Interdiffusion In Alloys Research Articles

High-throughput approach for investigating interdiffusion in medium- and high-entropy alloys

Interdiffusion experiments are usually time-consuming and tedious since diffusion couples must be annealed at several temperatures for a long time. The efforts required to study interdiffusion in multicomponent alloys increase dramatically as multiple diffusion couples are required to cover broad composition ranges and determine the diffusivities of individual elements in different chemical environments. To circumvent this challenge, we present a high-throughput approach applicable to single-phase and compositionally complex alloys, which are assumed to approximate ideal solid solutions. Here, a simple diffusion-multiple experiment combined with a physically based kinetic model is proposed to efficiently determine the diffusion coefficients of the constituent elements in quaternary CrFeCoNi alloys. Compared with tracer diffusivities reported in the literature, the results, thus, obtained do not differ by more than a factor of 2 and were obtained from a single interdiffusion experiment. In contrast, the diffusivities simulated with commercial mobility and thermodynamic databases are strongly overestimated by a factor ranging from 1 to 16. Therefore, our approach enables high-throughput determination of diffusivities and can help in the design of alloys for high-temperature applications where diffusion plays a key role.

Advances in Diffusion Barrier Coatings for High-Temperature Applications

Diffusion barrier coating (DBC) systems on heat resistant alloys consist of a multi-layer structure: an outer Al-reservoir layer and an inner diffusion barrier layer (DBL). The outer Al-reservoir layer forms a protective Al2O3 scale and DBL acts as a barrier layer against alloy interdiffusion. Three kinds of DBL were developed: Re on Ni-based superalloys; W on stainless steels; and Cr on Ni–Cr alloys. It was found that DBC systems have excellent mechanical properties (creep and fatigue), improving alloy substrate performance, and enhance the anti-exfoliation properties of YSZ in thermal barrier coatings (TBC) in addition to providing excellent oxidation resistance. At temperatures higher than 1300 °C, however, the DBC design based on kinetics (diffusion) is insufficient to form and maintain a protective Al2O3 scale. In this case a self-maintaining coating (SMC) system designed on the basis of thermodynamics (phase stability) is required. The SMC system formed on Nb–Hf (C-103) alloy consists of a multi-layer structure: an outer Re (Al, Si)1.8 and inner NbSi2 layers, plus a transient Nb5Si3 layers formed during oxidation. At temperatures higher than 1300 °C the Al2O3 can be formed by changing the Al/Si ratio in the Re (Al, Si)1.8 in which Si was supplied from the decomposition reaction of NbSi2 to Si + Nb5Si3 during selective oxidation of Al. It is proposed that coating alloys should be designed for considering not only high temperature oxidation, but also alloy substrate mechanical properties and anti-exfoliation of oxide scales, based on both kinetic principles (DBC system) and thermodynamics (SMC system).

The interdiffusion in liquid alloys of alkali metals with lead

The mutual diffusion in liquid cesium-lead alloys containing from 20 to 70 at.% Pb is investigated by a gamma-ray attenuation technique. The obtained data are compared with the results of similar studies for Li-Pb, Na-Pb, and K-Pb melts, carried out by us earlier. The concentration dependences of the interdiffusion coefficient for alkali-lead liquid systems demonstrate pronounced maxima in the vicinity of 20 or 50 at.% Pb. These phenomena confirm a tendency for chemical short-range ordering in liquid alloys.

A new approach for analysing interdiffusion in multicomponent alloys

Analysis of interdiffusion in multicomponent alloys is addressed by developing a new and elegant mathematical approach that is based on the fitting of composition profiles into a closed-form solution where interdiffusion coefficients are independent of composition. As examples, ternary metallic systems are analysed using one and two diffusion couples with the full set of interdiffusion coefficients being determined. Overall, the new fitting method gives excellent outcomes and allows the probing of multiple solutions (validated by back-testing) that exist when a single diffusion couple is used in multicomponent (>2) systems. Important findings of the present investigation show that small differences in composition profiles may lead to large differences in the interdiffusion coefficients. In addition, the newly developed approach is successfully applied to experimental results for the Cu-Ni-Zn alloys annealed at 775 °C for 48 h.

Novel Interdiffusion Analysis in Multicomponent Alloys - Part 2: Application to Quaternary, Quinary and Higher Alloys

A novel study of analysis interdiffusion in multicomponent alloys is investigated by means of closed form solutions and numerical simulations. Quaternary as well as selected CoCrFeMnNi (HEAs) quinary metallic systems are analysed using one, two and three diffusion couples with the full set of interdiffusion coefficients being calculated. A custom written Matlab fitting program (MFP) is used as the main tool for the simultaneous fitting into multiple composition profiles in both systems. The retrieved interdiffusion matrices are obtained using a newly developed approach that is interlinked with composition vectors, eigenvalues and eigenvector. On average, it can be concluded that the accuracy of the obtained matrices steadily improves with the increase of the number of couples used in the analysis.

Interdiffusion in CMSX-4 Related Ni-Base Alloy System at a Supersolvus Temperature

Interdiffusion in Ni-base superalloy CMSX-4 and alloys related to CMSX-4 was investigated at the temperature 1288 °C, which is 8 °C above the γ’-solvus temperature of this superalloy, 1280 °C. This temperature is of a special interest because it is a temperature of hot isostatic pressing applied to CMSX-4 and modeling of this process needs verified diffusion data for this specific temperature. Various diffusion couples were assembled from the investigated alloys, annealed at 1288 °C and studied by electron probe microanalysis. So far as the annealing temperature was higher than the γ’-solvus temperature of CMSX-4 and other investigated alloys have no strengthening γ’-phase, interdiffusion occurred in the fcc solid solutions of nickel. It was found that in the case when the γ’-forming and γ-stabilizing elements diffuse in the same direction (towards nickel) the diffusion rate accelerates, but when they diffuse in the opposite directions (counter diffusion) it slows down. Such an interdiffusion behavior is in agreement with the results predicted with diffusion simulation software Dictra.

Growth kinetics of σ-phase precipitates and underlying diffusion processes in CrMnFeCoNi high-entropy alloys

Key mechanisms and elementary diffusion processes that control the growth kinetics of σ precipitates in high-entropy alloys were investigated in the present study. For this purpose, an off-equiatomic Cr26Mn20Fe20Co20Ni14 alloy with an initially single-phase FCC structure was subjected to isothermal heat treatments, which are known to promote the formation of σ phase, i.e., aging between 600 °C and 1000 °C for times ranging from 0.1 h to 1000 h. The growth kinetics of σ precipitates at grain boundaries of the FCC matrix and those located within the interior of the grains were analyzed separately. The latter precipitates are found to grow through direct substitutional diffusion of Cr-solutes towards and Mn, Fe, Co, and Ni away from them and the growth rate of the allotriomorphs can be rationalized by the collector plate mechanism of interfacial diffusion-aided growth. From the growth-kinetics data obtained in the present study, lattice interdiffusion coefficients as well as diffusivities along crystalline defects were obtained. Above 800 °C, the growth kinetics are dominated by lattice interdiffusion of Cr in the FCC matrix described by DL = 9.8 × 10-4 exp[(-300 kJ/mol)/(RT)] m2/s. At lower temperatures, the growth kinetics are enhanced by fast interdiffusion along dislocation pipes, which temperature dependence is given by DD = 5.0 × 10-3 exp[(-205 kJ/mol)/(RT)] m2/s. The Cr-diffusivity along σ/FCC interphase boundaries deduced from the thickening kinetics of grain boundary precipitates can be represented by the Arrhenius relationship DI = 0.5 × 10-4 exp[(-145 kJ/mol)/(RT)] m2/s, which is similar to that found for grain boundary interdiffusion in metals and alloys.

A general approach to quantify the uncertainty of interdiffusion coefficients in binary, ternary and multicomponent systems evaluated using Matano-based methods

In this paper, we developed a general approach to quantify the uncertainties of interdiffusion coefficients in binary, ternary and multicomponent systems evaluated using the Boltzmann-Matano and related other methods together with the distribution functions. Various sources of errors from both experimental and calculation procedures and their propagation were fully considered and quantified in the finally obtained interdiffusion coefficients. Benchmark tests in hypothetical binary systems with three types of the preset D-c relations and three noise levels were utilized to validate the presently proposed approach, which was then successfully applied in the practical binary, ternary and high-entropy alloys. The comprehensive comparison between the presently calculated interdiffusivities in different alloys with the literature data indicated that the integration of Matano-based methods, the distribution function and the present approach represents a general ensemble solution for evaluation of the reliable interdiffusion coefficients and their uncertainties. Further discussion indicates that the accurate interdiffusion coefficients with reliable uncertainty are the “cornerstone” for the subsequent analysis on diffusion properties, i.e., the sluggish diffusion in high-entropy alloys, and the development of high-quality atomic mobility databases, and the impurity diffusion coefficients with uncertainties can be directly retrieved from the evaluated composition-dependent binary interdiffusion coefficients.

Growth Kinetics of Σ-Phase Precipitates and Underlying Diffusion Processes in Crmnfeconi High-Entropy Alloys

Key mechanisms and elementary diffusion processes that control the growth kinetics of σ precipitates in high-entropy alloys were investigated in the present study. For this purpose, an off-equiatomic Cr26Mn20Fe20Co20Ni14 alloy with an initially single-phase FCC structure was subjected to isothermal heat treatments, which are known to promote the formation of σ phase, i.e. aging between 600 °C and 1000 °C for times ranging from 0.1 h to 1000 h. The growth kinetics of σ precipitates at grain boundaries of the FCC matrix and those located within the interior of the grains were analyzed separately. The latter precipitates are found to grow through direct substitutional diffusion of Cr-solutes towards and Mn, Fe, Co, and Ni away from them and the growth rate of the allotriomorphs can be rationalized by the collector plate mechanism of interfacial diffusion-aided growth. From the growth-kinetics data obtained in the present study, lattice interdiffusion coefficients as well as diffusivities along crystalline defects were obtained. Above 800 °C, the growth kinetics are dominated by lattice interdiffusion of Cr in the FCC matrix described by DL = 9.8 × 10-4 exp[( 300 kJ/mol)/(RT)] m2/s. At lower temperatures, the growth kinetics are enhanced by fast interdiffusion along dislocation pipes, which temperature dependence is given by DD = 2.5 × 10-3 exp[( 210 kJ/mol)/(RT)] m2/s. The Cr-diffusivity along σ/FCC interphase boundaries deduced from the thickening kinetics of grain boundary precipitates can be represented by the Arrhenius relationship DI = 0.5 × 10-4 exp[( 145 kJ/mol)/(RT)] m2/s, which is similar to that found for grain boundary interdiffusion in metals and alloys.

Self- and interdiffusion in dilute liquid germanium-based alloys

Self- and inter-diffusion coefficients in liquid Ge and dilute Ge-based Ge–Si, Ge–Au, Ge–In, Ge–Ce and Ge–Gd alloys-containing 2 at% additions, respectively, are measured using a comprehensive approach of measuring techniques: quasi-elastic neutron scattering, in situ long-capillary experiments combined with x-ray radiography, and a long-capillary experiment under microgravity conditions. Resulting inter- and Ge self-diffusion coefficients are equal within error bars for each investigated alloy. The interdiffusion coefficients are smaller for the alloys containing Ce and Gd, However, no dependence of the atomic mass of the minor additions, that varies by about a factor of seven between Si and Au, on the diffusion coefficients could be observed. This demonstrates that in a loosely-packed metallic liquid with fast diffusive dynamics the diffusion mechanism is highly collective in nature.

Comments on Experimental Assessment of the Thermodynamic Factor for Diffusion in Cocrfeni and Cocrfemnni High Entropy Alloys

In this contribution, as a response to the paper in Scripta Materialia, v.157, p.81, 2018, we show that the pseudo-binary approach for analysis of interdiffusion in multicomponent alloys has its reference value of the Manning factor (vacancy-wind factor) that is very different from true binary interdiffusion. In true binary interdiffusion, this factor is usually compared with unity. In the pseudo-binary analysis this reference value must be changed to the inverse of N1+N2, where Ni are the compositions (mole fractions), and components 1 and 2 are the atomic components that have different terminal compositions in the corresponding experiment.

Determination of accurate interdiffusion coefficients in fcc Ag-In and Ag-Cu-In alloys: A comparative study on the Matano method with distribution function and the numerical inverse method with HitDIC

In this paper, 3 fcc binary Ag-In and 3 fcc ternary Ag-Cu-In diffusion couples were firstly prepared. Based on the measured composition-distance profiles, both the traditional Matano method with distribution functions and the numerical inverse method with HitDIC were then utilized to determine the accurate interdiffusion coefficients in fcc Ag-In alloys at 873 K, 973 K, and 1073 K and Ag-Cu-In alloys at 1073 K. The determined interdiffusivities in fcc Ag-In alloys increases as the composition of In increases. The impurity diffusivities of In in fcc Ag extrapolated from the evaluated interdiffusivities based on the Matano method agree well with the tracer experimental data from the literature. As for fcc Ag-Cu-In alloys, the three-dimensional main interdiffusivities planes at 1073 K were constructed over the investigated composition range. The diffusion rate of In is generally faster than that of Cu. Moreover, the main interdiffusivity of In increases with the increment of both In and Cu concentrations, while the main interdiffusivity of Cu increases with In concentration but decreases with Cu concentration. After that, a comprehensively comparative study on the two methods were performed. The interdiffusivities in both the fcc Ag-In and Ag-Cu-In alloys evaluated from the two methods are consistent with each other, indicating that both methods can result in accurate interdiffusivities in binary and ternary alloys. However, as the number of elements increases, the Matano method becomes inconvenient. While for the numerical inverse method with HitDIC, no such limitation exists, and it can be conveniently applied in alloys with any number of components.

Investigation of Interdiffusion in High Entropy Alloys: Application of the Random Alloy Model

High entropy alloys (HEAs) are composed of five or more principal elements with equal (or nearly equal) compositions. In this paper, interdiffusion phenomenon in the HEAs is investigated. Two composition dependent (as well as composition independent) interdiffusion matrices have been used for detailed studying of the diffusion behaviour in CoCrFeMnNi HEAs. These matrices are calculated according to the Darken and Manning formalisms and are used in combination with the explicit finite difference method (EFDM) to obtain interdiffusion profiles. First, the interdiffusion profiles are calculated for the case of the terminal binary diffusion couple. A significant difference in the composition profiles is found between predictions according to the Darken and Manning formalisms. Next, the interdiffusion problem in the 5-component alloy is addressed numerically by considering the interdiffusion coefficients as constant, independent of composition, in CoCrFeMnNi alloys for several diffusion couples (mainly quasi-binary and quasi-ternary). The simulated composition profiles are found to be in a very good agreement with the available experimental results [1, 2]. It should be pointed out that the independence on composition of the interdiffusion matrix should be used for diffusion couples under two conditions: relatively small changes in composition, and the non-zero/non-dilute terminal compositions. The composition dependent interdiffusion matrix should be used in the diffusion couple if the composition differences are large and/or zero/dilute terminal compositions. In this paper, the Darken and Manning formalisms are used for modelling the composition dependent interdiffusion matrices. The purpose of this modelling is to systematically investigate interdiffusion in CoCrFeMnNi alloys in diffusion couples with substantial changes in composition. The main application of the present research is in the prediction of possible interdiffusion profiles in the framework of the random alloy model.

The Vacancy-Wind Factor and the Manning Factor Occurring in Interdiffusion and Ionic Conductivity in Solids

In crystalline solids, during such processes as chemical interdiffusion in alloys, ionic conductivity and the annealing out of radiation damage there will inevitably be a net flux of vacancies. In most cases, when different species of atoms have different jump rates with vacancies within a net flux of vacancies, the phenomenon of the vacancy-wind effect will occur. This effect was first discovered in the 1960s by the late Dr John Manning. It is a subtle phenomenon that comes about because of the local redistribution of the equilibrium concentration of vacancies with respect to two or more species of drifting atoms in a driving force. The effect is captured in various ‘vacancy-wind factors’ (some of which are now sometimes called Manning factors) which formally arise from non-zero off-diagonal Onsager phenomenological transport coefficients and non-unity values of the tracer correlation factors. In this paper, the effect is reviewed and discussed.

The Sequence of the Phase Growth during Diffusion in Ti-Based Systems

Abstract The interdiffusion in Ti-based alloys was studied. It was shown that during diffusion at 1,123 K formation of four intermetallic phases occurs. The diffusion paths for six different diffusion couples were determined. Moreover, the entropy production was calculated – the approximation used for determination of the sequence of intermetallic phase formation. In theoretical analysis, the intrinsic diffusion coefficients were determined from the modified Wagner method.

A Novel Approach to Eliminate the Effect of External Stress on Interdiffusivity Measurement.

In this paper, the interdiffusivities in fcc Co–Ni alloys at 1373 K due to different types of diffusion couple experiments were firstly re-calculated via the unified Wagner method based on the measured composition profiles. Their maximum difference due to different approaches for diffusion couple preparation was found to be larger than one order of magnitude. Then, a comprehensive analysis on the effect of different preparation methods was performed. After that, a two-step diffusion couple technique in combination with the pragmatic numerical inverse method was proposed to determine the accurate interdiffusivities by eliminating the effect of external stress. Such a novel approach was successfully applied in the binary fcc Co–Ni alloys for demonstration purposes. Moreover, it is anticipated that such novel approach can be utilized as the standard method for accurate interdiffusivity measurement, and the resultant accurate interdiffusivities in different alloys may serve as a benchmark for the later experimental and theoretical studies.

Effect of Small Amount of Manganese on the Interdiffusivities in Fe-Al Alloys

The ability to weld aluminum and steel sheets depends strongly on the formation of intermetallic phases; a process that is, in turn, controlled by the interdiffusion of iron and aluminum across the welded interface. Understanding the interdiffusion behavior, and how it is influenced by tertiary elements such as manganese, will allow for better prediction of the properties of the spot weld. Hence, interdiffusion coefficients and activation energies for interdiffusion were determined in the α solid solution and B2 intermetallic phases of Fe-Al alloys in the presence of 1.5-2 at.% manganese with pseudo-binary diffusion couples investigated at 900-1095 °C. The interdiffusion coefficients in α were found to increase in the presence of Mn at all temperatures compared with those reported in the binary Fe-Al alloys. The activation energies for interdiffusion in α are correspondingly lower than those in the binary Fe-Al alloys. The increase in the main interdiffusion coefficients in the presence of Mn indicates that diffusional interactions between Fe and Al are increased in the presence of Mn. The expected increase in diffusional interactions of Fe and Al are found to be consistent with the thermodynamic interactions between Fe and Al in the binary Fe-Al and ternary Fe-Al-Mn system as estimated from the literature. The presence of Mn is found to decrease the solubility of Al in the α solid solution, which, in turn, is expected to decrease the growth rate of the intermetallic at the interface between steel and aluminum.

An augmented numerical inverse method for determining the composition-dependent interdiffusivities in alloy systems by using a single diffusion couple

Abstract

Enhanced calculation of eigen-stress field and elastic energy in atomistic interdiffusion of alloys

The structural evolution of alloys is affected by the elastic energy associated to eigen-stress fields. However, efficient calculations of the elastic energy in evolving geometries are actually a great challenge in promising atomistic simulation techniques such as Kinetic Monte Carlo (KMC) methods. In this paper, we report two complementary algorithms to calculate the eigen-stress field by linear superposition (a.k.a. LSA, Lineal Superposition Algorithm) and the elastic energy modification in atomistic interdiffusion of alloys (the Atom Exchange Elastic Energy Evaluation (AE4) Algorithm). LSA is shown to be appropriated for fast incremental stress calculation in highly nanostructured materials, whereas AE4 provides the required input for KMC and, additionally, it can be used to evaluate the accuracy of the eigen-stress field calculated by LSA. Consequently, they are suitable to be used on-the-fly with KMC. Both algorithms are massively parallel by their definition and thus well-suited for their parallelization on modern Graphics Processing Units (GPUs). Our computational studies confirm that we can obtain significant improvements compared to conventional Finite Element Methods, and the utilization of GPUs opens up new possibilities for the development of these methods in atomistic simulation of materials.

Examining the mechanical properties and superplastic behaviour in an Al-Mg-Sc alloy after processing by HPT

Experiments were conducted using the solution treated Al-3 % Mg-0.2 % Sc alloy in order to examine the mechanical properties and superplastic behaviour after processing by high-pressure torsion. Hardness values of ~200 Hv were detected in the edge of the samples after 10 turns of HPT, although the microhardness distribution was inhomogeneous along the diameter of the discs. Excellent superplastic properties were achieved in this Al alloy after HPT processing and further tensile testing at temperatures over the range from 523 to 673 K, demonstrating good agreement with the theoretical model for grain boundary sliding. High strain rate superplasticity was consistently observed at temperatures from 573 to 623 K, with elongations to failure up to ~800 % at 573 K and at a strain rate of 1.4×10-2 s-1. Further analysis of the experimental data revealed that the stress exponent at the testing conditions displaying elongations >400 % was ~2 thereby demonstrating good agreement with the theoretical model for grain boundary sliding. The calculated activation energies lie in the range from ~98 to ~118 kJ mol-1 and are similar to the value obtained for the same alloy after ECAP which is within the range for grain boundary diffusion in pure Al and interdiffusion in Al-Mg alloys