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.

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.

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.

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.

Interdiffusion in the Fe_2O_3-TiO_2 system

Interdiffusion in the Fe203-TiO2 system was investigated by the diffusion couple method in the temperature range of 1323 to 1473 K. The diffusion concentration curves of Ti4＋ cations were obtained by electron probe microanalysis, according to which the Boltzmann-Matano method optimized by Broeder was used to calculate the interdiffusion coeffi- cients. The interdiffusion coefficients almost increased linearly with the mole fraction of Ti4＋ cations increasing, and they were in the range of 10-12-10-11cm2-s-1. The increase of temperature could also lead to the increase of the interdiffusion coefficients at a constant concentration of Ti4＋ cations. It was also found that the thickness growth of the diffusion layer obeyed the parabolic rate law.

High-throughput studies and machine learning for design of β titanium alloys with optimum properties

Based on experimental data,machine learning(ML) models for Young's modulus,hardness,and hot-working ability of Ti-based alloys were constructed.In the models,the interdiffusion and mechanical property data were high-throughput re-evaluated from composition variations and nanoindentation data of diffusion couples.Then,the Ti-(22±0.5)at.%Nb-(30±0.5)at.%Zr-(4±0.5)at.%Cr(TNZC) alloy with a single body-centered cubic(BCC) phase was screened in an interactive loop.The experimental results exhibited a relatively low Young's modulus of(58±4) GPa,high nanohardness of(3.4±0.2) GPa,high microhardness of HV(520±5),high compressive yield strength of(1220±18) MPa,large plastic strain greater than 30%,and superior dry-and wet-wear resistance.This work demonstrates that ML combined with high-throughput analytic approaches can offer a powerful tool to accelerate the design of multicomponent Ti alloys with desired properties.Moreover,it is indicated that TNZC alloy is an attractive candidate for biomedical applications.

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.

Investigation of mechanical and diffusion properties in bcc Ti−Nb−Zr−Sn alloys via a high-throughput method

The mechanical and diffusion properties of bcc Ti−Nb−Zr−Sn alloys in the Ti-rich corner were analyzed through a high-throughput method with the combination of nanoindentation and diffusion couple techniques.Nine groups of quaternary Ti−Nb−Zr−Sn diffusion couples were prepared after annealing at 1273 K for 25 h.The composition-dependent mechanical properties were determined by nanoindentation and electron probe microanalysis(EPMA)techniques.Moreover,the corresponding interdiffusion coefficients were confirmed from the composition gradients of the quaternary diffusion couples using a pragmatic numerical inverse method.A composition-dependent database on the mechanical and diffusion properties was utilized to discuss the processability during the hot working.The results reveal that the solute elements Nb and Sn are strictly controlled to increase the hardness and wear resistance of Ti−Nb−Zr−Sn alloys,and the additional element Zr is mainly useful to improve the processability during the hot working.

High-throughput determination of mechanical and diffusion properties of Ti–Ta–Fe alloys

The mechanical and diffusion properties of Ti-Ta-Fe alloys in the Ti-rich region were investigated by utilizing a high-throughput method, with the combination of nanoindentation and diffusion couple techniques.Five groups of ternary Ti-Ta-Fe diffusion couples were prepared after annealing at 1273 K for 25 h. The composition-dependent mechanical properties of bcc Ti-Ta-Fe system were experimentally determined by means of nanoindentation and electron probe microanalysis(EPMA) techniques. Moreover, the interdiffusion coefficients of Ti-Ta-Fe alloys at 1273 K were confirmed from the composition gradients of the ternary diffusion couples with the support of a pragmatic numerical inverse method. A composition-dependent database on the mechanical and diffusion properties of Ti-Ta-Fe alloys was carefully established and utilized for the discussion of the processability during the hot working. The results indicated that the content of Fe should be controlled for the Ti alloys with high hardness and low Young’s modulus.

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.

Anisotropic diffusion of volatile pollutants at air-water interface

The volatile pollutants that spill into natural waters cause water pollution. Air pollution arises from the water pollution because of volatilization. Mass exchange caused by turbulent fluctuation is stronger in the direction normal to the air-water interface than in other directions due to the large density difference between water and air. In order to explore the characteristics of anisotropic diffusion of the volatile pollutants at the air-water interface, the relationship between velocity gradient and mass transfer rate was established to calculate the turbulent mass diffusivity. A second-order accurate smooth transition differencing scheme （STDS） was proposed to guarantee the boundedness for the flow and mass transfer at the air-water interface. Simulations and experiments were performed to study the trichloroethylene （C2HC13） release. By comparing the anisotropic coupling diffusion model, isotropic coupling diffusion model, and non-coupling diffusion model, the features of the transport of volatile pollutants at the air-water interface were determined. The results show that the anisotropic coupling diffusion model is more accurate than the isotropic coupling diffusion model and non-coupling diffusion model. Mass transfer significantly increases with the increase of the air-water relative velocity at a low relative velocity. However, at a higher relative velocity, an increase in the relative velocity has no effect on mass transfer.

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.

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.

DIFFUSION REACTIONS BETWEEN Cu AND NbTi-ALLOY

Diffusion reaction of superconductig composite NbTi/Cu assembled both mechanically and metallurgically,diffusion couples Ti/Cu and Nb/Cu have/been studied by means of EPMA.The results indicate that the initial interface state of the composite NbTi/Cu significantly affects the forming process of intermetallic compounds at the interface.In comparison with the metallurgically bound composite,the intermetallic com- pounds forms at a higher temperature in mechanically bound one.Therefore.the mechanical hinding process is beneficial to the production of NbTi/Cu superconducting composite. No intermetallic compounds have been observed in Nb/Cu system.The morphology of intermetallic phases and the sequence in which they form in Ti/Cu system are somewhat different from that in NbTi/Cu.The relationship between the thickness of compound layer and annealing time obeys the rule of y^(1.5) ∝ t.

Linearization of Systems of Nonlinear Diffusion Equations

We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.

Numerical simulation of intermediate phase growth in Ti/Al alternate foils

To investigate the diffusion reaction between Ti/Al solid diffusion couple, Ti/Al alternate foils formed by hot pressing were annealed at 525, 550, 575 and 600 °C for time ranging from 1 to 40 h. The experimental results show that TiAl3 was the only observed phase at Ti/Al interface. The interface thermodynamics favored the preferential formation of TiAl3 in Ti/Al couple. The growth of TiAl3 layer occurred mainly towards Al foil side and exhibited a parabolic law. Using the interdiffusion coefficients calculated based on the contribution of grain boundary diffusion, the growth of TiAl3 was simulated numerically with the finite difference method, and the simulated results were in good agreement with the experimental ones.

Directional growth behavior of a(Al) dendrites during concentration-gradientcontrolled solidification process in static magnetic field

The large and small sized Cu（solid）/Al（liquid） couples were prepared to investigate the directional growth behavior of primary a（Al） phase during a concentration-gradient-controlled solidification process under various static magnetic fields（SMFs）.The results show that in the large couples,the α（Al） dendrites reveal a directional growth character whether without or with the SMF.However,the 12 T magnetic field induces regular growth,consistent deflection and the decrease of secondary arm spacing of the dendrites.In the small couples,the α（Al） dendrites still reveal a directional growth character to some extent with a SMF of ≤5 T.However,an 8.8 T SMF destroys the directional growth and induces severe random deflections of the dendrites.When the SMF increases to 12 T,the a（Al） dendrites become quite regular despite of the consistent deflection.The directional growth arises from the continuous long-range concentration gradient field built in the melt.The morphological modification is mainly related to the suppression of natural convections and the induction of thermoelectric magnetic convection by the SMF.

Formation of Intermetallic Compound in Iron-Aluminum Alloys

The mechanism of iron and aluminum intermetallics formation in the reactive sintering of iron and aluminum mixing powders has been studied by investigating iron aluminum diffusion couples.The couples were treated at 600℃,700℃,800℃,900℃ and 1000℃ respectively.It was found that an Al rich intermetallics FeAl 3 has formed in iron adjacent to the interface of iron and aluminum by aluminum diffusion into iron at 600℃ (below the eutectic temperature),and that in the case above 700℃ (above the eutectic temperature) there was a liquid,an intermetallics Fe 2Al 5 has formed in both side of the interface.The diffusion of iron and aluminum atoms is companied with the Fe Al reaction during the treatment under the both conditions.The diffusion coefficients of iron and aluminum and the activation energy were determined.The mechanism of the intermetallics formation in the couples is also discussed.