Cross Interdiffusion Coefficients Research Articles

Diffusion-controlled growth and microstructural evolution between Pt and Pd containing B2-NiAl bondcoats and Ni-based single crystal superalloy

Pt-modified NiAl bond coats are used to extend the lifetime of blades in gas turbine engine applications. However, they suffer from the growth of deleterious precipitates within the interdiffusion zone. Partial substitution of Pt by Pd is advantageous in reducing the interdiffusion zone thickness between the bond coat and the superalloy, providing comparable oxidation properties, and critically reducing the propensity to form brittle (Pt,Ni)Al2 precipitates. In this study, we utilize the pseudo-binary diffusion couple method to estimate the interdiffusion coefficients of Ni and Al in Pd, Pd-Pt and Pt-modified nickel aluminides. Additionally, the main and cross-interdiffusion coefficients are estimated in the ternary diffusion couples. The estimated diffusion coefficients in the β-NiAl phase reflect on the thickness of the β phase in the superalloy bond coat interdiffusion zone. Pd reduces the pseudo-binary interdiffusion coefficients of Ni–Al and also decreases the main and cross-ternary interdiffusion coefficients. This correlates with the reduction of the interdiffusion zone thickness by Pd. The diffusion process is strongly assisted by point defects in this phase. Ab initio-informed defect calculations are done to explain diffusion retardation in the presence of Pd (compared to Pt) with decreased defect concentrations. Furthermore, through in-depth microstructure characterization performed by electron probe micro analyser, transmission electron microscopy, and atom probe tomography, the presence of σ, R and μ phases as TCP precipitates in the interdiffusion zone are identified. The results give insights into the coatings’ diffusional properties that influence the service life of the product.

Effect of Vacancy Defect Content on the Interdiffusion of Cubic and Hexagonal SiC/Al Interfaces: A Molecular Dynamics Study.

The mechanical properties of ceramic-metal nanocomposites are greatly affected by the equivalent properties of the interface of materials. In this study, the effect of vacancy in SiC on the interdiffusion of SiC/Al interfaces is investigated using the molecular dynamics method. The SiC reinforcements exist in the whisker and particulate forms. To this end, cubic and hexagonal SiC lattice polytypes with the Si- and C-terminated interfaces with Al are considered as two samples of metal matrix nanocomposites. The average main and cross-interdiffusion coefficients are determined using a single diffusion couple for each system. The interdiffusion coefficients of the defective SiC/Al are compared with the defect-free SiC/Al system. The effects of temperature, annealing time, and vacancy on the self- and interdiffusion coefficients are investigated. It is found that the interdiffusion of Al in SiC increases with the increase in temperature, annealing time, and vacancy.

Molecular Dynamics Study of Interdiffusion for Cubic and Hexagonal SiC/Al Interfaces

The mechanical properties of the SiC/Al interface are crucial in estimating the overall strength of this ceramic-metal composite. The present work investigates the interdiffusion at the SiC/Al interface using molecular dynamics simulations. One cubic and one hexagonal SiC with a higher probability of orientations in contact with Al are examined as two samples of metal-matrix nanocomposites with whisker and particulate reinforcements. These reinforcements with the Si- and C-terminated surfaces of the SiC/Al interfaces are also studied. The average main and cross-interdiffusion coefficients are evaluated using a single diffusion couple for each system. The effect of temperature and annealing time are analysed on the self- and interdiffusion coefficients. It is found that the diffusion of Al in SiC is similar in cubic and hexagonal SiC and as expected, the interdiffusion coefficient increases as the temperature and annealing time increase. The model after diffusion can be used to evaluate the overall mechanical properties of the interface region in future studies.

Ternary Diffusion and Thermodynamic Interaction in the β Solid Solutions of Ti–Al–Zr Alloys at 1473 K

Interdiffusion in Ti-rich β solid solutions in Ti–Al–Zr alloys was investigated at 1473 K. In the β Ti–Al–Zr alloys, the main interdiffusion coefficients (i.e., and , respectively) and the cross interdiffusion coefficients, (i.e., and , respectively) have positive values, as well as a slight concentration dependence. The values of are larger than those of . In Ti–Al–X (= V, Cr, Fe, Co, Zr) alloys, the values of the main coefficients are at 1473 K. Repulsive interactions occur between Al and X (= V, Cr, Fe, Co, Zr) atoms in the Ti–Al–X alloys, because the ratio values of the cross coefficients to the main ones are positive in sign. On the other hand, the interactions between Ti (solvent) and X (= V, Cr, Fe, Co, Zr) (or Al) atoms are attractive in the present alloys because the ratio of the converted interdiffusion coefficients is negative values.

High-throughput determination of mechanical and diffusion properties in the Ti–Nb–Fe alloys

Accurate Young's modulus, hardness, and interdiffusion coefficient are the necessary information for the design and production of biomedical multicomponent alloys. In this work, five sets of ternary Ti–Nb–Fe diffusion couples were prepared after annealing at 1273 K for 25 h. The composition-dependent Young's moduli and hardness in the bcc Ti–Nb–Fe system were experimentally determined by means of nanoindentation and electron probe microanalysis (EPMA) techniques. Moreover, the main and cross interdiffusion coefficients of Ti–Nb–Fe alloys at 1273 K were confirmed from the composition gradients of the diffusion couples by using a pragmatic numerical inverse method. A composition-dependent database on the mechanical and diffusion properties of Ti–Nb–Fe alloys was carefully established and utilized for the discussion of the processability during the hot workability. The results indicated that Fe concentration control could be very helpful for the development of Ti–Nb–Fe alloys with low Young's modulus, high hardness, and nice processability during the hot working.

A Direct Derivation of Fick's Law from Continuity Equation for Interdiffusion in Multicomponent Systems

A new analysis is presented where the interdiffusion flux J˜i of a component i is related to (n-1) independent concentration gradients for an isothermal, n-component diffusion couple with the aid of the continuity equation. This analysis may be considered as a derived statement of Fick's law applicable to the analysis of solid-solid and vapor-solid diffusion couples. New expressions are provided for both main and cross interdiffusion coefficients, D˜ijn(i,j=1,2,.....n−1), at section x in the diffusion zone involving the partial derivatives of [(J˜i)·(x−xo)] with respect to concentration Cj, where xo is the Matano plane. Such expressions for both binary and ternary interdiffusion coefficients are presented for various choices of the dependent concentration variable, Cn. The validity of the analysis is illustrated with a binary diffusion couple characterized by a constant interdiffusion coefficient. Diffusional interactions among components are reflected in the variations of [(J˜i)·(x−xo)] with Cj.

Correlation between estimated diffusion coefficients from different types of diffusion couples in multicomponent system

The interdiffusion coefficients can be estimated now purely experimentally from multicomponent diffusion profiles utilizing the recently proposed pseudo-binary and pseudo-ternary diffusion couple methods. One can estimate the composition dependent main interdiffusion coefficients over the composition range and main intrinsic diffusion coefficients at the Kirkendall marker plane from pseudo-binary diffusion couple. On the other hand, main and cross interdiffusion coefficients can be calculated from the pseudo-ternary diffusion couples. In this article, we have first proposed the method of estimation of the tracer diffusion coefficients at the cross of diffusion paths in pseudo-ternary diffusion couples by extending the approach propose by Lane and Kirkaldy in a ternary system but without neglecting the cross phenomenological terms of Onsager formalism. Following, one can even estimate the main and cross intrinsic diffusion coefficients, which is otherwise not possible following the Kirkendall marker experiments in this type of couple. Following we have derived the relation for estimation of the tracer diffusion coefficients at the Kirkendall marker plane in a pseudo-binary diffusion couple. We have chosen NiCoFeCr system to demonstrate the utilization of these methods by comparing the tracer diffusion coefficients estimated directly following radiotracer method. The relations derived in this article help to understand the correlation between estimated data in different types of diffusion couples by neglecting and considering the vacancy wind effect. This method can be now extended to the Al, Ga, Si containing systems in which the estimation of tracer diffusion coefficients following the radiotracer method is difficult/impossible because of various reasons.

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.

Diffusion, defects and understanding the growth of a multicomponent interdiffusion zone between Pt-modified B2 NiAl bond coat and single crystal superalloy

Composition-dependent diffusion coefficients are determined in B2-Ni(CoPt)Al system following the pseudo-binary and pseudo-ternary diffusion couple methods, which would not be possible otherwise in a quaternary inhomogeneous material fulfilling the conditions to solve the equations developed based on the Onsager formalism. The end-member compositions to produce ideal/near-ideal diffusion profiles are chosen based on thermodynamic details. The pseudo-binary interdiffusion coefficients of Ni and Al decrease in the presence of Co but increase in the presence of Pt. The pseudo-ternary interdiffusion coefficients indicate that the main interdiffusion coefficients increase significantly in the presence of Pt. Marginal changes of the cross interdiffusion coefficients substantiate a minor change of the diffusional interactions between the components. The thermodynamic driving forces show opposite trends with respect to composition as compared to the changes of the interdiffusion coefficients advocating a dominating role of the Pt(Co)-induced modifications of point defect concentrations. DFT-based calculations revealed that Pt alloying increases the Ni vacancy concentration and decreases the activation energy for the triple defect diffusion mechanism. These findings explain the increase in the thickness of the interdiffusion zone between the B2-Ni(Pt)Al bond coat and the single crystal superalloy René N5 because of Pt addition. Furthermore, the EPMA and TEM analyses reveal the growth of refractory elements-enriched precipitates.

First report on entire sets of experimentally determined interdiffusion coefficients in quaternary and quinary high-entropy alloys

Abstract

Diffusion research in HCP Mg–Al–Sn ternary alloys

Diffusion behavior in the HCP Mg–Al–Sn ternary alloys was experimentally investigated at 673 K and 723 K by analyzing solid-state diffusion couples. From the composition profiles analytically represented by error function expansion, the inter- and impurity diffusion coefficients were extracted by the Whittle-Green and generalized Hall methods respectively, which enable to establish the diffusion properties of the HCP Mg–Al–Sn alloys. The present results, together with the binary diffusion data of Mg–Al and Mg–Sn binaries, reveal that the average value of the main interdiffusion coefficient D˜SnSnMg over the investigated compositions is 1.39 times larger than D˜AlAlMg at 673 K and 1.36 times at 723 K, respectively, implying Sn diffuses comparably faster than Al in the HCP Mg–Al–Sn alloys. The main interdiffusion coefficients D˜AlAlMg and D˜SnSnMg and the impurity diffusion coefficient DSn(Mg−Al)* increases with increasing the content of diffusing element, either Al or Sn, however, DAl(Mg−Sn)* increases first and then decreases as the Sn composition increases. The cross interdiffusion coefficients are scattering, their composition dependences are not very conclusive, however, a trend that D˜AlSnMg and D˜SnAlMg become negligibly small or even negative was evidenced as the content of Al or Sn approaches 0.

Ternary Interdiffusion in β (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.

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 in Ternary Magnesium Solid Solutions of Aluminum and Zinc

Al and Zn are two of the most common alloying elements in commercial Mg alloys, which can improve the physical properties through solid solution strengthening and precipitation hardening. Diffusion plays a key role in the kinetics of these and other microstructural design relevant to Mg-alloy development. However, there is a lack of multicomponent diffusion data available for Mg alloys. Through solid-to-solid diffusion couples, diffusional interactions of Al and Zn in ternary Mg solid-solution at 400° and 450 °C were examined by an extension of the Boltzmann-Matano analysis based on Onsager’s formalism. Concentration profiles of Mg-Al-Zn ternary alloys were determined by electron probe microanalysis, and analyzed to determine the ternary interdiffusion coefficients as a function of composition. The magnitude of $$\tilde{D}_{ZnZn}^{Mg}$$ ternary interdiffusion coefficients was greater than that of $$\tilde{D}_{AlAl}^{Mg} ,$$ the magnitude of $$\tilde{D}_{ZnZn}^{Al}$$ ternary interdiffusion coefficients was greater than that of $$\tilde{D}_{MgMg}^{Al}$$ , and the magnitude of $$\tilde{D}_{MgMg}^{Zn}$$ was greater than that of $$\tilde{D}_{AlAl}^{Zn}$$ . Appreciable diffusional interactions among Mg, Al, and Zn were observed by variations in sign and magnitude of cross interdiffusion coefficients. In particular, Zn was found to significantly influence the interdiffusion of Mg and Al significantly: the $$\tilde{D}_{MgZn}^{Al}$$ and $$\tilde{D}_{AlZn}^{Mg}$$ ternary cross interdiffusion coefficients were both negative, and large in magnitude, in comparison to $$\tilde{D}_{MgMg}^{Al}$$ and $$\tilde{D}_{AlAl}^{Mg}$$ , respectively. Al and Mg were observed influence the interdiffusion of Mg and Al, respectively, with positive $$\tilde{D}_{MgAl}^{Zn}$$ and $$\tilde{D}_{AlMg}^{Zn}$$ interdiffusion coefficients, but their influence on the Zn interdiffusion was negligible.

Microstructural Development and Ternary Interdiffusion in Ni-Mn-Ga Alloys

NiMnGa alloys functioning as either ferromagnetic shape memory alloys or magnetocaloric materials have both practical applications and fundamental research value. In this study, solid-to-solid diffusion couple experiments were carried out to investigate the phase equilibria, microstructural development, and interdiffusion behavior in Ni-Mn-Ga ternary alloys. Selected diffusion couples between pure Ni, Ni25Mn75 and four ternary off-stoichiometric NiMnGa alloys (i.e., Ni52Mn18Ga30, Ni46Mn30Ga24, Ni52Mn30Ga18, Ni58Mn18Ga24) were assembled and annealed at 1073 K, 1123 K, and 1173 K (800 °C, 850 °C, and 900 °C) for 480, 240, and 120 hours, respectively. At these high temperatures, the β NiMnGa phase has a B2 crystal structure. The microstructure of the interdiffusion zone was examined by scanning electron microscopy and transmission electron microscopy. Concentration profiles across the interdiffusion zone were determined by electron probe micro analysis. Solubility values obtained for various phases were mostly consistent with the existing isothermal phase diagrams, but the phase boundary of the γ(Mn) + β two-phase region was slightly modified. In addition, equilibrium compositions for the γ(Ni) and α′ phases at 1173 K (900 °C) were also determined for the respective two-phase region. Both austenitic and martensitic phases were found at room temperature in each diffusion couple with a clear boundary. The compositions at the interfaces corresponded close to valence electron concentration (e/a) of 7.6, but trended to lower values when Mn increased to more than 35 at. pct. Average effective interdiffusion coefficients for the β phase over different compositional ranges were determined and reported in the light of temperature-dependence. Ternary interdiffusion coefficients were also determined and examined to assess the ternary diffusional interactions among Ni, Mn, and Ga. Ni was observed to interdiffuse the fastest, followed by Mn then Ga. Interdiffusion flux of Ni also has strong influences on the interdiffusion of Mn and Ga with large and negative cross interdiffusion coefficients, $$ \tilde{D}_{MnNi}^{Ga} $$ and $$ \tilde{D}_{GaNi}^{Mn} $$ . The $$ \tilde{D}_{NiNi}^{Ga} $$ and $$ \tilde{D}_{MnMn}^{Ga} $$ ternary interdiffusion coefficients exhibited minimum values near 52 at. pct Ni concentration.

Investigations of quaternary interdiffusion in a constituent system of high entropy alloys

Interdiffusion was investigated at 1000°C in a quaternary Fe-Ni-Co-Cr system, which is an essential constituent of many high-entropy alloys. The relative values of main and cross interdiffusion coefficients determined from concentrations and interdiffusion fluxes developed in a single diffusion couple indicate that significant diffusional interactions exist in this system. Thermodynamic interactions between the binary constituents were analyzed based on the activity coefficient relations and it is shown that the observed diffusional interactions of a component with others are consistent with relative thermodynamic interactions between them.

Interdiffusion and related atomic mobilities in fcc Cu–Fe–Co alloys

Diffusion couples for fcc Cu–Fe–Co ternary system are prepared, all of which are annealed at 1573K for 50h. Interdiffusion coefficients are evaluated at the intersection points of two independent diffusion paths sharing a common composition. Such main and cross interdiffusion coefficients are then used to inversely retrieve atomic mobilities of Cu, Fe and Co in fcc Cu–Fe–Co alloys, with the aid of available thermodynamic description. Further validation concerning the quality of atomic mobilities is conducted with computational simulations for diffusion couples, the results of which are compared with experimental data. This work contributes to the establishment of a general Co-based kinetic database for computational design of superalloys.

Atomic mobilities, interdiffusivities and their related diffusional behaviors in fcc Co–Cr–Ni alloys

Diffusion couples for fcc Co–Cr–Ni ternary system are prepared, all of which are annealed at 1573K for 50h. Interdiffusion coefficients are evaluated at the intersection points of two independent diffusion paths sharing a common composition. Such main and cross interdiffusion coefficients are then used to inversely retrieve atomic mobilities of Co, Cr and Ni in fcc Co–Cr–Ni alloys, with the aid of available thermodynamic description. Further validation concerning the quality of atomic mobilities is conducted with computational simulations for diffusion couples annealed at 1573K for 50h, the results of which are compared with experimental data. This work contributes to the establishment of a general Co- or Ni-based kinetic database for computational design of superalloys.

Interdiffusion and solid solution strengthening in Ni–Co–Pt and Ni–Co–Fe ternary systems

Diffusion couple experiments are conducted in Co–Ni–Pt system at 1200 °C and in Co–Ni–Fe system at 1150 °C, by coupling binary alloys with the third element. Uphill diffusion is observed for both Co and Ni in Pt rich corner of the Co–Ni–Pt system, whereas in the Co–Ni–Fe system, it is observed for Co. Main and cross interdiffusion coefficients are calculated at the composition of intersection of two independent diffusion profiles. In both the systems, the main interdiffusion coefficients are positive over the whole composition range and the cross interdiffusion coefficients show both positive and negative values at different regions. Hardness measured by performing the nanoindentations on diffusion couples of both the systems shows the higher values at intermediate compositions.

Interdiffusion and Growth of the Phases in CoNi/Mo and CoNi/W Systems

Deleterious topological-closed-packed (tcp) phases grow in the interdiffusion zone in turbine blades mainly because of the addition of refractory elements such as Mo and W in the Ni- and Co-based superalloys. CoNi/Mo and CoNi/W diffusion couples are prepared to understand the growth mechanism of the phases in the interdiffusion zone. Instead of determining the main and cross-interdiffusion coefficients following the conventional method, we preferred to determine the average effective interdiffusion coefficients of two elements after fixing the composition of one element more or less the same in the interdiffusion zone. These parameters can be directly related to the growth kinetics of the phases and shed light on the atomic mechanism of diffusion. In both systems, the diffusion rate of elements and the phase layer thickness increased because of the addition of Ni in the solid solution phase, probably because of an increase in driving force. On the other hand, the growth rate of the μ phase and the diffusion coefficient of the species decreased because of the addition of Ni. This indicates the change in defect concentration, which assists diffusion. Further, we revisited the previously published Co-Ni-Mo and Co-Ni-W ternary phase diagrams and compared them with the composition range of the phases developed in the interdiffusion zone. Different composition ranges of the tcp phases are found, and corrected phase diagrams are shown. The outcome of this study will help to optimize the concentration of elements in superalloys to control the growth of the tcp phases.