Zero-flux planes and flux reversals in Cu−Ni−Zn diffusion couples

Concentration profiles of isothermal diffusion couples in binary as well as multicomponent systems can be analyzed directly for interdiffusion fluxes without the need for a prior knowledge of interdiffusion coefficients. Such an analysis is presented and applied for the calculation of interdiffusion fluxes of each component at various sections of several diffusion couples in the Cu−Ni−Zn system investigated at 775°C. A major outcome of these calculations is the identification of “zero-flux planes” for the individual components within the diffusion zones of ternary couples. At a zero-flux plane the interdiffusion flux of a component goes to zero and on either side of the plane occurs a change or reversal in the direction of the interdiffusion flux of the component. The formation as well as the number of zero-flux planes of the components is dictated by the terminal alloys of the diffusion comple. The compositions of zero-flux planes for Ni and Cu identified in several Cu−Ni−Zn couples are found to correspond to composition points of intersection of diffusion paths and isoactivity lines drawn through the terminal alloys of the couples on a ternary isotherm. C. W. KIM, formerly a graduate student at Purdue University     

Interdiffusion and Diffusion Mobility for fcc Ni-Co-Al Alloys

Ternary fcc Ni-Co-Al diffusion couples annealed at 1173 K (900 °C), 1373 K (1100 °C), and 1573 K (1300 °C) have been studied by using electron probe microanalysis. The interdiffusion coefficients were extracted using the Sauer–Freise and Whittle–Green methods from the measured concentration profiles of binary and ternary diffusion couples, respectively. Based on the diffusion coefficients reported in the literature and those determined in the present work, the diffusion mobilities for fcc Ni-Co-Al alloys were assessed. In general, reasonable agreements were reached and the resulted mobility database can be used to study the diffusion behavior of the ternary fcc Ni-Co-Al alloys in a wide composition range.     

Interdiffusion in the Ni-Cr-Co-Mo system at 1300 °C

Interdiffusion was investigated with solid-solid diffusion couples in theα (fcc) region of the quaternary Ni-Cr-Co-Mo system at 1300 °C for the determination of diffusion paths and diffusional interactions among the components. The concentration profiles for a given couple exhibited a common cross-over composition, Y_c, which reflected the relative depths of diffusion in the terminal alloys. Interdiffusion fluxes were calculated directly from the concentration profiles, and the quaternary interdiffusion coefficients were calculated at selected compositions. Ni and Co exhibited uphill diffusion against their individual concentration gradients in a direction opposite to the interdiffusion of Cr. Quaternary diffusion paths were presented as a set of partial diffusion paths on the basis of relative concentration variables.     

Diffusion in β2 Fe-Ni-Al alloys

Diffusion in the β(bcc) phase field of the Fe-Ni-Al system was investigated at 1004°C with solid-solid diffusion couples assembled with β₂ alloys of selected composition. Experimental diffusion paths were determined for all couples and interdiffusion coefficients calculated at composition points corresponding to intersections of diffusion paths and maxima and minima of concentration profiles. The dependence of interdiffusion coefficients on composition was most clearly presented in terms of the parameter Fe/(Fe + Ni). The diffusive interactions between aluminum and nickel as represented by the cross coefficients were either positive or negative depending on the ternary composition. The Fe/(Fe + Ni) ratio appeared to be a significant parameter since iron and nickel atoms behave differently in affecting the degree of ordering in nonstoichiometric (Fe, Ni)Al alloys with less than 50 at. pct aluminum.     

Quaternary diffusion in the Cu−Ni−Zn−Mn system at 775°C

Quaternary diffusion was investigated in the α (fcc) region of the Cu−Ni−Zn−Mn system at 775°C with solid-solid diffusion couples assembled with alloys characterized by similar concentrations of one of the components. The concentration profiles of the quaternary couples were examined on the basis of a relative concentration variable for each component; the profiles for any given couple exhibited a common cross-over composition. The interdiffusion fluxes of the components were calculated directly from the concentration profiles. Interdiffusion of each component up its own concentration gradient was observed in several couples, while the zero-flux planes for the individual components were identified in selected couples. The common cross-over composition reflected the relative diffusion depths in the terminal alloys of the single-phase quaternary diffusion couples. The quaternary diffusion paths were presented on the basis of relative concentration variables for the individual components.     

Zero-flux planes and flux reversals in the Cu- Ni- Zn System at 775 °C

Ternary diffusion in the Cu-Ni-Zn system was investigated at 775 °C for the development of zero-flux planes (ZFP) and flux reversals of the individual components. ZFP’s, where the interdiffusion flux of either Cu, Ni, or Zn goes to zero, were identified in several series of single phase and multiphase solid-solid diffusion couples assembled with a (fcc),β (bcc), or γ (cubic) Cu-Ni-Zn alloys and characterized by terminal alloys of similar thermodynamic activity for one of the components. Profiles of interdiffusion fluxes were directly determined from concentration profiles. The diffusion path for a single phase couple with a ZFP was experimentally found to be invariant with diffusion time. The locations of ZFP’s within the diffusion zone of a couple corresponded to sections where the activity of a component was the same as its activity in either of the terminal alloys of the couple. Couples developing ZFP’s showed regions where a component diffused up its own activity gradient. The diffusional interactions among the components described by the ratios of cross to main ternary interdiffusion coefficients were determined directly from the slopes of the diffusion paths at various ZFP compositions. In several multiphase couples, discontinuous flux reversals for the components were also identified at theβ/a and γ/β interfaces. A discontinuous flux reversal for a component was observed at a planar interface, when the activity of the component at the interface corresponded to its activity in one of the terminal alloys of the couple.     

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 ( (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 ( and ) were negative in all three phases. In general, the coefficients were larger in magnitude than the coefficients; however, the magnitude of was greater than that of near the β/(β + γ) phase boundary on the ternary isotherm. In the β phase, the magnitude of (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.     

Diffusional and thermodynamic interactions in the Cu-Ni-Zn system at 775°C

Diffusion was investigated in both α(fcc) and β(bcc) phase regions of the Cu-Ni-Zn system at 775°C with solid-solid diffusion couples and interdiffusion coefficients were determined at several compositions. Intrinsic and interdiffusion coefficients were also estimated from available data on thermodynamic activities and tracer diffusivities for α Cu-Ni-Zn alloys; and the estimated coefficients were consistent with those experimentally determined. Large off-diagonal coefficients indicating strong interactions among the diffusing species were observed and could be appreciated in terms of the compositional dependence of the thermodynamic activities of the components.     

Average effective interdiffusion coefficients and the Matano plane composition

From an integration of the interdiffusion flux of a component over distance in the diffusion zone of an isothermal solid-solid diffusion couple, average effective interdiffusion coefficients can be evaluated over selected ranges of composition. An analysis is developed to inter-relate, in general, the average effective interdiffusion coefficients calculated for the composition ranges on either side of the Matano plane to the composition at the Matano plane. Characteristic depths for concentration profiles on either side of the Matano plane are employed to characterize the concentration profiles and their deviations from error function solutions. The analysis is applied to the concentration profiles of a binary Fe-C as well as a ternary Cu-Ni-Zn single-phase diffusion couple. From a knowledge of concentration profiles on one side of the Matano plane, profiles on the other side can be generated from an error function model based on the analysis.     

Experimental Investigation of the Ce-Mg-Mn Isothermal Section at 723 K (450 °C) via Diffusion Couples Technique

The isothermal section of the Ce-Mg-Mn phase diagram at 723 K (450 °C) was established experimentally by means of diffusion couples and key alloys. The phase relationships in the complete composition range were determined based on six solid–solid diffusion couples and twelve annealed key alloys. No ternary compounds were found in the Ce-Mg-Mn system at 723 K (450 °C). X-ray diffraction and energy-dispersive X-ray spectroscopy spot analyses were used for phase identification. EDS line-scans, across the diffusion layers, were performed to determine the binary and ternary homogeneity ranges. Mn was observed in the diffusion couples and key alloys microstructures as either a solute element in the Ce-Mg compounds or as a pure element, because it has no tendency to form intermetallic compounds with either Ce or Mg. The fast at. interdiffusion of Ce and Mg produces several binary compounds (Ce _x Mg _y ) during the diffusion process. Thus, the diffusion layers formed in the ternary diffusion couples were similar to those in the Ce-Mg binary diffusion couples, except that the ternary diffusion couples contain layers of Ce-Mg compounds that dissolve certain amount of Mn. Also, the ternary diffusion couples showed layers containing islands of pure Mn distributed in most diffusion zones. As a result, the phase boundary lines were pointing toward Mn-rich corner, which supports the tendency of Mn to be in equilibrium with all the phases in the system.     

Interdiffusion in Ni-Rich,Ni-Cr-Al alloys at 1100 and 1200 °C: Part I. Diffusion paths and microstructures

Interdiffusion in Ni-rich, Ni-Cr-Al diffusion couples was studied after annealing at 1100 and 1200 °C. Recession of γ′ (Ni₃Al structure), β (NiAl structure), or α (bcc) phases was also measured. Aluminum and chromium concentration profiles were measured in the γ (fcc) phase for most of the diffusion couples. The amount and location of Kirkendall porosity suggests that Al diffuses more rapidly than Cr which diffuses more rapidly than Ni in the γ phase of Ni-Cr-Al alloys. The location of maxima and minima in the concentration profiles of several of the diffusion couples indicates that both cross-term diffusion coefficients for Cr and Al are positive and that D_CrAl has a greater effect on the diffusion of Cr than does D_A1Cr on the diffusion of Al. The γ/γ + β phase boundary has also been determined for 1200 °C through the use of numerous γ/γ+ β diffusion couples.     

Ternary dissolution kinetics in the Fe-Ni-P system

The dissolution of (FeNi)₃P in the ternary Fe-Ni-P system has been studied by optical and electron microprobe techniques. Precipitates of (FeNi)₃P, initially in equilibrium with their ternary matrix (a at 750°C, y at 875°C), were examined after being partially dissolved by heating at 975°C. In addition, diffusion couples with starting compositions similar to the equilibrated ternary alloys were examined after also being heat treated at 975°C. Phosphide, (FeNi)₃P, dissolution in the α or γ phase is diffusion controlled at 975°C. The ternary dissolution paths observed in each of the diffusion couples are unique and the same as those observed in the comparable alloys. The dissolution rate of (FeNi)₃P is controlled by the diffusion rate of P in the α or y phases. The Ni interface compositions in (FeNi)₃P and α or γ and the dissolution path through the ternary are determined by the rate of dissolution and the major Ni ternary diffusion coefficients. It is possible to calculate both the dissolution path and rate for (FeNi)₃P by using the binary dissolution equations in combination with the Fe-Ni-P diagram and the major (ternary) diffusion coefficients. In addition, numerical solutions can be correctly calculated for diffusion controlled dissolution where impingement of overlapping gradients occurs. Formerly Graduate Assistant, Department of Metallurgy and Materials Science, Lehigh University, Bethlehem, Pennsylvania     

Thermodynamic and kinetic study of diffusion paths in the system Cu-Fe-Ni

An understanding and modeling of diffusion paths in ternary systems requires a combined thermodynamic and diffusion kinetic approach. The driving force for the intrinsic diffusion of each component is the gradient of the chemical potential (or activity) which can be calculated from the concentration profile if the thermodynamic properties of the system are known. For studying the diffusion behavior in ternary metallic systems, the Cu-Fe-Ni-system was chosen because of its experimental and thermodynamic simplicity. Concentration profiles and diffusion paths in single-phase areas and across an α/β interface were studied experimentally at 1000 °C using the diffusion couple technique. Coefficients for interdiffusion and tracer diffusion have been calculated at the intersection points of two independent diffusion paths with a common composition. A concentration dependence for the tracer diffusion coefficients for each component was calculated and found to be consistent with the literature data in the binary Cu-Ni and Fe-Ni systems. The calculated vacancy flux in the couples was consistent with the experimentally observed marker shift.     

Diffusion structures in multiphase Cu-Ni-Zn couples

Isothermal, multiphase diffusion was investigated with infinite diffusion couples in the Cu-Ni-Zn system at 775°C. The couples were assembled with disks of a β (bcc) ternary alloy sandwiched between disks of selected binary, Cu-Ni α (fcc)alloys and were annealed for 2 hr to 2 days. The diffusion structures were investigated metallographically and by electron probe analysis. The couples developed multiphase structures that showed transitions from planar interfaces to nonplanar morphologies with changes in composition of the α -terminal alloys. The various structures are described by the aid of composition paths. The velocity of planar interfaces is discussed in terms of intrinsic fluxes in the adjacent phases. This paper is based upon a thesis submitted by R. D. SISSON, JR. to Purdue University in partial fulfillment of the requirements of the M.S. Metallurgical Engineering degree.     

Multiphase diffusion in Fe−Ni−Al system at 1000°C: II. Interdiffusion coefficients for β and γ alloys

Ternary interdiffusion coefficients were determined at 1000°C at several Fe−Ni−Al alloy compositions with multiphase β(bcc)vs γ (fcc) diffusion couples which developed planar β/γ-interfaces. The coefficients, (i,j=Al or Ni) were calculated at compositions corresponding to points of intersections of diffusion paths with Fe taken as the dependent component. These coefficients varied with composition by 1 to 2 orders of magnitude in the β-phase but relatively little in the γ-phase. Empirical relations were derived to describe the composition dependence of the main coefficients. and . Interdiffusion coefficients with either Al or Ni as the dependent component were also evaluated. The relative diffusivities of the elements increase in the order, Fe, Ni, Al for both β- and γ-alloys. The ternary diffusion data were consistent with binary interdiffusion coefficients for Fe−Al and Fe−Ni alloys. G. H. CHENG, formerly a Graduate Student at Purdue University     

An analysis of interdiffusion in finite-geometry,two-phase diffusion couples in the Ni−W and Ag−Cu systems

The progress of homogenization in finite, multilayer diffusion couples was studied experimentally using both quantitative metallography to measure phase thicknesses and electron microprobe analysis to determine concentration-distance profiles. Ni?W couples having mean compositions in the nickel-rich terminal solid solution range (12.1 and 15.2 at. pct W) were studied after 4.43 to 240.7 hr interdiffusion treatments at 1156° and 1207°C. Ag?Cu couples having mean compositions in both of the terminal solid solution ranges (8.5 at. pct Cu and 2.1 at. pct Ag) were studied after 3.8 to 65.4 hr interdiffusion treatments at 760°C. Experimental data were in good agreement with calculations of interdiffusion based on equilibrium interface concentrations and concentration-independent interdiffusion coefficients. The good agreement between experimental data and calculated values for the Ni?W couples extended to times necessary for the achievement of essentially complete homogenization,i.e., through both the two-phase dissolution process and the subsequent stage of gradient elimination in the terminal solid solution phase.     

Interdiffusion and Atomic Mobility for Face-Centered-Cubic Co-Al Alloys

Interdiffusion in the face-centered-cubic (fcc) Co-Al binary alloys was studied by the diffusion-couple approach in the temperature range of 1173 K to 1573 K (900 °C to 1300 °C). Interdiffusion coefficients of the fcc Co-Al alloys were then evaluated by using the Sauer–Freise method. The effect of magnetic ordering on the Co-Al interdiffusion was observed at 1273 K (1000 °C) by examining the Arrhenius plots. The interdiffusion data were assessed to develop the atomic mobility for the fcc Co-Al alloys, and their validity was tested by simulating the diffusion-couple experiments.     

Interdiffusion, Intrinsic Diffusion, Atomic Mobility, and Vacancy Wind Effect in γ(bcc) Uranium-Molybdenum Alloy

U-Mo alloys are being developed as low enrichment uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) Program. In order to understand the fundamental diffusion behavior of this system, solid-to-solid pure U vs Mo diffusion couples were assembled and annealed at 923 K, 973 K, 1073 K, 1173 K, and 1273 K (650 °C, 700 °C, 800 °C, 900 °C, and 1000 °C) for various times. The interdiffusion microstructures and concentration profiles were examined via scanning electron microscopy and electron probe microanalysis, respectively. As the Mo concentration increased from 2 to 26 at. pct, the interdiffusion coefficient decreased, while the activation energy increased. A Kirkendall marker plane was clearly identified in each diffusion couple and utilized to determine intrinsic diffusion coefficients. Uranium intrinsically diffused 5-10 times faster than Mo. Molar excess Gibbs free energy of U-Mo alloy was applied to calculate the thermodynamic factor using ideal, regular, and subregular solution models. Based on the intrinsic diffusion coefficients and thermodynamic factors, Manning’s formalism was used to calculate the tracer diffusion coefficients, atomic mobilities, and vacancy wind parameters of U and Mo at the marker composition. The tracer diffusion coefficients and atomic mobilities of U were about five times larger than those of Mo, and the vacancy wind effect increased the intrinsic flux of U by approximately 30 pct.