Atomistic Monte Carlo Simulations Research Articles

A novel algorithm to study the impact of the mismatch on analog building blocks: a case study in basic 35 nm CMOS amplifiers

In this paper, the context of modeling of the impact of mismatch and statistical variations on analogue circuit building blocks is emphasized. The aim is to develop a new algorithm which predicts the statistical behavior of important parameters of an amplifier including output resistance, voltage gain and trans-conductance. The relative error of standard deviation of statistical parameters will remain less than 5% compared with the most accurate Monte-Carlo (MC) simulations using atomistic library model-cards. In comparison with other models which are based on the normal distribution of parameters, the proposed model does not need this limiting presumption. On the other hand, the proposed algorithm is more efficient compared with time consuming MC atomistic simulations.

Effect of Surface Modification on Water Adsorption and Interfacial Mechanics of Cellulose Nanocrystals.

With increasing environmental concerns about petrochemical-based materials, the development of high-performance polymer nanocomposites with sustainable filler phases has attracted significant attention. Cellulose nanocrystals (CNCs) are promising nanocomposite reinforcing agents due to their exceptional mechanical properties, low weight, and bioavailability. However, there are still numerous obstacles that prevent these materials from achieving optimal performance, including high water adsorption, poor nanoparticle dispersion, and filler properties that vary in response to moisture. Surface modification is an effective method to mitigate these shortcomings. We use computational approaches to obtain direct insight into the water adsorption and interfacial mechanics of modified CNC surfaces. Atomistic grand-canonical Monte Carlo simulations demonstrate how surface modification of sulfated Na-CNCs impacts water adsorption. We find that methyl(triphenyl)phosphonium (MePh3P+)-exchanged CNCs have lower water uptake than Na-CNCs, supporting experimental dynamic vapor sorption measurements. The adsorbed water molecules show orientational ordering when distributed around the cations. Steered molecular dynamics simulations quantify traction-separation behavior of CNC-CNC interfaces. We find that exchanging sodium for MePh3P+ effectively changes the surface hydrophilicity, which in turn directly impacts interfacial adhesion and traction-separation behavior. Our analysis provides guidelines for controlling moisture effects in cellulose nanocomposites and nanocellulose films through surface modifications.

The effect of different organic solvents on sodium ion storage in carbon nanopores.

In this study fully atomistic grand canonical Monte Carlo (GCMC) simulations have been employed to study the behaviour of an electrolyte salt (NaPF6) and different non-aqueous (organic) solvents in carbon nanopores, to reveal the structure and storage mechanism. Organic solutions of Na+ and PF6- ions at 1 M concentration were considered, based on the conditions in operational sodium ion batteries and supercapacitors. Three organic solvents with different properties were selected: ethylene carbonate (EC), propylene carbonate (PC), and ethyl methyl carbonate (EMC). The effects of solvents, pore size and surface charge were quantified by calculating the radial distribution functions and ionic density profiles. It is shown that the organic solvent properties and nanopore confinement can affect the structure of the organic electrolyte solution. For the pore size range (1-5 nm) investigated in this paper, the surface charge used in this study can alter the sodium ions but not the solvent structure inside the pore.

Shape-dependent surface magnetism of Co-Pt and Fe-Pt nanoparticles from first principles

In this paper, we have performed the first-principles density functional theory calculations to predict the magnetic properties of the CoPt and FePt nanoparticles in cuboctahedral, decahedral, and icosahedral shapes. The modeled alloy nanoparticles have a diameter of 1.1 nm and consist of 31 $5d$ Pt atoms and 24 $3d$ Co (or Fe) atoms. For both CoPt and FePt, we found that the decahedral nanoparticles had appreciably lower surface magnetic moments than the cuboctahedral and icosahedral nanoparticles. Our analysis indicated that this reduction in the surface magnetism was related to a large contraction of atomic spacing and high local Co (or Fe) concentration in the surface of the decahedral nanoparticles. More interestingly, we predicted that the CoPt and FePt cuboctahedral nanoparticles exhibited dramatically different surface spin structures when noncollinear magnetism was taken into account. Our calculation results revealed that surface anisotropy energy decided the fashion of surface spin canting in the CoPt and FePt nanoparticles, confirming previous predictions from atomistic Monte Carlo simulations.

An empirical potential for simulating vacancy clusters in tungsten

We present an empirical interatomic potential for tungsten, particularly well suited for simulations of vacancy-type defects. We compare energies and structures of vacancy clusters generated with the empirical potential with an extensive new database of values computed using density functional theory, and show that the new potential predicts low-energy defect structures and formation energies with high accuracy. A significant difference to other popular embedded-atom empirical potentials for tungsten is the correct prediction of surface energies. Interstitial properties and short-range pairwise behaviour remain similar to the Ackford-Thetford potential on which it is based, making this potential well-suited to simulations of microstructural evolution following irradiation damage cascades. Using atomistic kinetic Monte Carlo simulations, we predict vacancy cluster dissociation in the range 1100–1300 K, the temperature range generally associated with stage IV recovery.

Multiscale modelling of precipitation in concentrated alloys: from atomistic Monte Carlo simulations to cluster dynamics I thermodynamics

In a recent paper, the authors showed how the clusters free energies are constrained by the coagulation probability, and explained various anomalies observed during the precipitation kinetics in concentrated alloys. This coagulation probability appeared to be a too complex function to be accurately predicted knowing only the cluster distribution in Cluster Dynamics (CD). Using atomistic Monte Carlo (MC) simulations, it is shown that during a transformation at constant temperature, after a short transient regime, the transformation occurs at quasi-equilibrium. It is proposed to use MC simulations until the system quasi-equilibrates then to switch to CD which is mean field but not limited by a box size like MC. In this paper, we explain how to take into account the information available before the quasi-equilibrium state to establish guidelines to safely predict the cluster free energies.

Improved atomistic Monte Carlo models based onab-initio-trained neural networks: Application to FeCu and FeCr alloys

We significantly improve the physical models underlying atomistic Monte Carlo (MC) simulations, through the use of ab initio fitted high-dimensional neural network potentials (NNPs). In this way, we can incorporate energetics derived from density functional theory (DFT) in MC, and avoid using empirical potentials that are very challenging to design for complex alloys. We take significant steps forward from a recent work where artificial neural networks (ANNs), exclusively trained on DFT vacancy migration energies, were used to perform kinetic MC simulations of Cu precipitation in Fe. Here, a more extensive transfer of knowledge from DFT to our cohesive model is achieved via the fitting of NNPs, aimed at accurately mimicking the most important aspects of the ab initio predictions. Rigid-lattice potentials are designed to monitor the evolution during the simulation of the system energy, thus taking care of the thermodynamic aspects of the model. In addition, other ANNs are designed to evaluate the activation energies associated with the MC events (migration towards first-nearest-neighbor positions of single point defects), thereby providing an accurate kinetic modeling. Because our methodology inherently requires the calculation of a substantial amount of reference data, we design as well lattice-free potentials, aimed at replacing the very costly DFT method with an approximate, yet accurate and considerably more computationally efficient, potential. The binary FeCu and FeCr alloys are taken as sample applications considering the extensive literature covering these systems.

A new scaling approach for the mesoscale simulation of magnetic domain structures using Monte Carlo simulations

A new scaling approach has been proposed for the spin exchange and the dipole–dipole interaction energy as a function of the system size. The computed scaling laws are used in atomistic Monte Carlo simulations of magnetic moment evolution to predict the transition from single domain to a vortex structure as the system size increases. The width of a 180° – domain wall extracted from the simulated structures is in close agreement with experimentally values for an F–Si alloy. The transition size from a single domain to a vortex structure is also in close agreement with theoretically predicted and experimentally measured values for Fe.

Inhibition of carbonation attack in cement-based matrix due to adding graphene oxide

Transport properties of cementitious materials are very important as they effectively influence the durability of these materials. Carbonation rate depends on the ease of carbon dioxide (CO2) movement from outer to internal surfaces. In this study, graphene oxide (GO) was incorporated in cement matrix to improve resistance of cementitious mix against carbon dioxide attack. The results showed very low carbonation depth of cementitious mix with GO (GM), only 8% of carbonation depth of the control cement mixture without GO (CM) after 6 months’ carbonation period. The most notable finding was the limited carbonation depth of GM despite the increasing of exposure to CO2. As carbonation depth increased for CM with time, full carbonation occurred after 24 months. However, GM showed no progress in carbonation front. This significant result can be attributed to interlocking influence of the CO2 molecules. Moisture loss monitoring confirms that GO sheets can act as reservoirs for water (H2O) molecules which limit transport of CO2 towards calcium phases of cement hydration. Physical interlocking was examined through molecule dynamic modelling, Monte Carlo atomistic simulation was conducted to evaluate the effects of GO sheets on carbon dioxide adsorption by cement matrix. The results showed that GO sheets reduce van der Waals adsorption energy of CO2 molecules. In addition, concentration of CO2 molecules around GO sheets was higher than the other porous areas which indicates the capability of these sheets for adsorbing of the gaseous molecule because of their high surface area.

Probing core and shell contributions to exchange bias inCo/Co3O4nanoparticles of controlled size

Coupling at the interface of core/shell magnetic nanoparticles is known to be responsible for the exchange bias (EB) and the relative sizes of core and shell components are supposed to influence the associated phenomenology. In this work, we have prepared core/shell structured nanoparticles with the total averaged diameter around $\sim$ 27 nm and a wide range of shell thicknesses through the controlled oxidation of Co nanoparticles well dispersed in an amorphous silica host. Structural characterizations give compelling evidence of the formation of Co$_3$O$_4$ crystallite phase at the shells surrounding the Co core. Field cooled hysteresis loops display nonmonotonous dependence of the exchange bias $H_E$ and coercive $H_C$ fields, that become maximum for a sample with an intermediate shell thickness, at which lattice strain is also maximum for both the phases. Results of our atomistic Monte Carlo simulations of the particles with the same size and compositions as in experiments are in agreement with the experimental observations and have allowed us to identify a change in the contribution of the interfacial surface spins to the magnetization reversal giving rise to the maximum in $H_E$ and $H_C$.

Precipitation in a copper matrix modeled byab initiocalculations and atomistic kinetic Monte Carlo simulations

A kinetic Monte Carlo approach is used to study the influence of Cr, Fe, Al, or Mg addition on the precipitation in a Cu–Ni–Si alloy. The simulation method is based on a vacancy diffusion model. The crucial parameters of this method are the pairwise mixing energies of all contained elements which are determined by ab initio calculations. The number of dissolved atoms in equilibrium state is used to estimate the influence of Cr, Fe, Al, or Mg on the electrical conductivity. In order to estimate the influence of the alloying elements on strength ab initio calculations of misfit strain at the Cu/Ni3Si interface are performed. The atomistic kinetic Monte Carlo (AKMC) simulations reveal that Cr, Fe, Al, and Mg atoms are located at different positions: Mg and Al atoms are preferably located at the interface of Ni–Si precipitates and Cu matrix, Cr atoms diffuse into Ni–Si precipitates, and Fe atoms form Fe clusters surrounded by Ni–Si shells. Cr addition leads to a significantly reduced fraction of atoms dissolved in the matrix which indicates an increase of electrical conductivity, whereas Mg addition results in a high misfit strain at the Cu/Ni3Si interface which can contribute to increased strength.

Cell-veto Monte Carlo algorithm for long-range systems.

We present a rigorous efficient event-chain Monte Carlo algorithm for long-range interacting particle systems. Using a cell-veto scheme within the factorized Metropolis algorithm, we compute each single-particle move with a fixed number of operations. For slowly decaying potentials such as Coulomb interactions, screening line charges allow us to take into account periodic boundary conditions. We discuss the performance of the cell-veto Monte Carlo algorithm for general inverse-power-law potentials, and illustrate how it provides a new outlook on one of the prominent bottlenecks in large-scale atomistic Monte Carlo simulations.

An object kinetic Monte Carlo model for the microstructure evolution of neutron‐irradiated reactor pressure vessel steels

This work presents a full object kinetic Monte Carlo framework for the simulation of the microstructure evolution of reactor pressure vessel (RPV) steels. The model pursues a “gray‐alloy” approach, where the effect of solute atoms is seen exclusively as a reduction of the mobility of defect clusters. The same set of parameters yields a satisfactory evolution for two different types of alloys, in very different irradiation conditions: an Fe–C–MnNi model alloy (high flux) and a high‐Mn, high‐Ni RPV steel (low flux). A satisfactory match with the experimental characterizations is obtained only if assuming a substantial immobilization of vacancy clusters due to solute atoms, which is here verified by means of independent atomistic kinetic Monte Carlo simulations. The microstructure evolution of the two alloys is strongly affected by the dose rate; a predominance of single defects and small defect clusters is observed at low dose rates, whereas larger defect clusters appear at high dose rates. In both cases, the predicted density of interstitial loops matches the experimental solute‐cluster density, suggesting that the MnNi‐rich nanofeatures might form as a consequence of solute enrichment on immobilized small interstitial loops, which are invisible to the electron microscope.

Size and thickness effect on magnetic structures of maghemite hollow magnetic nanoparticles

The effect of surface anisotropy on the magnetic ground state of hollow maghemite nanoparticles is investigated using atomistic Monte Carlo simulation. The computer modeling is carried on hollow nanostructures as a function of size and shell thickness. It is found that the large contribution of the surface anisotropy imposes a “throttled” spin structure where the moments located at the outer surface tend to orient normal to the surface while those located at the inner surface appear to be more aligned. For increasing values of surface anisotropy in the frame of a radial model, the magnetic moments become radially oriented either inward or outward giving rise to a “hedgehog” configuration with nearly zero net magnetization. We also show the effect of the size of hollow nanoparticle on the spin behavior where the spin non-collinearity increases (for fixed value of surface anisotropy) as the diameter of the hollow nanoparticle increases due to the significant increase in surface-to-volume ratio, the thickness being constant. Moreover, the thickness of the hollow nanoparticle shell influences the spin configuration and thus the relation between surface anisotropy and the size or the thickness of the hollow nanoparticle is established.

Te homogeneous precipitation in Ge dislocation loop vicinity

High resolution microscopies were used to study the interactions of Te atoms with Ge dislocation loops, after a standard n-type doping process in Ge. Te atoms neither segregate nor precipitate on dislocation loops, but form Te-Ge clusters at the same depth as dislocation loops, in contradiction with usual dopant behavior and thermodynamic expectations. Atomistic kinetic Monte Carlo simulations show that Te atoms are repulsed from dislocation loops due to elastic interactions, promoting homogeneous Te-Ge nucleation between dislocation loops. This phenomenon is enhanced by coulombic interactions between activated Te2+ or Te1+ ions.

Atomic-based phase-field method for the modeling of radiation induced segregation in Fe–Cr

We present a quantitative phase-field modeling of radiation-induced segregation in Fe–Cr alloys. The evolution of chemical and point defect concentration fields are described by an Onsager formalism combined to a Cahn–Hilliard like diffusion equation for the introduction of non-uniform driving forces. Both the Onsager transport coefficients and the driving force parameters are extracted from atomic Monte Carlo simulations with point defect diffusion models fitted on DFT calculations, in a composition range between 0 and 20at.% Cr and in a temperature range between 600 and 1000K. Phase-field simulations are able to quantitatively reproduce the evolution of segregation profiles obtained from direct atomistic kinetic Monte Carlo simulations, while being typically two orders of magnitude faster. It is shown that a precise parameterization of the concentration-dependent Onsager transport coefficients, thermodynamic factors, and equilibrium point defect concentrations is crucial for the phase-field method to be quantitative.

Modeling and Optimization of Bilayered TaOxRRAM Based on Defect Evolution and Phase Transition Effects

A comprehensive physical model on the resistive switching (RS) behaviors of bilayered TaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> -based RS access memory [resistive random access memory (RRAM)] is presented. In the model, the effects of the generation and recombination (G-R) of oxygen vacancies ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{{\rm{O}}}$ </tex-math></inline-formula> ), phase transition (P-T) between Ta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> and TaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and the interaction (I-A) between Ta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> and TaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> layers are involved to explain the RS behaviors based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ab initio</i> calculations. An atomistic Monte Carlo simulation method based on the model is developed to investigate the dynamic physical processes and reproduce the experimental phenomena. The impacts of G-R and P-T as well as the I-A effects on the RS behaviors of a bilayered Ta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> /TaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> structure and the device performances are identified. This paper indicates that the G-R effect dominates the RS behaviors, and self-compliance is due to the I-A effect. Based on the simulations, the optimization guidance of a bilayered TaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> -based RRAM is presented.

Composition and stress of SiGe nanostructures on curved substrates

Recent experimental studies of Ge nanoislands on silicon-on-insulator (SOI) substrates have provided a defect-free strain relaxation mechanism through the bending of the substrate. Here, using atomistic Monte Carlo simulations and analytical modeling, we couple this relaxation mechanism with interdiffusion and alloying and observe composition profiles that are completely different from those observed in flat nanoislands. Moreover, for comparable SOI and island thicknesses, intermixing can be greatly reduced and Ge content in the islands is highly preserved.

Dislocation core structures in (0001) InGaN

Threading dislocation core structures in c-plane GaN and InxGa1−xN (0.057 ≤ x ≤ 0.20) films were investigated by aberration-corrected scanning transmission electron microscopy. a-type dislocations are unaffected by alloying with indium and have a 5/7-atom ring core structure in both GaN and InxGa1−xN. In contrast, the dissociation lengths of (a + c)-type dislocations are reduced, and new 7/4/9-atom ring and 7/4/8/5-atom ring core structures were observed for the dissociated (a + c)-type dislocations in InxGa1−xN, which is associated with the segregation of indium near (a + c)-type and c-type dislocation cores in InxGa1−xN, consistent with predictions from atomistic Monte Carlo simulations.

Radiation-accelerated precipitation in Fe–Cr alloys

The kinetics of phase separation in Fe–Cr alloys under irradiation is modeled by Atomistic kinetic Monte Carlo simulations that include the formation, migration and elimination of vacancies and self-interstitials at point defects sinks. The evolution of the sink density is modeled by cluster dynamics, and taken into account in the Monte Carlo simulations by a rescaling of the time. The results are in good agreement with available experimental observations of neutron irradiation at 290 °C. The irradiation is found to accelerate the kinetics of phase separation by orders of magnitude, with an acceleration factor given by the increase in point defect concentrations. The microstructure evolution is qualitatively the same as during isothermal annealing, except in the vicinity of point defect sinks. The effects of equilibrium and radiation induced segregations at grain boundaries are considered. The ballistic mixing occurring in displacement cascades is modeled, and is found to be insufficient to produce the dissolution of chromium rich precipitates at 290 °C, even at high dose rates. Therefore, it cannot explain the absence of precipitation observed during ion irradiations.