Zero-flux Planes Research Articles

Delineating soil moisture dynamics within an evapotranspiration surface barrier using spatial‐temporal analysis

AbstractEvapotranspiration (ET) surface barriers store infiltrated precipitation during the recharge period and release the stored water to the atmosphere via ET. The primary purpose of a surface barrier is to reduce or eliminate drainage to the underlying waste zone. The objective of this study is to analyze the spatial and temporal dynamics of soil moisture within an ET surface barrier based on observed and simulated data. This study characterizes the water movement processes using contour plots of soil moisture content and flux rate in the depth‐time domain. Zero‐flux planes (ZFPs) divide the depth‐time domain into stored water, ET, and drainage zones. Some flow dynamics (e.g., flow rate and direction) that were not observed in the field were elaborated with simulation results to identify the depth of the recharge front of infiltrated water, the release front of stored water, and the bottom of the ET zone. The ET‐drainage divide marks the bottom of the ET zone and the top of the drainage zone. The results showed that the temporal analysis of soil moisture storage could indicate the degree of usage of the storage capacity of a surface barrier. The spatial‐temporal analyses of soil moisture content and flux rate can characterize the durations of the recharge/release processes and the depth of the stored water. Quantification of these processes and related zones provides beneficial understanding of the state and dynamics of soil moisture for a range of weather and vegetation conditions and is useful in optimizing the design of an ET surface barrier.

华北山区典型人工林土壤水势动态和水分运移规律

大规模植树造林工程有效缓解了我国北方水土流失等问题，但伴随植被生长和降水格局变化，水循环过程发生明显改变。土壤水分运动是水循环的关键过程，研究变化环境下人工林植被土壤水分运移规律，对植被生态恢复具有重要意义。基于2014-2018年多时间尺度（半小时、天、月和年）华北山区崇陵流域典型人工侧柏林和荒草土壤剖面水势监测数据，阐明不同植被覆盖下土水势动态变化规律，提出土壤水分运移和植被水分利用模式。研究结果表明：侧柏林土壤水势日变幅显著低于荒草植被，但土水势日变幅随土壤深度增加而减小的速率90 a侧柏依次大于60 a侧柏和荒草；月、年尺度侧柏林不同深度土水势变化对降水的响应大于荒草地，其中60 a侧柏林年均土水势与年降雨量显著线性相关（P<0.05）。由水势梯度和零通量面多年平均变化可知，90 a侧柏林0-50 cm土壤水呈下渗趋势，根系水力提升促使50-100 cm土壤水向上蒸散；60 a侧柏林0-20 cm、70-100 cm以及枯水年30-70 cm土壤水均以蒸散为主，根系可同时吸收利用表层和深层土壤水分；荒草地0-20 cm土壤水分蒸发强烈，且为根系主要吸水深度，20-100 cm土壤水稳定下渗。相比60 a侧柏林和荒草，90 a侧柏林的土壤调蓄能力增强，与荒草互被可减少植被间水分竞争，充分利用土壤水，从而减少流域内地表径流和土壤侵蚀量。;Large scale afforestation alleviates soil erosion effectively in North China. The water cycle has been consequently modified under plant growth and changing precipitation regimes. Soil water dynamics is critical to investigate the water cycle of planted forests under changing environment for plant restoration. In this study, multi-time scale (i.e. half-hourly, daily, monthly, and annual scales) analysis of soil water potential (SWP) was conducted based on long-term measurement of the SWP between 2014 and 2018 under 60 a and 90 a arborvitae (Platycladus orientalis) planted forests as well as weeds as a reference in Chongling catchment in the mountain area of North China. The temporal variations in vertical gradients of SWP and zero flux planes (ZFPs) were analyzed to propose the patterns of soil water movement and plant water utilization for three representative vegetation types. Results showed that the diurnal variation of the SWP appeared as a unimodal curve with a peak occurring between 13:00 and 14:00. Daily variation in the SWP of arborvitae was significantly small compared to that of weeds. Daily changes of SWP decreased with the increase of soil depth, while the declining rate was larger under 90 a arborvitae than that under 60 a arborvitae and weeds. It was evident that the SWP decreased gradually from April to June, reaching a minimum value of -305.3 cm with the standard deviation (SD) of 58.3 cm. Nevertheless, the SWP increased rapidly from July to August ((-215.7±105.9) cm) and then remained high during September to October ((-210.6±51.9) cm). The responses of SWP at different soil depths to precipitation under arborvitae at monthly and annual scale were greater than those under weeds. There was a significant linear relationship between the annual mean SWP and annual precipitation under 60 a arborvitae (P<0.05). Based on the depth distributions of SWP gradients and ZFPs in the experimental years, soil water infiltration was estimated to mainly appear at upper 50 cm depth but root hydraulic lift facilitated soil moisture moving upwards in the 50-100 cm layer under 90 a arborvitae. The soil moisture in the 0-20 cm and 70-100 cm layers as well as that in the 30-70 cm layer in dry year mainly moved upwards and were taken up by plant roots under 60 a arborvitae. Strong evaporation and root water uptake primarily occurred at the top of 20 cm for weeds, while soil water infiltrated steadily in the 20-100 cm layer. It was found that soil water storage capacity under 90 a arborvitae was stronger than that under 60 a arborvitae and weeds, as it had smaller soil bulk density and increased the saturated soil water content. The planted forest of 90 a arborvitae coexisting with weeds could reduce water competition among different species and improve the water use efficiency. Surface runoff as well as soil erosion would be further reduced in the catchment. This study demonstrated the modifications of soil water dynamics and water utilization of the representative planted forests on the basis of long-term observations and multi-time scale analysis of SWP in Chongling catchment. It provided new insights into ecological restoration and water management in North China under changing environment.

Investigations of Ternary Interdiffusion in β (BCC) Phase Field of Ti-Al-Mo Alloy System

Solid–solid diffusion couples were investigated at 1100 °C for determination of ternary interdiffusion coefficients at several compositions of the BCC phase field of Ti-Al-Mo system. Some of the diffusion couples developed zero flux planes (ZFP), which indicate the presence of strong diffusional interactions in this system. The composition of ZFP corresponds to the cross-over point of the diffusion path of the couple with the iso-activity line passing through one of the terminal alloys. Ternary interdiffusion coefficients were evaluated at several compositions at which the diffusion paths of the couples intersected each other. The strong diffusional interactions were also evident in large values of cross interdiffusion coefficients. Large negative values of $$ \tilde{D}_{\text{TiAl}}^{\text{Mo}} $$ indicate that the interdiffusion flux of titanium is enhanced up the gradient of aluminum and reduced down its gradient. An empirical relation is proposed between the ternary interdiffusivities and composition. The diffusion profiles were regenerated reasonably well using finite difference method based on empirically fitted composition dependent diffusion data. Availability of such composition–diffusivity relations in ternary systems would help in more accurate predictive design of the alloys and processes as it avoids the assumptions of negligible cross effects and need of complex extrapolations from lower order systems.

Multicomponent Diffusion Studies in Selected High Temperature for IN718/BNi-2/316L Diffusion Couple

The phenomenology of multicomponent diffusion studies was carried out in the IN718/BNi-2/AISI 316L joined couple at bonding temperature 1050 °C for bonding time 45 min. This study has been employed for the determination of interdiffusion fluxes, zero-flux planes and chemical potential gradient for multicomponent system of IN718/BNi-2/316L. The chemical composition of phases in the diffusion zone were analyzed by energy-dispersive spectroscopy, and the mobility parameter was extracted from Thermo-Calc software, DICTRA module. Interdiffusion fluxes of individual components, e.g., Ni, Cr, Fe, Si, B, Ti and Nb, were determined directly from the experimental concentration profiles and were examined in the light of diffusional interactions. The calculated flux result revealed that boron diffusion toward IN718 alloy was more than 316L alloy in the presence of other alloying elements. In addition, this observation was evaluated thermodynamically using the chemical potential gradient that was calculated for each component. The chemical potential results showed that the chemical potential gradient of boron in the presence IN718 elements was lower than chemical potential gradient of boron in the presence 316L elements.

An Overview of Selected Phenomena in Multicomponent Diffusion

There exist several interesting phenomena and observations reported in literature for isothermal diffusion in multicomponent systems. Such phenomena include uphill diffusion, development of zero-flux planes and flux reversals for individual components, flux reversals at interfaces, and instability at interfaces and multiphase layer development. In addition, uncommon diffusion structures exhibiting unusual diffusion paths can develop in both single phase and multiphase diffusion assemblies. An overview of such phenomena is presented to highlight the role of interactions among diffusing components with the aid of selected diffusion studies carried out in multicomponent alloy systems, aluminides, silicides, and nuclear fuels.

Atomic mobilities, zero-flux planes and flux reversals in fcc Cu–Fe–Ni alloys

Based on the thermodynamic description, the atomic mobilities of Cu, Fe and Ni are inversely parameterized from the experimental data on tracer diffusion and interdiffusion. The quality of atomic mobilities obtained in the present work has been verified through extensive comparisons between the calculated and measured tracer diffusion coefficients, interdiffusion coefficients, concentration profiles and diffusion paths in ternary Cu–Fe–Ni alloys. With such thermodynamic and kinetic descriptions of fcc Cu–Fe–Ni alloys, it is convenient to computationally study the presence and evolution of zero-flux planes (ZPFs) with respect to the lattice-fixed frame of reference as well as the number-fixed frame of reference, the results of which shed light on novel Cu-based and Fe-based alloy design for industry.

Uphill diffusion, zero-flux planes and transient chemical solitary waves in garnet

Diffusion profiles in minerals are increasingly used to determine the duration of geological events. For this purpose, the distinction between growth and diffusion zoning is critical; it requires the understanding of complex features associated with multicomponent diffusion. Seed-overgrowth interdiffusion experiments carried out in the range 1,050–1,250°C at 1.3 GPa have been designed to quantify and better understand Fe–Mg–Ca interdiffusion in garnet. Some of the diffusion profiles measured by analytical transmission electron microscope show characteristic features of multicomponent diffusion such as uphill diffusion, chemical solitary waves, zero-flux planes and complex diffusion paths. We implemented three different methods to calculate the interdiffusion coefficients of the D matrix from the experimental penetration curves and determined that with Ca as the dependent component, the crossed coefficients of the D matrix are negative. Experiments and numerical simulations indicate that: (1) uphill diffusion in garnet can be observed indifferently on the three components Fe, Mg and Ca, (2) it takes the form of complementary depletion/repletion waves and (3) chemical waves occur preferentially on initially flat concentration profiles. Derived D matrices are used to simulate the fate of chemical waves in time, in finite crystals. These examples show that the flow of atoms in multicomponent systems is not necessarily unidirectional for all components; it can change both in space along the diffusion profile and in time. Moving zero-flux planes in finite crystals are transitory features that allow flux reversals of atoms in the diffusion zone. Interdiffusion coefficients of the D matrices are also analyzed in terms of eigenvalues and eigenvectors. This analysis and the experimental results show that depending on the composition of the diffusion couple, (1) the shape of chemical waves and diffusion paths changes; (2) the width of the diffusion zone for each component may or may not be identical; and (3) the width of diffusion calculated at a given D and duration may greatly vary. D matrices were retrieved from thirteen sets of diffusion profiles. Data were cast in Arrhenius relations. Linear regressions of the data yield activation energies equal to 368, 148, 394, 152 kJ mol−1 at 1 bar and frequency factors Do equal to 2.37 × 10−6, −4.46 × 10−16, −1.31 × 10−5, 9.85 × 10−15 m2 s−1 for $$ \tilde{D}_{FeFe}^{Ca} $$ , $$ \tilde{D}_{FeMg}^{Ca} $$ , $$ \tilde{D}_{MgFe}^{Ca} $$ , $$ \tilde{D}_{MgMg}^{Ca} $$ , respectively. These values can be used to calculate interdiffusion coefficients in Fe–Mg–Ca garnets and determine the duration of geological events in high temperature metamorphic or magmatic garnets.

Selected Analyses and Observations in Multicomponent Diffusion

Selected isothermal diffusion studies in ternary and quaternary systems are reviewed in order to present analytical and experimental approaches adopted for the determination of interdiffusion fluxes of components, interdiffusion coefficients, diffusional interactions among components, and internal consistency in the experimental data. Several interesting phenomena and observations including uphill diffusion, zero-flux planes and flux reversals, and double serpentine diffusion paths are illustrated with selected single phase Cu-Ni-Zn, Fe-Ni-Al and Cu-Ni-Zn-Mn diffusion couples. The main challenges involved in the experimental determination of interdiffusion data from multicomponent diffusion couples and in the application of such data are also addressed.

Evolution of Concentration Profiles and Diffusion Paths in Single-Phase Multicomponent Multilayered Assemblies

An analysis of multilayered assemblies set up with multicomponent alloys selected in a single phase field has been recently developed on the basis of a matrix of constant interdiffusion coefficients. This analysis employs a transfer matrix method and is applicable to a study of evolution of concentration profiles and diffusion paths as a function of time for multilayered diffusion assemblies (MDAs) where any number of finite layers is sandwiched between two bulk terminal alloys. The analysis is utilized in this study to simulate concentration profiles and diffusion paths for MDAs assembled with (fcc) Cu-Ni-Zn alloys with two terminal alloys, A and B, sandwiching an alloy layer C in the middle. For short diffusion times the diffusion path of the ternary MDA, A/C/B, corresponds to two segments corresponding to the diffusion paths of the infinite diffusion couples, A/C and C/B. At longer times the diffusion zones of the two individual couples overlap and the diffusion path of the MDA varies continuously with time. The evolution of the concentration profiles and diffusion paths is presented and each intermediate path configuration is associated with a unique ratio of the middle layer thickness to the square root of diffusion time. The simulated concentration profiles clearly show the development of uphill diffusion and zero-flux planes (ZFP) for the individual components due to diffusional interactions among the components. At very long times, the diffusion path of the MDA approaches that of the infinite couple A/B between the two terminal alloys.

An Examination of Diffusion Paths in Terms of Interdiffusion Fluxes and Interdiffusion Coefficients

Selected diffusion couples investigated in the Cu-based and Fe-based multicomponent systems are examined for diffusion path development, zero-flux planes, uphill diffusion, and internal constraints for diffusion paths. The couples are analyzed for interdiffusion fluxes and interdiffusion coefficients with the aid of the “MultiDiFlux” program. Eigenvalues and eigenvectors are also determined from the interdiffusion coefficients determined over various ranges of composition in the diffusion zone. Slopes of diffusion paths at selected sections, including the path ends, are related to interdiffusion coefficients, interdiffusion fluxes and/or eigenvectors. These relations are explored with selected single phase diffusion couples in the Cu-Ni-Zn and Fe-Ni-Al systems and the calculated path slopes are compared with those directly determined from the concentration profiles. Relations between the gradient of interdiffusion flux and the concentration gradient are examined for each component in a two-phase Cu-Ni-Zn diffusion couple. The research is supported by the National Science Foundation.

Interdiffusion structures and paths for multiphase Fe-Ni-Al diffusion couples at 1000 °C

Diffusion studies were carried out in the Fe-Ni-Al system at 1000 °C using solid-solid diffusion couples assembled with β (B2), γ (fcc) single phase, and (β + γ) two-phase alloys. The diffusion couples were encapsulated in quartz tubes under vacuum and annealed for 48 hours. The diffusion structures were examined by optical and scanning electron microscopy. For all β vs (β + γ) couples, growth of the β phase was observed as the (β + γ) two-phase region recessed with the dissolution of the γ phase. For multiphase couples assembled with two (β + γ) terminal alloys, demixing of the (β + γ) two-phase alloys occurred with the formation of single-phase β and γ layers. The development of an interphase boundary between the (β + β′) two-phase region and the γ phase is reported for the first time for a Fe-Ni-Al diffusion couple assembled with single-phase, β, and γ terminal alloys. Various diffusion structures for the couples were related to their diffusion paths constructed from concentration profiles determined by electron probe microanalysis. Interdiffusion fluxes of individual components were determined directly from the experimental concentration profiles and examined in light of diffusional interactions and the development of zero-flux planes and flux reversals. In addition, the boundaries for the miscibility gap between the ordered β and disordered β′ phases of the Fe-Ni-Al system at 1000 °C were determined with the aid of diffusion couples that developed β and β′ phases in the diffusion zone.

Calculating of Diffusion Paths in Ternary Systems Using Effective Interdiffusion Coefficients of Components

The peculiarities of practical application of effective interdiffusion coefficients of components for calculating diffusion paths in ternary systems are analysed. It is shown that infinite values of the interdiffusion coefficients at zero concentration gradient’s points do not remarkably affect the accuracy of calculation in the case of a correct choice of variables. At zero-flux planes where the respective effective interdiffusion coefficient is equal to zero, no calculation problems arise, as evidently zero-flux planes can occur simultaneously only for one of the components. The results of calculation of diffusion paths for diffusion couples in the ternary systems Cu-Fe-Ni and Co-Fe-Ni using respective effective interdiffusion coefficients are presented. These results demonstrate a good accuracy of such kind of calculations even in the case of very strong deviation from linearity of the diffusion path.

Zero-Flux Plane Kinetics at Multicomponent Interfaces

Zero flux planes (ZFP's) are the locations in a diffusion couple where fluxes of individual components vanish. The conditions required for developing ZFP's between interdiffusing multicomponent alloys are now well understood through the works of Dayananda and Morral. In this paper we analyze the kinetics of multicomponent diffusion near ZFP's. In contrast to the usual mixing that occurs between end-member alloys in a diffusion couple, where the average component compositions are approached through “global” exchange of atoms, the presence of a stationary ZFP requires instead that mixing of the blocked component occurs through the release of a pair of coupled diffusion waves. In classical (thick) couples these waves spread symmetrically away from the Matano plane. The wave pair consists of a “depletion” wave that reduces the blocked component concentration in the component-rich alloy, and a conjugate “repletion” wave that increases the concentration in the adjacent component-poor alloy. Curiously, each of these waves establishes the average (equilibrium) concentration unilaterally on either side of the Matano plane. A stationary ZFP precludes net transport of one component across the Matano plane—a circumstance that has practical and theoretically interesting implications for the design of stable multicomponent films and coatings that must resist diffusive loss of a component.

Dynamics of multicomponent diffusion with zero flux planes

Multicomponent diffusion induces zero flux planes (ZFPs) that are locations in a diffusion couple where fluxes of individual components vanish. We analyze the kinetics of multicomponent diffusion near ZFPs. In contrast to the usual mixing that occurs between alloys in a diffusion couple, where the average component compositions are approached through ‘global’ exchange of atoms, the presence of a ZFP requires that mixing of the blocked component occurs through the release of coupled diffusion waves consisting of a ‘depletion’ wave that reduces the blocked component concentration in the component-rich alloy, and a ‘repletion’ wave that increases the concentration in the component-poor alloy. Each wave establishes the average (equilibrium) concentration unilaterally on either side of the Matano plane. Multicomponent diffusion behaviors, such as slowed diffusive spreading and reduced atomic transport, are associated with the near collocation of multiple ZFPs, and the proximity of a zero flux plane for the major component.

Diffusion studies in the β (B2), β′ (bcc), and γ (fcc) Fe-Ni-Al alloys at 1000 °C

Diffusion studies were carried out in the Fe-Ni-Al system at 1000 °C with solid-solid diffusion couples assembled with β (B2), β′ (bcc), and γ (fcc) single-phase alloys for the development of diffusion structures, diffusion paths, and for the determination of interdiffusion and intrinsic diffusion coefficients. The diffusion structures were examined by optical and scanning electron microscopy, and the concentration profiles were determined by electron microprobe analysis. Diffusion couples included several series of β vs γ and β′ vs γ diffusion couples characterized by a common terminal alloy bonded to several terminal alloys with varying compositions. The development of planar and nonplanar interfaces, as well as two-phase layers, as observed in various couples, were related to the diffusion paths. The interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the diffusional interactions among components were examined in the light of zero-flux planes (ZFPs) and flux reversals, which were identified in several couples. Ternary interdiffusion coefficients ( $$\tilde D_{i,j}^{Fe} $$ (i, j = Al, Ni)), with Fe considered as the dependent concentration variable, were evaluated at composition points of the intersection of diffusion paths of single-phase couples and of multiphase couples that developed planar interfaces. The interdiffusion coefficients were the largest in magnitude for the β′ alloys, especially near the β/β′ miscibility gap, and decreased for the β and γ alloys. In the β and γ phases, the main interdiffusion coefficient for Al was larger than those for Ni and Fe. Also, Fe interdiffused faster than Ni in the Fe-rich β and β′ phases. The cross-interdiffusion coefficients ( $$\tilde D_{AlNi}^{Fe} $$ and $$\tilde D_{NiAl}^{Fe} $$ ) were negative in all three phases. In general, the $$\tilde D_{AlNi}^{Fe} $$ coefficients were larger in magnitude than the $$\tilde D_{NiAl}^{Fe} $$ coefficients; however, the magnitude of $$\tilde D_{NiAl}^{Fe} $$ was greater than that of $$\tilde D_{AlNi}^{Fe} $$ near the β/(β + γ) phase boundary on the ternary isotherm. In the β phase, the magnitude of $$\tilde D_{i,j}^{Fe} $$ (i, j=Al, Ni) coefficients increased over 1 to 2 orders of magnitude with a decrease in the Al concentration and increase in the Fe/Ni concentration ratio. Interdiffusion coefficients, extrapolated from the ternary coefficients for binary alloys, were consistent with those in literature. Intrinsic diffusion coefficients were also determined at selected compositions. In addition, tracer diffusion coefficients were estimated for the binary Fe-Al and Ni-Al alloys at selected compositions, from an extrapolation of ternary interdiffusion coefficients.

Interdiffusion and diffusion structure development in selected refractory metal silicides

Abstract Solid–solid diffusion couples set up with disks of Mo, W, Re, Nb, or Ta in contact with disks of a single crystal of MoSi 2 were annealed at selected temperatures between 1300° and 1700°C for diffusion structure, determination of interdiffusion coefficients and energies of activation for interdiffusion in various silicides developed in the couples. The couples were analyzed and characterized by SEM and optical microscopy, microprobe analysis, X-ray diffraction and orientation imaging microscopy. From the interdiffusion fluxes determined directly from the concentration profiles, integrated and average effective interdiffusion coefficients were calculated for the components in the various binary and ternary silicide layers. The Mo vs. MoSi 2 couples developed Mo 5 Si 3 and Mo 3 Si layers with non-planar interface morphologies; the Mo 5 Si 3 layer exhibited oriented growth and microcracking. The W vs. MoSi 2 couples developed W 5 Si 3 and (W,Mo) 5 Si 3 layers with little microcracking. The diffusion structure of Re vs. MoSi 2 diffusion couples consisted of layers of Re 2 Si, (Re,Mo)Si and (Re,Mo) 5 Si 3 phases and cracks were blunted in the (Re,Mo) 5 Si 3 layer. The Nb vs. MoSi 2 couples developed the Nb 5 Si 3 and (Nb,Mo) 5 Si 3 phase layers with porosity in the diffusion zone. Layers of Ta 2 Si, Ta 5 Si 3 and (Ta,Mo) 5 Si 3 phases were observed in the Ta vs. MoSi 2 couples. The activation energies ( Q ) for the interdiffusion of both Si and W are calculated to be about 360 and 450 kJ mol −1 in the W 5 Si 3 and (W,Mo) 5 Si 3 layers, respectively. Values of Q for the interdiffusion of both Re and Si are about 190 kJ mol −1 in the Re 2 Si phase, 325 kJ mol −1 in the (Re,Mo)Si phase, and 270 kJ mol −1 in the (Re,Mo) 5 Si 3 phase. For the interdiffusion of Si and Nb in the (Nb,Mo) 5 Si 3 phase, Q values are about 300 and 240 kJ mol −1 , respectively; Q is about 265 kJ mol −1 in the binary Nb 5 Si 3 phase. Zero-flux planes (ZFP) and uphill diffusion are observed for Mo in the (Re,Mo)Si and (Me,Mo) 5 Si 3 layers where Me=W, Re, Nb or Ta; in these layers, the ternary cross coefficient D MoMe Si is about as large as the main ternary interdiffusion coefficient D MoMo Si and the interdiffusion of Mo is enhanced down the Me concentration gradient.

Investigation of the Homovalent Impurity in Aluminum to Form Alloys With Enhanced Interconnect Reliability

ABSTRACTDiffusion-induced failures such as stress-induced voiding and electromigration (EM) are a major concern for interconnect metallization in silicon integrated circuits. The addition of solute elements to aluminum interconnects often leads to “blocking” of high diffusivity paths such as grain boundaries and thus to an improvement in the resistance to electromigration failure. This research investigates Al-In, Al-La, and Al-In-La alloys to improve interconnect EM resistance. The choice of these alloying elements is based on the fact that they have negligible solid solubility in aluminum and are homovalent. Lower solubilities may lead to grain boundary stuffing and hence to improved EM resistance. In addition, the homovalency minimizes the adverse effect on the metal resistivity from addition of impurities to aluminum. Multicomponent diffusion principles are used to tailor aluminum-based ternary alloy compositions which would exhibit the multicomponent effect of zero flux planes (ZFPs), or regions in the reaction zone of a diffusion couple where the flux of a component goes to zero. This study involves modeling the occurrence of ZFPs for aluminum in several diffusion couples of Al-In-La, thus limiting the bulk diffusive spreading of aluminum so that the electromigration behavior can be inhibited or eliminated. This paper presents our experimental findings and discusses the modeling approach to determine ternary alloys exhibiting ZFPs.

Multicomponent diffusion studies in selected high-temperature alloy systems

The phenomenology of multicomponent diffusion is reviewed with special emphasis on the approaches employed for the determination of interdiffusion fluxes, zero-flux planes and flux reversals for the individual components without the need for the interdiffusion coefficients. The development of a zero-flux plane (ZFP), where the interdiffusion flux of a component can go to zero and exhibit a change in diffusion direction on the two sides of the plane is illustrated with selected diffusion couples in systems such as FeNiAl, FeNiCr and the significance of the ZFP phenomena will be discussed in the light of thermodynamic and diffusional interactions among the components. Interdiffusion studies carried out with NiCoCrMo quaternary alloys at 1300 °C for the determination of interdiffusion fluxes and diffusion paths are presented and the development of a ZFP for cobalt is discussed in the light of interdiffusion coefficients. Selected diffusion experiments carried out at 1100 °C with an NiCr alloy coated with MCrAlY coatings are also presented and discussed for the recession of the coating layer in the light of the aluminum content of the coatings. Diffusional interactions between aluminum and chromium are discussed in the light of uphill diffusion observed for these elements and a ZFP developed for chromium.

Zero-flux planes and flux reversals in multicomponent diffusion

The development of zero-flux planes (ZFP) and flux reversals of individual components is a phenomenon commonly encountered during isothermal diffusion in multicomponent systems. At a zero-flux plane, the interdiffusion flux of a component goes to zero and exhibits a flux reversal from one side of the plane to the other. The identification of ZFP’s is based on the determination of interdiffusion fluxes directly from the concentration profiles of diffusion couples without the knowledge or use of interdiffusion coefficients. The development of ZFP and flux reversals is reviewed and presented for both single-phase and multiphase isothermal diffusion couples in selected Cu-base multicomponent systems. The significance of ZFP is discussed with the aid of diffusion paths and thermodynamic data.

Predicting the occurrence of zero flux planes

Zero flux planes have been observed in many multicomponent diffusion couples following interdiffusion. Recently, it was shown with a constant diffusivity theory that their occurrence can be predicted by knowing the terminal alloy compositions and the square root diffusivity. In the present work, the theory is tested by applying it to previous obervations on the Cu-Ni-Zn system and it is found to predict correctly the occurrence of zero flux planes in 21 out of 24 concentration profiles. Also, a qualitative discussion is given of how variations in diffusivity with composition can modify the constant diffusivity predictions.