Effective Interdiffusion Coefficients Research Articles

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.

Interdiffusion and Reaction between Pure Magnesium and Aluminum Alloy 6061

Using solid-to-solid couples investigation, this study characterized the reaction products evolved and quantified the diffusion kinetics when pure Mg bonded to AA6061 is subjected to thermal treatment at 300°C for 720 hours, 350°C for 360 hours, and 400°C for 240 hours. Characterization techniques include optical microscopy, scanning electron microscopy with X-ray energy dispersive spectroscopy, and transmission electron microscopy. Parabolic growth constants were determined for γ-Mg17Al12, β-Mg2Al3, and the elusive ε-phase. Similarly, the average effective interdiffusion coefficients of major constituents were calculated for Mg (ss), γ-Mg17Al12, β-Mg2Al3, and AA6061. The activation energies and pre-exponential factors for both parabolic growth constant and average effective interdiffusion coefficients were computed using the Arrhenius relationship. The activation energy for growth of γ-Mg17Al12 was significantly higher than that for β-Mg2Al3 while the activation energy for interdiffusion of γ-Mg17Al12 was only slightly higher than that for β-Mg2Al3. Comparisons are made between the results of this study and those of diffusion studies between pure Mg and pure Al [1] to examine the influence of alloying additions in AA6061.

Nanoscale diffusion in Pt/56Fe/57Fe thin-film system

Low-temperature diffusion of Fe in Pt/56Fe/57Fe thin films (grown on MgO (100) substrate) was investigated between 703K and 813K using secondary neutral mass spectrometry. The activation energy of the effective interdiffusion coefficients, evaluated by the “centre-gradient” method, is 1.53±0.25eV reflecting a strong contribution from grain boundaries. This is also supported by the observed deep penetrations of Pt into the 56Fe layer, from which the grain boundary diffusion coefficients for Pt in Fe were also estimated and 1.45±0.25eV activation energy was obtained. A simple model, including the effect of grain boundaries to the overall intermixing at the original sharp interfaces in nanocrystalline films, is developed. This predicts that at short annealing times the grain boundary diffusion dominates, and bulk diffusion coefficients can be determined only in long time limit. At intermediate annealing times, when the grain boundaries are saturated but the bulk diffusion is still negligible, there are no changes in the composition profiles. This yields good qualitative agreement with the experimental data and offers explanation for the time and temperature dependence of the interdiffusion coefficients obtained in similar systems.

Interfacial reactions and diffusion path in gold–tin–nickel system during eutectic or thermo-compression bonding for 200 mm MEMS wafer level hermetic packaging

In this work, Au–Sn eutectic bonding and Au–Sn thermo-compression bonding are studied for applications in hermetic packaging at wafer level. Eutectic bonding experiments were performed under vacuum or pure nitrogen at temperatures between 310 and 400 °C while thermo-compression bonding experiments were performed under vacuum at 270 °C. Nickel layers 350 nm thick are used as wetting layers on both cap and device sides. During these experiments, the interaction of electrodeposited Au–Sn alloy with nickel layers is studied either in solid or liquid state. The diffusion paths at 270 °C as well as during isothermal solidification of the joint at 310, 350 and 400 °C are determined in relation with the thicknesses of the reaction layers formed at the interfaces and the microstructure of the joint. The effective interdiffusion coefficient in the ζ-Au5Sn phase is deduced at 270 and 310 °C. Moreover, the melting and solidification process of electrodeposited Au/Sn layers with an overall eutectic composition were studied by Differential Scanning Calorimetry in a specific configuration that does not involve the interaction of Au–Sn alloy with the nickel layer. Bonded wafers with good mechanical properties were characterized by cross-section Scanning Electron Microscopy using Energy Dispersive X-ray mode. The mechanical strength of the seal was checked by blade plate insertion technique.

Interfacial mixing of nickel vanadium multilayers induced by cold rolling

During the cold rolling of multilayers of Ni and V with an average composition Ni70V30, Ni30V70 and Ni57V43, deformation induces phase transformation and an interfacial mixing. After repeated cold rolling at room temperature, X-ray diffraction (XRD) and scanning transmission electron microscope (STEM) results demonstrate that between pure Ni and V layers a metastable fcc solid solution phase forms in Ni70V30, a metastable bcc solid solution phase forms in Ni30V70 and metastable fcc and bcc solid solution phases form in Ni57V43 with suppression of nucleation of intermetallic phases. At an intermediate stage of the reaction when both pure Ni and V still remain, a smoothly varying composition profile was determined from the electron energy loss spectrum (EELS) across the multilayers. The composition dependent effective interdiffusion coefficient that was calculated based on the obtained profile was found to increase monotonically from 1.2×10−15cm2/s to 1.6×10−13cm2/s with increase of Ni mole fraction. Compared to the stored energy due to dislocation and interfaces, the excess chemical free energy from the interfacial mixing is the largest portion of total stored energy from deformation, which represents a form of mechanochemical transduction.

Interdiffusion in nanometric Fe/Ni multilayer films

[Fe (3.1 nm)/Ni (3.3 nm)]20 multilayer films were prepared by DC magnetron sputtering onto oxidized Si(100) substrates. The Fe and Ni layers were shown to both be face-centered cubic by x-ray diffraction. Interdiffusion of the Fe and Ni layers in the temperature range of 300–430 °C was studied by x-ray reflectivity. From the decay of the integral intensity of the superlattice peak, the activation energy and the pre-exponential term for the effective interdiffusion coefficient were determined as to 1.06 ± 0.07 eV and 5 × 10−10 cm2/s, respectively. The relevance of the measured interdiffusion coefficient to the laboratory timescale synthesis of L10 ordered FeNi as a rare-earth free permanent magnet is discussed.

Interdiffusion and impurity diffusion in polycrystalline Mg solid solution with Al or Zn

Interdiffusion and impurity diffusion in Mg binary solid solutions, Mg(Al) and Mg(Zn) were investigated at temperatures ranging from 623 to 723K. Interdiffusion coefficients were determined via the Boltzmann–Matano Method using solid-to-solid diffusion couples assembled with polycrystalline Mg and Mg(Al) or Mg(Zn) solid solutions. In addition, the Hall method was employed to extrapolate the impurity diffusion coefficients of Al and Zn in pure polycrystalline Mg. For all diffusion couples, electron microprobe analysis was utilized for the measurement of concentration profiles. The interdiffusion coefficient in Mg(Zn) was higher than that of Mg(Al) by an order of magnitude. Additionally, the interdiffusion coefficient increased significantly as a function of Al content in Mg(Al) solid solution, but very little with Zn content in Mg(Zn) solid solution. The activation energy and pre-exponential factor for the average effective interdiffusion coefficient in Mg(Al) solid solution were determined to be 186.8 (±0.9)kJ/mol and 7.69×10−1 (±1.80×10−1)m2/s, respectively, while those determined for Mg(Zn) solid solution were 139.5 (±4.0)kJ/mol and 1.48×10−3 (±1.13×10−3)m2/s. In Mg, the Zn impurity diffusion coefficient was an order of magnitude higher than the Al impurity diffusion coefficient. The activation energy and pre-exponential factor for diffusion of Al impurity in Mg were determined to be 139.3 (±14.8)kJ/mol and 6.25×10−5 (±5.37×10−4)m2/s, respectively, while those for diffusion of Zn impurity in Mg were determined to be 118.6 (±6.3)kJ/mol and 2.90×10−5 (±4.41×10−5)m2/s.

Diffusion paths in single-phase ternary metal systems

An analysis of diffusion paths in single-phase ternary metal systems Co–Fe–Ni and Cu–Fe–Ni on the basis of the phenomenological interdiffusion model using effective interdiffusion coefficients is presented. The peculiarities of practical application of effective interdiffusion coefficients of components for calculating diffusion paths in ternary systems are analysed. It is done on the basis of the relationship between effective interdiffusion coefficients and the diffusion paths. The results were found to be in good agreement with experimental data for the ternary systems Co–Ni–Fe and Cu–Ni–Fe. It is shown that deviation of the diffusion path from linearity in ternary single-phase diffusion couple in the system Cu–Ni–Fe mainly depends on the thermodynamic properties of the system.

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.

Calculating of Diffusion Profiles in Ternary Systems Using Effective Interdiffusion Coefficients of Components

A method has been developed for calculating diffusion profiles in ternary systems by using effective interdiffusion coefficients of components and Boltzmanns solution for diffusion equation with variable diffusion coefficient. Using this method the concentration profiles for several diffusion couples in the systems Fe-Co-Ni and Cu-Fe-Ni are calculated as examples and some peculiarities of these calculations are discussed, particularly, how to solve some possible difficulties, which may sometimes arise at calculation procedures. It is shown that having the data on effective interdiffusion coefficients and their concentration dependence for at least two components in a ternary diffusion couple, the concentration profiles for all three components can be calculated with good accuracy.

Interdiffusion in the Mg-Al System and Intrinsic Diffusion in β-Mg2Al3

Solid-to-solid diffusion couples were assembled and annealed to examine the diffusion between pure Mg (99.96 pct) and Al (99.999 pct). Diffusion anneals were carried out at 573 K, 623 K and 673 K (300 °C, 350 °C and 400 °C) for 720, 360, and 240 hours, respectively. Optical and scanning electron microscopes were used to identify the formation of the intermetallic phases, γ-Mg17Al12, and β-Mg2Al3, as well as the absence of the e-Mg23Al30 in the diffusion couples. The thicknesses of the γ-Mg17Al12 and β-Mg2Al3 phases were measured and the parabolic growth constants were calculated to determine the activation energies for growth. Concentration profiles were determined with electron microprobe analysis using pure elemental standards. Composition-dependent interdiffusion coefficients in Mg-solid solution, γ-Mg17Al12, β-Mg2Al3, and Al-solid solutions were calculated based on the Boltzmann-Matano analysis. Integrated and average effective interdiffusion coefficients for each phase were also calculated, and the magnitude was the highest for the β-Mg2Al3 phase, followed by γ-Mg17Al12, Al-solid solution, and Mg-solid solution. Intrinsic diffusion coefficients based on Huemann’s analysis (e.g., marker plane) were determined for the ~ Mg-62 at. pct Al in the β-Mg2Al3 phase. Activation energies and the pre-exponential factors for the interdiffusion and intrinsic diffusion coefficients were calculated for the temperature range examined. The β-Mg2Al3 phase was found to have the lowest activation energies for growth and interdiffusion among all four phases studied. At the marker location in the β-Mg2Al3 phase, the intrinsic diffusion of Al was found to be faster than that of Mg. Extrapolations of the impurity diffusion coefficients in the terminal solid solutions were made and compared with the available self-diffusion and impurity diffusion data from the literature. Thermodynamic factor, tracer diffusion coefficients, and atomic mobilities at the marker plane composition were approximated using the available literature values of Mg activity in the β-Mg2Al3 phase.

Effect of Pt on interdiffusion and mechanical properties of the γ and γ′ phases in the Ni–Pt–Al system

The effect of Pt on the growth kinetics of the γ′-[Ni(Pt)]3Al ordered intermetallic phase and the γ-Ni(Pt, Al) solid solution diffusion rates of the species, hardness and elastic modulus was examined by employing the diffusion couple experimental technique. Experiments were conducted by using the β-Ni(Pt)Al phase and Ni(Pt) alloy couples, each of which had a fixed amount of Pt (5, 10 and 15 at. %) in both the end members so that the Pt content is more or less constant throughout the interdiffusion zone. The results suggest that the growth kinetics of both phases and the average effective interdiffusion coefficients of Ni and Al increase with the increase in Pt content. Nanoindentation studies across the compositional gradients show that the mechanical properties of the intermetallic phase in the superalloy are relatively insensitive to the presence of Pt but are more sensitive to the Ni/Al ratio. In contrast, the marked variation in the hardness of the γ phase were noted, increasing markedly with Al concentration in a given couple and also increasing with increasing Pt content. Possible causes for the observed variations are discussed.

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.

Intrinsic and Interdiffusion in Cu-Sn System

Solid-solid diffusion couples assembled with disks of copper, tin and intermetallics (Cu3Sn and Cu6Sn5) were employed to investigate the Kirkendall effect in the copper-tin system at the temperature of 200 °C. In the Cu(99.9%)/Sn diffusion couple, inert alumina particles used as markers were identified in the Cu6Sn5 phase, while microvoids were observed at the Cu/Cu3Sn interface. The Cu(99.9%)/Sn and Cu(99.9%)/Cu6Sn5 diffusion couples annealed at 200 °C for 10 days were analyzed for intrinsic diffusion coefficients of Cu and Sn in the Cu6Sn5 and Cu3Sn phases, respectively with due consideration of changes in molar volume. Interdiffusion, integrated and effective interdiffusion coefficients were also calculated for the intermetallic phases. Diffusion couples annealed at 125-400 °C for various times were analyzed for the kinetic parameters such as growth rate constants and activation energies for the formation of Cu3Sn and Cu6Sn5 phases. Uncertainties in the calculated intrinsic diffusivities of Cu and Sn arise mainly from the non-planar morphologies of the interfaces and the non-planar distribution of the markers. Intrinsic diffusion coefficients based on average locations of the marker plane indicate that Cu is the faster diffusing component than Sn in both the Cu3Sn and Cu6Sn5 phases.

Site Preference and Diffusion in Ni<sub>3</sub>Al Alloyed with Ir, Ta or Re at 1200°C

Diffusion in L12-Ni3Al with ternary alloying additions of Ir, Ta and Re was investigated at 1200°C using solid-to-solid diffusion couples, and examined with respect to site preference in ordered intermetallic compound. In addition to determination of average ternary interdiffusion coefficients [1-3], average effective interdiffusion coefficients were determined directly from the experimental concentration profiles. Ni has the largest magnitude of average effective interdiffusion coefficient, followed by Al, Ir, Re and Ta. The average effective interdiffusion coefficients for Ir, Re and Ta are much smaller than those for Ni and Al. Tracer diffusion coefficients determined by extrapolation technique, and available literature also followed the same trend. The relative tendency of Ni, Al, Ir, Re and Ta to occupy the -Ni and -Al sites are correlated to these diffusion coefficients, with due consideration for diffusion mechanisms and coordination of atoms.

The effective interdiffusivity, structure, and magnetic properties of [Fe∕Pt]n multilayer films

This paper reports the influence of the deposition temperature and the wavelength of the periodicity on the effective interdiffusivity, microstructure, and magnetic properties of annealed [Fe∕Pt]n multilayer films (MLs). It was found that both the deposition temperature and periodicity of [Fe∕Pt]n MLs have a significant influence on the effective Fe–Pt interdiffusivity, microstructure, and magnetic properties of the annealed films. It was also observed that the magnitude of the effective interdiffusion coefficient, the L10 grain size, and the long-range order parameter were positively correlated. This result suggests that nonequilibrium reaction kinetics are desirable for the reduced temperature formation of the L10 FePt phase.

The Influence of Thermodynamic Properties of Alloys on Effective Interdiffusion Coefficients in Ternary Systems

To prove the validity of Dayananda’s phenomenological model of interdiffusion in ternary systems the effective interdiffusion coefficients for a few diffusion couples in the system Cu-Ni-Fe, annealed at 1000 oC, are calculated on the basis of this model using available tracer diffusion and thermodynamic data. It is found that the calculated values of effective interdiffusion coefficients are in reasonable agreement with experimental values extracted independently from experimental concentration--penetration curves. Using the relationship between effective interdiffusion coefficients, tracer diffusion coefficients and thermodynamic factors, it is shown that thermodynamic properties of alloys play a significant role in interdiffusion processes in the system Cu-Fe-Ni.

Thermodynamic Aspects of Diffusion Paths in Ternary Systems

Description of diffusion paths is one of the most interesting and topical problems in experimental investigations of interdiffusion in multicomponent systems and, particularly, in ternary systems. The relationship between effective interdiffusion coefficients and diffusion paths in ternary systems has been discussed earlier but the specific influence of the mobility and thermodynamic properties of components on the characteristics of the diffusion path is still unclear. In this paper an attempt is made to clarify the separate influences of mobility and thermodynamics on the behavior of diffusion paths in ternary systems and the corresponding correlation is found. It is shown that in most cases the deviation of the diffusion path from linearity (an ideal system) is related to the deviation of the thermodynamic properties from the ideal. The results obtained are analyzed on the basis of thermodynamic data for the ternary system Cu-Fe-Ni.

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.

Diffusional analysis of a multiphase oxide scale formed on a Mo-Mo3Si-Mo5-SiB2 alloy

Diffusional analyses were performed to understand the oxidation at 1300 °C of a multiphase Mo-13.2Si-13.2B (at.%) alloy. During oxidation, a protective glass scale formed with an intermediate layer of (Mo+glass) between the base alloy and external glass scale. Compositional profiles across the (Mo+glass) layer and the external glass scale were determined, and interdiffusion fluxes and effective interdiffusion coefficients for the various components were determined by using “MultiDiFlux” software. The motion of the (alloy/Mo+glass) and (Mo+glass/glass) interphase boundaries after passivation was examined. Additionally, vapor-solid diffusion experiments at 1300 °C were carried out with single-phase Mo3Si and T2 specimens in addition to a multiphase Mo-10Si-10B (at.%) alloy. These specimens were exposed to vacuum to induce silicon loss resulting in the formation of a Mo layer. An average effective interdiffusion coefficient of Si in Mo at 1300 °C was estimated from the Mo3Si-vapor couple to be in the order of 8×10−17 m2/s.