Interdiffusion Fluxes Research Articles

Interdiffusion and atomic mobility studies in Ni-rich fcc Ni−Al−Mn alloys

By employing nine groups of bulk diffusion couples together with electron probe microanalysis technique, the composition dependence of ternary interdiffusion coefficients in Ni-rich fcc Ni−Al−Mn alloys at 1373 K was determined via the Matano–Kirkaldy method. The experimental interdiffusion coefficients were critically assessed to obtain the atomic mobilities of Ni, Al and Mn in fcc Ni−Al−Mn alloys by using the DICTRA (DIffusion-Controlled TRAnsformations) software package. The reliability of these mobilities was validated by comprehensive comparison between the model-predicted diffusion properties and the experimental data. The obtained atomic mobilities could be used to describe various diffusion phenomena in fcc Ni–Al–Mn alloys, such as the concentration profiles, interdiffusion flux and diffusion paths.

Interdiffusion and reaction between uranium and iron

Metallic uranium alloy fuels cladded in stainless steel are being examined for fast reactors that operate at high temperature. In this work, solid-to-solid diffusion couples were assembled between pure U and Fe, and annealed at 853K, 888K and 923K where U exists as orthorhombic α, and at 953K and 973K where U exists as tetragonal β. The microstructures and concentration profiles developed during annealing were examined by scanning electron microscopy and electron probe microanalysis, respectively. U6Fe and UFe2 intermetallics developed in all diffusion couples, and U6Fe was observed to grow faster than UFe2. The interdiffusion fluxes of U and Fe were calculated to determine the integrated interdiffusion coefficients in U6Fe and UFe2. The extrinsic (KI) and intrinsic growth constants (KII) of U6Fe and UFe2 were also calculated according to Wagner’s formalism. The difference between KI and KII of UFe2 indicate that its growth was impeded by the fast-growing U6Fe phase. However, the thin UFe2 played only a small role on the growth of U6Fe as its KI and KII values were determined to be similar. The allotropic transformation of uranium (orthorhombic α to tetragonal β phase) was observed to influence the growth of U6Fe directly, because the growth rate of U6Fe changed based on variation of activation energy. The change in chemical potential and crystal structure of U due to the allotropic transformation affected the interdiffusion between U and U6Fe. Faster growth of U6Fe is also examined with respect to various factors including crystal structure, phase diagram, and diffusion.

Phase equilibria, diffusion growth and diffusivities in Ni-Al-Pt system using Pt/β-NiAl diffusion couples

AbstractThe phase equilibria, diffusion growth and diffusivities in the Ni-Al-Pt system at 1 150, 1 200 and 1 250 °C were studied using Pt/β-NiAl diffusion couples. Based on the measured concentration profiles coupled with the local equilibrium hypothesis, the tie-lines between neighboring phases were determined. Two intermediate phases, Pt3Al and α-NiPt(Al), are found to develop between the Pt and β-NiAl couples. The thicknesses of Pt3Al and α-NiPt(Al) layers varies linearly with the square of annealing time, indicating that the growth of Pt3Al and α-NiPt(Al) are diffusion-controlled. The calculated Arrhenius equations of the parabolic growth constants, k, for the Pt3Al and β-NiPt(Al) phases are obtained, respectively. The average ternary inter-diffusivities of the Pt3Al and β-NiAl phases at different temperatures are determined from an integration of inter-diffusion fluxes calculated directly from the experimental concentration profiles.

Interface Movement and Microstructure Evolution of Interdiffusion in the Binary Alloy Diffusion Couples

The phase field simulation of interface movement and interdiffusion microstructure in a binary diffusion couples was developed. The diffusion couples with nonequilibrium concentration for single phase or single phase and two-phase including the temperature and mobility effects were studied. It’s shown that the interface movement and the atoms diffusion direction were determined by the magnitude of relative concentration difference between the initial concentration and the equilibrium concentration, the distance of interface movement and interdiffusion flux increases as the temperature or the mobility increasing, and the large mobility makes the particles coarsening faster.

Atomic mobility, diffusivity and diffusion growth simulation for fcc Cu–Mn–Ni alloys

On the basis of the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of Cu, Mn and Ni in fcc Cu–Mn–Ni alloys were assessed as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between the calculated results and the experimental data show that a good agreement is obtained for various diffusivities in binary and ternary systems, including impurity diffusion coefficients, tracer diffusion coefficients and interdiffusion coefficients. The atomic mobilities obtained can also be used to describe various diffusion phenomena for a series of binary and ternary diffusion couples, such as concentration profiles, the Kirkendall shift, the interdiffusion flux and diffusion paths.

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).

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.

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 in L12-Ni3Al Alloyed with Re

Ternary interdiffusion in L12-Ni3Al with ternary alloying addition of Re was investigated at 1473 K using solid-to-solid diffusion couples. Interdiffusion flux of Ni, Al, and Re were directly calculated from experimental concentration profiles and integrated for the determination of average ternary interdiffusion coefficients. The magnitude of main interdiffusion coefficients \( \bar{\tilde{D}}_{\text{NiNi}}^{\text{Al}} \) and \( \bar{\tilde{D}}_{\text{AlAl}}^{\text{Ni}} \) was determined to be much larger than that of the main interdiffusion coefficient \( \bar{\tilde{D}}_{\text{ReRe}}^{\text{Al (or Ni)}}. \) A moderate tendency for Re to substitute for Al sites was reflected by its influence on interdiffusion of Al, quantified by large and positive \( \bar{\tilde{D}}_{\text{AlRe}}^{\text{Ni}} \) coefficients. Similar trends were observed from ternary interdiffusion coefficients determined by Boltzmann-Matano analysis. Profiles of concentrations and interdiffusion fluxes were also examined to estimate binary interdiffusion coefficients in Ni3Al, and tracer diffusion coefficients of Re (5.4 × 10−16 ± 2.3 × 10−16 m2/s) in Ni3Al.

On interdiffusion in the multicomponent β-NiAl phase

Diffusion coefficients of the multicomponent β-NiAl phase at 850, 950 and 1050 °C have been estimated as a function of composition by means of analyzing interdiffusion fluxes from concentration profiles which are obtained from the pack-aluminizing diffusion couples. The results indicate that values of D AlNi int and D AlCo int are strongly composition dependent and values of D AlCr int are slightly composition dependent. There exist significant differences in values of D AlNi int between obtained in this study and reported in the literature for the binary NiAl phase. These differences become larger as the temperature decreases. This can be explained by the variation of the thermodynamic properties of the multicomponent β-NiAl phase, which results from the solid solution of the alloying elements present in the nickel-based superalloy. The changes in the electronic structure due to the atomic size mismatch between the solute and solvent atoms may partially be responsible for these differences.

Ternary and Quaternary Interdiffusion in γ (fcc) Fe-Ni-Cr-X (X = Si, Ge) Alloys at 900°C

Interdiffusion in Fe-Ni-Cr (fcc γ phase) alloys with small additions of Si and Ge at 900°C was studied using solid-to-solid diffusion couples. Alloy rods of Fe-24 at.%Ni, Fe-24 at.%Ni- 22at.%Cr, Fe-24 at.%Ni-22at.%Cr-4at.%Si and Fe-24 at.%Ni-22at.%Cr-1.7at.%Ge were cast using arc-melt, and homogenized at 900°C for 168 hours. Sectioned alloy disks from the rods were polished, and diffusion couples were assembled with in Invar steel jig, encapsulated in Argon after several hydrogen flushes, and annealed atz 900°C for 168 hours. Polished cross-sections of the diffusion couples were characterized to determine experimental concentration profiles using electron probe microanalysis with pure elemental standards. Interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the moments of interdiffusion flux profiles were examined to determine the average ternary and quaternary interdiffusion coefficients. Effects of alloying additions on the interdiffusional behavior of Fe-Ni- Cr-X alloys at 900°C are presented with due consideration for the formation of protective Cr2O3 scale.

Effects of Ir or Ta Alloying Addition on Interdiffusion of L1 2–Ni 3Al

Ternary interdiffusion in L1 2–Ni 3Al with ternary alloying additions of Ir and Ta was investigated at 1473 K using solid-to-solid diffusion couples. Average ternary interdiffusion coefficients were determined from an integration of interdiffusion fluxes calculated directly from experimental concentration profiles. The magnitude of D ˜ ¯ NiNi and D ˜ ¯ AlAl coefficients was determined to be much larger than that of D ˜ ¯ IrIr and D ˜ ¯ TaTa coefficients. Ir substituting in Ni-site influenced the interdiffusion of Ni significantly, and D ˜ ¯ NiIr Al coefficients were determined to be large and positive. On the other hand, Ta substituting for Al influenced the interdiffusion of Al significantly, and D ˜ ¯ AlTa Ni coefficients were determined to be large and positive. An excellent agreement was found with ternary interdiffusion coefficients determined by Boltzmann–Matano analysis. Profiles of concentrations and interdiffusion fluxes were also examined to estimate binary interdiffusion coefficients in Ni 3Al, and tracer diffusion coefficients of Ir (14.7 × 10 −16 ± 1.4 × 10 −16 m 2/s) and Ta (2.6 × 10 −16 ± 2.4 × 10 −16 m 2/s) in Ni 3Al.

Modeling the Interdiffusion and Reactive-Diffusion Processes in Multicomponent Systems

Some long-standing problems concerning the diffusion in open systems are resolved in the context of Darken and Wagner methods with Nernst–Planck flux. Explicitly, the known results on the reactive and interdiffusion processes are significantly extended as follows: (1) the diffusion fluxes are defined in the volume fixed reference frame that is rigorously defined, (2) the Darken method is extended and allows analyzing the nonideal alloys showing different molar volumes, (3) the boundary conditions take into account both the interdiffusion and reactive diffusion, and (4) the flux constraints are used to couple processes occurring at different time scales. We demonstrate solutions of the interdiffusion in the Fe-Ni-Cu alloy and heterogeneous reaction between the multicomponent alloy and oxidant. The interdiffusion fluxes can be computed starting from the Fick’s constitutive diffusion flux formula to the combined Darken–Onsager approach. This method allows modeling pure interdiffusion in multicomponent systems as well as a wide class of the reaction-diffusion problems associated with solid-state chemistry, corrosion, surface treatment, etc.

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.

Ternary Interdiffusion in L1<sub>2</sub>-Ni<sub>3</sub>Al with Ir Alloying Addition

Average ternary interdiffusion coefficients in Ni3Al with Ir additions have been determined using solid-to-solid diffusion couples annealed at 1200°C for 5 hours. Disc shaped alloy specimens were prepared by the vacuum arc melting at compositions of Ni-24Al, Ni-25Al, Ni-26Al, Ni-23.5Al-1Ir, Ni-24.5Al-1Ir, Ni-23Al-2Ir, Ni-23Al-2Ir, Ni-24Al-2Ir, Ni-23Al-3Ir (at.%). Surfaces of alloys were polished down to 1200 grit and diffusion couples were assembled in Si3N4 jig for initial bonding heat treatment at 1200°C for 0.5 hours. Additional diffusion anneal was carried out at 1200°C for 4.5 hours outside of Si3N4 jig so that diffusion couples can be water quenched. Concentration profiles of individual components were measured by electron probe microanalysis using pure standard of Ni, Al and Ir. Interdiffusion flux of individual component was determined directly from the experimental concentration profiles, and the moments of interdiffusion flux were examined to calculate the average ternary interdiffusion coefficients, D˜ ij k either with Al or Ni as dependent component. Calculated interdiffusion coefficients suggest that Ir-alloyed Al2O3-forming oxidation resistant coatings would be beneficial to reduce the interdiffusion flux of Ni from superalloy substrates to the coating, and reduce the interdiffusion flux of Al from the coating to the superalloy substrate.

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 in (fcc) Ni-Cr-X (X = Al, Si, Ge or Pd) Alloys at 700°C

Interdiffusion at 700°C for Ni-22at.%Cr (fcc γ phase) alloys with small additions of Al, Si, Ge, or Pd was examined using solid-to-solid diffusion couples. Rods 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 alloys were cast using arc-melt and homogenized at 900°C for 168 hours. The diffusion couples were assembled with alloy disks in Invar steel jig, encapsulated in Argon after several hydrogen flushes, and annealed at 700°C for 720 hours. Experimental concentration profiles were determined from polished cross-sections by using electron probe microanalysis with pure standards of Ni, Cr, Al, Si, Ge and Pd. Interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the moments of interdiffusion fluxes were examined to determine average ternary interdiffusion coefficients. Effects of ternary alloying additions on the interdiffusional behavior of Ni-Cr-X alloys at 700°C are presented in the light of the diffusional interactions and the formation of protective Cr2O3 scale.

Reactive Diffusion between Solid Fe and Liquid Zn at 723 K

Reactive diffusion between solid Fe and liquid Zn was experimentally examined using Fe/Zn diffusion couples prepared by an immersion technique. Using this technique, a pure iron sheet was immersed in a molten pure Zn bath with a constant temperature of T=723 K (450°C) for various times up to t=7.2×103 s (2 h). The microstructure of the cross section of the Fe/Zn diffusion couple was observed by scanning electron microscopy, and the chemical composition of each phase was determined by electron probe microanalysis. Interface concentrations of Fe for the ζ-FeZn13 and δ-FeZn7–10 phases at the ζ/δ interface, cζδ and cδζ, and for the liquid-Zn (L) phase at the ζ/L interface, cLζ, determined from the diffusion couples were found to be extremely higher than the corresponding equilibrium values, especially in the early stage of t<300 s, and the difference gradually decreased during immersion. The deviations from the equilibrium values for the cζδ and cLζ were proportional to the interdiffusion flux across the ζ phase layer.

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.

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.