Diffusion Coefficient Of Atoms Research Articles

Self-diffusion of Fe and Pt in L10-Ordered FePt: Molecular Dynamics simulation

Vacancy-mediated lattice diffusion coefficients of Fe and Pt atoms in the chemically ordered L10-FePt phase at temperatures between 1300 and 1600 K were evaluated by means of Molecular Dynamics (MD) simulations. Due to the anisotropic structure of the L10-ordered FePt phase, Fe and Pt diffusion fluxes and the resulting self-diffusion coefficients were considered along and perpendicular to the [001] crystallographic direction. In view of a very low vacancy concentration in real FePt single crystals, steady state conditions of the simulated process were approximated by specifically scaling the self-diffusion coefficients estimated for higher vacancy concentrations to the equilibrium vacancy concentration. This procedure involved the calculation of vacancy formation energies which appeared temperature dependent. The validity of this approach was thoroughly tested and the final results were analyzed and compared to the relevant literature data. The evaluated temperature dependent Fe and Pt self-diffusion coefficients showed Arrhenius behavior, however, their values were much lower than the reported experimental ones. Apart from the inevitable effect of the applied quasi-empirical potentials, the discrepancies might originate from the fact that while the MD simulations addressed a single crystal of FePt defected exclusively with vacancies and antisites, the existence of fast diffusion paths along linear and planar defects cannot be excluded in real materials.

Quantitative three-dimensional phase-field modeling of dendritic solidification coupled with local ensemble transform Kalman filter

Prediction of dendrite growth during alloy solidification is important for controlling the microstructures and mechanical properties of alloys. To this end, quantitative phase-field (QPF) models have been developed to accurately predict dendrite growth. However, a comprehensive method to calibrate the parameters of the QPF models has not been established. In this study, QPF modeling of dendritic solidification coupled with a data assimilation method based on the local ensemble transform Kalman filter (LETKF) is proposed. This modeling could simultaneously estimate multiple parameters and improve the prediction of dendrite growth. The modeling was applied to simulations of isothermal dendritic solidification in Fe–C–Mn ternary alloys. The results show that the solid–liquid interfacial energy and diffusion coefficients of solute atoms in a liquid phase can be estimated from the shapes of the growing dendrites. The accuracy of parameter estimation depends on the growth rate of the primary dendrite arm instead of the dendrite shape. This study demonstrates that LETKF-based data assimilation improves the prediction of solute concentration fields. The proposed QPF modeling paves a promising way to improve the prediction accuracy of conventional QPF models and derive new knowledge from the experimental data obtained by in-situ observations of growing dendrites.

Microstructure evolution and mechanical properties of Al-8wt. % Si semi-solid billet fabricated by powder metallurgy liquid phase reaction sintering

Abstract The Al-8wt. % Si semi-solid billets were successfully prepared by a new liquid phase reaction sintering process with Al and Si elemental powders. The reaction mechanism of the Al and Si elemental powders was investigated, and the thermodynamics and dynamics of the reaction process were studied. The effect of the microstructure evolution on the mechanical properties was analyzed. In the reaction process, the reaction product Al(Si)(L) liquid phase wets the Al particles well, and the liquid phase content increased with increasing reaction temperature and time. It was found that the kinetic model given by ψ = 4.6 × 105exp(-1.05 × 105/RT)t1/3 can accurately predict the actual liquid phase formation fraction. With increasing reaction temperature, the viscosity of the liquid phase decreases and the Si atom diffusion coefficient increases. This will increase the formation rate of the liquid phase and decrease the length of lath Si. The increased liquid phase content increases the strength of the billet and decreases its elongation. The shear crack is the main reason for the instability of the billets during the deformation process. Acting as a crack source, Si particles accelerate the generation and propagation of cracks, and promote the instability fracture of the billet.

Atomic-Scale Mechanism Investigation of Mass Transfer in Laser Fabrication Process of Ti-Al Alloy via Molecular Dynamics Simulation

This article deals with a Ti-Al alloy system. Molecular dynamics simulation was used to simulate and explore the mass transfer behavior during the laser fabrication process at atomic scale. The research goal is to investigate the mass transfer mechanism at atomic scale and the movement of solute atoms during the laser fabrication process. The mean square displacement (MSD), radial distribution function (RDF), atomic number density, and atomic displacement vector were calculated to characterize it. The results show that the TiAl alloy is completely melted when heated up to 2400 K, and increasing the temperature past 2400 K has little effect on mass transfer. As the heating time increases, the diffusion coefficient gradually decreases, the diffusion weakens, and the mass transfer process gradually stabilizes. In Ti-Al binary alloys, the diffusion coefficients of different solute atoms are related to the atomic fraction. During the melting process, the alloy particle system has a greater diffusion coefficient than the elemental particle system.

Influence of applied electric field on atom diffusion behavior and mechanism for W/NiFe interface in diffusion bonding of Steel/NiFe interlayer/W by spark plasma sintering

Influence of applied electric field on atom diffusion behavior and mechanism for W/NiFe interface in diffusion bonding of Steel/NiFe interlayer/W by spark plasma sintering was studied using the first-principles calculations. The result indicates that applied electric field reduces d-orbital electron concentrations of W atom and Ni atom effectively, and then weakens W-W metallic bonding/Ni-Ni metallic bonding and Nisp-W metallic bonding/Wsp-Ni metallic bonding for W/NiFe diffusion interface, which decides the vacancy formation energy and solute atom migration energy. Therefore, the diffusion activation energy composed by vacancy formation energy and solute atom migration energy was reduced and leading to the increasing interfacial atom diffusion coefficient. Moreover, because W atom is more susceptible to applied electric field due to the smaller stability of d-orbital electrons than Ni atom, the decline degrees of W-W and Nisp-W metallic bonding strength are larger than those of Ni-Ni and Wsp-Ni metallic bonding strength. Therefore, the accelerating effect for Ni atom diffusing into W slab is larger than W atom diffusing into NiFe slab on W/NiFe interface, presented as that the diffusion activation energies for them decrease by 0.37 eV and 0.07 eV, and the diffusion coefficients at 1400 K increase by 26.72 times and 2.23 times, respectively.

Study on micro-mechanism of carbon atom diffusion in surface nanocrystallization low carbon alloy steel using molecular dynamics simulation

Molecular dynamics (MD) simulation was successfully used to explore the mechanism of carbon atom diffusion in supersonic fine particle bombardment (SFPB) pretreated low carbon alloy steel during vacuum carburization. Results of experiment and simulation demonstrated that the plastic deformation was occurred and high surface energy achieved on the surface of low carbon alloy steel during the process of SFPB. The defects were formed inside the crystal including vacancies, 1/2 <111>, <100> and <110> types of dislocations, and the number of defects gradually increased with the increase of bombardment time and speed. Compared with defect-free materials, the large number of defects increase the diffusion coefficient by several orders of magnitudes. The internal defects of the material, including vacancies, dislocations and grain boundaries induce the rise of carbon atom diffusion coefficient, accordingly. While the effect of dislocation types was not obvious to diffusion coefficient. The carburizing temperature has a significant effect on the carbon atom diffusion rate of SFPB pretreated samples, when comparing with that of non-pretreated ones.

Investigation of atomic diffusion behavior of Mo/Au interface

The atomic diffusion behavior of Mo/Au interface was investigated by using molecular dynamics (MD) simulations which combines classical diffusion theory and molecular dynamics simulation, mutual diffusion coefficient and radial distribution function of Mo atoms and Au atoms were obtained. The results indicate that Au atoms can diffuse into Mo layer, while Mo atoms diffuse onto the surface of Au layer extremely difficult. The mutual diffusion coefficients and degree of atomic disorder (Mo and Au atoms) increase with the increase of diffusion temperature. The results were verified by scanning electron microscope (SEM) and X-ray photoelectron spectroscopy (XPS) analysis. The Mo 3d characteristic peaks can not be detected on the surface of Mo/Au film at annealing temperature below 673 K, which indicates that Mo atoms can not reach the surfaces of Au layers through the atomic diffusion behavior. The experimental results agree well with the simulation results. However, Mo/Au film structure has been destroyed due to aggregated Au grains at annealing temperature 973 K. Therefore, the experimental results should be taken into account in MD simulations.

Atomic diffusion behavior and diffusion mechanism in Fe–Cu bimetal casting process studied by molecular dynamics simulation and experiment

A molecular dynamics (MD) method with an embedded atomic method (EAM) was proposed to study the atomic diffusion behavior and diffusion mechanism in the Fe–Cu bimetal casting process. The results indicated that the diffusion coefficient of the Cu atoms was larger than that of the Fe atoms at the same temperature, but the Fe atoms predominantly diffused into the Cu side in the process of diffusion bonding. Moreover, the relationship between diffusion distance and temperature was predicted by the established model, and the optimal temperature for interface diffusion bonding of Fe–Cu bimetal ranged from 1473K to 1753 K. The diffusion behavior was mainly due to vacancies, which played a key role in the formation of the Cu cluster, and the accumulation of Cu atoms decreased the system energy. Finally, FeAcknowledgmentsCu bimetal casting was prepared to validate the simulated results of the diffusion behavior and diffusion distance, and the simulated results were consistent with the experimental ones.

Accelerated kinetic Monte Carlo: A case study; vacancy and dumbbell interstitial diffusion traps in concentrated solid solution alloys.

Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and ⟨100⟩ dumbbell interstitials in Ni-Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy's non-monotonic behavior. In contrast, the difference between formation energies of Ni-Ni, Ni-Fe, and Fe-Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition-based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one-is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.

Improving the performance of phase-change memory by grain refinement

Many experiments have shown that three-dimensional-confined grain refinement (GR) textures in phase-change memory reduce power consumption and improve endurance performance. However, a lack of knowledge on the GR mechanisms and their influence on device performances challenges designs that concurrently enhance the comprehensive device performances using the same impurity-doped strategy. Here, we experimentally observe dramatic GR in carbon-doped Ge2Sb2Te5 (GST), which also presents reduced power consumption and enhanced endurance performances. We provide low power consumption evidence that thermal conductivity controls the thermal transport heat loss and is proportional to the size of nanoscale grains because the boundary severely scatters phonons. Our simulations indicate that the short carbon chains in the boundary interlace with each other and trend to form trialkyl carbon atoms that constitute the basic local environment of graphene. The stable sheet consists of aggregated carbon, which is even stable above the melting temperature of GST and acts as a second-phase drag to refine the grain size. The enhanced endurance is explained by the restricted migration from the stable carbon sheet, which is verified by the greatly reduced diffusion coefficient of the host atoms in the boundary because of the less shielding effect from the core electrons in carbon and strong bonds formed between host and carbon atoms. Our findings show that the reduced power consumption and enhanced endurance from GR engineering are feasible in phase-change memory, which has been largely overlooked.

First-principles calculations on adsorption-diffusion behavior of Boron atom with tungsten surface

In this work, adsorption-diffusion behavior of Boron atom along and into W surface as well as the basic Boron atom absorption-diffusion behavior in W bulk were studied using first-principles density functional theory and climbing image nudged elastic band (CI-NEB) method. The result indicates that the octahedral interstice is the most stable position for B atom absorption and the energy barrier for B atom diffusing between two neighboring octahedral interstices in W bulk is 2.476 eV. For the adsorption behavior of Boron atom on W surface, Hollow site is the most stable adsorption position for W (100) surface and W (110) surface, while Hollow-II Site is the most stable adsorption position for W (111) surface. When B atom diffusing along W surface, the energy barrier for B atom diffusing along W (100) surface is the largest followed by W (110) surface and W (111) surface. During B atom diffusion into W surface, the needed energies for B atom diffusing into W (100) surface, W (110) surface and W (111) surface are 2.231 eV, 1.87 eV and 1.63 eV, respectively. After B atom diffuses to the 3rd, 3rd and 4th atomic layer below W (100) surface, W (110) surface and W (111) surface, the subsequent diffusion behavior shows the bulk diffusion characteristic. Beside, atomic diffusion coefficient D indicates that no matter diffusing along or into W surface, W (111) surface provides the best diffusion condition.

First-principles molecular dynamics studying the solidification of Ti-6Al-4V alloy

Solidification process plays a significant role in macroscopic properties of metallic materials. However, the understanding of this process at the atomic level is still far from complete. In this work, for the first time, the first-principles molecular dynamics simulations are carried out to systematically explore the structural evolution and transport properties of Ti-6Al-4V alloy, one of the commonly used alloys for selective laser melting technology, upon cooling from 2400 K to 1300 K. Firstly, the melting range of this alloy is predicted by simulated density to be about 1850–1950 K, which is in good agreement with the experimental value of 1875–1925 K. Afterwards, the local atomic structure variation with temperature is statistically analyzed by structure factors, partial radial distribution functions, coordination number, bond angle distributions, and Voronoi tessellation. It reveals that Ti-6Al-4V alloy experiences a phase transition from 2400 K to 1300 K. The system changes from a liquid dominated by the icosahedral-like cluster to a solid with body-centered cubic structure, where the 〈0, 5, 2, 6〉 and 〈0, 4, 4, 6〉 polyhedra play an important role. Eventually, the diffusion coefficients of Ti, Al, and V are estimated to investigate the kinetic property of liquid Ti-6Al-4V alloy. From 2400 K to 1950 K, the diffusion coefficients of atoms all obey Arrhenius function, and V atom has the largest diffusion coefficient, followed by the Ti atom, which is very close to the self-diffusion coefficient of pure liquid Ti, and finally the Al atom. This abnormal mass dependence of diffusion coefficient is well explained by activation energy. In conclusion, the present work provides insights into the understanding of structural dynamics and the kinetic properties of such alloy melts, which could guide selective laser melting technology to obtain desired microstructure.

Empirical interatomic potential for Fe-C system using original Finnis-Sinclair potential function

The Finnis-Sinclair (FS) potential is one of the three-body potentials and the potential function is the simplest in them. We developed the FS potential for an Fe-C binary system without changing the original form of the function. The potential parameters for the Fe-C and C-C interactions were determined to fit the physical properties (structural parameters, bulk modulus and cohesive energy) of five iron carbides (γ′-Fe4C, θ-Fe3C, χ-Fe5C2ο-Fe7C3 and NaCl type-FeC). The developed potential reproduced fourteen iron carbides and migration energy barriers of interstitial carbon atoms in body-centered cubic (bcc) and face-centered cubic (fcc) irons. Moreover, the reproducibility of the phonon densities of states for the iron atoms of cementite (θ-Fe3C) and hexagonal-Fe7C3 (h-Fe7C3) was confirmed and the diffusion coefficient of carbon atoms in bcc iron was good agreement with the experimental value.

Multi-phase-field modelling of electromigration-induced void migration in interconnect lines having bamboo structures

Predicting the evolution of voids induced by electromigration (EM) in interconnect lines is an important aspect of improving the reliability of miniaturized integrated circuits. In this paper, we propose a new multi-phase-field (MPF) model to simulate void evolution in polycrystalline interconnect lines on a three-dimensional (3D) basis. This model was validated by comparing simulations of 3D void migration in a single crystal copper line with analytical solutions. We also performed a parametric study intended to elucidate the key factors associated with void evolution leading to line breakage. This study determined that critical void evolution in copper straight interconnect lines having a bamboo structure depends on the ratio of the diffusion coefficient of atoms at the grain boundaries to that at the void surfaces. Simulations in which multiple voids migrated by EM in a bamboo line mimicking a via site in an integrated circuit showed that such voids tend to accumulate and break the interconnect line above the via. By comparing simulation results to experimental data, this work also confirmed that the MPF model can predict the break point of an interconnect line as caused by EM.

Atomistic Simulations and Experimental Investigations of the Diffusion Behavior of Steel/ZCuPb20Sn5 Bimetals

A hybrid verification method consisting of experiments and molecular dynamics simulations was implemented to investigate the diffusion behaviour of steel/ZCuPb20Sn5 bimetals. The effects of different carbon steels (Q235 steel, 45 steel, and T8 steel), pouring temperatures, and holding times on their microstructures and mechanical properties were studied to obtain the optimum process parameters. The experimental results indicated that the pouring temperature and holding time played an imperative role in improving the shear strength of the steel/copper bimetallic composite. The highest bonding strength of all the steel/copper bimetallic composites was obtained at 1523 K and the holding time of 40 min. Moreover, the carbon steel of 45 steel with a ZCuPb20Sn5 interface exhibited the highest bonding strength because of the appropriate pearlite content along with the preferable structure and micro-hardness for the considered diffusion width and bonding strength. Meanwhile, the diffusion distance of copper atoms in the carbon steel matrix was smaller than that of iron atoms in the ZCuPb20Sn5 matrix. In the simulation results, the diffusion coefficient of Cu atoms was smaller than that of Fe atoms, but the diffusion distance of Fe atoms in the Cu bulk was larger than that of Cu atoms in the Fe bulk; this showed a significant agreement with the experimental result.

Effect of Mo Nanoparticles on the Growth Behavior of the Intermetallic Compounds Layer in Sn3.0Ag0.5Cu/Cu Solder Joints.

The reliability of solder joints, which is affected largely by the interfacial intermetallic compounds layer, is of great importance to the performance of electronic devices. In this paper, a novel composite solder with Mo nanoparticles doped in Sn3.0Ag0.5Cu solder was prepared. Solder/Cu joints were prepared using Sn3.0Ag0.5Cu solder or Mo nanoparticles reinforced solder with Cu substrates. The effect of the nanoparticles on the growth of intermetallic compounds during isothermal aging was investigated. It was found that the addition of Mo nanoparticle markedly suppressed the increase in thickness of the interfacial intermetallic compounds layer during isothermal aging. The atomic diffusion coefficients during isothermal aging in Sn3.0Ag0.5Cu solder and in the novel doped solder were determined experimentally. Mo nanoparticles were found to decrease the diffusion coefficient in the composite solder. The high specific surface area of the nanoparticles makes them easily adsorbed and hinders the diffusion of Sn and Cu atoms. This is consistent with an increase in the diffusion activation energy due to the addition of Mo nanoparticles in Sn3.0Ag0.5Cu solder.

Intermediate range structure of amorphous Cu2GeTe3: ab initio molecular dynamics study

We have investigated the intermediate range structure of amorphous Cu2GeTe3 based on ab initio molecular dynamics simulations. The highest population of ring size is three, which makes the triangle structure. This ring consists of mainly Cu2Te. Rings may also consist of CuCuCu, Cu2Ge, and CuGeTe, where approximately 88% of Cu atoms in the system are related with the three-membered ring. The second highest population of ring size is five. Three- and five-membered rings in the amorphous phase originate from six-membered ring in the crystalline phase. This situation can enhance the phase transition between crystalline and amorphous phases. In the phase change process, Cu atoms may diffuse in the amorphous state with changing bonds. The diffusion coefficient of Cu DCu is estimated to be approximately 0.12 × 10−9 m2 s−1. Such high diffusion coefficient of Cu atoms is contributed from only 10% of Cu atoms in the amorphous phase.

ReaxFF Molecular Dynamics Simulations on Silicon Suboxide as Anode Material for Lithium-Ion Batteries

Amorphous silicon suboxides (a-SiOy, y < 2) have attracted much attention as promising anode materials for rechargeable energy storage devices. We performed ReaxFF molecular dynamics simulations (ReaxFF MD) to examine the structural evolution, volume expansion, and diffusion properties in amorphous LixSiOy bulks, and to reveal the impact of oxygen content on its performance. Our results suggest that the inserted Li atoms preferentially disintegrate Si–Si connections in Si-rich oxide (a-SiO0.5), while they tend to break Si–O connections in O-rich silicon oxide (a-SiO). Besides, our study demonstrates that a higher concentration of O atoms in a-SiOy reduces its relative expansion upon lithiation, which is desirable for the application of electrode materials. However, we also find that the diffusion properties weaken with increasing O content. At the same level of O concentration, the diffusion coefficient of Li atoms () increases with lithiation, while at the same level of Li concentration, decreases with the increasing of O content. Our simulation results provide important insights into the role of O in a-SiOy at the atomistic level.

Regulating the helium bubble nucleation in the titanium tritides by environment temperature during the early aging period

The nucleation of helium bubbles in the early aging stage of tritium storage materials will have an important influence on the bubble growth behavior in the whole of aging. Herein, the nucleation of helium bubbles was adjusted by environment temperature at the first 15 days immediately after preparation of polycrystalline titanium tritide films. The influence of the environment temperature on the nucleation of helium bubbles were studied by X-ray diffraction (XRD), positron annihilation spectroscopy (PAS), thermal helium desorption spectroscopy (THDS) and scanning transmission electron microscopy (STEM). Results demonstrate that the helium bubble nucleation is significantly affected by the environment temperature of −60 °C, 20 °C and 120 °C. The higher the environment temperature, the lower number density of helium bubble in the titanium tritide films. The helium bubble nucleation mechanism is strongly correlated to the helium atom diffusion coefficient that is controlled by the environment temperature. During the following aging, the rate of helium atoms captured by a single helium bubble increases in titanium tritides with low number density bubbles, which accelerates the growth of helium bubbles in the matrix. However, the low number density bubbles also decrease the capture probability of free helium atoms by helium bubbles, resulting in the increase of helium atoms diffusing to infinite size defects such as grain boundaries macroscopically, and accelerating the evolution of helium in titanium tritides.

Theoretical Calculations of the Diffusion and Friction Coefficients for Neutral Atoms that Moving in a Laser Field

This research aimed to study the friction and diffusion coefficients of neutral atoms that moving and interact with a laser field .The Mathcad 14 program used to calculate the results. The theoretical model was solved and shown the effect of different optical parameters on the diffusion and friction of neutral atoms .The different values of ellipticity (Ɛ) were used to find the friction and diffusion coefficients ,for each value of ellipticity we found that the relationship between the natural width of excited level( γ) and the difference(δ) between the frequency of laser field(ω) and the atomic resonance (ω0 ) has strong effect on the friction coefficient of atoms .The effect of Rabi frequency (Ω ) on the diffusion coefficient has been investigated .In this research the results showed that each of the parameters δ and Ω has effect on the diffusion of atom and the Rabi frequency has more influence. The dependence of the friction and diffusion coefficients on the natural width of the excited level was studied. The measuring of the friction and diffusion coefficients of atom very important to control the movement and then localize it, this have many applications in physics fields.