Multiscale Calculations Research Articles

Neural-Parareal: Self-improving acceleration of fusion MHD simulations using time-parallelisation and neural operators

The fusion research facility ITER is currently being assembled to demonstrate that fusion can be used for industrial energy production, while several other programmes across the world are also moving forward, such as EU-DEMO, CFETR, SPARC and STEP. The high engineering complexity of a tokamak makes it an extremely challenging device to optimise, and test-based optimisation would be too slow and too costly. Instead, digital design and optimisation must be favoured, which requires strongly-coupled suites of multi-physics, multi-scale High-Performance Computing calculations. Safety regulation, uncertainty quantification, and optimisation of fusion digital twins is undoubtedly an Exascale grand challenge. In this context, having surrogate models to provide quick estimates with uncertainty quantification is essential to explore and optimise new design options. But there lies the dilemma: accurate surrogate training first requires simulation data. Extensive work has explored solver-in-the-loop solutions to maximise the training of such surrogates. Likewise, innovative methods have been proposed to accelerate conventional HPC solvers using surrogates. Here, a novel approach is designed to do both. By bootstrapping neural operators and HPC methods together, a self-improving framework is achieved. As more simulations are being run within the framework, the surrogate improves, while the HPC simulations get accelerated. This idea is demonstrated on fusion-relevant MHD simulations, where Fourier Neural Operator based surrogates are used to create neural coarse-solver for the Parareal (time-parallelisation) method. Parareal is particularly relevant for large HPC simulations where conventional spatial parallelisation has saturated, and the temporal dimension is thus parallelised as well. This Neural-Parareal framework is a step towards exploiting the convergence of HPC and AI, where scientists and engineers can benefit from automated, self-improving, ever faster simulations. All data/codes developed here are made available to the community.

Energetic Landscape and Terminal Emitters of Phycobilisome Cores from Quantum Chemical Modeling.

Phycobilisomes (PBs) are giant antenna supercomplexes of cyanobacteria that use phycobilin pigments to capture sunlight and transfer the collected energy to membrane-bound photosystems. In the PB core, phycobilins are bound to particular allophycocyanin (APC) proteins. Some phycobilins are thought to be terminal emitters (TEs) with red-shifted fluorescence. However, the precise identification of TEs is still under debate. In this work, we employ multiscale quantum-mechanical calculations to disentangle the excitation energy landscape of PB cores. Using the recent atomistic PB structures from Synechoccoccus PCC 7002 and Synechocystis PCC 6803, we compute the spectral properties of different APC trimers and assign the low-energy pigments. We show that the excitation energy of APC phycobilins is determined by geometric and electrostatic factors and is tuned by the specific protein-protein interactions within the core. Our findings challenge the simple picture of a few red-shifted bilins in the PB core and instead suggest that the red-shifts are established by the entire TE-containing APC trimers. Our work provides a theoretical microscopic basis for the interpretation of energy migration and time-resolved spectroscopy in phycobilisomes.

Assessing the accuracy and efficacy of multiscale computational methods in predicting reaction mechanisms and kinetics of SN2 reactions and Claisen rearrangement

This study investigates the application of quantum mechanical (QM) and multiscale computational methods in understanding the reaction mechanisms and kinetics of SN2 reactions involving methyl iodide with NH2OH and NH2O−, as well as the Claisen rearrangement of 8-(vinyloxy)dec-9-enoate. Our aim is to evaluate the accuracy and effectiveness of these methods in predicting experimental outcomes for these organic reactions. We achieve this by employing QM-only calculations and several hybrids of QM and molecular mechanics (MM) methods, namely QM/MM, QM1/QM2, and QM1/QM2/MM methodologies. For the SN2 reactions, our results demonstrate the importance of explicitly including solvent effects in the calculations to accurately reproduce the transition state geometry and energetics. The multiscale methods, particularly QM/MM and QM1/QM2, show promising performance in predicting activation energies. Moreover, we observe that the size of the MM active region significantly affects the accuracy of calculated activation energies, highlighting the need for careful consideration during the setup of multiscale calculations. In the case of the Claisen rearrangement, both QM-only and multiscale methods successfully reproduce the proposed reaction mechanism. However, the activation free energies calculated using a continuum solvation model, based on single-point calculations of QM-only structures, fail to account for solvent effects. On the other hand, multiscale methods more accurately capture the impact of solvents on activation free energies, with systematic error correction enhancing the accuracy of the results. Furthermore, we introduce a Python code for setting up multiscale calculations with ORCA, which is available on GitHub at https://github.com/iranimehdi/pdbtoORCA.

Multiscale Modeling of Plutonium Radiation Chemistry in Nitric Acid Solutions. 1. Cobalt-60 Gamma Irradiation of Pu(IV).

Careful manipulation of the plutonium oxidation states is essential in the study and utilization of its rich redox chemistry. To achieve this level of control, a comprehensive mechanistic understanding of radiation-induced plutonium redox chemistry is critical due to the unavoidable exposure of plutonium to ionizing radiation fields, both inherent and from in-process applications. To this end, we have developed an experimentally evaluated multiscale computer model for the prediction of gamma radiation-induced Pu(IV) redox chemistry in concentrated nitric acid solutions (1.0, 3.0, and 6.0 M). Under these acidic, aqueous solution conditions, cobalt-60 gamma irradiation afforded marginal net conversion of Pu(IV) to Pu(VI), the extent of which was dependent on the concentration of HNO3 and absorbed gamma dose. Multiscale calculations, which are in excellent agreement with experimental data, indicate that this observation is due to a combination of inherent plutonium disproportionation reactions and several radiation-induced processes, including redox cycling between Pu(IV) and Pu(III), as achieved by the reduction of Pu(IV) by nitrous acid and hydrogen peroxide, the oxidation of Pu(III) by nitrate and hydroxyl radicals, and the sequential oxidation of Pu(IV) to Pu(V) and Pu(VI) by the remaining available yield of nitrate radicals.

Solid–liquid phase transition simulated by the lattice Boltzmann model: from pore scale to representative elementary volume scale

Purpose This paper aims to establish a lattice Boltzmann (LB) method for solid-liquid phase transition (SLPT) from the pore scale to the representative elementary volume (REV) scale. By applying this method, detailed information about heat transfer and phase change processes within the pores can be obtained, while also enabling the calculation of larger-scale SLPT problems, such as shell-and-tube phase change heat storage systems. Design/methodology/approach Three-dimensional (3D) pore-scale enthalpy-based LB model is developed. The computational input parameters at the REV scale are derived from calculations at the pore scale, ensuring consistency between the two scales. The approaches to reconstruct the 3D porous structure and determine the REV of metal foam were discussed. The implementation of conjugate heat transfer between the solid matrix and the solid−liquid phase change material (SLPCM) for the proposed model is developed. A simple REV-scale LB model under the local thermal nonequilibrium condition is presented. The method of bridging the gap between the pore-scale and REV-scale enthalpy-based LB models by the REV is given. Findings This coupled method facilitates detailed simulations of flow, heat transfer and phase change within pores. The approach holds promise for multiscale calculations in latent heat storage devices with porous structures. The SLPT of the heat sinks for electronic device thermal control was simulated as a case, demonstrating the efficiency of the present models in designing and optimizing SLPT devices. Originality/value A coupled pore-scale and REV-scale LB method as a numerical tool for investigating phase change in porous materials was developed. This innovative approach allows for the capture of details within pores while addressing computations over a large domain. The LB method for simulating SLPT from the pore scale to the REV scale was given. The proposed method addresses the conjugate heat transfer between the SLPCM and the solid matrix in the enthalpy-based LB model.

Multiscale calculations reveal new insights into the reaction mechanism between KRASG12C and α, β-unsaturated carbonyl of covalent inhibitors

Utilizing α,β-unsaturated carbonyl group as Michael acceptors to react with thiols represents a successful strategy for developing KRASG12C inhibitors. Despite this, the precise reaction mechanism between KRASG12C and covalent inhibitors remains a subject of debate, primarily due to the absence of an appropriate residue capable of deprotonating the cysteine thiol as a base. To uncover this reaction mechanism, we first discussed the chemical reaction mechanism in solvent conditions via density functional theory (DFT) calculation. Based on this, we then proposed and validated the enzymatic reaction mechanism by employing quantum mechanics/molecular mechanics (QM/MM) calculation. Our QM/MM analysis suggests that, in biological conditions, proton transfer and nucleophilic addition may proceed through a concerted process to form an enolate intermediate, bypassing the need for a base catalyst. This proposed mechanism differs from previous findings. Following the formation of the enolate intermediate, solvent-assisted tautomerization results in the final product. Our calculations indicate that solvent-assisted tautomerization is the rate-limiting step in the catalytic cycle under biological conditions. On the basis of this reaction mechanism, the calculated kinact/ki for two inhibitors is consistent well with the experimental results. Our findings provide new insights into the reaction mechanism between the cysteine of KRASG12C and the covalent inhibitors and may provide valuable information for designing effective covalent inhibitors targeting KRASG12C and other similar targets.

Optimizing nanoporous metallic actuators through multiscale calculations and machine learning

Nanoporous materials (NMs) immersed in electrolytes can achieve approximately 1 % deformation at a low operating voltage of about 1 V. The actuation renders them promising artificial muscles. The actuation performance significantly hinges on the structure and size of nanopores and ligaments in NMs. Consequently, designing an optimal configuration is imperative for excellent performance. The actuation mechanism of NMs involves the coupling of multiple fields at various length scales, posing a formidable challenge to conventional simulation and design approaches. To surmount this challenge, we have developed a computational framework capable of conducting concurrent and sequential multiscale calculations. By utilizing artificial neural network (ANN) surrogate models trained on data obtained through the finite element method (FEM), the framework achieves optimized values for both actuation strain and effective Young's modulus within a designated design space. The constitutive model, which establishes the relationship between surface stress and charges in FEM, is derived from the surface eigenstress model and symbolic regression. This involves utilizing data calculated through joint density functional theory. This framework not only ensures the desired properties but also demonstrates its potential for effectively addressing other multiscale optimization problems.

Features and insights for molecular structure of Chinese Taixi anthracite at atomic scales

This work presents insights into the molecular structure of Chinese Taixi anthracite (TXA) at atomic scales. The comprehensive analysis of materials characterizations and data fitting & calculations are performed to reveal microscopic characteristics and structural parameters of TXA. Then the planar and three-dimensional molecular structure models of TXA are con with the help of computer-aided molecular design and multi-scale molecular simulation calculations. The chemical structure characteristics of TXA are systematically analyzed, such as the carbon framework, main functional groups, and typical chemical bonding features. It is found that aromatic carbons are the main skeleton of organic matter, combined with some aliphatic carbons mainly in form of methyl, methylene and methine. Conceptualized single molecular description of TXA is determined to be C763H397O21N8. Representative two-dimensional and three-dimensional molecular structural models are also constructed to describe the apparent molecular structural features of TXA. Finally, molecular structural models are further verified by the elemental composition, nuclear magnetic resonance, Fourier transform infrared, and bond concentration of TXA. In addition, we summarized microstructure features of coal with various metamorphism. This work could provide theoretical guidance for understanding the microstructure of TXA and building the correlation between coal structure and functional properties to achieve efficient utilization of coal resources.

Development and application in multiscale and multiphysics methodologies in Spain: Present and future trends

In the field of reactor physics analysis, the coupling of multiple physics phenomena plays a crucial role in enhancing the accuracy of predictions and understanding complex systems. Multiphysics refers to the study and analysis of physical phenomena that involve multiple interconnected physical processes occurring simultaneously in a nuclear system to ensure essential aspects of reactor design, safety analysis, and optimization, among others. Multiphysics encompasses various domains of physics, such as Thermal-Hydraulics, Neutronics, Structural Mechanics, Radiation Transport, Chemistry, and Materials Science. On the other hand, the Multiscale approach involves combining high-fidelity models with lower-fidelity ones to accurately capture the relevant physical phenomena in a Nuclear Power Plant (NPP). Multiscale involves three main scales: system level, core level, and detailed analysis scale. This paper presents an overview of the main research performed by Spanish groups in the field of multiphysics and multiscale calculations, particularly on thermal–hydraulic analysis. This revision is focused mainly on two key aspects: thermal–hydraulic multiscale coupling and thermal–hydraulic / neutronic coupling. The paper also includes the expected future trends in this field.

Systematic experiments and multiscale simulation calculations reveal chemical stability differences in dry/wet nanofiltration membranes

This study investigated the chemical stability differences between dry and wet nanofiltration membranes when immersed in strong acid and base environments. Systematic experimental studies were conducted on both types of nanofiltration (NF) membranes, supplemented by Molecular Dynamics (MD) simulations and Density Functional Theory (DFT) calculations. The results indicate that wet NF membranes, soaked in deionized water for a week, exhibit higher chemical stability compared to dry membranes treated only with air. Traditional air heating causes membrane pore contraction and excessive crosslinking. However, after a week of immersion in water, the polyamide (PA) layer gradually becomes a loose and well-extendable PA layer. MD simulations revealed that H+ and OH− ions possess lower diffusion coefficients and extended residence times in dry NF membranes, making them more prone to damage. Additionally, DFT calculations disclosed that the Gibbs free energy (ΔG) for amide bond hydrolysis in wet NF membranes, in the presence of water molecules, is elevated, significantly delaying their hydrolysis rate under extreme conditions. This study highlights the pivotal role of membrane wetness in the chemical durability of NF membranes and offers a novel perspective for improving membrane lifespan and efficiency.

Tailoring ammonia capture in MOFs and COFs: A multi-scale and machine learning comprehensive investigation of functional group modification.

Our study aims to examine the impact of ligand functionalization on the ammonia adsorption properties of MOFs and COFs, by combining multi-scale calculations with machine learning techniques. Density Functional Theory calculations were performed to investigate the interactions between ammonia (NH3) and a comprehensive set of 48 strategically chosen functional groups. In all of the cases, it is observed that functionalized rings exhibit a stronger interaction with ammonia molecule compared to unfunctionalized benzene, while -O2Mg demonstrates the highest interaction energy with ammonia (15 times stronger than the bare benzene). The trend obtained from the thorough DFT screening is verified via Grand Canonical Monte-Carlo calculations by employing interatomic potentials derived from quantum chemical calculations. Isosteric heat of adsorption plots provide a comprehensive elucidation of the adsorption process, and important insights can be taken for studies in fine-tuning materials for ammonia adsorption. Furthermore, a proof of concept machine learning (ML) analysis is conducted, which demonstrates that ML can accurately predict NH3 binding energies despite the limited amount of data. The findings derived from our multi-scale methodology indicate that the functionalization strategy can be utilized to guide synthesis towards MOFs, COFs, or other porous materials for enhanced NH3 adsorption capacity.

A Vision for the Future of Multiscale Modeling.

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

Navigating the landscape of enzyme design: from molecular simulations to machine learning.

Global environmental issues and sustainable development call for new technologies for fine chemical synthesis and waste valorization. Biocatalysis has attracted great attention as the alternative to the traditional organic synthesis. However, it is challenging to navigate the vast sequence space to identify those proteins with admirable biocatalytic functions. The recent development of deep-learning based structure prediction methods such as AlphaFold2 reinforced by different computational simulations or multiscale calculations has largely expanded the 3D structure databases and enabled structure-based design. While structure-based approaches shed light on site-specific enzyme engineering, they are not suitable for large-scale screening of potential biocatalysts. Effective utilization of big data using machine learning techniques opens up a new era for accelerated predictions. Here, we review the approaches and applications of structure-based and machine-learning guided enzyme design. We also provide our view on the challenges and perspectives on effectively employing enzyme design approaches integrating traditional molecular simulations and machine learning, and the importance of database construction and algorithm development in attaining predictive ML models to explore the sequence fitness landscape for the design of admirable biocatalysts.

First-principles simulation of excitation energy transfer and transient absorption spectroscopy in the CP29 light-harvesting complex.

The dynamics of delocalized excitons in light-harvesting complexes (LHCs) can be investigated using different experimental techniques, and transient absorption (TA) spectroscopy is one of the most valuable methods for this purpose. A careful interpretation of TA spectra is essential for the clarification of excitation energy transfer (EET) processes occurring during light-harvesting. However, even in the simplest LHCs, a physical model is needed to interpret transient spectra as the number of EET processes occurring at the same time is very large to be disentangled from measurements alone. Physical EET models are commonly built by fittings of the microscopic exciton Hamiltonians and exciton-vibrational parameters, an approach that can lead to biases. Here, we present a first-principles strategy to simulate EET and transient absorption spectra in LHCs, combining molecular dynamics and accurate multiscale quantum chemical calculations to obtain an independent estimate of the excitonic structure of the complex. The microscopic parameters thus obtained are then used in EET simulations to obtain the population dynamics and the related spectroscopic signature. We apply this approach to the CP29 minor antenna complex of plants for which we follow the EET dynamics and transient spectra after excitation in the chlorophyll b region. Our calculations reproduce all the main features observed in the transient absorption spectra and provide independent insight on the excited-state dynamics of CP29. The approach presented here lays the groundwork for the accurate simulation of EET and unbiased interpretation of transient spectra in multichromophoric systems.

Identification of Multiscale Vortex Structures and Transition Fluid Features in CFD and Numerical Astrophysics

The need for effective postprocessor analysis of the results of extensive calculations on supercomputers remains extremely high when using new complex computing systems in modeling super- and hypersonic gas flows, predictive modeling of heat and mass transfer processes in jet engines and new energy devices, in solving multiscale problems for astrophysical simulation. Requirements for improving the quality and versatility of new software and visualization codes are increasing with the transition to exascale computing, which requires the improvement of new service systems, in particular systems for visualizing and analyzing the results of multi-scale calculations with dramatically increased input and output data. This paper considers the experience of using an authorized visualization system in the practice of solving some tasks with vortex flow structures and unpredictable instability.

Preorganized Internal Electric Field Promotes a Double-Displacement Mechanism for the Adenine Excision Reaction by Adenine DNA Glycosylase.

Adenine DNA glycosylase (MutY) is a monofunctional glycosylase, removing adenines (A) misinserted opposite 8-oxo-7,8-dihydroguanine (OG), a common product of oxidative damage to DNA. Through multiscale calculations, we decipher a detailed adenine excision mechanism of MutY that is consistent with all available experimental data, involving an initial protonation step and two nucleophilic displacement steps. During the first displacement step, N-glycosidic bond cleavage is accompanied by the attack of the carboxylate group of residue Asp144 at the anomeric carbon (C1'), forming a covalent glycosyl-enzyme intermediate to stabilize the fleeting oxocarbenium ion. After departure of the excised base, water nucleophiles can be recruited to displace Asp144, completing the catalytic cycle with retention of stereochemistry at the C1' position. The two displacement reactions are found to mostly involve the movement of the oxocarbenium ion, occurring with large charge reorganization and thus sensitive to the internal electric field (IEF) exerted by the polar protein environment. Intriguingly, we find that the negatively charged carboxylate group is a good nucleophile for the oxocarbenium ion, yet an unactivated water molecule is not, and that the electric field catalysis strategy is used by the enzyme to enable its unique double-displacement reaction mechanism. A strong IEF, pointing toward 5' direction of the substrate sugar ring, greatly facilitates the second displacement reaction at the expense of elevating the barrier of the first one, thereby allowing both reactions to occur. These findings not only increase our understanding of the strategies used by DNA glycosylases to repair DNA lesions, but also have important implications for how internal/external electric field can be applied to modulate chemical reactions.

Atomic motion behavior calculation and bonding mechanism analysis of explosive welding of high-strength and high-hardness titanium alloy Ti6Al4V/aluminum alloy 7075

The explosive welding technology of titanium alloy Ti6Al4V/aluminum alloy 7075 is the most valuable research problem in the field of Ti/Al explosive welding. In this paper, the smooth particle hydrodynamics and molecular dynamics algorithms are used to conduct multi-scale numerical calculations on the explosive welding of Ti6Al4V and 7075. The interface morphology, interface atomic movement, lattice changes and crystal defects are comprehensively analyzed. With the calculation as a reference, the Ti6Al4V/7075 composite with a flat interface is prepared. The calculation results indicate that with the transformation of titanium aluminum crystal structure, a large number of various dislocations, mainly 1/6〈110〉dislocations, are generated on the titanium side; During explosive welding, uniform and stable element diffusion occurred. Element diffusion mainly occurred in the unloading stage when the pressure was 0. The melting zone and ablation zone were composed of TiAl and TiAl3, respectively; The fundamental reason for the combination of Ti6Al4V/7075 is the diffusion of elements and the solid-phase binding of atoms.

Origin of Low-Lying Red States in the Lhca4 Light-Harvesting Complex of Photosystem I.

The antenna complexes of Photosystem I present low-lying states visible as red-shifted and broadened absorption and fluorescence bands. Among these, Lhca4 has the most evident features of these "red" states, with a fluorescence band shifted by more than 25 nm from typical LHC emission. This signal arises from a mixing of exciton and charge-transfer (CT) states within the excitonically coupled a603-a609 chlorophyll (Chl) dimer. Here we combine molecular dynamics, multiscale quantum chemical calculations, and spectral simulations to uncover the molecular mechanism for the formation and tuning of exciton-CT interactions in Lhca4. We show that the coupling between exciton and CT states is extremely sensitive to tiny variations in the Chl dimer arrangement, explaining both the red-shifted bands and the switch between conformations with blue and red emission observed in single-molecule spectroscopy. Finally, we show that mutating the axial ligand of a603 diminishes the exciton-CT coupling, removing any red-state fingerprint.

Construction of a new n-body potential and multi-scale investigations of the direct alloying behaviors for immiscible W/Cu system

Achieving direct alloying at the tungsten/copper (W/Cu) interface is crucial for the fabrication of laminar metal matrix composite (LMMC) plasma-facing components (PFCs) of fusion reactors based on immiscible W/Cu systems. Our previous work has accomplished direct alloying between immiscible W and Cu, forming a diffusion layer with a thickness of approximately 22–32 nm at the interface. The performance of the interface directly affects the lifetime and reliability of W/Cu LMMC. Multi-scale calculations are designed since some interface properties cannot be directly measured or observed experimentally in real-time and in situ. Firstly, a new potential is constructed to overcome the limitations that the existing W/Cu potential cannot accurately describe the W/Cu alloying process. Secondly, molecular dynamics (MD) simulations use the new potential to study interfacial properties and calculate the diffusion depth at the W/Cu interface. Lastly, combining MD, FEM, and image visualization techniques, a multi-scale method of the crack propagation rate at the W/Cu interface is used to predict the thermal fatigue life of W/Cu LMMC PFCs prepared by nano-active structure-induced alloying. Our simulation results agree with experimental values and literature results, demonstrating the reliability of the new W/Cu potential and the accuracy of our designed multi-scale method. Directly alloyed W/Cu LMMCs have the potential to be utilized in fusion reactors.

Synthetic first-principles studies from phase equilibria to microstructural formation in the Fe-Pt L10 phase

Electronic-structure calculations, the cluster-variation method of statistical mechanics, and the phase-field method were combined in attempted first-principles calculations of phase equilibria and microstructural evolution associated with the disorder-$\mathrm{L}{1}_{0}$ transition of the Fe-Pt system. The calculated disorder-$\mathrm{L}{1}_{0}$ transition temperature was within $\ensuremath{\sim}10$ K difference from the experimental value, and the locus of spinodal ordering temperature is placed in the phase diagram. The calculated microstructure demonstrates preferential growth of the ordered domain along the 100> direction and, in the later period, an anisotropic morphology of an antiphase domain structure develops. We offered an interpretation from the atomistic point of view for this morphology. We therefore achieved consistent first-principles multiscale calculations of phase equilibria and microstructural evolution, bridging microscopic to mesoscopic scales without any adjusting parameters.