High entropy alloys (HEAs) are equimolar multi-principal-element alloys (MPEAs) that are different from traditional solvent-based multicomponent alloys based on the concept of alloy design. Based on initial work by Yeh and co-workers, HEAs were postulated to exhibit four “core” effects: high entropy, sluggish diffusion, lattice distortion, and cocktail effect. Out of these four proposed core effects, “high entropy” and “sluggish diffusion” effects were most debated in the literature as these core effects directly affect the thermodynamic and kinetic understanding of HEAs. The initial work on HEAs by several researchers utilized these effects to indirectly support the experimentally observed “unique” properties, without independent investigation of these core effects. The presumed implications of these core effects resulted in justification or generalization of properties to all HEAs, e.g., all HEAs should exhibit high temperature stability based on high entropy effect, high temperature strength owing to limited grain growth, good diffusion barrier application due to sluggish diffusion kinetics, etc. However, many recent studies have challenged these core effects, and suggested that not all HEAs were observed to exhibit these core effects.
Kinetic Monte Carlo simulations are a useful tool to predict and analyze the ionic conductivity in crystalline materials. We present here the basic functionalities and capabilities of our recently published Monte Carlo software for solid state ionics called MOCASSIN, exemplified by simulations of several model systems and real materials. We address the simulation of tracer correlation factors for various structures, the correlation in systems with complex migration mechanisms like interstitialcy or vehicle transport, and the impact of defect interactions on ionic conductivity. Simulations of real materials include a review of oxygen vacancy migration in doped ceria, oxygen interstitial migration in La-rich melilites, and proton conduction in acceptor doped fully hydrated barium zirconate. The results reveal the impact of defect interactions on the ionic conductivity and the importance of the defect distribution. Combinations of these effects can lead to unexpected transport behavior in solid state ionic materials, especially for multiple mobile species. Kinetic Monte Carlo simulations are therefore useful to interpret experimental data which shows unexpected behavior regarding the dependence on temperature and composition.
A novel study of interdiffusion analysis in multicomponent alloys is presented. A custom written Matlab fitting program (MFP) is used as the main tool for the present study. The interdiffusion matrices are obtained using a newly developed mathematical approach based on the fitting into the closed form solution for the composition profiles. Overall, the new fitting method gives very good outcomes and allows the probing of multiple solutions (validated by back tests) that exist when a single diffusion couple is used in a multicomponent system. An important finding of the present investigations is that small differences in composition profiles may lead to large differences in the interdiffusion coefficients.
We review the results of our Monte Carlo simulation studies carried out within the past two decades in the area of atomic-migration-controlled phenomena in intermetallic compounds. The review aims at showing the high potential of Monte Carlo methods in modelling both the equilibrium states of the systems and the kinetics of the running processes. We focus on three particular problems: (i) the atomistic origin of the complexity of the ‘order-order’ relaxations in γ’-Ni3Al; (ii) surface-induced ordering phenomena in γ-FePt and (iii) ‘order—order’ kinetics and self-diffusion in the ‘triple-defect’ β-NiAl. The latter investigation demonstrated how diverse Monte Carlo techniques may be used to model the phenomena where equilibrium thermodynamics interplays and competes with kinetic effects.
Tracer diffusion is one of most reliable techniques for providing basic kinetic data in solids. In the present review, selected direct methods, in particular the radiotracer measurements as a superior technique due to its high sensitivity, Secondary-Ion-Mass-Spectroscopy (SIMS) profiling, X-Ray Diffraction measurements and Rutherford Backscattering Spectrometry are presented and discussed. Special attention is put on the radiotracer technique describing the currently used sectioning techniques in detail with a focus on the experimental applications and complications. The relevant experimental results are exemplary shown. Furthermore, the most recent developments and advances related to the combined tracer/inter-diffusion measurements are highlighted. It is shown that this approach offers possibilities to provide the concentration-dependent tracer diffusion coefficients of the constituting elements in multi-component alloys in high-throughput experiments. Possibilities of estimating the tracer diffusion coefficients following different types of diffusion couple methods in binary and multicomponent systems are briefly introduced. Finally, specificity of SIMS analysis of diffusion in fine-grained materials are carefully analyzed. If applicable, a direct comparison of the results obtained by different techniques is given.
A novel study of analysis interdiffusion in multicomponent alloys is investigated by means of closed form solutions and numerical simulations. Quaternary as well as selected CoCrFeMnNi (HEAs) quinary metallic systems are analysed using one, two and three diffusion couples with the full set of interdiffusion coefficients being calculated. A custom written Matlab fitting program (MFP) is used as the main tool for the simultaneous fitting into multiple composition profiles in both systems. The retrieved interdiffusion matrices are obtained using a newly developed approach that is interlinked with composition vectors, eigenvalues and eigenvector. On average, it can be concluded that the accuracy of the obtained matrices steadily improves with the increase of the number of couples used in the analysis.
In this paper, a brief history of the contributions of many of the major researchers in the field of solid state diffusion is presented starting from 1829 up to the present day. People who are still making significant contributions to the field are mentioned. The authors are well aware that such an attempt is necessarily incomplete and inevitably based on personal knowledge and flavour.
The kinetic properties such as diffusivity and viscosity of the metal melt are the foundations to reveal the structure evolutions and the glass formation abilities during solidification of the investigated alloy, thus, to control the microstructures, defects and properties of materials. In this work, ab initio molecular dynamics simulations were utilized to investigate the kinetic and thermodynamic properties and the structural relaxations of Fe-X (X = 10-15 wt% Al, Cr, Mn and Ti, or 1-2wt% B and C) melts under various temperature and external pressure, which are in line with the interested concentration range of multi-component Fe-based alloys. The kinetics and structural relaxations are characterized by mean squared displacement, velocity autocorrelation function and self-intermediate scattering function. The thermodynamics properties including entropy and heat capacity are calculated by combining the vibrational and electronic contributions based on vibrational and electronic density of states. The predicted kinetics and thermodynamics properties under high temperature and pressure agree well with the experimental and theoretical results while the connection among structural relaxations and diffusion are revealed based on the Stokes-Einstein relation and the Hall-Wolynes (HW) relation. This work provides an insight into the structure-property relationships of metal melts, which are essential in the development of advanced multi-component Fe-based alloys.
CoSb based compounds have gained much importance in the fields of thermoelectric devices. In this work, we have conducted the solid–state conventional bulk diffusion couple experiments. To study the phase evolutions, Co/Sb diffusion couples are annealed at 450–550 °C. The interdiffusion zone is analysed using field emission gun equipped scanning electron microscope and the composition measurements are done in electron probe micro−analyser to confirm the growth of various product phases. The marker experiment indicates that the CoSb3 phase grows mainly by diffusion of Sb in the binary Co–Sb system. Growth of the CoSb3 phase is discussed based on assessment correlating the difference in mobilities of species with the high homologous temperature, crystal structure of the phase, and the concept of sublattice diffusion mechanism in line compounds.
An analysis of aCasson fluid flowing over a porous exponentially stretching surface with radiation has been studied. A non-Newtonian fluid model was developed for the flow and similarity analysis used in the transformation process. The model of partial differential equations was transformed into ordinary differential equations and reduced into a system of first order differential equations which was then solved using the Fourth-order Runge-Kutta algorithm alongside the Newton Raphson shooting method. The results have been presented graphically and in tabular form for various controlling parameters of the problem. It is observed that general control can be achieved by the permeability of the surface and the value of the Casson parameter.
This article investigates the boundary layer flow and heat transfer of an electrically conducting Casson fluid over a stretching wedge by considering the effects of suction/injection, velocity and thermal slips and thermal radiation. By applying the appropriate similarity transformations,the governing partial differential equations are transformed to highly non-linear ordinary differential equations. These resulting similarity equations are then solved by a new analytic method namely DTM-BF, based on differential transformation method (DTM) and base function (BF). A comparativestudy of the present numerical results has been made with the already published results available in the literature. The effects of various governing parameters on the flow and heat transfer characteristics have been discussed graphically.
The effect of viscous dissipation on heat transfer through nano-fluid in a vertical wavy channel filled with porous media has been studied. The consequential differential equations are simplified by the R-K method of 6th order. The numerical obtained results are shown in the graphs. The significant results of fluid flow and heat transfer rate and its properties are shown graphically. Nusslet values are calculated a for varying the governing parameters φ Da, Gr, ε, Ec and the remaining parameters are to be constants.
The discrete Frenkel-Kontorova model for the movement of a foreign atom in a solid, obtained in the local chains approximation, led to the movement of the atom in the Frenkel-Kontorova ( F-K ) soliton form. This model made it possible to reveal the structure of the F-K soliton, to design the shapes of nanostructures and to take into account their influence on the F-K soliton. The transition to field variables leads the Frenkel-Kontorova equation to the sine-Gordon equation for the displacement field of an atom having solutions also in the form of a soliton. This equation and its solution (soliton) contains coefficients depending on the shape and size of nanostructures. The transition to the sine-Gordon equation allowed us to use the results of Theodorakopoulos 's works related to the consideration of the interaction of elastic vibration modes with a soliton. This made it possible to calculate the diffusion coefficient of the soliton and find the dependence of the diffusion coefficient on the shape and size of nanostructures and temperature.
Polymeric plastic boxes (named Front Opening Unified Pods (FOUP)) were widely used in semiconductor manufacture to maintain the cleanliness of processed wafer substrates in a controlled mini-environment. Polymeric materials, however, are able to sorb airborne molecular contaminants (AMCs) and subsequently to outgas the sorbed AMCs backward to FOUP’s atmosphere, causing the transfer of AMCs to sensitive stored substrates, named cross-contamination. As a type of AMCs, the NH3 cross-contamination could cause a severe yield loss to integrated circuits (crystals (haze), resist-development defects (T-topping) or metallic corrosion). Experiments were carried out to establish the NH3 sorption and desorption kinetics in polyetherimide (PEI), Entegris Barrier Material (EBM)), and EBM/carbon nanotubes (EBMCNT) at NH3 concentration of 800-ppbv, 21°C, and relative humidity of 40%. The transport coefficients i.e. solubility and diffusivity (DNH3 and SNH3) were then determined. The study on NH3 provides an additional guideline to choose the best raw materials for FOUP formulation in taking into account the potential cross-contamination of AMCs. Numerical simulation model based on obtained solubility and diffusivity values was conducted to demonstrate NH3 concentration profiles in FOUP walls during contamination and FOUP decontamination, which are inaccessible by conventional experiments.
In the present paper, we investigated mathematical model of the magnetohydrodynamic flow and heat transfer in an electro-conductive polymer on the externalsurface of a semi-infinite vertical plate under radial magnetic field. Thermal radiation andconvective heating effects are considered at the semi-infinite plate surface with modifiedboundary conditions. The Williamson viscoelastic model is employed which isrepresentative of certain industrial polymers. The non-dimensional, transformedboundary layer equations for momentum and energy are solved with the second orderaccurate implicit Keller box finite difference method under appropriate boundaryconditions. Validation of the numerical solutions is achieved via benchmarking withearlier published results. The influence of Williamson viscoelastic fluid parameter,magnetic body force parameter, convective heating, radiation parameter, stream wisevariable and Prandtl number on thermos-fluid characteristics are studied graphically. Themodel is relevant to the simulation of magnetic polymer materials processing.
