Interdiffusion and Diffusion Mobility for Fcc Ni-Co-Mo Alloys

Ternary fcc Ni-Co-Mo diffusion couples annealed at 1273 and 1473 K have been scanned to measure composition profiles by using electron probe microanalysis. The interdiffusion coefficients were extracted using the Whittle–Green method from the measured composition profiles of the ternary diffusion couples. Based on the diffusion coefficients reported in the literature and data determined in the present work, the diffusion mobilities for fcc Ni-Co-Mo alloys were assessed. In addition, diffusion paths and composition profiles were simulated with presently assessed mobility parameters. In general, reasonable agreements have been reached and the resulted mobility database can be used to investigate the diffusion behavior of the ternary fcc Ni-Co-Mo alloys in wide composition and temperature ranges.     

Analysis of multicomponent diffusion couples for interdiffusion fluxes and interdiffusion coefficients

A procedure for the analysis of an isothermal, multicomponent, solid-solid diffusion couple is presented for the direct determination of interdiffusion fluxes of all components over the entire diffusion zone and for the evaluation of main and cross interdiffusion coefficients over regions selected in the diffusion zone. The average effective interdiffusion coefficients for the individual components are also determined over the selected compositional ranges. A user-friendly computer program called MultiDiFlux has been developed to carry out all of the analysis and calculations. With the aid of this program, selected diffusion couples in the ternary Cu-Ni-Zn system were analyzed for interdiffusion fluxes and ternary interdiffusion coefficients, and were assessed for up-hill diffusion, zero-flux plane development, and diffusional interactions among components. The interdiffusion coefficients determined over various regions of the diffusion zone are used by the program to regenerate the concentration profiles of the couple.     

Co-Cr-V三元系富Co侧fcc相的互扩散及原子迁移率参数研究

本研究制备了一系列Co-Cr-V合金,在1200℃下扩散处理259200 s。利用EPMA技术测定了各扩散偶的浓度-距离曲线,并根据测得的浓度-距离曲线用Whittle and Green方法计算了Co-Cr-V三元系在1200℃下的互扩散系数。基于本研究的实验数据和文献报道的热力学信息和相关子二元系的动力学参数,利用DICTRA软件优化得到Co-Cr-V体系fcc相的扩散迁移率参数。运用优化得到的原子迁移率参数计算互扩散系数,并与实验数据比对,取得较好的一致性,从而验证了所得迁移率参数的可靠性。同时运用该迁移率参数计算了各扩散偶的浓度-距离曲线和扩散路径,计算结果与实验数据均符合良好,进一步验证了参数的合理性和准确性。     

Ni-Cr-W三元系富Ni侧fcc相的互扩散及原子迁移率参数研究

利用电子探针微量分析与Whittle-Green方法确定了在1200℃下退火72 h的Ni-Cr-W三元合金体系的互扩散系数。通过DICTRA软件包对实验互扩散系数进行评估以确定原子迁移率。通过全面分析比较模型预测的扩散特性和实验数据的良好一致性验证了原子迁移率的合理性。Ni-Cr-W三元体系中的扩散现象,如扩散路径和浓度-距离曲线可以通过获得的原子迁移率合理地描述,进一步证明了本研究所获得的原子迁移率参数的可靠性。     

Interdiffusion and Atomic Mobility Studies in Ni-Rich fcc Ni-Co-Al Alloys

The ternary interdiffusion coefficients in fcc Ni-Co-Al alloys at 1373 K were determined using Whittle and Green method together with electronic-probe microanalysis. With the help of DICTRA software, the experimental diffusion coefficients were critically assessed to obtain the atomic mobilities of Ni, Co and Al in fcc Ni-Co-Al alloys. Comprehensive comparisons between calculated and experimental diffusion coefficients showed that the experimental data could be well reproduced by the atomic mobilities obtained in the present work. The developed diffusion mobilities were further validated by the calculation of the concentration profiles and diffusion paths in diffusion couples.     

Computational Study of Atomic Mobility in Co-Fe-Ni Ternary Fcc Alloys

The generalized Boltzmann-Matano method has been used to evaluate the interdiffusion coefficients at 1100 °C for the fcc phase of the Co-Fe-Ni ternary system from the concentration profiles developed from single-phase diffusion couple. The evaluated interdiffusion coefficients, together with other experimental data in the literature, have been assessed to develop an atomic mobility database for the fcc phase of the Co-Fe-Ni ternary. The atomic mobility database, in conjunction with the CALPHAD-base thermodynamics, has been used to simulate a number of ternary diffusion couple experiments. Comprehensive comparisons between the calculated and experimental data show that excellent agreement is obtained not only for the general diffusion data of ternary diffusion couple, such as the interdiffusion coefficients and the concentration profiles, but also for much of in-depth diffusion behavior, like the diffusion path, the interdiffusion flux and the shift of the Kirkendall plane.     

A transfer-matrix method for analysis of multicomponent diffusion with any number of components

A transfer-matrix method (TMM) is presented for the development of concentration and flux profiles in multicomponent diffusion involving any numbern of components. From interdiffusion fluxes or concentration gradients available at an initial positionx _s, the authors derive expressions for the transfer matrix and its integral so that the concentrations or interdiffusion fluxes of the components can be obtained at any coordinatex. The TMM requires data for interdiffusion coefficients, which are obtained as average values over selected regions by the method of moments developed by Dayananda. Expressions for the concentrations are also obtained from initial conditions on the fluxes or the concentration gradients. The method is also applicable to the case when all the concentrations are known at two ends of a region over which the diffusion coefficients are considered constant. The integration of the fluxes over time, or over the coordinatex, can be evaluated using the transfer-matrix approach, provided the value of the interdiffusion flux is given at a given coordinate. The TMM is applicable to any number of components and can be regarded as a compact generalization of the solutions available for ternary diffusion couples with constant interdiffusion coefficients. An application of the method is illustrated with the experimental data for a ternary Cu-Ni-Zn diffusion couple, and the results are compared with those based on the Fujita-Gosting solution. This article was presented at the Multicomponent-Multiphase Diffusion Symposium in Honor of Mysore A. Dayananda, which was held during TMS 2006, 135th Annual Meeting and Exhibition, March 12–16, 2006, in San Antonio, TX. The symposium was organized by Yongho Sohn of University of Central Florida, Carelyn E. Campbell of National Institute of Standards and Technology, Richard D. Sisson, Jr., of Worcester Polytechnic Institute, and John E. Morral of Ohio State University.     

On Interdiffusion in FeNiCoCrMn High Entropy Alloy

Interdiffusion was studied in FCC FeNiCoCrMn high entropy alloy (HEA) system with the help of two quinary diffusion couples annealed at 1000 °C for 100 hours. The terminal alloys of the two couples were selected based upon the knowledge of binary thermodynamic interactions so as to have enhancement or reduction of interdiffusion of particular components. Interdiffusion fluxes of nickel and manganese, which have highest negative binary enthalpy of mixing, were observed to be enhanced up the gradients of each other and reduced down the gradients of each other. Regions of uphill interdiffusion observed for chromium and iron and presence of a zero flux plane observed for iron in one of the diffusion couples indicate the existence of strong diffusional interactions in this HEA. Quinary interdiffusion coefficients were also calculated at various compositions of the FeNiCoCrMn system based upon Manning’s model, utilizing the knowledge of tracer diffusivities of constituent elements and thermodynamic factors. The calculated cross interdiffusion coefficients were shown to be consistent with the diffusional interactions observed in the two diffusion couples. Nickel and Manganese, which are slowest and fastest diffusing species in the FeNiCoCrMn HEA and, which also possess highly negative binary enthalpy of mixing were observed to play particularly significant role in determining the diffusional interactions in this HEA system. Validity of the interdiffusion coefficients evaluated by Manning’s approach was established by regenerating the concentration profiles of the experimental diffusion couples based on transfer matrix method (TMM).     

Interdiffusion analysis for NiAl versus superalloys diffusion couples

Solid-to-solid diffusion couples, β-NiAl (B2) versus various commercial superalloys (i.e., CM247, GTD-111, IN-939, IN-718, and Waspalloy) were examined to quantify the rate of Al interdiffusion as a function of initial superalloy composition. The diffusion couples were assembled with Invar steel jig encapsulated in Ar by sealing in quartz capsules and annealed at 1050 °C for 96 h. Concentration profiles measured by electron probe microanalysis in the single-phase β-NiAl region were used to determine interdiffusion fluxes and effective interdiffusion coefficients of individual components in the single-phase β-NiAl side of the couple. The values determined using experimental concentration profiles of the single-phase β-NiAl side of the couple were used to predict effective interdiffusion coefficients in multiphase superalloy side of the couple based on mass balance and local continuity of interdiffusion fluxes. Microstructural and compositional stability of protective coatings (e.g., NiCoCrAlY and NiAl) as a function of superalloys composition are discussed based on effective interdiffusion coefficients predicted from diffusion couple studies. This article was presented at the Multicomponent-Multiphase Diffusion Symposium in Honor of Mysore A. Dayananda, which was held during TMS 2006, 135th Annual Meeting and Exhibition, March 12–16, 2006, in San Antonio, TX. The symposium was organized by Yongho Sohn of University of Central Florida, Carelyn E. Campbell of National Institute of Standards and Technology, Richard D. Sisson, Jr., of Worcester Polytechnic Institute, and John E. Morral of Ohio State University.     

Intrinsic diffusion simulation for single-phase,multicomponent systems

A one-dimensional, finite difference simulation based on Darken’s treatment of intrinsic diffusion for single-phase, multicomponent systems is described. For the study of intrinsic diffusion using semi-infinite diffusion couples for binary systems, the input to the simulation includes the initial concentration distributions, the molar volume and the intrinsic diffusion coefficients for the two components as a function of composition. The simulation provides as the output all the results that are obtained from a typical interdiffusion experiment including the concentration profiles, the Kirkendall shift and interdiffusion fluxes of the components as a function of position and time. In addition, the intrinsic and vacancy fluxes, and the lattice shifts and lattice velocity profiles are also obtained at all positions within the diffusion zone. Since the simulation can handle variations in molar volume, information regarding fluxes and mean velocities in various reference frames are also provided. The internal consistency of the simulation is tested with the aid of an analytical model for a binary system where the interdiffusion coefficient and the ratio of the intrinsic diffusion coefficients are constant.     

Investigation of interdiffusion and kirkendall effect in the Co-Ni-Fe system: III. Dependence of diffusion parameters on the initial conditions

Dependences of the parameters of interdiffusion (effective coefficients, diffusion paths, Kirkendall shift) on the variation of the initial compositions of a diffusion couple have been studied on the concrete example of the Co-Fe-Ni system. The experimental results obtained show that the diffusion paths in the three-component system depend substantially on the selection of initial conditions, even when the initial alloys of the “narrower” diffusion couple lie on the diffusion path of the “wider” pair. At the same time, when represented in reduced concentrations, the diffusion paths of all these diffusion couples practically coincide. The latter makes it possible to predict the type of diffusion paths for any diffusion couple whose initial com- position lies in the same concentration region. In one of the diffusion couples studied, the instability of the Kirkendall plane was revealed, which thus far was observed only in binary systems.     

Interdiffusion and Atomic Mobilities of fcc Co-V-Mo Alloys: Measurement and Modeling

Based on 18 bulk diffusion couples, the composition-dependent interdiffusion coefficients in the fcc Co-V-Mo alloys at 1273, 1373 and 1473 K were obtained from the intersection points of the diffusion couples by means of EPMA technique coupled with the Whittle and Green method. With the experimentally determined interdiffusion coefficients and the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of fcc Co-V-Mo alloys were assessed by means of Diffusion Controlled Transformation (DICTRA) software. The quality of the assessed atomic mobilities was confirmed by the comprehensive comparisons between various DICTRA-calculated diffusion behaviors and the experimental ones, including concentration profiles and diffusion paths.     

An examination of a multicomponent diffusion couple

New expressions relating the interdiffusion flux of a component to its own concentration gradient in a multicomponent diffusion couple have been derived and applied to a diffusion couple investigated in the Cu-Ni-Zn system. From these relations, effective interdiffusion coefficients were determined at selected sections in the diffusion zone directly from the locations of the sections relative to the Matano plane. The Cu-Ni-Zn couple was analyzed for interdiffusion fluxes and interdiffusion coefficients with the aid of “MultiDiFlux” program developed for the analysis of interdiffusion in multicomponent systems. The couple was examined for zero-flux plane development, interdiffusion against activity gradients, and diffusion path representation. Diffusion path slopes at selected sections in the diffusion zone were related to the interdiffusion coefficients; slopes at path ends were determined from eigenvectors evaluated from limiting ratios of interdiffusion fluxes. Expressions for internal consistency among the concentration profiles or flux profiles of the individual components were also developed in terms of the terminal alloy compositions and applied to the Cu-Ni-Zn couple in the diffusion zone. This article was presented at the Multicomponent-Multiphase Diffusion Symposium in Honor of Mysore A. Dayananda, which was held during TMS 2006, 135th Annual Meeting and Exhibition, March 12–16, 2006, in San Antonio, TX. The symposium was organized by Yongho Sohn of University of Central Florida, Carelyn E. Campbell of National Institute of Standards and Technology, Richard D. Sisson, Jr., of Worcester Polytechnic Institute, and John E. Morral of Ohio State University.     

Ni-Nb-Ti三元系富Ni侧fcc相的互扩散及原子迁移率参数研究

本研究利用EPMA技术测定了Ni-Nb-Ti三元系富Ni侧合金在1000℃下的扩散数据,并使用Whittle and Green方法计算了Ni-Nb-Ti三元系在1000℃下的互扩散系数。通过DICTRA软件优化得到Ni-Nb-Ti三元系的fcc相的原子迁移率参数,运用优化得到的的原子迁移率计算出的互扩散系数与实验数据具有较好的一致性,从而验证了所得的原子迁移率参数的可靠性。同时通过运用迁移率参数拟合各扩散偶的的浓度-距离曲线和扩散路径,进一步验证了参数的合理性。     

Ternary Interdiffusion in <Emphasis Type="Italic">β</Emphasis> (BCC) Phase of the Ti-Al-Nb System

Interdiffusion coefficients are reported at various compositions in the β (BCC) phase of the Ti-Al-Nb system using solid–solid diffusion couples assembled at three different temperatures of 1060 °C, 1100 °C and 1170 °C. The interdiffusion fluxes were determined after fitting the experimental concentration profiles with MultiDiFlux software and the ternary interdiffusion coefficients were evaluated at various compositions using Kirkaldy’s approach. The interdiffusion of Nb was the slowest, while Ti and Al showed similar interdiffusion kinetics. The main interdiffusion coefficients for the three components are positive. The cross interdiffusion coefficients of Ti and Nb are comparable in magnitude to their respective main terms indicating the presence of strong diffusional interactions in this system. The cross coefficient \(\tilde{D}_{\text{TiNb}}^{\text{Al}}\) is positive indicating that the interdiffusion flux of Ti is enhanced down the concentration gradient of Nb. The negative value of the cross-term \(\tilde{D}_{\text{TiAl}}^{\text{Nb}}\) indicates that the interdiffusion flux of Ti is enhanced up the gradient of Al. The tracer diffusion coefficient of Al increases with temperature and decreasing Nb content in binary Ti-Nb alloys. Binary interdiffusivities calculated at Ti-Nb compositions by extrapolation are reasonably consistent with the values reported in the literature.     

Interdiffusion in γ (face-centered cubic) Ni-Cr-X (X=Al, Si, Ge, or Pd) alloys at 900 °C

Interdiffusion in nickel (Ni)-chromium (Cr) (face-centered cubic γ phase) alloys with small additions of aluminum (Al), silicon (Si), germanium (Ge), or palladium (Pd) was investigated using solid-to-solid diffusion couples. Ni-Cr-X alloys having compositions of Ni-22at.% Cr, Ni-21at.%Cr-6.2at.%Al, Ni-22at.%Cr-4.0at.%Si, Ni-22at.%Cr-1.6at.%Ge, and Ni-22at.%Cr-1.6at.%Pd were manufactured by arc casting. The diffusion couples were assembled in an Invar steel jig, encapsulated in Ar after several hydrogen purges, and annealed at 900 °C in a three-zone tube furnace for 168 h. Experimental concentration profiles were determined from polished cross sections of these couples by using electron probe microanalysis with pure element standards. Interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the moments of interdiffusion fluxes were examined to determine the average ternary interdiffusion coefficients. The effects of ternary alloying additions on the diffusional behavior of Ni-Cr-X alloys are presented in the light of the diffusional interactions and the formation of a protective Cr₂O₃ scale. This article was presented at the Multicomponent-Multiphase Diffusion Symposium in Honor of Mysore A. Dayananda, which was held during TMS 2006, the 135th Annual Meeting and Exhibition, March 12–16, 2006, in San Antonio, TX. The symposium was organized by Yongho Sohn of University of Central Florida, Carelyn E. Campbell of National Institute of Standards and Technology, Richard D. Sisson, Jr., of Worcester Polytechnic Institute, and John E. Morral of Ohio State University.     

A numerical inverse method for calculating the interdiffusion coefficients along a diffusion path in ternary systems

A numerical method has been developed to extract the composition-dependent interdiffusion coefficients from the concentration profiles in a single diffusion couple. The procedure is based on the minimization of the difference between the profiles calculated by a finite difference scheme and the experimental profiles. Tests performed on computed profiles, with noise added to simulate experimental concentration scatter, demonstrate the improvements this procedure provides compared with the classic inverse methods. In particular, the interdiffusion coefficient values are obtained along the whole diffusion path, instead of only at the intersection point of independent paths or instead of mean coefficient values.     

Concentration dependence of interdiffusion coefficients in Cu-Fe-Ni system

Conventional and effective interdiffusion coefficients have been determined in a Cu-Fe-Ni system for 1000°C based on our experimental data [13] on the distribution of concentrations of components in six diffusion couples of this system. The possibilities of applying these coefficients to interpret peculiar features of interdiffusion in ternary systems are analyzed. It has been demonstrated that effective interdiffusion coefficients are in a certain correlation with thermodynamic characteristics of the system.