Cross Interdiffusion Coefficients Research Articles

Interdiffusion behavior in sigma-phase using Ni3Al/Mo diffusion couples

The sigmaNiMo( Al) phase was formed using Ni3Al/Mo diffusion couples at 1423, 1473 and 1523 K. The growth of formed phase and the concentration-distance profiles for each component in the diffusion couples were examined by electron probe microanalysis (EPMA). The activation energy for the parabolic growth of ? phase is found to be 525.3 kJ/mol. The concentration dependence and average ternary interdiffusion coefficients in single ?-NiMo(Al) phase were calculated, and the Arrhenius equations of the D for the ?-NiMo(Al) phase are calculated, the diffusional interaction between Ni, Mo and Al in ?-NiMo(Al) phase was studied by the crossinterdiffusion coefficients. Moreover, these results were utilized to explain the ? phase formation and growth in ?? phase.

Interdiffusion behavior between Nb and MoSi 2 intermetallic compound

The interdiffusion behavior in Nb/MoSi 2 diffusion couples was studied in temperature interval 1250–1400 °C. The average binary interdiffusion coefficients in Nb 5Si 3 phase were determined from the interdiffusion fluxes calculated directly from experimental concentration profiles. The concentration dependence ternary interdiffusion coefficients in (Nb,Mo) 5Si 3 phase were calculated over the selected compositional ranges. Strong diffusional interaction between Nb and Mo in (Nb,Mo) 5Si 3 phase had been unfolded by the cross-interdiffusion coefficients D ˜ NbMo Si and D ˜ MoNb Si . The ternary interdiffusion coefficients were also examined to estimate binary interdiffusion coefficients and tracer diffusion coefficients of Nb and Mo in M 5Si 3 (M = Nb, Mo).

Determination of Average Ternary Interdiffusion Coefficients Using Moments of Interdiffusion Flux and Concentration Profiles

We developed a method of rigorous solution of the Onsager’s flow equations using moments of the interdiffusion-parameter integrands for the determination of average ternary interdiffusion coefficients. The analysis developed by Dayananda and Sohn [1] is the basis for this refined approach. Average main and cross interdiffusion coefficients are determined over selected regions in the diffusion zone using the diffusion-distance moments of the interdiffusion flux flow equations. Thermodynamic stability of solid solutions in the light of interdiffusion phenomenon is taken as validation criteria to identify accurate and reliable values of the ternary interdiffusion coefficients. Regulations are proposed for successful application of the analysis method to various ternary diffusion couples in Ni- and Fe-based intermetallics.

Interdiffusion within the β-phase region of the Ni–Co–Cr–Al quaternary system

Interdiffusion coefficients within the β-phase region of the nickel–cobalt–chromium–aluminum (Ni–Co–Cr–Al) quaternary system were estimated by square root diffusivity analysis. The obtained results indicated that the cross interdiffusion coefficients D ij ( i ≠ j, i, j = Al, Cr, Co) other than D AlCo were less than the main interdiffusion coefficients D ij ( i = j), and that the values of D Ali were greater than those of D Cri and D Coi . This finding suggests that the addition of chromium decreases the interdiffusion coefficients of aluminum and cobalt, but the addition of cobalt did not cause an obvious change in the interdiffusion coefficients of aluminum and chromium in the β-phase region. The different effects associated with the additions of chromium and cobalt were qualitatively discussed in light of the relationship between the thermodynamic properties of the system and Wagner's interaction parameter. The results revealed that the different effects could be ascribed to the stronger thermodynamic interactions between aluminum and cobalt compared to that between aluminum and chromium.

Interdiffusion in β phase in the ternary Ti–Al–Fe system alloys

The interdiffusion in Ti-rich β Ti–Al–Fe alloys has been investigated in the temperature range from 1323 to 1473 K. The main interdiffusion coefficients, D˜TiAlAl and D˜TiFeFe, and cross interdiffusion coefficients, D˜TiAlFe and D˜TiFeAl, have positive values in the ternary alloys, and they have slight concentration dependence. The values of D˜TiFeFe are larger than those of D˜TiAlAl, D˜TiAlAl, and the values of D˜TiFeAl are also larger than those of D˜TiAlFe. The repulsive interactions exist between Al and Fe atoms in the Ti–Al–Fe alloys, because the ratio values of cross coefficient to main one are positive in sign. On the other hand, the interactions between Ti (solvent) and Al (or Fe) atoms are attractive in the present alloy, since the ratio of converted interdiffusion coefficients in the ternary alloys show negative values.

Ternary diffusion and thermodynamic interaction in the β solid solutions of Ti–Al–Co alloys

The interdiffusion in Ti-rich β Ti–Al–Co alloys has been investigated in the temperature range from 1323 to 1473 K. The main interdiffusion coefficients, DAlAlTi and DCoCoTi, and cross interdiffusion coefficients, DAlCoTi and DCoAlTi, have positive values in the ternary alloys, and these four interdiffusion coefficients have slight concentration dependence. The values of DCoCoTi are larger than those of DAlAlTi, and the values of DCoAlTi are also larger than those of DAlCoTi. The repulsive interactions exist between Al and Co atoms in the Ti–Al–Co alloys, because the ratio values of cross coefficient to main one are positive in sign. On the other hand, the interactions between Ti (solvent) and Al (or Co) atoms are attractive in the present alloy, since the ratio of converted interdiffusion coefficients in the ternary alloys shows negative values.

Cross Interdiffusion Coefficients in Nickel- and Iron-Based Ternary Alloys

It is known that two main interdiffusion coefficients, ık Dii and ık Djj , as well as two cross interdiffusion coefficients, ık Dij and ık Dji , are necessary for understanding the atomic diffusion for ternary system. Here, k is the host element of ternary system, and i and j are solute elements. These four interdiffusion coefficients are obtained from a series of experiments using two kinds of ternary diffusion couples. In general, it is believed that ık Dij and ık Dji indicate the same sign to each other, but there are a lot of experimental data showing that ık Dij and ık Dji indicate opposite sign [1]. In such a case, the physical meaning of the cross interdiffusion coefficient has not always been understood thoroughly. The purposes of this study are to measure the interdiffusion coefficients by a series of experiments and to elucidate the physical meaning of the two cross interdiffusion coefficients on the basis of the consideration about the relationship between the thermodynamic functions and the cross interdiffusion coefficients. It is concluded that ık Dij exhibits the opposite sign to ık Dji without contradicting the Onsarger’s reciprocity theorem when the ( 2 2 ) c j ∂ G ∂c shows the opposite sign to ( 2 2 ) c i ∂ G ∂c . Here, c G is Gibbs free energy of the ternary system.

Diffusion of Refractory Elements in Ni—X—Y (X, Y: Co, Re, Ru, W) Ternary Alloys

Ni-based superalloys are strengthed by refractory elements such as Re, Ru and W [1]. Thus, the information on the interdiffusion coefficient as well as the thermodynamic interaction between the refractory elements is important for the future alloy design. In this study, interdiffusion coefficients of the refractory elements in Ni-X-Y (X, Y=Co, Re, Ru, W) ternary systems were estimated by a series of experiments. In the all systems studied in the present works, the main interdiffusion coefficients were much larger than the cross interdiffusion coefficients. In some systems, two cross interdiffuion coefficients had opposite signs each other. For example, in Ni-Co-Ru system, the main interdiffusion coefficients are 2.7 10 14 ~ Ru = × − CoCo D and 15 6.8 10 ~ Ru = × − RuRu D , while the cross interdiffusion coefficients are 16 6.6 10 ~ Ru = − × − CoRu D and 16 8.9 10 ~ Ru = × − RuCo D at 1523K. In Ni-Co-Ru and Ni-Re-Co systems, the activation energies and frequency factors for two main interdiffusion coefficients. For example, Q (kJ ) Co = 268 , 5 ( 2 1 ) 0( ) 4.4 10 D = × − m s − Co , 3 ( 2 1 ) 0( ) 2.9 10 D = × − m s − Ru in Ni-Co-Ru system.

Diffusion of Refractory Elements in Ternary Iron Alloys

Interdiffusion coefficients of the refractory elements in Fe-W-Re and Fe-Cr-X (X=Mo, W) ternary alloys have been measured on the basis of the modified Boltzmann-Matano method for ternary system. Both the cross interdiffusion coefficients, Fe ReW ~D and Fe WRe ~D were negative in Fe-W-Re ternary alloys. This result indicates that attractive interaction exists between W and Re atoms in iron alloys [1]. This is consistent with our previous experimental results that Re suppresses W diffusion in Fe-15Cr alloy [1]. In addition, the value of cross interdiffusion coefficient Fe CrW ~D was positive in Fe-Cr-W diffusion system, whereas Fe MoCr ~D was negative in Fe-Cr-Mo diffusion system.

Interdiffusion of Refractory Elements in Fe-Cr-X (X-Mo, W) and Fe-Mo-W Ternary Iron Alloys

Interdiffusion coefficients of the refractory elements in Fe-Cr-X (X=Mo, W) and Fe-Mo-W ternary alloys were measured on the basis of the modified Boltzmann-Matano method for ternary systems. The cross interdiffusion coefficient, ildeDCrWFe was positive in Fe-Cr-W ternary alloy, indicating that W accelerates interdiffusion between Fe and Cr atoms. On the other hand, the cross interdiffusion coefficient, ildeDCrMoFe was negative in Fe-Cr-Mo ternary alloys, indicating that Mo suppresses interdiffusion between Fe and Cr atoms. In addition, the cross interdiffusion coefficient, ildeDWMoFe was positive in Fe-Mo-W diffusion system. This result implies that Mo addition accelerates interdiffusion between Fe and W.

Diffusion of Re and Ru in the γ′ Phase of Ni Based Alloys

The diffusion of Re and Ru in the � 0 -Ni3Al phase has been investigated at a range of temperatures 1423–1523 K by using the pseudo-binary diffusion couples. It was found that the concentration gradient of Re appeared to promote the uphill diffusion of Al, whereas that of Ru did not promote the Al uphill diffusion. The cross interdiffusion coefficients of ~ D Ni and ~ D Ni were independent of the matrix ordering since they were comparable qualitatively between those in the � 0 -Ni3Al and in the � -Ni phases. The tracer diffusion coefficients for Re and Ru in Ni3Al were estimated by extrapolation and the obtained activation energies were consistent with the site preferences of the elements reported in the literature. Further, the results of this work suggest that the diffusion of Ru in Ni3Al is mostly governed by the diffusion in Ni sublattice and the diffusion of Re is mainly controlled by the formation of anti-site defects in the Ni sublattice with negligible contribution of the anti-site bridge mechanism. [doi:10.2320/matertrans.MRA2007632]

Diffusion and γ′ Phase Coarsening Kinetics in Ruthenium Containing Nickel Based Alloys

The present paper reports the interdiffusion of Re, W, Ru and Co in the binary and pseudo-binary Ni based alloys at 1523 K and the � 0 phase coarsening kinetics of model superalloys at 1324 K. Both Re and W concentration gradients caused Ru uphill diffusion in the respective pseudo-binary diffusion couple, whereas Ru concentration gradient promoted uphill diffusion for W but not for Re. Interestingly, Re uphill diffusion occurred under the influence of Co concentration gradient but the reverse effect was not observed. The cross interdiffusion coefficients qualitatively determined from the uphill diffusion profiles were in reasonable agreement with those reported previously. Comparison of the interdiffusion coefficients in the binary and the pseudo-binary diffusion couples showed that Ru and W decreased the diffusivity of each other whereas Co appeared to be more powerful barrier atoms than Ru to decrease the Re diffusivity. Furthermore, it was evident that the coarsening kinetics of the � 0 phase in both Ru-free and Ru-containing model superalloys were controlled by diffusion and Ru was found to have no effect on the rate constant of the � 0 phase coarsening. [doi:10.2320/matertrans.MRA2007283]

Interdiffusion in the β phase region of the Ni–Al–Cr system

This paper describes an investigation of the interdiffusion behavior in the beta single-phase region of the Ni-Al-Cr system by the modified Boltzmann-Matano method. The interdiffusion coefficient matrix is estimated and the cross-interdiffusion coefficients found to be smaller than the main interdiffusion coefficients at the examined composition ranges. Combining the thermodynamic calculation of the isochemical potential lines reveals that the thermodynamic interaction between Al and Cr in Al-rich beta-Nl(AI,Cr) is possibly negligible. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Computation of solidification paths in multiphase alloys with back-diffusion

Mathematical modeling of microsegregation in multicomponent alloys is a considerable challenge since solidification implies generally the formation of many different solid phases, each one changing the dynamics of phase transformation as the morphology becomes very complex and the kinetics phenomena more diverse. Before sophisticated models based on the resolution of partial differential mass conservation equations can give reliable predictions in multiphase alloys, there is a need to calculate solidification paths based on the incremental mass conservation equation and the back-diffusion parameters. The incremental mass balance proposed in this contribution was written without considering a specific migration mechanism. This decoupling allowed an easy integration of a microsegregation model enabling the evaluation of back-diffusion parameters. In this paper, Ohnaka’s microsegregation model was chosen because it allows a simple and elegant inclusion of the cross interdiffusion coefficients in the calculation of back-diffusion parameters. The model assumes that complete mixing prevails in the liquid phase and that equilibrium conditions can be applied for a sub-system having a composition defined according to the mobility of species and a set of empirical parameters. A large range of solidification paths lying between Scheil and global equilibrium conditions can be calculated and used to explain experimental observations. The model was applied on a ternary Al–Mg–Mn alloy for comparison purposes, with the software DICTRA. An excellent agreement between the two models was obtained using similar assumptions. The scheme was also applied on AA6111 and allowed us to understand large deviations observed between the amounts of secondary phases obtained with DSC experiments and those predicted by Scheil or equilibrium conditions.

Interdiffusion in Ni-Co-Re and Ni-Co-Ru Systems

The diffusion in Ni-Co-Re and Ni-Co-Ru systems have been investigated in the temperature range 1323–1523 K through the determination of the interdiffusion coefficients. The main interdiffusion coefficients of these systems were larger than the cross interdiffusion coefficients, indicating that the influences of the own concentration gradients of the elements were generally still dominant. From the ratio of the cross interdiffusion coefficient to the main one, j ~ D k = ~ D k j, it was found that the effect of Co on the diffusion of Re was more appreciable than that of Ru. Moreover, by the comparison between the diffusion in the binary Ni-Re and in the ternary Ni-Co-Re, it was clear that the presence of Co reduced the Re diffusivity in Ni. The results of this work reflect two folds; the attractive force exists between Co and Re, and the interatomic bonding of Co-Re seems to be stronger than that of Ni-Re. [doi:10.2320/matertrans.MRA2007116]

Diffusion of Refractory Elements in Ni–X–Y (X, Y: Re, W, Ru, Al) Ternary Alloys

Interdiffusion coefficients of the refractory elements in Ni–X–Y (X, Y ¼ W, Re, Ru, Al) ternary systems, which are the fundamental systems of Ni-based superalloys, were estimated by a series of experiments using diffusion couples. The modified ternary Boltzmann–Matano method was employed for analyzing the experimental data. The cross interdiffusion coefficients were smaller than the main interdiffusion coefficients in all systems. Especially, the cross interdiffusion coefficient ~ D Ni is much smaller by an order of magnitude than the main interdiffusion coefficient ~ D Ni in Ni–Ru–Re system. This result indicates that the thermodynamical interaction parameter (Wagner’s interaction

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.

Diffusion of Refractory Elements in Ni-Al-X (X:Re,W) Ternary Alloys

In order to investigate the diffusivity of both W and Re in Ni-based superalloys, interdiffusion coefficients in Ni-Al-X (X=Re, W) ternary system, which is the fundamental system of Ni-based superalloys, were measured by an experiment using diffusion couples. A modified ternary Boltzmann-Matano method was employed for the evaluation of the interdiffusion coefficients. In the γ phase of Ni-2.5Al-4.3Re and of Ni-2.4Al-3.3W (mol%), the major interdiffusion coefficients were estimated to be \\ ildeDReReNi=2.2×10−15 m2/s and \\ ildeDWWNi=9.9×10−15 m2/s. It is found that \\ ildeDReReNi is much smaller than \\ ildeDWWNi. Also cross interdiffusion coefficients, |\\ ildeDReAlNi|<|\\ ildeDWAlNi| and \\ ildeDReAlNi,\\ ildeDWAlNi<0 were obtained in the γ phase. The interdiffusion coefficients give the Wagner’s interaction parameter between Re and Al, and between W and Al as εReAl<εWAl<0, indicating that the ordering tendency exists between Al and Re, and between Al and W.

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.

A new analysis for the determination of ternary interdiffusion coefficients from a single diffusion couple

Concentration profiles that develop in a ternary diffusion couple during an isothermal anneal can be analyzed directly for average ternary interdiffusion coefficients. A new analysis is presented for the determination of average values for the main and cross-interdiffusion coefficients over selected regions in the diffusion zone from an integration of interdiffusion fluxes, which are calculated directly from experimental concentration profiles. The analysis is applied to selected isothermal diffusion couples investigated with α (fcc) Cu-Ni-Zn alloys at 775 °C, β (bcc) Fe-Ni-Al alloys at 1000 °C, and γ (fcc) Ni-Cr-Al alloys at 1100 °C. Average ternary interdiffusion coefficients treated as constants are calculated over composition ranges on either side of the Matano plane and examined for the diffusional interactions among the diffusing components. The ternary interdiffusion coefficients determined from the new analysis are observed to be consistent with those determined by the Boltzmann-Matano analysis at selected compositions in the diffusion zone. The ternary interdiffusion coefficients are also employed in analytical solutions based on error functions for the generation of concentration profiles for the selected diffusion couples. The generated profiles are a good representation of the experimental profiles including those exhibiting uphill diffusion or zero-flux plane (ZFP) development for the individual components. Uncertainties in the values of the interdiffusion coefficients calculated on the basis of the new analysis are found to be minimal.