Formation and Growth Kinetics of Intermediate Phases in Ni-Al Diffusion Couples

Formation and growth of the intermediate phases in the Ni-Al diffusion couples prepared by pouring technique were investigated. Electron probe microanalysis, scanning electron microscopy and X-ray diffraction were used to characterize the product phases in the joints. The results show that two intermediate phases form in the sequence of NiAl3 and Ni2Al3 during solidification. After annealed, Ni2Al3 and NiAl3 still exist in the joints of the couples. The reasons for the formation of Ni2Al3 and NiAl3, as well as the absence of NiAl, Ni5Al3 and Ni3Al were discussed, respectively. The growth kinetics of both product phase layers indicates that their growth obeys the parabolic rate law. The activation energies and frequency factors for NiAl3 and Ni2Al3 phases were also calculated according to the Arrhenius equation.

Preparation of Y-Zr-Hf,Y-Zr-Nb Ternary Diffusion Couples and Phase Diagrams Determination

Work has been done in preparing ternary diffusion couple containing one rare earth element.Though rare earth is highly reactive,we have successfully prepared two ternary diffusion couples containing yttrium by means of special technique.By using electron microprobe analysis(EMPA),the two isothermal sections of Y-Zr-Hf and Y-Zr-Nb ternary systems at 1273K have been determined.The section of Y-Zr-Hf system consists of three one-phase regions,three two-phase regions and one three-phase region.And that of Y-Zr-Nb system consists of two one-phase regions and one two-phase region.The effeet of some factors on EMP measuring ac- curacy was also discussed.

Self-organized layered growth phenomena of diffusion couples with spinodal decomposition in binary alloys

In order to investigate the formation mechanisms of the layered growth phenomena in diffusion couples with spinodal decomposition,a phase field model combined with elastic strain field was employed.Microstructure evolutions of diffusion couple with spinodal decomposition in binary alloys were numerically simulated by considering concentration fluctuation and elastic anisotropy.The simulation results indicate that the number of the periodical layers decreases with the increase of initial concentration fluctuation,even with large elastic anisotropy.The growth of layered microstructures can be attributed to the directional diffusion enhanced by initially discontinuous chemical potential at the interface.

Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface(downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.

Cellular Automata-based Chloride Ion Diffusion Simulation of Concrete Bridges under Multi-factor Coupling Actions

In order to accurately simulate the diffusion of chloride ion in the existing concrete bridge and acquire the precise chloride ion concentration at given time, a cellular automata （CA）-based model is proposed. The process of chloride ion diffusion is analyzed by the CA-based method and a nonlinear solution of the Fick＇s second law is obtained. Considering the impact of various factors such as stress states, temporal and spatial variability of diffusion parameters and water-cement ratio on the process of chloride ion diffusion, the model of chloride ion diffusion under multi-factor coupling actions is presented. A chloride ion penetrating experiment reported in the literature is used to prove the effectiveness and reasonability of the present method, and a T-type beam is taken as an illustrative example to analyze the process of chloride ion diffusion in practical application. The results indicate that CA-based method can simulate the diffusion of chloride ion in the concrete structures with acceptable precision.

Analytical evaluation of steady-state solute distribution in through- diffusion and membrane behavior test under non-perfectly flushing boundary conditions

The through-diffusion and membrane behavior testing procedure using a closed-system apparatus has been widely used for concurrent measurement of diffusion and membrane efficiency coefficients of low-permeability clay-based barrier materials.However,the common assumption of perfectly flushing conditions at the specimen boundaries could induce errors in analyses of the diffusion coefficients and membrane efficiencies.In this study,an innovative pseudo three-dimensional(3D)analytical method was proposed to evaluate solute distribution along the boundary surfaces of the soil-porous disks system,considering the non-perfectly flushing conditions.The results were consistent with numerical models under two scenarios considering different inflow/outflow positions.The proposed model has been demonstrated to be an accurate and reliable method to estimate solute distributions along the bound-aries.The calculated membrane efficiency coefficient and diffusion coefficient based on the proposed analytical method are more accurate,resulting in up to 50%less relative error than the traditional approach that adopts the arithmetic mean value of the influent and effluent concentrations.The retar-dation factor of the clay specimen also can be calculated with a revised cumulative mass approach.Finally,the simulated transient solute transport matched with experimental data from a multi-stage through-diffusion and membrane behavior test,validating the accuracy of the proposed method.

Determination of phase diagrams using the diffusion couple technique

It has been demonstrated that the diffusion couple technique is a powerful and efficient approach in establishing phase relationships of ternary systems. Accurate data on the phase equilibria can be obtained if the appropriate alloys are employed as end members of the diffusion couple. It is desirable to combine the diffusion couple technique with an investigation of the afterwards selected equilibrated alloys so that the precision and reliability of the obtained information about a ternary isotherm could be guaranteed.

Comparison of the interface reaction behaviors of CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) solid-state systems based on the diffusion couple method

The formation mechanism of calcium vanadate and manganese vanadate and the difference between calcium and manganese in the reaction with vanadium are basic issues in the calcification roasting and manganese roasting process with vanadium slag.In this work,CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples were prepared and roasted for different time periods to illustrate and compare the diffusion reaction mechanisms.Then,the changes in the diffusion product and diffusion coefficient were investigated and calculated based on scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) analysis.Results show that with the extension of the roasting time,the diffusion reaction gradually proceeds among the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples.The regional boundaries of calcium and vanadium are easily identifiable for the CaO–V_(2)O_(5) diffusion couple.Meanwhile,for the MnO_(2)–V_(2)O_(5) diffusion couple,MnO_(2) gradually decomposes to form Mn_(2)O_(3),and vanadium diffuses into the interior of Mn_(2)O_(3).Only a part of vanadium combines with manganese to form the diffusion production layer.CaV_(2)O_(6) and MnV_(2)O_(6) are the interfacial reaction products of the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples,respectively,whose thicknesses are 39.85 and 32.13μm when roasted for 16 h.After 16 h,both diffusion couples reach the reaction equilibrium due to the limitation of diffusion.The diffusion coefficient of the CaO–V_(2)O_(5) diffusion couple is higher than that of the MnO_(2)–V_(2)O_(5) diffusion couple for the same roasting time,and the diffusion reaction between vanadium and calcium is easier than that between vanadium and manganese.

STUDY ON THE DIFFUSION OF Cu^(2+)-H^+ COUPLE IN A CATION EXCHANGE MEMBRANE——A RAPID METHOD TO DETERMINE SELF-DIFFUSION COEFFICIENTS OF COUNTER-IONS WITH UNEQUAL VALENCE

1 INTRODUCTIONKnowledge of the basic transport phenomena of ions in an ion exchange membrane isimportant for the application of such a membrane.Various studies on the developmentof mathematical models for predicting and correlating membrane transport rate havebeen published in recent years.More exact estimation of the diffusion coefficientshas been the subject of chief concern in many of these papers.For a bi-ionic systemwith the same valence,Sato et al.gave a method for estimating diffusion coefficients

Investigation on the temperature-dependent diffusion growth of intermetallic compounds in the Mg-Al-Zn system:Experiment and modeling

With the rapid development of Mg alloys,deeper understanding to the thermodynamic and diffusional kinetic behavior of intermetallic compounds(IMCs)is important for studying the effect of alloying elements to the microstructure evolution.Specially,a systematic quantitative investigation on the diffusional growth of IMCs is of great necessity.However,the works studying the elemental diffusion behaviors of multiple-element IMCs are rare in magnesium alloy systems.The current work takes the ternary Mg-Al-Zn system as research target,and combines the diffusion couple technique,phase stability diagrams,in-situ observation technique and numerical inverse method to investigate the temperature-dependent kinetic coefficients.The parabolic growth constant(PGC)and interdiffusion coefficients for Mg solid-solution phase andγ-Mg_(17)Al_(12),β-Mg_(2)Al_(3),ε-Mg_(23)Al_(30),MgZn_(2),Mg_(2)Zn_(3),τ-Mg_(32)(Zn,Al)49 andφ-Mg_(5)Zn_(2)Al_(2) IMCs in the Mg-Al-Zn alloy system are determined.By comparing the current experimental with calculation results,the rate-controlling factor of the temperature-dependent diffusion growth ofφ,τandεternary IMCs in the Mg-Al-Zn system is further discussed in detail.

Diffusion coefficient of Ti^4+ in calcium ferrite/calcium titanate diffusion couple

This study investigated the interdiffusion of calcium ferrite/calcium titanate system in the time range of 0-120 min by the diffusion couple method in a CO/N2 reducing atmosphere at 700℃.The results show that after the diffusion reaction occurred,no longitudinal agglomerations were present on the substrate surface on the calcium titanate side.When the diffusion time was increased to 105 min,a net vacancy flow from calcium titanate to calcium ferrite might have occurred,causing the surface of the calcium ferrite substrate to collapse.The thickness of the diffusion layer of the calcium ferrite/calcium titanate system was about 17-48μm,which conforms to the parabolic law of diffusion.The diffusion coefficient and the Ti^4+concentration in the calcium ferrite/calcium titanate system are related.This shows an increase in the diffusion coefficient with the increase of Ti^4+concentration,and the diffusion coefficient value was in the range of 10^−12-10^−11 cm^2·s^−1.

Simulation Study of Passive Rod Diffusion in Active Bath:Nonmonotonic Length Dependence and Abnormal Translation-Rotation Coupling

Diffusion of tracer particles in active bath has attracted extensive attention in recent years.So far,most studies have considered isotropic spherical tracer particles,while the diffusion of anisotropic particles has rarely been involved.Here we investigate the diffusion dynamics of a rigid rod tracer in a bath of active particles by using Langevin dynamics simulations in a two-dimensional space.Particular attention is paid to how the translation(rotation)diffusion coefficient D_(T)(D_(R))change with the length of rod L and active strength Fa.In all cases,we find that rod exhibits superdiffusion behavior in a short time scale and returns to normal diffusion in the long time limit.Both D_(T) and D_(R) increase with Fa,but interestingly,a nonmonotonic dependence of D_(T)(D_(R))on the rod length has been observed.We have also studied the translation-rotation coupling of rod,and interestingly,a negative translation-rotation coupling is observed,indicating that rod diffuses more slowly in the parallel direction compared to that in the perpendicular direction,a counterintuitive phenomenon that would not exist in an equilibrium counterpart system.Moreover,this anomalous(diffusion)behavior is reentrant with the increase of Fa,suggesting two competitive roles played by the active feature of bath particles.

Analytical solution for coupled diffusion of three-components liquid in porous pellet

The coupled three-components liquid diffusion within a porous pellet was investigated. The coupled diffusion model was given according to irreversible thermodynamics, and the rigorous solutions of the model subject to the homogeneous boundary conditions of the first kind are derived by employing Hankel transform technique and the standard technique resolving ordinary differential system. The method can also be used to solve the other coupled diffusion problems within a pellet with different kinds of boundary conditions. Then the case computations were conducted. The calculation results show that the effect of interdiffussion on the concentration of components depends upon the diffusion time strongly, after a long diffusion period, a very small cross diffusion coefficient will induce the observable change of concentration profile, and that, when the cross coefficients are close to 5%7% of the main coefficients, the significant effect of coupled diffusion on the concentration profiles of components is observed. The case computations also show that interdiffussion can induce non-monotonous concentration profiles. So, for the diffusion taking place within ternary system, the concentration profiles obtained by the analysis of interdiffussion can be very different from that obtained by the equivalent binary system analysis method.

Effect of alternative magnetic field on the diffusion layer growth in Al/Zn couple

The influence of an alternative magnetic field on the growth of the diffusionlayer in Al-Zn diffusion couple was studied. The thickness of the diffusion layer was examined. Theresults show that the alternative magnetic field increases the thickness of the diffusion layer andthe effect increases with the intensity and frequency of the alternative magnetic field increasing. The growth of the diffusion layer obeys the parabolic rate law and the growth rateincreases with the application of the alternative magnetic field. This growth rate change ismanifested through a change in the frequency factor k_0 and not through a change in the activationenergy Q. The frequency factor k_0 for the diffusion layer growth with the alternative magneticfield is 5.03 cm^2/s and the one without the magnetic field is 3.84 cm^2/s.

Intervention against information diffusion in static and temporal coupling networks

Information diffusion in complex networks has become quite an active research topic.As an important part of this field,intervention against information diffusion processes is attracting ever-increasing attention from network and control engineers.In particular,it is urgent to design intervention schemes for the coevolutionary dynamics between information diffusion processes and coupled networks.For this purpose,we comprehensively study the problem of information diffusion intervention over static and temporal coupling networks.First,individual interactions are described by a modified activitydriven network(ADN)model.Then,we establish a novel node-based susceptible-infected-recovered-susceptible(SIRS)model to characterize the information diffusion dynamics.On these bases,three synergetic intervention strategies are formulated.Second,we derive the critical threshold of the controlled-SIRS system via stability analysis.Accordingly,we exploit a spectral optimization scheme to minimize the outbreak risk or the required budget.Third,we develop an optimal control scheme of dynamically allocating resources to minimize both system loss and intervention expense,in which the optimal intervention inputs are obtained through optimal control theory and a forward-backward sweep algorithm.Finally,extensive simulation results validate the accuracy of theoretical derivation and the performance of our proposed intervention schemes.

Coupling for Markovian switching jump-diffusions

This work is concerned with coupling for a class of Markovian switching jump-diffusion processes.The processes under consideration can be regarded as a number of jump-diffusion processes modulated by a Markovian switching device.For this class of processes,we construct a successful coupling and an order-preserving coupling.

Numerical solution to T-φ_S-C_L coupling in binary dendrite solidification with any solid-back diffusion effects

A previous numerical solution method to the strong nonlinear T φ S C L coupling for a Scheil type binary solidification process was extended and modified for single phase dendrite solidifications of any nominal alloy composition(in a composition range of single phase or eutectic solidification) and with any solid back diffusion extents. Numerical sample computations were performed on Al Cu system with different nominal compositions from almost pure Al to nearly eutectic and with different solid diffusion coefficients, which are factitiously enlarged or decreased in eight orders of magnitude. The calculation results exhibit the feasibility, capability and efficiency of the proposed numerical scheme in modeling an arbitrary binary dendrite solidification problem.

Atomic interdiffusion in Ni-Cu system under high magnetic field

The effect of high magnetic field on the atomic interdiffusion in Ni-Cu system was studied using the Cu/Ni/Cu diffusion couples. During the atomic interdiffusion in Ni-Cu system, it was found that the interdiffusion coefficients increased with the increase of molar fraction of Ni atoms in the interdiffusion zones when the couples were annealed with or without the magnetic field. It was noted that all corresponding interdiffusion coefficients under the magnetic field are smaller than those without the magnetic field. The results demonstrate that the magnetic field retards the atomic interdiffusion in Ni-Cu system. This retardation is achieved through reducing the frequency factors but not changing the interdiffusion activation energies.

GLOBAL EXISTENCE OF SOLUTIONS FOR A STRONGLY COUPLED REACTION-DIFFUSION SYSTEM

This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.

Role of Kirkendall effect in diffusion processes in solids

In the 1940s, KIRKENDALL showed that diffusion in binary solid solutions cannot be described by only one diffusion coefficient. Rather, one has to consider the diffusivity of both species. His findings changed the treatment of diffusion data and the theory of diffusion itself. A diffusion-based framework was successfully employed to explain the behaviour of the Kirkendall plane. Nonetheless, the complexity of a multiphase diffusion zone and the morphological evolution during interdiffusion requires a physico-chemical approach. The interactions in binary and more complex systems are key issues from both the fundamental and technological points of view. This paper reviews the Kirkendall effect from the circumstances of its discovery to recent developments in its understanding, with broad applicability in materials science and engineering.