Atomistic simulations of grain boundary segregation in nanocrystalline yttria-stabilized zirconia and gadolinia-doped ceria solid oxide electrolytes

Hybrid Monte Carlo–molecular dynamics simulations are carried out to study defect distributions near Σ5(3 1 0)/[0 0 1] pure tilt grain boundaries (GBs) in nanocrystalline yttria-stabilized zirconia and gadolinia-doped ceria. The simulations predict equilibrium distributions of dopant cations and oxygen vacancies in the vicinity of the GBs where both materials display considerable amounts of dopant segregation. The predictions are in qualitative agreement with various experimental observations. Further analyses show that the degree of dopant segregation increases with the doping level and applied pressure in both materials. The equilibrium segregation profiles are also strongly influenced by the microscopic structure of the GBs. The high concentration of oxygen vacancies at the GB interface due to lower vacancy formation energies triggers the dopant segregation, and the final segregation profiles are largely determined by the dopant–vacancy interaction.     

Atomistic Monte Carlo simulations on the influence of sulphur during high-temperature decarburization of molten iron–carbon alloys

We report a Monte Carlo simulation study of the molten Fe–C–S system with the aim of developing a theoretical understanding of the influence of sulphur during decarburization reactions in Fe–C alloys. Focussing specifically on the role played by free surfaces, computer simulations were based on the hexagonal atomistic model of Fe–C–S system using isotropic atomic interaction parameters; free surfaces were characterized by a missing layer of atoms. Three geometrical configurations, namely a liquid bath, a prismatic block and a spherical droplet, were investigated. Simulations were carried out as a function of melt carbon and sulphur concentration, temperatures and surface/volume ratios of the simulation cell. Sulphur atoms were found to preferentially concentrate in the top few layers, with the second layer showing the highest amounts of sulphur; very little sulphur was observed in the bulk liquid. This trend was observed in all three simulation configurations over a wide carbon/sulphur concentration range and temperatures. Significant levels of iron were observed in the top surface layer. The influence of free surfaces on atomic concentration profiles was found to be a strong function of the surface/volume ratio. The surface segregation of S was more pronounced for small exposed surfaces and was much smaller for liquids with large exposed surfaces. The presence of surface-active sulphur resulted in a major re-distribution of carbon. Carbon tended to concentrate deeper in the bulk, with the surface region being severely depleted of carbon. In addition to several new findings and a better understanding of liquid surfaces, these simulations have helped overcome major limitations of Sain and Belton’s model. Key experimental results on decarburization have been explained within the framework of our simulations. These simulation results have significant implications for surface decarburization reactions and carbon-boil phenomena in smelting technologies.     

Atomistic simulations of surface segregation of defects in solid oxide electrolytes

We performed atomistic simulations of yttria-stabilized zirconia (YSZ) and gadolinia-doped ceria (GDC) to study the segregation of point defects near (1 0 0) surfaces. A hybrid Monte Carlo–molecular dynamics algorithm was developed to sample the equilibrium distributions of dopant cations and oxygen vacancies. The simulations predict an increase of dopant concentration near the surface, which is consistent with experimental observations. Oxygen vacancies are also found to segregate in the first anion layer beneath the surface and to be depleted in the subsequent anion layers. While the ionic size mismatch between dopant and host cations has been considered as a driving force for dopant segregation to the surface, our simulations show that the correlation between individual point defects plays a dominant role in determining their equilibrium distributions. This correlation effect leads to more pronounced dopant segregation in GDC than in YSZ, even though the size mismatch between dopant and host cations is much greater in YSZ than in GDC.     

Atom probe tomography investigation of heterogeneous short-range ordering in the ‘komplex’ phase state (K-state) of Fe–18Al (at.%)

We study an Fe–18Al (at.%) alloy after various thermal treatments at different times (24–336 h) and temperatures (250–1100 °C) to determine the nature of the so-called ‘komplex’ phase state (or “K-state”), which is common to other alloy systems having compositions at the boundaries of known order-disorder transitions and is characterised by heterogeneous short-range-ordering (SRO). This has been done by direct observation using atom probe tomography (APT), which reveals that nano-sized, ordered regions/particles do not exist. Also, by employing shell-based analysis of the three-dimensional atomic positions, we have determined chemically sensitive, generalised multicomponent short-range order (GM-SRO) parameters, which are compared with published pairwise SRO parameters derived from bulk, volume-averaged measurement techniques (e.g. X-ray and neutron scattering, Mössbauer spectroscopy) and combined ab-initio and Monte Carlo simulations. This analysis procedure has general relevance for other alloy systems where quantitative chemical-structure evaluation of local atomic environments is required to understand ordering and partial ordering phenomena that affect physical and mechanical properties.     

Pt-Rh二元合金系表面偏聚的分析型EAM模型计算

应用分析型EAM多体势和Monte Carlo模拟方法研究了Pt-Rh合金系的表面偏聚情况．模拟结果显示，不同Pt含量的合金以及不同的表面，最外层都富集Pt原子，次外层富集Rh原子，剖面成分呈振荡分布．(111)面和(100)面的成分偏聚量差别较大：(111)面的Pt原子偏聚量较(100)面小得多，且前者只有最表面3层原子发生偏聚，而后者的成分偏聚影响表面至少10层．模拟结果与已有理论和实验结果符合得很好．     

Grain growth in thin metallic films

Grain growth in thin films deposited on a substrate was studied theoretically. The thrust of the model proposed is the effect of vacancy generation accompanying grain growth on the rate of the process. In addition, the magnitude of a tensile stress developing in the film was considered. It was shown that due to the contribution of vacancies to the free energy of the system, discernible grain growth is preceded by an “incubation” period, during which the grain structure can be considered as stable, as the rate of growth is relatively small over this incubation time. During this time, the vacancy concentration remains nearly constant, staying at a level much higher than the thermal equilibrium concentration. Based on numerical analysis, a simple expression for the incubation time in terms of the vacancy sink spacing, temperature and grain boundary characteristics was derived. With this formula, the stability of the grain structure of a thin film can be assessed for given conditions.     

Substitutional diffusion and Kirkendall effect in binary crystalline solids containing discrete vacancy sources and sinks

We investigate vacancy-mediated diffusion in a binary substitutional alloy by explicitly accounting for discrete vacancy sources and sinks. The regions between sources and sinks are treated as binary crystals with a perfect lattice structure containing a dilute concentration of vacancies. The sources and sinks are assumed ideal, maintaining an equilibrium vacancy concentration in their immediate vicinity. Diffusion within the perfect lattice is described with a diffusion-coefficient matrix determined by kinetic Monte Carlo simulations for a binary, thermodynamically ideal alloy in which the components have different vacancy-exchange frequencies. Continuum simulations are performed for diffusion couples with discrete grain boundaries acting as vacancy sources and sinks. Effective grain coarsening due to the Kirkendall effect is observed even in the absence of Gibbs-Thomson driving forces. As in standard ternary systems, uphill diffusion is observed. We also find that the drift of the lattice frame of reference as a result of the Kirkendall effect increases with the source/sink density. Upon increasing the density of vacancy sources and sinks, we recover the conventional treatment of substitutional diffusion, which assumes a dense and uniform distribution of vacancy sources and sinks that maintain an equilibrium vacancy concentration throughout the solid. The inverse Kirkendall effect, where the slower component segregates at grain boundaries acting as vacancy sinks, is also observed in the simulations.     

Development of glue-type potentials for the Al–Pb system: phase diagram calculation

Empirical many-body potentials of the glue-type have been constructed for the Al–Pb system using the “force matching” method. The potentials are fitted to experimental data, physical quantities derived from ab initio linear muffin-tin orbitals calculations and a massive quantum mechanical database of atomic forces generated using ultrasoft pseudopotentials in conjunction with ab initio molecular statics simulations. Monte Carlo simulations using these potentials have been employed to compute an Al–Pb phase diagram which is in fair agreement with experimental data.     

Impact of diffusion on concentration profiles around near-critical nuclei and implications for theories of nucleation and growth

In order to better understand the interplay of diffusion and interfacial processes in nucleation phenomena we have performed kinetic Monte Carlo simulations of a lattice gas model with realistic but generic microscopic dynamics. These simulations are used to probe the complete dynamic range extending from diffusion-limited through interface-limited kinetics. Most phenomenological theories describing nucleation, growth and/or coarsening focus on either the diffusion-limited or interface-limited regime. Calculations are performed on initially monodisperse clusters placed into solutions of uniform concentration. In agreement with predictions, our simulations show the appearance of regions of enhanced solute concentration around clusters smaller than the critical size, and of solute depletion around clusters larger than the critical size. The range and magnitude of these effects are largely controlled by the ratios of the rate of free diffusion to those of interfacial attachment and detachment processes. Furthermore, these simulations show that the rate of cluster growth depends strongly on the diffusion rate and correlates well with the local solute concentration at the cluster surface, over the entire dynamic range studied. In “diffusion-limited” phenomenological models the solute concentration at the cluster surface is assumed to be determined by the radius of the cluster, through a local-equilibrium condition. Our results indicate that in the intermediate regime in which the rates of diffusion and interfacial processes are similar, such assumptions are qualitatively incorrect and so models that assume either fully diffusion-limited or fully interface-limited growth and coarsening should not be used. We show, in particular, that the recently proposed “coupled-flux model” correctly and naturally describes the underlying physics over the complete dynamic range and therefore is generally preferable.     

Migration and correlation in highly defective systems: Fast-diffusion in lithium oxide

The high-temperature superionic phase of lithium oxide is characterized by a high concentration of Frenkel defects and a diffusion mechanism involving several types of atomic jumps. We have calculated the tracer-correlation factor and analyzed the migration paths of the Li ions obtained by molecular dynamics (MD). A kinetic Monte Carlo code, simulating the lithium vacancy diffusion, has been developed and used to predict the correlation factor as a function of the atomic fraction of defects. There is a good agreement with the result directly obtained by MD. The analysis of the jump paths shows that the direct exchange between a vacancy and a migrating atom is the main part of the diffusion mechanism. The other atomic jumps, although complex, mostly imply vacancies. The Li⁺ fast-diffusion proceeds by a vacancy mechanism involving several jump types.     

Effects of atomic relaxation and the electronic structure of niobium (100) and (110) surfaces

A comparative analysis of the atomic relaxation and electronic structure of niobium (100) and (110) surfaces has been carried out using the VASP-PAW method. The relaxation-induced changes in interlayer spacings of surface layers demonstrate an oscillating behavior but they substantially differ for the two analyzed surfaces; namely for the (110) surface with the closest atomic packing two outermost surface layers are contracted by 4.3% and the relaxation becomes noticeable for three outer layers, while for the more “open” (100) surface these quantities equal 13.1 and six layers, respectively. An analysis of the layer-by-layer distribution of the densities of states, spatial distribution of the charge density, and densities of states at the Fermi level indicates that the most considerable changes near Fermi level take place for (100) surface.     

Monte Carlo simulations and experimental observations of templated grain growth in thin platinum films

Monte Carlo (MC) simulations were used to model microstructural evolution in Pt thin films with epitaxial seed grains buried in a polycrystalline matrix. The key to achieving purely epitaxial films via templated grain growth in such materials is the lateral coalescence of the seeds into a single epitaxial grain. The primary factors in determining whether this event takes place, for a given set of interfacial mobility/energy functions, are the relative initial sizes of the seed grains and polycrystalline matrix grains, and the initial degree of surface coverage of the epitaxial seeds. These characteristics are evaluated by varying the films’ initial microstructural parameters, including seed grain size, seed number density, seed surface coverage and polycrystalline matrix grain size. Additional simulations were carried out to investigate the effect of varying the energy and the mobility of seed–matrix interfaces. The critical values of seed–matrix grain size depend on the energy/mobility used, though seed coalescence remains the key criterion for epitaxial grain growth.     

Monte Carlo simulation of grain boundary segregation and decohesion in NiAl

Grand canonical Monte Carlo simulations are performed to study grain boundary segregation in the ordered intermetallic compound NiAl. The embedded atom method is applied to model atomic interactions in NiAl. The structure and chemical composition of Σ=5 (210) [001] and Σ=5 (310) [001] symmetrical tilt grain boundaries are studied as functions of the bulk composition at 1200 K. The grain boundaries tend to be enriched in Ni. Deviations of the bulk composition from the stoichiometry towards Ni-rich compositions increase local disorder and enhance Ni segregation at the grain boundaries. In one of the boundaries, the Ni segregation induces a structural transformation to a new metastable grain boundary structure. The effect of grain boundary disorder and segregation on grain boundary decohesion is evaluated by simulated tensile tests.     

Continuum simulations of the formation of Kirkendall-effect-induced hollow cylinders in a binary substitutional alloy

We examine binary substitutional diffusion in cylindrical diffusion couples in which free surfaces are considered explicit vacancy sources and sinks. The central region of the cylinder is initially occupied by an atomic species with a larger hop frequency, while the outer region is occupied by another atomic species with a smaller hop frequency. Equilibrium vacancy concentration is maintained at free surfaces that serve as vacancy sources and sinks. In the crystal, diffusion is governed by the standard diffusion equations with analytically evaluated diffusion coefficients. The void growth dynamics and hollow cylinder formation stemming from the Kirkendall effect are simulated. Our results show that the Kirkendall void growth involves two competing factors. One is the net inward vacancy flux that favors void growth. The other is the Gibbs–Thomson effect that favors void shrinkage. We compute the critical initial radius for void growth above which the Kirkendall effect dominates over the Gibbs–Thomson effect. The fully grown void radius and the elapsed time to the fully grown size are also predicted for different fast-diffuser volume fractions and fast-to-slow diffuser atomic hop frequency ratios.     

A MONTE CARLO SIMULATION OF THE CVD DIAMOND FILM

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Electrochemical polishing as a 316L stainless steel surface treatment method: Towards the improvement of biocompatibility

A 316L stainless steel (316L-SS) surface was electrochemically polished (EP) in an electrolyte of a new chemical composition at different cell voltages, with the aim of improving its corrosion resistance and biocompatibility. X-ray photoelectron spectroscopy results revealed that the EP-formed oxide films were characterized by a significantly higher atomic Cr/Fe ratio and film thickness, in comparison to the naturally-grown passive oxide film formed on the untreated (control) 316L-SS surface. As a result of the increase in the oxide film thickness and relative Cr enrichment, the EP-treated 316L-SS surfaces offered a notable improvement in general corrosion resistance and pitting potential. In addition, the attachment of endothelial cells (ECs) and smooth muscle cells (SMCs) to the 316L-SS surfaces revealed a positive effect of electropolishing on the preferential attachment of ECs, thus indicating that the EP surfaces could be endothelialized faster than the control (unmodified) 316L-SS surface. Furthermore, the EP surfaces showed a much lower degree of thrombogenicity in experiments with the platelet-rich plasma. Therefore, the use of the electrochemical polishing technique in treating a 316L-SS surface, under the conditions presented in this paper, indicates a significant improvement in the surface’s performance as an implant material.     

Monte Carlo simulations of the structure of Pt-based bimetallic nanoparticles

Pt-based bimetallic nanoparticles have attracted significant attention as a promising replacement for expensive Pt nanoparticles. In the systematic design of bimetallic nanoparticles, it is important to understand their preferred atomic structures. However, compared with unary systems, alloy nanoparticles present greater structural complexity with various compositional configurations, such as mixed-alloy, core–shell, and multishell structures. In this paper, we developed a unified empirical potential model for various Pt-based binary alloys, such as Pd–Pt, Cu–Pt, Au–Pt and Ag–Pt. Within this framework, we performed a series of Monte Carlo (MC) simulations that quantify the energetically favorable atomic arrangements of Pt-based alloy nanoparticles: an intermetallic compound structure for the Pd–Pt alloy, an onion-like multishell structure for the Cu–Pt alloy, and core–shell structures (Au@Pt and Ag@Pt) for the Au–Pt and Ag–Pt alloys. The equilibrium nanoparticle structures for the four alloy types were compared with each other, and the structural features can be interpreted in terms of the interplay of their material properties, such as the surface energy and heat of formation.