Monte Carlo simulations of copper clustering in Fe–Cu alloys under irradiation

We present the computational approach for studying the microstructures of Cu clusters in Fe–Cu alloys by combining the molecular dynamics (MD) simulation and Monte Carlo methods. The MD simulation is used to characterize the primary damage resulting from the displacement cascade in Fe. Then, using the Metropolis Monte Carlo methods, the microstructure of the Cu clusters is predicted under the assumption that the system will evolve towards the equilibrium state. The formation of the Cu clusters is apparent for Fe–Cu alloys of a higher Cu content (1.0 w/o), whereas the degree of Cu clustering is not significant for the lower Cu content (0.1 w/o) alloys. The atomic configuration of the Cu–vacancy complex under irradiation, produced by this simulation, is in a fair agreement with the experiments. The simulation is expected to provide important information on the Cu-cluster morphology, which is useful for experimental data analysis.     

Decomposition kinetics in Fe–Cu dilute alloys. Monte Carlo simulation using concentration-dependent interactions

A generalization of the statistical (Monte Carlo) simulation technique for determining the structure of alloys is proposed. It takes into account the dependence of effective interactions between the atoms of a dissolved chemical element on their local concentration. Using the ab initio parametrization of the model, the decomposition of the bcc Fe–Cu alloy accompanied by the formation of Cu nanoprecipitates is studied. It is shown that the concentration dependence of effective interactions significantly affects the decomposition kinetics by displacing its onset to longer times in agreement with the experiment.     

Comparing kinetic Monte Carlo simulations with cluster dynamics: What can we learn about precipitation? Application to AlZr alloys

Kinetic Monte Carlo simulations of precipitation in AlZr alloys are compared with predictions of cluster dynamics based on an enhanced thermodynamic model. A methodology and various tools are proposed to learn as much as possible from such comparisons. Important deviations between the two methods are investigated and interpreted through the role of different mechanisms.     

Monte Carlo simulations of dynamic phase transitions in ultrathin Blume–Capel films

Dynamic phase transition phenomena in ultrathin films described by the Blume–Capel model have been investigated using Monte Carlo simulations. Hysteresis loops, micromagnetic structures, and hysteresis loop area curves, as well as dynamic correlation between the magnetization and the external field have been studied as functions of the field, as well as the film parameters. The variation of critical coupling of the modified film surface at which the transition temperature becomes independent of film thickness has been clarified for varying system parameters. Frequency dispersion of hysteresis loop area has been found to obey a power law for low and moderate frequencies for both ordinary and enhanced surfaces.     

Precipitation in α -Fe based Fe-Cu-Ni-Mn-alloys: behaviour of Ni and Mn modelled by ab initio and kinetic Monte Carlo simulations

A kinetic Monte Carlo approach is used to study the behaviour of Ni and Mn solutes in $\alpha$ -Fe containing Cu, Ni and Mn foreign atoms. The simulation method is based on a vacancy diffusion model. Regarding precipitation, the crucial parameters of this method are the mixing energies of all contained elements. These are determined using ab initio calculations taking into account temperature by varying the lattice constant. It is found that the behaviour of Ni and Mn solutes which can form NiMn-precipitates, NiMn-shells around Cu precipitates or stay in solution changes significantly with small changes in the mixing energies.     

Monte Carlo simulation of the kinetics of decomposition and the formation of precipitates at grain boundaries of the general type in dilute BCC Fe–Cu alloys

The kinetics of decomposition of a polycrystalline Fe–Cu alloy and the formation of precipitates at the grain boundaries of the material have been investigated theoretically using the atomistic simulation on different time scales by (i) the Monte Carlo method implementing the diffusion redistribution of Cu atoms and (ii) the molecular dynamics method providing the atomic relaxation of the crystal lattice. It has been shown that, for a small grain size (D ~ 10 nm), the decomposition in the bulk of the grain is suppressed, whereas the copper-enriched precipitates coherently bound to the matrix are predominantly formed at the grain boundaries of the material. The size and composition of the precipitates depend significantly on the type of grain boundaries: small precipitates (1.2–1.4 nm) have the average composition of Fe–40 at % Cu and arise in the vicinity of low-angle grain boundaries, while larger precipitates that have sizes of up to 4 nm and the average composition of Fe–60 at % Cu are formed near grain boundaries of the general type and triple junctions.     

Monte Carlo particle-based simulations of deep-submicron n-MOSFETs with real-space treatment of electron–electron and electron–impurity interactions

In modern deep-submicron devices, for achieving optimum device performance, the doping densities must be quite high. This necessitates a careful treatment of the short- and long-range electron–electron and electron–impurity interactions. We have shown before that by using a corrected Coulomb force, in conjunction with a proper cutoff range, one can properly account for the short-range portion of the force. Our approach naturally incorporates multi-ion contributions, local distortions in the scattering potential due to the movement of the free charges, and carrier-density fluctuations. The doping dependence of the low-field electron mobility obtained from 3D resistor simulations closely followed the experimental results, thus proving the correctness of our approach. Here, we discuss how discrete impurity effects affect the threshold voltage of ultra-small n-channel MOSFETs with gate lengths ranging from 50 to 100 nm. We find that the fluctuations in the threshold voltage increase with increasing the oxide thickness and substrate doping. The averaging effect over the width of the device leads to significantly smaller fluctuations in the threshold voltage for devices with larger gate width. The observed trends are in agreement with the experimental findings.     

Early stages of precipitation and microstructure control in Mg–rare earth alloys

Hardening precipitation frequently occurs in Mg–rare earth (RE) alloys after heat treatment in the 150–200°C range. Early stages of precipitation have been studied in detail by transmission electron microscopy in two Mg–RE alloys (Mg–Y–Gd and Mg–Y–Nd). Two types of structures may be involved in the precipitation sequence: a DO₁₉ phase and the so-called orthorhombic β′ phase. The structural relationship between DO₁₉ and β′ phases has been established in underaged and overaged states from the observations at peak ageing. We show that the earliest precipitates play a key role in the selection of phases developing in overaged states. Depending on the habit plane of the precipitates present in the early states, either the DO₁₉ or the β′ phase will grow in further ageing. The Mg–Y–Gd and Mg–Y–Nd alloys illustrate the different microstructures resulting from such selection. Due to the selective growth of the β′ phase, the Mg–Y–Gd alloys are characterized by a fine scale microstructure which provides improved mechanical properties.     

Monte Carlo simulations in the isothermal—isobaric ensemble: the requirement of a ‘shell’ molecule and simulations of small systems

A modification of the widely used Monte Carlo method for determining thermophysical properties in the isothermal-isobaric ensemble is presented. The new Monte Carlo method, now consistent with recent derivations describing the proper statistical mechanical formulation of the constant pressure ensemble for small systems, requires a ‘shell’ molecule to uniquely identify the volume of the system, thereby avoiding the redundant counting of configurations. Ensemble averages obtained with the new algorithm differ from averages calculated with the old Monte Carlo method, particularly for small system sizes, although both sets of averages become equal in the thermodynamic limit. Monte Carlo simulations in the constant pressure ensemble applied to the Lennard-Jones fluid demonstrate these differences for small systems. Peculiarities of small systems are also discussed, revealing that ‘shape’ is an important thermodynamic variable. Finally, an extension of the Monte Carlo method to mixtures is presented.     

Parallel three-dimensional Monte Carlo simulations for effects of precipitates and sub-boundaries on abnormal grain growth of Goss grains in Fe–3%Si steel

Using parallel three-dimensional Monte Carlo simulations, we investigated the effects of precipitates and sub-boundaries on abnormal grain growth (AGG) of Goss grains based on real orientation data of primary recrystallized Fe–3%Si steel. The simulations showed that AGG occurred in the presence of precipitates which inhibited the grain growth of matrix grains, whereas it did not in the absence of precipitates. The role of precipitates in enhancing AGG is to maintain a relatively high fraction of high energy boundaries between matrix grains, which increases the probability of sub-boundary-enhanced solid-state wetting of an abnormally growing grain. The microstructure evolved by the simulation could reproduce many realistic features of abnormally growing grains, such as the formation of island and peninsular grains and merging of abnormally growing grains which appeared to be separated initially on the cross-section.     

Calculation of the Kirkwood–Frohlich correlation factor and dielectric constant of methanol using a statistical model and density functional theory

The geometries of methanol monomer and methanol clusters, (CH₃OH) _m , m = 2–10, were optimized using the DFT/B3LYP/6-31++G(d,p) method. For each m > 2, a number of conformers were found to satisfy the optimization condition, showing no imaginary frequency in their calculated IR spectra. With increasing m, five- and six-membered rings begin to appear with open chain branches and the calculated IR spectra approach the experimentally observed IR spectrum of liquid methanol. Using the average energy of formation of one hydrogen bond and a statistical model, the Kirkwood–Frohlich (K–F) correlation factor (g) and dielectric constant (ε) were calculated for each methanol cluster. From a plot of ε versus cluster size (m), the bulk dielectric constant was obtained by extrapolation to m→∞. The value of g averaged over all conformers is in almost complete agreement with the g value obtained in an earlier molecular dynamics simulation study by Fonseca and Ladanyi [J. Chem. Phys. 93, 8148 (1990)]. Using this value of g in the K–F equation, the dielectric constant (ε) of methanol was calculated and found to be in fair agreement with (～17% lower than) the experimental value and also with an earlier molecular dynamics simulation [Mol. Phys. 94, 435 (1998)]. The calculated ε follows the same trend in variation with temperature as the experimental ε in the range 288–318 K.     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.     

Displacement fields around Guinier–Preston 1 zones in Al–Cu alloys: investigations using MD and ADF-STEM image simulations

The displacements of atoms around Guinier–Preston 1 (GP1) zones in Al–Cu alloys at a temperature of 295?K have been investigated using molecular dynamics (MD) simulations. The magnitude of the displacements at the first Al layer adjacent to a GP1 zone reached 24% strain and this value decreased with distance from the zone to zero at about 40th Al layer. Strain fields near a GP1 zone were evaluated by calculating strain tensors around individual atoms. The obtained strain maps suggested that the equilibrium Cu content in a GP1 zone should be 100%. The atomic configurations determined by MD simulations were utilised for multislice image simulations of annular dark-field scanning transmission electron microscopy (ADF-STEM) to investigate the effect of foil thickness and the depth position of a GP1 zone in a foil on ADF-STEM images. The atomic displacements in ADF-STEM images were smaller than the MD result due to foil thickness and electron channelling.     

Monte Carlo simulation of radiation damage produced in iron and vanadium by primary knock on atom ‘PKA’

Atomic scale simulation of radiation damage of pure iron and vanadium has been studied using the JA-IPU code based on Monte Carlo simulation. In response to gamma, neutron and any charged particle irradiation, energetic atoms knocked off their lattice position also generate atomic cascades inside the material besides the projectiles. The atomic cascade initiated by the primary knock on atoms (PKAs) of energy in the range 0–50?keV have been simulated in case of iron and vanadium metals. More realistic energy segregation has been achieved by incorporating electronic energy loss (EEL) along with nuclear stopping in the code. It is revealed that the effect of EEL is definite and different at low PKA energy as compared with high energy. The flip over energy is ～8?keV in iron and ～20?keV in the case of vanadium. This difference is found to be more in the case of the displacements than in the case of the defects. Cascade efficiency of vanadium calculated from the JA-IPU code has also been compared with the molecular dynamic simulation and found to be nearly the same.     

Influence of impurity elements on the nucleation and growth of Si in high purity melt-spun Al–Si-based alloys

The nucleation and growth of Si has been investigated by TEM in a series of high purity melt spun Al–5Si (wt%)-based alloys with a trace addition of Fe and Sr. In the as-melt-spun condition, some twinned Si particles were found to form directly from the liquid along the grain boundary. The addition of Sr into Al–5Si-based alloys promotes the twinning of Si particles on the grain boundary and the formation of Si precipitates in the α-Al matrix. The majority of plate-shaped and truncated pyramid-shaped Si precipitates were also found to nucleate and grow along {111}_α-Al planes from supersaturated solid solution in the α-Al matrix. In contrast, controlled slow cooling decreased the amount of Si precipitates, while the size of the Si precipitates increased. The orientation relationship between these Si precipitates and the α-Al matrix still remained cube to cube. The β-Al₅FeSi intermetallic was also observed, depending on subsequent controlled cooling.     

Energy distribution of cosmic rays in the Earth’s atmosphere and avionic area using Monte Carlo codes

Cosmic rays cause significant damage to the electronic equipments of the aircrafts. In this paper, we have investigated the accumulation of the deposited energy of cosmic rays on the Earth’s atmosphere, especially in the aircraft area. In fact, if a high-energy neutron or proton interacts with a nanodevice having only a few atoms, this neutron or proton particle can change the nature of this device and destroy it. Our simulation based on Monte Carlo using Geant4 code shows that the deposited energy of neutron particles ranging between 200 MeV and 5 GeV are strongly concentrated in the region between 10 and 15 km from the sea level which is exactly the avionic area. However, the Bragg peak energy of proton particle is slightly localized above the avionic area.     

Structure of Na2S–GeS2 glasses studied by using neutron and X-ray diffraction and reverse Monte Carlo modeling

Neutron and X-ray diffraction measurements were performed to investigate the structure of Na₂S–GeS₂ glasses synthesized by mechanical alloying. The Ge–S coordination numbers calculated from the total correlation functions show that GeS₄ tetrahedra form the basic framework structure of Na₂S–GeS₂ glasses. In addition, a three-dimensional structural model of the (Na₂S)₅₀(GeS₂)₅₀ glass was obtained by using reverse Monte Carlo (RMC) simulation on neutron and X-ray diffraction data, and it was compared with the RMC model previously obtained for a (Li₂S)₅₀(GeS₂)₅₀ glass. The results show that the Ge–S framework structures in the two glasses are almost the same in the short and intermediate ranges; that is, the Ge–S framework structures are formed mainly by the connection of corner-sharing GeS₄ tetrahedra. Many of the Na ions are coordinated by four S atoms, which are non-bridging S atoms and/or bridging S atoms.     

Synthesis and characterization of multi–wall carbon nanotubes supported-hydrated iron phosphate cathode material for lithium–ion cells by a novel homogeneous precipitation method

Iron phosphate (FePO₄) is a promising candidate for the cathode material in lithium-ion cells due to its easy synthesis and low cost. However, the intrinsic drawbacks of FePO₄ material (i.e., the low electronic conductivity and the low lithium-ion diffusion coefficient) result in poor capacity. To overcome the shortcomings, multi-wall carbon nanotubes (MWNTs) supported hydrated iron phosphate nanocomposites (FePO₄·2H₂O/MWNTs) are prepared using a novel homogeneous precipitation method. Meanwhile, the formation mechanism of highly dispersed and ultrafine FePO₄·2H₂O nanoparticles is discussed in detail. Electrochemical measurements show that FePO₄·2H₂O/MWNTs nanocomposites have a superior discharge capacity and stability. For example, FePO₄·2H₂O/MWNTs nanocomposites exhibit a high initial discharge capacity (129.9?mAhg^?1) and a stable capacity retention (114.3?mAhg^?1 after 20 cycles). The excellent electrochemical performance is attributed to the small particle size of FePO₄·2H₂O nanoparticles, the good electronic conductivity of MWNTs, and the three-dimensional conductive network structure of FePO₄·2H₂O/MWNTs nanocomposites.     

Comparison of Monte Carlo simulation and direct multistep scattering theory in (e,e′p) nuclear reactions

Two methods to deal with final state interactions in (e,e′p) reactions in nuclei are compared. One of them uses a Monte Carlo semiclassical approach while the other uses a statistical quantum mechanical approach. The comparison serves to give support to both approaches, showing at the same time their limitations.