### Fundamental algorithms

#### 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 (Cu_{50}Zr_{50} and Cu_{20}Zr_{80}). 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, 064303-1-7 (2012).

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.