Hybrid Monte Carlo Simulations Research Articles

DNA-damage RBE assessment for combined boron and gadolinium neutron capture therapy.

Neutron capture therapy (NCT) by 10B and 157Gd agents is a unique irradiation-based method which can be used to treat brain tumors. Current study aims to quantitatively evaluate the relative biological effectiveness (RBE) and dose distributions during the combined BNCT and GdNCT modalities through a hybrid Monte Carlo (MC) simulation approach. Snyder head phantom as well as a cubic hypothetical tumor was at first modeled by Geant4 MC Code. Then, the energy spectra and dose distribution relevant to the released secondary particles during the combined Gd/BNCT were scored for different concentrations of 157Gd and 10B inside tumor volume. Finally, the scored energy spectra were imported to the MCDS code to estimate both RBESSB and RBEDSB values for different 157Gd concentrations. The results showed that combined Gd/BNCT increases the fluence-averaged RBESSB values by about 1.7 times when 157Gd concentration increments from 0 to 2000µg/g for both considered cell oxygen levels (pO2=10% and 100%). Besides, a reduction of about 26% was found for fluence-averaged RBEDSB values with an increment of 157Gd concentration in tumor volume. From the results, it can be concluded that combined Gd/BNCT technique can improve tumor coverage with higher dose levels but in the expense of RBEDSB reduction which can affect the clinical efficacy of the NCT technique.

Chemical short-range order enhances fracture toughness of medium entropy alloy CoCrNi

Using hybrid molecular dynamics and Monte Carlo simulations, we examine the role of lattice distortion (LD) and chemical short-range ordering (CSRO) on the development of defects ahead of a mode I crack in medium entropy alloy CoCrNi. We show that CSRO noticeably increases fracture toughness. The result can be explained by the effect of CSRO on lowering LD and increasing intrinsic stacking fault energy and the direct impact CSRO has on the energetic barriers for emitting partial dislocations and forming nanotwins from CoCr clusters on the crack tip. CSRO allows the nanotwin domains to further support inelastic deformation, such as dislocation glide and amorphization, leading to stable crack-tip plasticity and postponement of softening. These findings imply that the superior fracture toughness in CoCrNi can be attributed to the non-negligible CSRO that naturally exists.

A meta-heuristic approach for reliability-based design optimization of shell-and-tube heat exchangers

This study introduces a new framework for optimizing Shell-and-Tube Heat Exchanger (STHE) layouts using a reliability-based design optimization (RBDO) approach. The framework combines a control variate-based surrogate model and a hybrid metaheuristic algorithm. The proposed hybrid algorithm, k-means clustering and whale optimization algorithm (kWOA), was evaluated using CEC’2020 and a case study for optimizing STHE design under static conditions. kWOA showed superior performance in minimizing STHE's total annual cost and solving benchmark functions effectively. In our case study, the RBDO framework optimized the STHE design under two scenarios with target failure probabilities of 1% and 5%, resulting in cost increases of 112% and 82%, respectively, compared to deterministic optimization (DO). The integration of the RBDO approach with the STHE mathematical model, considering factors like inlet flow temperatures, mass flow rates, and fouling resistance, demonstrated the framework's ability to balance the trade-off between cost and reliability under uncertainty. Hybrid control variate radial basis function (RBF) models and Monte Carlo Simulation (MCS) were used to assess safety levels, showing the RBDO framework's superiority in improving safety and significantly reducing failure probability from 89% to 1% and 5%. The RBDO framework offers a robust approach for designing STHEs that achieve optimal performance while ensuring high reliability under uncertain conditions.

Simulation, Structural, Thermal and Mechanical Properties of the FeTiTaVW High Entropy Alloy

Developing new materials to be applied in extreme environments is an opportunity and a challenge for the future. High entropy alloys are new materials that seem promising approaches to work in nuclear fusion reactors. In this work, FeTaTiVW high entropy alloys were developed and characterized with Molecular Dynamic and Hybrid Molecular Dynamic Monte Carlo simulations. The simulation results show that phase separation originates a lower potential energy per atom and a high level of segregation compared to those of a uniform solid solution. Moreover, the experimental diffractogram of the milled powder shows the formation of a body-centred cubic-type structure and the presence of TiO2. In addition, the microstructure of the consolidated material evidenced three phases: W-rich, Ti-rich, and a phase with all the elements. This phase separation observed in the microstructure agrees with the Hybrid Molecular Dynamic Monte Carlo simulation. Moreover, the consolidated material’s thermal conductivity and specific heat are almost constant from 25 °C to 1000 °C, and linear expansion increases with increasing temperature. On the other hand, specific heat and thermal expansion values are in between CuCrZr and W values (materials chosen for the reactor walls). The FeTaTiVW high entropy alloy evidences a ductile behaviour at 1000 °C. Therefore, the promising thermal properties of this system can be attributed to the multiple phases and systems with different compositions of the same elements, which is exciting for future developments.

A Hybrid Monte Carlo study of argon solidification

Abstract A GPU-based implementation of the Hybrid Monte Carlo (HMC) algorithm is presented to explore its utility in the chemistry of solidification at the example of liquid to solid argon. We validate our implementation by comparing structural characteristics of argon fluid-like phases from HMC and MD simulations. Examining solidification, both MD and HMC show similar trends. Despite observable differences, MD simulations and HMC agree within the errors during the phase transition. Introducing voids decreases the solidification temperature, aiding in the formation of a well-structured solids. Further, our findings highlight the importance of larger system sizes in simulating solidification processes. Simulations with a temperature dependent potential show ambiguous results for the solidification which may be attributed to the small system sizes. Future work aims to expand HMC capabilities for complex chemical phenomena in phase transitions.

Localization of overdamped bosonic modes and transport in strange metals

The strange metal phase of correlated electrons materials was described in a recent theory by a model of a Fermi surface coupled a two-dimensional quantum critical bosonic field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained for a wide range of intermediate temperatures, including the linear in temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at lower temperatures. For an [Formula: see text]-component boson with [Formula: see text], we use multiple graphics processing units (GPUs) to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to the emergence of the physics of the random transverse-field Ising model at low temperatures, as has been proposed by Hoyos, Kotabage, and Vojta. This regime is controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a "quantum critical phase" away from the quantum critical point, as observed in several cuprates. For the [Formula: see text] Ising scalar, the mean-field treatment is not applicable, and so we use Hybrid Monte Carlo simulations running on multiple GPUs; we find a rounded transition and localization physics, with strange metal behavior in an extended region around the transition.

Effect of Cr and Ni on mechanical response and microstructural evolution of nanocrystalline ferrite: A molecular dynamics study

Microalloying plays a critical role in improving the mechanical properties of steel. To offer a better theoretical guide for experimental research at the atomic level, this paper investigated the synergistic mechanism of adding trace amounts of alloy Cr and Ni and the microstructure evolution of nanocrystalline ferrite during the mechanical response process. First-principles calculations were implemented to investigate electronic properties. Hybrid molecular dynamics and Monte Carlo simulations were employed to explore the deformation mechanism under uniaxial tension and scratching. Specifically, comprehensive differences between doped and pure nanocrystalline ferrites were explored regarding local stress-strain state, dislocation evolution, twin expansion, and grain boundary activity. The results show that Cr- and Ni-doped nanocrystalline ferrite has higher strength and better wear resistance. The potential mechanism is that the addition of Cr and Ni enhances the atomic bonding strength with Fe atoms, hinders the movement of dislocations caused by lattice distortion, and suppresses grain boundary slip and migration, thereby improving the resistance to plastic deformation and grain boundary stability. Theoretical calculations based on microstructure indicate that compared to solid solution strengthening, Ni-induced grain boundary strengthening plays a dominant role in improving yield strength. Under large deformation, the trend of mechanical response is reversed. The suppression of dislocation motion by Cr reduces the dislocation density and dislocation entanglement, resulting in flow stress and local scratch force being smaller than that of pure samples. However, the formation of more nanoscale twins and twin-dislocation interactions enhances strain-hardening ability during tensile. Finer nanostructured subgrains are formed under scratching. These results provide valuable insights into the understanding of the strengthening mechanism and plastic deformation mechanism of Cr-Ni system low alloy steel under dynamic loading.

Forecasting monthly rainfall using hybrid time-series models and Monte Carlo simulation amidst security challenges: a case study of five districts from northern Nigeria

AbstractNigeria’s agricultural sector relies heavily on rainfall, but insecurity in various regions poses significant challenges. This study aims to address this issue by identifying secure, rain-rich areas in northern Nigeria to support sustainable agriculture. Two models, one integrating classical statistical methods (polynomial and Fourier series fittings) and another using a hybrid approach (artificial neural networks, polynomial, and Fourier series fittings), were employed to analyze historical rainfall data from 1981 to 2021 in the selected districts (Kano, Zaria, Bida, Nguru, and Yelwa) known for their rainfall levels and security stability. The study demonstrates that the machine learning-classical hybrid model outperforms existing models, including the classical-classical hybrid and benchmark models like Iwok’s (2016) model, Fourier series, and SARIMA models. Multi-step ahead forecasting with this hybrid model reveals potential changes in rainfall patterns. Notably, Kano, Zaria, Bida, and Yelwa are expected to experience increased rainfall from 2022 to 2026, while Nguru may initially witness decreased rainfall, with improvement in the final year (2026). In conclusion, this study introduces an effective approach for rainfall modeling and forecasting, facilitating the identification of secure agricultural regions in northern Nigeria. These findings carry implications for crop production and agricultural development, contributing to climate resilience efforts and assisting stakeholders in strategic decision-making for regional agricultural investments.

Hybrid Monte Carlo simulation with Fourier acceleration of the N = 2 principal chiral model in two dimensions

Motivated by the similarity to QCD, specifically the property of asymptotic freedom, we simulate the dynamics of the SU(2) × SU(2) model in two dimensions using the Hybrid Monte Carlo algorithm. By introducing Fourier Acceleration, we show that critical slowing down is largely avoided and increases the simulation efficiency by up to a factor of 300. This yields numerical predictions at a precision exceeding that of existing studies and allows us to verify the onset of asymptotic scaling.

Impact of gadolinium concentration and cell oxygen levels on radiobiological characteristics of gadolinium neutron capture therapy technique in brain tumor treatment.

Neutron capture therapy (NCT) with various concentrations of gadolinium (157Gd) is one of the treatment modalities for glioblastoma (GBM) tumors. Current study aims to evaluate how variations of 157Gd concentration and cell oxygen levels can affect the relative biological effectiveness (RBE) of gadolinium neutron capture therapy (GdNCT) technique through a hybrid Monte Carlo (MC) simulation approach. At first, Snyder phantom including a spherical tumor was simulated by Geant4 MC code and relevant energy electron spectra to different 157Gd concentrations including 100, 250, 500, and 1000 ppm were calculated following the neutron irradiation of simulated phantom. Scored energy electron spectra were then imported to Monte Carlo damage simulation (MCDS) code to estimate RBE values (both RBESSB and RBEDSB) at different gadolinium concentrations and oxygen levels from 10 to 100%. The results indicate that variations of 157Gd can affect the energy spectrum of released secondary electrons including Auger electrons. Variation of gadolinium concentration from 100 to 1000 ppm in tumor region can change RBESSB and RBEDSB values by about 0.1% and 0.5%, respectively. Besides, maximum variations of 4.3% and 2% were calculated for RBEDSB and RBESSB when cell oxygen level changed from 10 to 100%. From the results, variations of considered gadolinium and oxygen concentrations during GdNCT can influence RBE values. Nevertheless, due to the not remarkable changes in the intensity of Auger electrons, a slight difference in RBE values would be expected at various 157Gd concentrations, although considerable RBE changes were calculated relevant to the oxygen alternations inside tumor tissue.

Mechanism of elemental segregation around extended defects in high-entropy alloys and its effect on mechanical properties

Elemental segregation around extended defects is common in high-entropy alloys (HEAs) composed of multi-principal elements, which profoundly impacts their mechanical properties. In HEAs, the driving force for segregation usually competes with chemical short-range ordering (CSRO) formation, making it challenging to elucidate the segregation mechanisms. In this study, we systematically investigate the chemical composition changes around extended defects, including dislocations, stacking faults, and grain boundaries (GBs) in CoNiCrFe HEAs, to explore the chemical-structure-mechanical relationship utilizing hybrid Monte Carlo and molecular dynamic (MC/MD) simulations and theoretical analysis. We find a pronounced Cr enrichment and Co/Ni/Fe depletion around all defects considered in this work. A correlation between the degree of structural disorder and the chemical segregation/depletion phenomenon in the proximity of extended defects has been uncovered. Our results show that due to the extreme chemical complexity in HEAs, CSRO inevitably contributes to the elemental rearrangement and affects segregation. Consequently, the segregation behavior in HEAs is mainly controlled by interactions between different atomic pairs, and the segregation entropy also plays a dominant role. By decoupling the strengthening contribution from elemental segregation and CSRO, we demonstrate and highlight that the strengthening in HEAs can be modulated by elemental segregation. The positive impact of element segregation on interfacial properties - improved ultimate tensile strength and elongation, has been evidenced through experimental comparisons of CoNiCrFe with different Fe additions. This work elucidates the mechanism of heterogenous elemental distributions in HEAs where elemental segregation and CSRO coexist, paving the way for manipulating their mechanical properties by modulating the compositional variations.

A comparative study on the oxidation behavior and failure mechanisms of conventional NiCoCrAl alloy and in-situ composite AlCoCrFeNi2.1 eutectic high-entropy alloy at 1300 °C

We present a comparative study on oxidation behavior and failure mechanisms of conventional NiCoCrAl alloys doped with Y and Hf (CNA) and in-situ composite AlCoCrFeNi2.1 eutectic high-entropy alloy doped with Y and Hf (ISC-EHEA) at 1300 °C. We demonstrate that the ISC-EHEA has much stronger resistance to surface rumpling and oxide spallation than CNA. Hybrid molecular dynamics (MD) and Monte Carlo (MC) simulations show that the diffusion coefficients of the metal elements in the Al-depletion layer of the ISC-EHEA are 50 % lower than those in the CNA. The low diffusion coefficients lead to low growth stress in the thermally grown Al2O3 scale on the ISC-EHEA and improve the creep resistance of the metal in contact with the scale, thus preventing the occurrence of rumpling. The oxidation rate constant of the ISC-EHEA is ∼32 % lower in comparison to those of the CNA, which is attributed to the coarser columnar Al2O3 grains that effectively mitigate grain boundary diffusion. The rumpling-free metal/oxide interface, the low residual stress and the low oxide growth rate for the ISC-EHEA result in strong resistance to scale spallation. Owing to the strong scale/alloy bonding at the interface and the build-up of strain energy during prolonged oxidation, damage in the Al2O3 scale on the ISC-EHEA is initiated as surface cracks rather than interface decohesion. When re-oxidized at 1300 °C, the ingress of oxygen along the surface cracks results in fast growth of new oxides at the metal/oxide interface, which causes local stress concentration, interface crack propagation and scale spallation.

Possibilistic–Probabilistic Risk-Based Smart Energy Hub scheduling considering cyber security in advanced metering infrastructures

Future energy systems will be more efficient because of the energy transition of which, decarbonization, decentralization, and digitalization are important aspects. In addition, cyber security becomes more important in the digitalized energy system as cyber-attacks increase. Since the Smart Energy Hub (SEH) is well known as an efficient type of smart digitalized energy system, cyber security is of great importance in SEH operation. In this paper, a novel possibilistic–probabilistic​ SEH model is proposed to evaluate the effect of cyber-attacks on the demand side of the energy system. The presented model is called Possibilistic–Probabilistic Risk-based Smart Energy Hub scheduling model considering Cyber Security in the Advanced Metering Infrastructure (PPRSEHAMICS). It contains different uncertainties regarding renewable generations, demand response programs, gas fuel, wind turbines, and energy prices. The uncertainty of demand response programs is represented using the Z-number as a possibilistic–probabilistic method. Other uncertainties are represented using a scenario-based hybrid approach and Monte Carlo Simulation. Also, the downside risk constraint (DRC) approach is used to model the behavior of the SEH operator in the presence of uncertainties, so the operation and risk costs are simultaneously optimized. Furthermore, a novel Monte Carlo-based FDI detection/correction method is proposed in order to determine and mitigate the effects of cyber-attacks. The proposed model is formulated as a Mixed-Integer Linear Programming (MILP) problem and the GAMS environment is used to solve it. In this paper, different scenarios are considered to evaluate the effects of demand response (DR) programs, SEH operator behavior, false data injection, and correction on the operation cost and risk-in-cost of smart energy hub systems. In the first stage, the obtained results demonstrate that using DR accompanied by DRC yields the optimum operation strategy where the operation cost and risk are maintained at an acceptable point. Further, simulation results suggest that FDI attacks can deviate the operation cost and risk by a substantial amount, and the proposed Monte Carlo-based detection/correction method mitigates almost 79 percent of the false data while keeping the convergence speed in an acceptable range. Moreover, modeling the participation rate of the demand response program by the Z- number approach increases the validity of the results and the applicability of the proposed model.

A hybrid Monte Carlo simulation risk model for oil exploration projects

A new 3-D Hybrid Monte Carlo Simulation (MCS) Risk Model is proposed in this study. The wind, wave, current, climate change, and tsunami sub-models of the Three-Dimensional Hydrodynamic Transport and Water Quality Model HYDROTAM-3D are interrelated with MCS, to obtain probability distributions for the simulation of environmental conditions. This is the only model that can incorporate the tsunami, storm, and sea level rise risks in oil exploration projects. The spill risk index (SRI) of 50 blue barrels spilled due to a blowout from the rig/port during fuel supply was circa 1 ton/ship as Tier I with an average annual occurrence probability of 1.0 × 10−6. The discharge of 4000 bbls for 6 h was modeled, resulting in the SRI of 546 metric tons from the riser blowout with SRI = 0.2 per meter, indicating a Tier II risk. The mean arrival time of this spill was found by MCS as 145 min.

Comparing the DNA-damage RBE of intraoperative and conventional electron beams using a hybrid simulation approach

Purpose Employing electron beam for radiotherapy purposes now has been established as one of the standard cancer treatment modalities. Both dedicated intraoperative and conventional electron beams can be employed in patient irradiation. Due to the differences between accelerating structure and electron beam delivery of dedicated intraoperative radiotherapy (IORT) machines and conventional ones, the initial energy spectra of the produced electron beam by these machines may be different. Accordingly, this study aims to evaluate whether these spectral differences can affect the relevant relative biological effectiveness (RBE) values of intraoperative and conventional electron beams. Materials and methods A hybrid Monte Carlo simulation approach was considered. At first, the head LIAC12 machine (as an IORT accelerator) and Varian 2100C/D (as a conventional accelerator) were simulated by MCNPX code and electron energy spectra at different depths and off-axis distances were scored for two nominal electron energies of 6 and 12 MeV at the field sizes of 6 and 10 cm. Then, the calculated spectra were imported to MCDS code to estimate the induced DNA-damage RBE values. Finally, the obtained RBE values for intraoperative and conventional electron beams were compared together. Results The results showed that the RBE values of the intraoperative electron beam are superior to those obtained for conventional electron beam at the same energy/field size combination. Variations of the depth can regularly affect the RBE value for both conventional and intraoperative electron beams, while no ordered variation trend was observed for RBE with changing the off-axis distance. Variations of electron energy and field size can also influence the RBE value for both types of studied electron beams. Conclusions From the results, it can be concluded the structural differences between the dedicated IORT and conventional Linacs can lead to distinct initial electron energy spectra for intraoperative and conventional electron beams. These physical differences can finally lead to different RBE values for intraoperative and conventional electron beams at the same energy and field size.

Hybrid molecular dynamic Monte Carlo simulation and experimental production of a multi-component Cu–Fe–Ni–Mo–W alloy

High-entropy alloys are a class of materials intensely studied in the last years due to their innovative properties. Their unconventional compositions and chemical structures hold promise for achieving unprecedented combinations of mechanical properties. The Cu–Fe–Ni–Mo–W multicomponent alloy was studied using a combination of simulation and experimental production to test the possibility of formation of a simple solid solution. Therefore, Molecular Dynamics and hybrid Molecular Dynamic/Monte Carlo simulations from 10K up to the melting point of the alloy were analyzed together with the experimental production by arc furnace and powder milling. The Molecular Dynamics simulations starting with a bcc type-structure show the formation of a single-phase bcc solid solution type-structure, whereas using Monte Carlo one, generally produced a two-phase mixture. Moreover, the lowest potential energy was obtained when starting from a fcc type-structure and using Monte Carlo simulation giving rise to the formation of a bcc Fe–Mo–W phase and a Cu–Ni fcc type-structure. Dendritic and interdendritic phases were observed in the sample produced by arc furnace while the milled powder evidence an separation of two phases Cu–Fe–Ni phase and W–Mo type-structures. Samples produced by both methods show the formation of bcc and a fcc type-structures. Therefore, the Monte Carlo simulation seems to be closer with the experimental results, which points to a two-phase mixture formation for the Cu–Fe–Ni–Mo–W multicomponent system.

Charge order in the kagome lattice Holstein model: a hybrid Monte Carlo study

The Holstein model is a paradigmatic description of the electron-phonon interaction, in which electrons couple to local dispersionless phonon modes, independent of momentum. The model has been shown to host a variety of ordered ground states such as charge density wave (CDW) order and superconductivity on several geometries, including the square, honeycomb, and Lieb lattices. In this work, we study CDW formation in the Holstein model on the kagome lattice, using a recently developed hybrid Monte Carlo simulation method. We present evidence for sqrt{3}times sqrt{3} CDW order at an average electron filling of 〈n〉 = 2/3 per site, with an ordering wavevector at the K-points of the Brillouin zone. We estimate a phase transition occurring at Tc ≈ t/18, where t is the nearest-neighbor hopping parameter. Our simulations find no signature of CDW order at other electron fillings or ordering momenta for temperatures T ≥ t/20.

Propagation of a vector wavelet through von Kármán-type random elastic media: Monte Carlo simulation by using the spectrum division method

SUMMARY For the study of the random velocity fluctuation of the solid Earth medium, it is useful to measure the collapse of a seismic wavelet with increasing travel distance and the excitation of coda waves. Radiative transfer theory (RTT) is a powerful tool for synthesizing the propagation of a seismic wavelet in random media statistically characterized by the power spectral density function (PSDF) of the fractional velocity fluctuation. The Born scattering coefficient is a key building block of RTT. As the centre wavenumber of a wavelet increases, the phase shift across the correlation length increases and the Born approximation leads to an extremely large forward scattering exceeding the applicable range of the perturbation method. In such a case, the Eikonal approximation is able to explain the envelope broadening with increasing travel distance; however, it can not explain the coda excitation. To overcome the difficulty, we have proposed a hybrid Monte Carlo (MC) simulation for scalar waves. In the case of von Kármán-type random media, when the centre wavenumber is higher than the corner wavenumber, taking the centre wavenumber as a reference, we divide the PSDF into two spectral components. Applying the Born and Eikonal approximations to the high- and low-wavenumber spectral components, we statistically evaluate the wide-angle scattering and the narrow-angle ray bending, respectively. The proposed MC simulation serially using two kinds of scattering processes successfully synthesizes the time trace of the wave energy density from the onset to the late coda. The travel-distance fluctuation derived from the one-way propagation of the Eikonal approximation is also important. This paper extends this method for the propagation of a vector wavelet in random elastic media. We suppose that random fractional fluctuations of the P- and S-wave velocities and the mass density are linearly proportional to each other, which maintains the linear polarization of an Swave throughout the scattering process. Using the hybrid MC simulation with the spectrum division, we synthesize three-component energy density time traces for the anisotropic radiation from a moment tensor source, from which we derive three-component root mean square (RMS) velocity amplitude time traces at different azimuths. In parallel, we synthesize the propagation of a vector wavelet in many realized random elastic media by the finite-difference simulation, then we calculate three-component RMS velocity amplitude time traces. Using them as a benchmark, we confirm the validity of the proposed MC simulation for specific cases.

Robustness of the Skyrmion Phase in a Frustrated Heisenberg Antiferromagnetic Layer against Lattice Imperfections and Nanometric Domain Sizes

By employing GPU-implemented hybrid Monte Carlo simulations, we study the robustness of the skyrmion lattice phase (SkX) in a frustrated Heisenberg antiferromagnetic (AFM) layer on a triangular lattice with a Dzyaloshinskii–Moriya interaction in the external magnetic field against the presence of lattice imperfections (nonmagnetic impurities) and lattice finiteness. Both features are typical of experimentally accessible magnetic materials and require theoretical investigation. In the pure model of infinite size, SkX is known to be stabilized in a quite wide temperature-field window. We first study the effects of such imperfections on the SkX stability and compare them with those in the nonfrustrated ferromagnetic counterpart. The partial results of this part appeared in the conference proceedings [M. Mohylnaand M. Žukovič, Proceedings of the 36th International ECMS International Conference on Modelling and Simulation, ECMS, 2022]. We further look into whether SkX can also persist in finite clusters, i.e., zero-dimensional systems of nanometric sizes. In general, both the presence of magnetic vacancies as well as the finiteness of the system tend to destabilize any ordering. We show that in the present model, SkX can survive, albeit in a somewhat distorted form, in the impure infinite system up to a fairly large concentration of impurities, and, in the pure finite systems, down to sizes comprising merely tens of particles. Distortion of the SkX phase due to the formation of bimerons, reported in the ferromagnetic model, was not observed in the present frustrated AFM case.

Enhanced nanocrystalline stability of BCC iron via copper segregation

Nanocrystalline alloys are known for their high density of grain boundaries (GBs), which results in low thermal stability and a tendency for coarsening. In this work, we investigated Fe–Cu alloys to explore the effects of Cu concentration on the thermal stability of nanocrystalline samples. Using hybrid molecular dynamics (MD) and Monte Carlo (MC) simulations, annealing treatments of nanocrystalline samples with varied Cu concentrations were conducted. The simulation results revealed that Cu atoms tended to accumulate at GBs. Subsequently, the model with Cu segregation was subjected to mechanical creep loading at various temperatures. Through the analysis of atomic structure evolution during creep deformation, it was found that Cu segregation efficiently stabilizes GBs and restricts their movement. The present findings highlight that the thermal stability of nanocrystalline Fe–Cu alloys can be effectively improved by introducing suitable Cu segregation at GBs.