Interdiffusion Data Research Articles

Analysis of Interdiffusion and Intrinsic Diffusion in Multicomponent Alloys to Obtain Information about Diffusion Mechanisms

In this paper, we present and discuss some of the theoretical procedures that have been established recently for binary and ternary alloy systems for the purposes of analyzing chemical diffusion data (interdiffusion and intrinsic diffusion) alone and chemical diffusion data in combination with tracer diffusion data. Emphasis is put on extracting information about diffusion mechanisms by way of tracer correlation factors/vacancy-wind factors. Examples are taken from the intrinsic diffusion, interdiffusion and tracer diffusion data in the Ag-Cd and Ag-Cd-Zn, Fe-Ni-Cr and Cu-Fe-Ni alloy systems.

Atomic mechanisms of interdiffusion in metallic multilayers

Interdiffusion data (activation energies and pre-exponential factors) for different metal–metal multilayers (MLs) published in the literature and our own results on Fe/Pt MLs are reviewed. The analysis of the available data suggests that vacancy diffusion is the main interdiffusion mechanism in metallic MLs. An empirical relation between the activation energy for interdiffusion in metallic multilayers, the average activation energy of vacancy diffusion and the activation energy for in-plane grain-boundary diffusion is proposed.

Theoretical analysis of experimental tracer and interdiffusion data in Cu–Ni–Fe alloys

In this paper, we present strategies to extract fundamental atomistic information from measured diffusion coefficients in a ternary alloy system. The strategies are exemplified with Cu–Ni–Fe alloys at 1271K where recent extensive interdiffusion coefficients and tracer diffusion coefficients for all three components have become available. We develop new defining phenomenological expressions for the vacancy-wind factors in terms of the diffusion coefficients. We show that the measured tracer diffusion coefficients can be processed using the Manning and Moleko, Allnatt and Allnatt random alloy diffusion kinetics formalisms (with and without the assumption of the Gibbs–Duhem relation between the thermodynamic activities) to give jump frequencies, tracer correlation factors, vacancy-wind factors and phenomenological coefficients. It is shown for example that Cu is generally the most correlated component in its diffusion behavior and that the off-diagonal phenomenological coefficients can be as high as 64% of the smallest of the diagonal phenomenological coefficients. It is also shown that the Darken formalism (which ignores off-diagonal phenomenological coefficients) is in fact a reasonable approximation for expressing the diagonal phenomenological coefficients in terms of the tracer diffusion coefficients. It is then shown how the measured interdiffusivities can be processed with these formalisms to give tracer diffusivities, vacancy-wind factors and phenomenological coefficients. Finally, we show how a straightforward strategy starting with the Darken analysis that is then followed by the Manning or Moleko, Allnatt and Allnatt analysis can be used to gain access to the vacancy-wind factors and the off-diagonal phenomenological coefficients.

Essentials in diffusion behavior of nickel- and titanium-aluminides

Recently we have extensively investigated bulk and grain boundary diffusion in technologically important Ni- and Ti-aluminides. These compounds exhibit different lattice structures and different types and concentrations of lattice defects on their sublattices (vacancies, anti-structure atoms of constitutional and/or thermal origin). The study therefore provides fundamental insight into the interdependence of diffusion behavior and diffusion mechanisms on structure and ordering. An overview is presented, including the direct tracer diffusion measurements of the transition metal component and the determination of the Al diffusivity through interdiffusion data and by using Al-substituting solutes, like Ga. The interpretation of the experiments is strongly supported by EAM-potential calculations of defect properties and Monte-Carlo simulations of possible diffusion mechanisms. Among other features, the experimentally established curvature in the Arrhenius plot of Ti self-diffusion in TiAl, the surprising effect of the missing diffusion enhancement from structural Ni-vacancies in Al-rich NiAl, the paradoxically appearing deep minimum of the chemical diffusion coefficient in stoichiometric NiAl, and interphase diffusion along oriented Ti 3Al/TiAl interfacesare successfully explained.

Interdiffusion of the platinum-group metals in nickel at elevated temperatures

Rates of interdiffusion of the platinum group metals Ir, Pd, Pt, Rh and Ru with nominally pure nickel have been characterised. Interdiffusion coefficients are estimated by analysing the measured diffusion profiles. In the composition range studied (no greater than 10 wt.% of the platinum group metal), the interdiffusion coefficients display little concentration dependence, but the values can differ by an order of magnitude. In order to rationalise the dependence of the interdiffusion coefficient on atomic number, the data are compared with values for other elements which are already in the literature. A systematic trend is observed: elements furthest from the centre of the period display the largest values and elements at the centre the smallest. It appears therefore that the magnitude of the interdiffusion coefficient correlates strongly with the atomic radius of the interdiffusing transition metal species. Our results suggest the existence of a binding energy between the vacancies and the impurity species. We believe that the interdiffusion data are of considerable use to those designing new and novel grades of superalloy for high temperature applications.

Influence of depth resolution on the interdiffusion data in thin film bilayer and multilayer Ag/Pd structures

This paper reports results of the interdiffusion studies in thin film Ag/Pd bilayer and multilayer structures, deposited onto the SiO2 and Cu substrates. Interdiffusion coefficients have been obtained from the changes of slopes of depth profiles at the interface of the two layers, from the rate of rise of diffusant concentration in the plateau region of the profile and from the change of the concentration distribution in the Ag/Pd multilayer structure. In all cases the depth resolution has been determined and its influence on the interdiffusion data has been studied. The values of the activation energy and the pre-exponential diffusivity term in the Arrhenius equation have been extrapolated to zero depth.

Auger electron spectroscopy investigations of the effect of degradation of depth resolution and its influence on the interdiffusion data in thin film Au/Ag, Cu/Ag, Pd/Au and Pd/Cu multilayer structures

Auger depth profile investigations of interdiffusion in the bilayer and multilayer Au/Ag, Cu/Ag, Pd/Au and Pd/Cu thin film structures in the temperature range 423–573K have been reported. Bilayers and multilayers have been obtained by successive evaporation onto the SiO2 and Cu substrates with different surface topographies. The thickness of bilayers was changed from 50 to 200nm, whereas the thickness of particular layers of the multilayer structure was changed from 20 to 80nm. Interdiffusion data have been derived from the change of the slope of the profile at the interface of two layers, from the rate of rise of diffusant concentration inside the upper layer and from the change of the concentration amplitude in the multilayer structure. In all cases, the depth resolution was monitored and its influence on the interdiffusion data was studied.

Diffusion in the C15-type intermetallic Laves phase NbCo 2

Abstract Self-diffusion of both constituents in the Laves phase NbCo2 has been explored using the tracer method and the radioisotopes 57Co and 95Nb in combination with sputter and grinder sectioning. The temperature dependences of the Co diffusivity in Nb31Co69 and Nb29Co71 (two compositions inside the phase field of NbCo2) and of the Nb diffusivity in Nb31Co69 are reported. All activation enthalpies are of similar magnitude. Nb diffusion in NbCo2 is significantly slower than Co diffusion. Co diffusion itself is considerably faster in the alloy with higher Co content. The diffusion results are discussed in connection with the structure of and the scarce information available about atomic defects in NbCo2. We propose that diffusion is mediated by thermal vacancies. Furthermore, the results are compared with self-diffusion data for the C14-type Laves compounds MgZn2 and Tife2, with interdiffusion data obtained from multiphase diffusion experiments in our laboratory, and with self-diffusion in the also close-packed L12 intermetallics.

Diffusion in the C15-type intermetallic Laves phase NbCo2

Abstract Self-diffusion of both constituents in the Laves phase NbCo2 has been explored using the tracer method and the radioisotopes 57Co and 95Nb in combination with sputter and grinder sectioning. The temperature dependences of the Co diffusivity in Nb31Co69 and Nb29Co71 (two compositions inside the phase field of NbCo2) and of the Nb diffusivity in Nb31Co69 are reported. All activation enthalpies are of similar magnitude. Nb diffusion in NbCo2 is significantly slower than Co diffusion. Co diffusion itself is considerably faster in the alloy with higher Co content. The diffusion results are discussed in connection with the structure of and the scarce information available about atomic defects in NbCo2. We propose that diffusion is mediated by thermal vacancies. Furthermore, the results are compared with self-diffusion data for the C14-type Laves compounds MgZn2 and Tife2, with interdiffusion data obtained from multiphase diffusion experiments in our laboratory, and with self-diffusion in the also close-packed L12 intermetallics.

Influence of depth resolution on interdiffusion measurements in polycrystalline Cu/Pd multilayers

Interdiffusion in the Cu/Pd multilayer system was studied in the temperature range 120–250 °C by means of Auger electron spectroscopy together with simultaneous argon ion sputtering. Interdiffusion coefficients have been calculated on the basis of changes of the concentration amplitude of the multilayer structure, as well as from variation of the composition at the interface of two consecutive layers of the multilayer. The depth resolution has also been determined and its influence on the interdiffusion data has been evaluated and discussed. Copyright © 2000 John Wiley & Sons, Ltd.

AES studies of interdiffusion in thin-film copper–palladium multilayer structures

The process of interdiffusion in thin film Cu–Pd multilayer system was studied in the temperature range of 393–493K for different annealing times using Auger electron spectroscopy (AES) in conjunction with an argon ion sputtering. The changes in Auger depth profiles caused by heating have been converted into compositional changes of diffusing species. On the basis of the concentration distribution of Pd and Cu inside the Pd–Cu multilayer structure the interdiffusion coefficients have been obtained in the studied temperature range. Interdiffusion data have been discussed and compared with diffusion parameters obtained by using different methods.

Use of lattice mole fraction to analyze interdiffusion data in strongly ordered triple-defect B2 intermetallic phases

Many transition metal aluminides and indides such as NiAl, CoAl, PdAl and PdIn exhibit an ordered bcc (or B2) structure and yet exist over wide ranges of homogeneity. In this class of compounds, the transition metals normally occupy one of the two sublattices, i.e. the {alpha}-sublattice [0,0,0] and the Al or In atoms on the {beta}-sublattice [1/2,1/2,1/2]. The predominant point defects in this class of intermetallic phases are vacancies on the {alpha}-sublattice and anti-site transition metal atoms on the {beta}-sublattice. The vacancy concentration affects the probability of finding an atom on a lattice site, and plays an important role in the movement of atoms. In view of the potential existence of rather high concentrations of constitutional vacancies in the lattice, the objective of the present communication is to introduce a new concentration variable, lattice mole fraction, for analyzing interdiffusion data determined experimentally in a diffusion couple.

Interdiffusion in nanometer-scale multilayers investigated byin situlow-angle x-ray diffraction

An in situ low-angle x-ray diffraction technique is used to investigate interdiffusion phenomena in various metal-metal and metal-amorphous Si nanometer-scale compositionally modulated multilayers ~ML’s !. The temperature-dependent interdiffusivities are obtained by accurately monitoring the decay of the first-order modulation peak as a function of annealing time. Activation enthalpies and preexponential factors for the interdiffusion in the Fe-Ti, Ag-Bi, Fe-Mo, Mo-Si, Ni-Si, Nb-Si, and Ag-Si ML’s are determined. Activation enthalpies and preexponential factors for the interdiffusion in the ML’s are very small compared with that in amorphous alloys and crystalline solids. The relation between the atomic-size difference and interdiffusion in the ML’s are investigated. The observed interdiffusion characteristics are compared with that in amorphous alloys and crystalline a-Zr, a-Ti, and Si. The experimental results suggest that a collective atomic-jumping mechanism govern the interdiffusion in the ML’s, the collective proposal involving 8‐15 atoms moving between extended nonequilibrium defects by thermal activation. The role of the interdiffusion in the solid-state reaction in the ML’s is also discussed. @S0163-1829~99!01516-7# Multilayers ~ML’s ! are of technologically useful physical properties and potential application in microelectronic device. 1‐3 ML’s can also provide a model system for scientists to investigate fundamental phenomena such as interface properties, stabilization of nonequilibrium structure and strains, and coupling interactions in magnetism and transport behavior. Therefore, the interdiffusion study in the compositionally modulated ML’s are interesting subjects. 3‐7 From a scientific point of view the diffusion mechanism in ML’s is still poorly understood, and a knowledge of the interdiffusion data and mechanism is highly desired for understanding the physical properties and phenomena in the ML’s. From a technological viewpoint, the knowledge of the interdiffusion is an important prerequisite for application of the ML’s. The discovery of solid-state interfacial reaction ~SSIR! in the thin films has further added to the importance of interdiffusion investigations in these materials. However, despite many years of effort, the interdiffusivity in the ML’s has remained poorly quantified. 7 This is because of the measurement difficulties associated with low diffusivity ~less than 10 223 m 2 /s) in the ML’s at low-annealing temperature. The difficulties are even higher in the amorphous ML’s because the measurements must be done at a sufficiently low temperature to avoid crystallization in amorphous ML’s. The difficulties inherent to diffusion experiments in amorphous ML’s can also be due to the metastability, which implies small mean-squared displacements. Rutherford backscatter

Self-Diffusion of Both Components in the Intermetallic Laves Phase NbCo2

ABSTRACTSelf-diffusion of57Co and95Nb in the cubic Laves phase NbCo2 has been studied using the radiotracer method. The temperature dependences of the self-diffusivities are described for Nb31Co69 by,and for Nb29Co71 by,The diffusivity of 95Nb in Nb31Co69 is considerably lower than that of 57Co. The latter increases significantly with increasing Co content.The results are discussed in terms of vacancy mediated diffusion in connection with structural aspects of the Laves phase together with the scarce information available for defects in NbCo2. The results are compared with interdiffusion data from our laboratory and with self-diffusion in the also close-packed L12 intermetallics.

Diffusion and phase diagram in binary alloys

The relationship betwwen diffusion and phase diagram is discussed in more detail for AgAu and AuNi alloys. For each alloy tracer diffusion and interdiffusion data have been compared with the corresponding phase diagram. Tracer diffusion is related to the solid-liquid phase transition. Ag and Au tracer diffusivities D∗(x) in AgAu alloys and melting temperature T m( x) of AgAu show opposite curvatures. The same holds for D∗ of Au and Ni in AuNi alloys and indicates a vacancy diffusion mechanism. Interdiffusion depends on the critical temperature of the solid-solid phase transition of the phase diagram. The curvature of interdiffusivity D( x) is determined by the sign of T c( x) or the interaction energy ε of the regular alloy. The calculations agree well with the experimental data.

Single-phase interdiffusion in intermetallic compound CoTi

Intermetallic compounds have recently attracted much attention as practical materials. Although much effort has been devoted to understand mechanical properties, investigations on diffusion in intermetallics are relatively scarce. The knowledge of diffusion behavior is of interest for production of these materials and for their practical use. Interdiffusion data are available in the literature of CoTi. However, the data were determined from multiphase diffusion couples and the measured interdiffusion data are more or less effective diffusion coefficients, because inherent interfacial reaction could not be excluded in the diffusion process. Therefore, interdiffusivity in intermetallic compounds should be determined from diffusion experiments using single-phase interdiffusion couples. CoTi fulfills the necessary requirements for single-phase interdiffusion, since the intermetallic compound has a wide homogeneity range and is sufficiently ductile to prepare diffusion couples by welding. The present paper reports the result of the interdiffusivity measure in B2-type intermetallic compound CoTi.

Diffusion in the Ce-Nd system

To date, information on interdiffusion in intralanthanide systems is limited. Interdiffusion studies have been reported for the Pr-Nd, La-Pr, and La-Ce systems. Yet, no data is available for the Ce-Nd system. This paper reports the results of Ce-Nd diffusion couples annealed at 425 C, 550 C, and 650 C. Both intrinsic and interdiffusion data have been calculated, as well as activation energy information as a function of composition. Comments will be made on how well the composition of the boundaries of the [({gamma}Ce) + ({beta}Ce, {alpha}Nd)] two-phase region in the Ce-Nd phase diagram agree with diffusion couple results.

FeMg interdiffusion in olivine up to 9 GPa at T = 600–900°C; experimental data and comparison with defect calculations

Interdiffusion data at high pressures are needed to provide good estimates of the closure temperatures of geothermometers based on FeMg exchange in olivine in contact with other phases and to understand the pressure dependence of high-temperature deformation in olivine. We report here measurements of the interdiffusion coefficient of Fe Mg in San Carlos olivine of mean composition Mg (Mg + Fe) = 0.90 , in the range of temperatures T = 600–900°C and pressures P = 0.5–9 GPa. The measurements were performed by preparing olivine samples covered by a thin layer of fayalite. These specimens were annealed in a uniaxial split-sphere apparatus (USSA-2000). The FeMg interdiffusion profiles were analysed by Rutherford back-scattering (RBS). The results yield a pre-exponential factor D 0 = 7.7 × 10 −8cm 2s −1 (7.7 × 10 −12 m 2 s −1), and an activation energy E ∗ = 147 ± 58 kJmol −1 (or 62 ± 58 (2 SD) kJ mol −1 if a p O 2 1 6 correction is performed), corresponding to the expression D = D 0 exp( −E ∗ RT ) exp(ϵX Fe)exp ( −PV ∗ RT ) . Our data are fitted best with ϵ = 3; X Fe = Fe (Fe + Mg) is between zero and one (in the present experiments X Fe is around 0.1), P is the pressure and V ∗ is found to be −0.5 ± 0.6 cm 3 mol −1 (or 1 ± 0.9 cm 3 mol −1 if a p O 2 1 6 correction is performed), i.e. about zero in the P and T range investigated. Comparisons between the present results, obtained at relatively low temperature under extrinsic conditions for diffusion, with other FeMg interdiffusion data at high temperature (1125°C or more) under intrinsic conditions allow us to deduce that the migration activation volume for point defects is V M ∗ ≈ 0 whereas that for formation is V F ∗ ≈ 5.5 cm 3 mol −1 . This has important implications for the creep sensitivity to pressure. Numerical simulations involving energy minimizations and performed with the CASCADE and PARAPOCS codes confirm these conclusions: one finds V M ∗ ≈ 0 and V F ∗ ≈ 4.8 cm 3 mol −1 . The activation energy E ∗ deduced from the experiments as well as the pre-exponential factor D 0 now permit precise estimation of the closure temperatures of geothermometers based on the FeMg exchange between olivine and spinel.

Constraints on the thermal history of the Allende parent body as derived from olivine-spinel thermometry and Fe/Mg interdiffusion in olivine

Attempts are made to determine the extent of thermal metamorphism on the Allende parent body. The chemical composition of olivine and coexisting spinel in type II chondrules and Fe-rich isolated olivine grains from the Allende meteorite were analysed with an electron microprobe. The Fe/Mg exchange reaction between olivine and spinel yields upper limits for peak metamorphic temperatures on the Allende parent body of approximately 800 K. This may represent the closure temperature for Fe/Mg interdiffusion in olivine and spinel. Steep Fe/Mg concentration gradients in Allende olivine of various textural settings provide an independent method for estimating peak metamorphic temperatures. Modelling of Fe/Mg interdiffusion in olivine leads to an upper limit of peak metamorphic temperatures between 600 and 750 K, assuming a duration of the thermal event of 106 years. The extrapolation of experimentally determined diffusion data to low temperatures and low oxygen fugacities is the major cause for the uncertainties in the calculated equilibration temperatures. A critical evaluation of existing Fe/Mg interdiffusion data and equations proposed for low temperature extrapolation suggests that the lower value of 600 K is more realistic.

Application of the square root diffusivity to diffusion in Ni-Cr-Al-Mo alloys

The square root diffusivity matrix [r] and diffusivity matrix [D] have been measured for a Ni-4.0 at. pct Cr-6.3 at. pct Al-3.5 at. pct Mo quaternary alloy at 1100 °C. Using a constant diffusivity analysis, the diffusivities were obtained from three diffusion couples having small initial concentration differences of 5 at. pct or less. When elements of [r] were substituted into the error function solution of the diffusion equation, it was found that the predicted concentration profiles were accurate to within ±0.1 at. pct of measured values. Also, it was found that Mo tends to reduce the diffusion kinetics of Cr and Al in Ni-base alloys. These results suggest that these methods of analyzing diffusion data and predicting interdiffusion data can be applied to alloys containing more than four components.