38 (2023) 107708-1-10.

β titanium alloys have a wide range of applications, including in aerospace and transport. The β phase is stable only at high temperatures, and the phase stability can be improved by adding stabilizers. However, the β-phase-stabilization effects of β stabilizers have not yet been clearly elucidated. Here, I report the ab initio prediction of the energetic phase stability of β titanium alloys with Mo, V, W, Nb, and Ta as additive β stabilizer elements. The stability is predicted using a combination of atomistic simulation via density functional theory and continuum micromechanics (Eshelby’s ellipsoidal inclusion analysis). In particular, I consider the heterogeneity of the secondary ω and α phases (precipitation) in the β matrix. All β stabilizer species led to a significant energetic and elastic stabilization of the β phase. Mo and W additives stabilized the β phase relatively stronger and secondary ω and α precipitates may hardly nucleate in β phase in high concentrate condition. Although V, Nb, and Ta additives stabilized the β phase significantly, the β phase remained metastable. Regarding the morphology of these secondary phases, V helped α precipitation and Ta helped ω precipitation. The possibility of a coexistence of ω and α in the β matrix was suggested for Nb addition. The strain fields around the precipitates were also investigated and the results suggested that α precipitates cause a large residual strain around it though ω precipitates do not.

Akio Ishii,“Morphology prediction of elastically interacting Zr hydride precipitates and cracks in alpha-Zr using atomistically informed Eshelby's ellipsoidal inclusion”, Computational Materials Science, 231 (2024) 112568-1-8.

We propose an atomistically informed Eshelby's inclusion analysis to investigate the morphology of secondary phases, which elastically interacted with each other through their respective local strain fields. Using the proposed method, we predict the morphology of delta-hydride precipitates and cracks, which interacted in the alpha–Zr matrix. Planar cracks nucleate along the basal-normal delta-hydride disk. And at the crack tip, the prismatic-normal delta-hydride disk also nucleates depending on the stress condition around the crack, constructing the hydride-crack network. The findings contribute to the understanding of the fracture mechanism of Zr alloys, such as delayed hydride cracking, which is caused by Zr hydride.

Akio Ishii,“Ab initio prediction of temperature-dependent stability of heterogeneous B19' phase in TiNi alloy using atomistically informed Eshelby's ellipsoidal inclusion”, Materials Today Communications, 35 (2023) 105861.

In this study, we energetically predicted the temperature-dependent stability of the heterogeneous B19′ phase in the B2 matrix of TiNi alloys using density functional theory (DFT) and phonon analysis informed Eshelby's ellipsoidal inclusion. The temperature-dependent eigenstrains and elastic constants for Eshelby's ellipsoidal inclusion were calculated using DFT and phonon analysis under a quasi-harmonic approximation. The stable orientation of the disk-shaped B19' phase in the B2 matrix and its total strains were evaluated with respect to temperature using Eshelby's ellipsoidal inclusion analysis. Using the total strains, the elastically deformed atomic structure of the heterogeneous B19' phase in the B2 matrix was determined, and its temperature-dependent free energy was calculated using DFT calculations and phonon analysis. Comparing the temperature-dependent free energies of the B2 and elastically deformed B19' structures, we successfully predicted that the transformation between the two phases occurs at 300 K, which agrees with experimental observations. Moreover, it is shown that the temperature-dependent difference in the elastic constants between the B19′ phase and B2 matrix influences the phase transformation, which is the origin of the shape-memory effect of TiNi alloy.

Akio Ishii,“Ab initio morphology prediction of Zr hydride precipitates using atomistically informed Eshelby’s ellipsoidal inclusion”, Computational Materials Science, 211, (2022) 111500-1-14.

We energetically predicted the morphology of Zr hydride precipitates in a hexagonal close-packed (HCP) Zr matrix. Considering Zr hydride precipitates as ellipsoids, we used Eshelby’s ellipsoidal inclusions to calculate the elastic energy increment due to the presence of Zr hydride precipitates in the Zr matrix, in which the elastic anisotropy and inhomogeneity of the elastic constants between Zr and Zr hydride were considered. We compared the difference in the elastic energy increment between the ellipsoidal inclusions with different shapes: plates (mimicked by penny-shape ellipsoids), needles (mimicked by longitudinal ellipsoids) and sphere, and orientations to detect the stable structure with the minimum elastic energy increment. Eigenstrains of each Zr hydride and elastic constants of Zr hydrides and HCP Zr for Eshelby’s ellipsoidal inclusion analysis were determined using atomistic simulations based on a density functional theory calculation, achieving a parameter free 𝑎𝑏 𝑖𝑛𝑖𝑡𝑖𝑜 morphology prediction. The morphology predictions were implemented for two cases: with and without shear components of eigenstrain (𝑤∕ and 𝑤∕𝑜 shear). The ⟨1̄210⟩ longitudinal needle for the 𝛾 hydride (𝑤∕𝑜 shear) and plate (or disk) on the plane, which is 20◦ to 30◦ tilted about ⟨1̄210⟩-axis from basal plane (0001), for 𝛿 and 𝜖 hydrides (𝑤∕ shear) were successfully predicted as stable shapes and orientations of the precipitates under zero external stress conditions, qualitatively consistent with experimental observations. The external circumferential tensile stress on the basal plane reduces the elastic energy of [0001] parallel Zr hydride plates, which is also qualitatively consistent with the reoriented 𝛿 hydride precipitates observed in the experiment. On the other hand, predicted external stress for the reorientation of Zr hydride is quite high, around 10 GPa. This is inconsistent with experimental observation and further investigation is necessary. Generally, our predictions based on elasticity theory appear qualitatively consistent with experimental observations, suggesting an elastic origin of the morphology of Zr hydride precipitates in the HCP Zr matrix.

Fan-Shun Meng, Jun-Ping Du, Shuhei Shinzato, Hideki Mori, Peijun Yu, Kazuki Matsubara, Nobuyuki Ishikawa, and Shigenobu Ogata,“General-purpose neural network interatomic potential for the α-iron and hydrogen binary system: Toward atomic-scale understanding of hydrogen embrittlement”, Physical Review Materials, 5, 11 (2021) 113606-1-16.

To understand the physics of hydrogen embrittlement at the atomic scale, a general-purpose neural network interatomic potential (NNIP) for the α-iron and hydrogen binary system is presented. It is trained using an extensive reference database produced by density functional theory (DFT) calculations. The NNIP can properly describe the interactions of hydrogen with various defects in α-iron, such as vacancies, surfaces, grain boundaries, and dislocations; in addition to the basic properties of α-iron itself, the NNIP also handles the defect properties in α-iron, hydrogen behavior in α-iron, and hydrogen-hydrogen interactions in α-iron and in vacuum, including the hydrogen molecule formation and dissociation at the α-iron surface. These are superb challenges for the existing empirical interatomic potentials, like the embedded-atom method based potentials, for the α-iron and hydrogen binary system. In this study, the NNIP was applied to several key phenomena necessary for understanding hydrogen embrittlement, such as hydrogen charging and discharging to α-iron, hydrogen transportation in defective α-iron, hydrogen trapping and desorption at the defects, and hydrogen-assisted cracking at the grain boundary. Unlike the existing interatomic potentials, the NNIP simulations quantitatively described the atomistic details of hydrogen behavior in the defective α-iron system with DFT accuracy. (Potential files download)

Akio Ishii, “Spatial and temporal heterogeneity of Kohlrausch–Williams–Watts stress relaxations in metallic glasses”, Computational Materials Science, 198 (2021) 110673-1-5.

We perform a molecular dynamics (MD) stress relaxation simulation for Zr₅₀Cu₄₀Al₁₀ metallic glass to confirm that the time dependency of stress relaxation conforms with the Kohlrausch–Williams–Watts (KWW) equation, and to derive the temperature dependency of the Kohlrausch exponent β^KWW. We also calculate local plastic deformation based on atomic strain, then discuss the morphology of relaxation and calculate the probability density of stress relaxation with respect to the characteristic time of relaxation from the number of deformed atoms. Afterward, we derive the time dependency of stress relaxation as a mode-averaged decay function, which expresses spatial and temporal heterogeneity. Both the results of simulation and calculation reproduce the KWW relaxation form and are in good agreement, confirming the spatially and temporally heterogeneous nature of KWW relaxation. The heterogeneity of the stress relaxation of metallic glass is determined by local stress changes caused by microscopic local plastic deformation.

Zeqi Shen, Jun-Ping Du, Shuhei Shinzato, Yuji Sato, Peijun Yu, Shigenobu Ogata, “Kinetic Monte Carlo simulation framework for chemical short-range order formation kinetics in a multi-principal-element alloy”, Computational Materials Science, 198 (2021) 110670-1-8.

Multi-principal-element alloys—so-called high-entropy alloys (HEAs)—contain multiple equiatomic or nearly equiatomic elements and are attracting increasing attention in basic and applied research because of their superior mechanical properties. Recently, the existence of chemical short-range order (CSRO)/local chemical ordering in HEAs has been experimentally confirmed and its effects on the mechanical properties of HEAs have been studied. However, the formation process and kinetics of CSRO have not yet been fully clarified. In the present study, we propose a simulation framework to study CSRO formation kinetics based on Monte Carlo and kinetic Monte Carlo simulation methods. Applying the simulation framework to quinary face-centered-cubic multi-principal-element alloys described by Lennard–Jones interatomic model potentials, we obtained the temperature-dependent CSRO formation kinetics via vacancy diffusion and constructed a time–temperature–CSRO degree diagram, which enables the CSRO of HEAs to be tailored via thermal processing.

Masahiro Yamamoto, Akio Ishii, Shuhei Shinzato, Shigenobu Ogata and Taisuke Ozaki, “First-principles adaptive-boost accelerated molecular dynamics simulation with effective boost potential construction methods: a study of Li diffusion in Si crystal”, Japanese Journal of Applied Physics, 59 (2020) 125002-1-6.

First-principles molecular dynamics (FPMD) simulation is a powerful tool for studying the mechanical, chemical,and thermal properties of materials. However, because of the fundamental time-scale limitation of molecular dynamics and the high computational cost of density functional theory, many of the rare events that dominate these properties cannot be directly investigated. We have developed an accelerated FPMD based on FPMD and the adaptive boost (AB) method, which remove the fundamental drawback of FPMD: time-scale limitation. We also propose a novel boost potential construction algorithms that allows an accurate boost potentialto be constructed with a limited number of FPMD samplings. In this study, to confirm the validity of the method,we compute the diffusion of a Li atom in a Si crystal. The temperature-dependent diffusivity was obtained and the activation enthalpy was calculated from an Arrhenius plot and compared with reported experimental diffusivities.

Akio Ishii, “Energetics of heterogeneous Mg {101-2} deformation twinning migration using an atomistically informed phase-field model”, Computational Materials Science, 183 (2020) 109907-1-14.

We have constructed an atomistically informed phase-field model for the quantitative energetic analysis of phase transformations. In our model, to describe the general phase transformation with a non-linear correlation between displacive and diffusive modes, we have defined two order parameters, ϒ and Φ, which describe the lattice distortion (displacive mode) and shuffling (diffusive mode), respectively. Our method provides a way to introduce the energetics from atomistic simulations to the phase-field model, describes ϒ and Φ in an atomic model, and derives phase-field parameters from the free energy calculated by atomistic simulation. As an application of our model, we used the energetics obtained from atomistic simulations using a density functional theory potential, and we calculated the free energy change during the heterogeneous {101-2} twin migration of hexagonally close-packed (HCP) Mg, which can be considered as a lattice distortion and shuffling mixed phase transformation, by combining our phase-field model with the nudged elastic band method. The activation energy, and the critical nucleus size of the heterogeneous {101-2} twin migration under a set stress were derived. The critical c-axis tensile stress (athermal stress), at which the activation energy becomes zero, is consistent with the experimental yield stress of {101-2} for the twinning deformation of HCP Mg nanopillars in tensile tests. The critical nucleus size of the heterogeneous {101-2} twin migration is on the range of nanometers under several hundred megapascals stress, which is consistent with the experimental observation of nanotwins.

Shuhei Shinzato, Masato Wakeda, Shigenobu Ogata, "An atomistically informed kinetic Monte Carlo model for predicting solid solution strengthening of body-centered cubic alloys", International Journal of Plasticity, 122 (2019) 319-337.

In order to predict solid solution strengthening in body-centered cubic dilute substitutional alloys, we developed an atomistically informed kinetic Monte Carlo (kMC) model for screw dislocation motion, which is a major determinant of the yield strength of the BCC alloys. The kMC model only requires parameters obtainable using atomic simulations. The parameters in the developed kMC model were actually determined for Fe–Si dilute alloys using atomistically derived activation energies of kink-pair nucleation and kink migration as well as their stress dependencies. The activation energies were computed using the nudged elastic band method with developed interatomic potentials based on first-principles density functional theory. Eventually, the critical resolved shear stress (CRSS), activation volume of the dislocation glide, and their temperature and solute concentration dependencies were directly obtained by two dimensional kMC dislocation glide simulations. Our kMC model qualitatively reproduced the trends of experimentally observed temperature and concentration dependencies of CRSS, and thus it can naturally describe solid solution strengthening, and softening without any empirical information. In addition, the limitations of the two dimensional model, including single slip and lack of non-Schmid effect, are discussed, which results in quantitative difference with the experimental CRSS.

Hiroshi Miyoshi, Hajime Kimizuka, Akio Ishii, Shigenobu Ogata, "Temperature-dependent nucleation kinetics of Guinier-Preston zones in Al-Cu alloys: An atomistic kinetic Monte Carlo and classical nucleation theory approach", Acta Materialia, 179 (2019) 262-272.

Guinier-Preston (GP) zones, which form in Al-Cu alloys, exhibit characteristic patterns of Cu-rich, disk-shaped atomic clusters along the {100} planes. GP zones have received much attention not only for their precipitation-hardening effect on the Al matrix, but also from fundamental interest in the physics and chemistry of the nanoscale organization of solute atoms. In this study, we established an atomistic kinetic Monte Carlo (kMC) modeling technique for exploring the nucleation and formation processes of GP zones in Al-Cu alloys by constructing an effective on-lattice multibody potential for a dilute Al-Cu-vacancy system by density functional theory calculations. Our model can describe the clustering of Cu atoms via successive exchanges with vacancies and reproduce the characteristic planar nanoprecipitates along the {100} planes in a manner consistent with the crystallographic nature of the GP zones in the early-stage aging of Al-Cu alloys. The time evolution and critical nucleus size of Cu clusters were characterized at various temperatures based on the kMC results. Consequently, we predicted the existence of an optimum temperature (i.e., nose temperature) for the formation of Cu clusters at which the cluster growth was maximized, which was attributable to the interplay between the critical nucleation barrier and the diffusion rate. In addition, the critical nucleus size and temperature for cluster formation were examined based on classical nucleation theory along with the developed multibody potential. These provided an insight into the competition between the enthalpic and entropic effects on the formation of GP zones in the Al-Cu system.

Yuji Sato, Chiaki Nakai, Masato Wakeda, and Shigenobu Ogata, “Predictive modeling of Time-Temperature-Transformation diagram of metallic glasses based on atomistically-informed classical nucleation theory”, Scientific Reports, 7 (2017) 7194-1-9.

Theoretical prediction of glass forming ability (GFA) of metallic alloys is a key process in exploring metallic alloy compositions with excellent GFA and thus with the ability to form a large-sized bulk metallic glass. Molecular dynamics (MD) simulation is a promising tool to achieve a theoretical prediction. However, direct MD prediction continues to be challenging due to the time-scale limitation of MD. With respect to practical bulk metallic glass alloys, the time necessary for quenching at a typical cooling rate is five or more orders of magnitude higher than that at the MD time-scale. To overcome the time-scale issue, this study proposes a combined method of classical nucleation theory and MD simulations. The method actually allows to depict the time-temperature-transformation (TTT) diagram of the bulk metallic glass alloys. The TTT directly provides a prediction of the critical cooling rate and GFA. Although the method assumes conventional classical nucleation theory, all the material parameters appearing in the theory were determined by MD simulations using realistic interatomic potentials. The method is used to compute the TTT diagrams and critical cooling rates of two Cu-Zr alloy compositions (Cu50Zr50 and Cu20Zr80). The results indicate that the proposed method reasonably predicts the critical cooling rate based on the computed TTT.

Akio Ishii, Ju Li, and Shigenobu Ogata, “Shuffling-controlled versus strain-controlled deformation twinning: The case for HCP Mg twin nucleation”, International Journal of Plasticity, 82 (2016) 32-43.

The atomistic pathways of deformation twinning can be computed ab initio , and quantified by two variables: strain which describes shape change of a periodic supercell, and shuffling which describes non-affine displacements of the internal degrees of freedom. The minimum energy path involves juxta-position of both. But if one can obtain the same saddle point by continuously increasing the strain and relaxing the internal degrees of freedom by steepest descent, we call the path strain-controlled, and vice versa. Surprisingly, we find the View the MathML source{1012}〈1011〉 twinning of Mg is shuffling-controlled at the smallest lengthscale of the irreducible lattice correspondence pattern, that is, the reaction coordinate at the level of 4 atoms is dominated by non-affine displacements, instead of strain. Shuffling-controlled deformation twinning is expected to have different temperature and strain-rate sensitivities from strain-controlled deformation twinning due to relatively weaker strength of long-range elastic interactions, in particular at the twin nucleation stage. As the twin grows large enough, however, elastic interactions and displacive character of the transformation should always turn dominant.

Kazuki Matsubara, Hajime Kimizuka, and Shigenobu Ogata, "First-Principles Analysis of Thermal Expansion Behavior of Mg Based on the Quasi-Harmonic Approximation Considering Structural Anisotropy", Journal of the Society of Materials Science, 63-2 (2014) 188-193 [in Japanese].

The temperature dependence of thermal expansion of hexagonal close-packed Mg was analyzed based on the quasi-harmonic approximation (QHA) using first-principles density functional theory calculations. To consider the structural anisotropy of a Mg single crystal, we introduced two individual structural parameters into the QHA scheme so that static total energy and lattice vibration frequencies of the system were numerically described by the approximate polynomials as a function of the lattice parameters a and c. We found that our approach can successfully reproduce the thermal expansion behavior of Mg over the wide temperature range by adopting the second- and higher-order polynomial to describe the lattice vibration, in a manner consistent with the experimental measurements. The nonlinear dependence of the lattice vibration frequencies on the axial strain was suggested to play an important role in understanding the thermal expansion anisotropy due to the anharmonicity in the interatomic interactions.

Hajime Kimizuka, and Shigenobu Ogata, "Predicting Atomic Arrangement of Solute Clusters in Dilute Mg Alloys", Materials Research Letters, 1-4 (2013) 213-219.

Theoretical prediction of the heterogeneous atomic structures in multicomponent alloys is one of the most challenging issues in materials science. Here we present a first-principles demonstration of this by constructing an on-lattice effective multibody potential model to describe the energetics of hexagonal close-packed Mg crystals containing stacking faults (SFs) with Al and Gd substitutions. Remarkably, we showed that our intuitive model can describe the segregation of solute atoms to SFs and reproduce the characteristic short-range chemical order in dilute Mg-Gd and Mg-Al-Gd systems, including long-period stacking ordered structures, in a manner consistent with recent scanning transmission electron microscopy measurements.

Shigenobu Ogata, "Prediction of Mechanical Properties of Materials from First-Principles", Journal of the Japan Society of Mechanical Engineers A, 78-791 (2012) 934-944. [in Japanese]

Current ability and expecting future development of Frst-principles predictive modeling for studying mechanicalproperties of materials is comprehensively discussed by means of introducing recent publications and reports. Particulary,I pick up topics for the elastic properties (e.g., elastic constants, elastic strain engineering, ideal strength), the plastic properties, (e.g., dislocation core properties, stacking faults, twinning), and the interfacial properties, (e.g., strength of grain boundaies, strength of interfaces composed of dissimilar matereials), which are necessary to understand materials behavior under external loadings.

Akio Ishii, Shigenobu Ogata, Hajime Kimizuka, and Ju Li, "Adaptive-boost molecular dynamics simulation of carbon diffusion in iron", Physical Review B, 85-6 (2012) 064303-1-7.

We have developed an accelerated molecular dynamics (MD) method to model atomic-scale rare events. In this method, a smooth histogram of collective variables is first estimated by canonical ensemble molecular dynamics calculations, and then a temperature-dependent boost potential is iteratively constructed to accelerate the MD simulation. This method not only allows us to observe the rare events but also to evaluate the profile of free energy and trial frequency along the reaction coordinate. We employed this method to study carbon diffusion in bcc iron and evaluated carbon's temperature-dependent diffusivity. The obtained diffusivities agree well with the experimental measurements. Even at low temperature for which, to the best of our knowledge, no experimental data are available, the diffusivity can be evaluated accurately. Additionally, we study carbon diffusion inside the edge dislocation core in bcc iron, and demonstrate the applicability of the method to rare events on a rugged free-energy surface.

Akio Ishii, Hajime Kimizuka, and Shigenobu Ogata, "Multi-replica Molecular Dynamics Modeling", Computational Materials Science, 54-1 (2012) 240-248.

We propose a new unified modeling concept, multi-replica molecular dynamics (MRMD), which is a collective designation for molecular dynamics (MD) or particle dynamics (PD) that simultaneously follows the time evolution of two or more replica systems. Numerous methods in various fields (physics, chemistry, biology, materials science, astronomy, etc.) can be classified in MRMD, such as parallel replica methods, the nudged elastic band method, path integral methods, replica exchange methods, and the multi-walker metadynamics method. However, the relations between these MRMD methods have not been clarified, and a global understanding or unified methodological framework remains to be presented. Therefore, herein, we discuss the relations between various MRMD methods to provide a comprehensive understanding of these methods. Then, with this understanding, we describe a concise implementation of MRMD into conventional domain- and particle-decomposition parallel MD program codes, instead of the somewhat intuitive replica-parallel implementation. Finally, we demonstrate examples of different MRMD calculations performed using our parallel MRMD program “ParaMrMD.”

Hiroki Ushida, Shigenobu Ogata, and Hajime Kimizuka, "Molecular Dynamics Stability Analysis of fcc Crystal Against Local Share Deformation", Journal of the Society of Materials Science, Japan, 60-1 (2011) 71-78. [in Japanese].

We propose a framework that can be used to study the local thermodynamic stability of materials at finite temperatures, by reconstructing free energy surface based on metadynamics, constraint molecular dynamics and local atomic deformation tensor analysis methods. We apply the proposed framework to fcc embedded atom copper models, and estimate the activation energies, volumes, and critical local deformation tensor for a stacking fault nucleation event in copper single crystal.