Diffusion in ordered alloys and intermetallic compounds

The effect of large vacancy concentration on intrinsic and interdiffusion coefficients: A first-principle study of B2-NiAl

Interdiffusion coefficients in copper-rich copper-antimony solid solutions containing up to 5 at% of Sb have been determined by Matano’s method in the temperature range between 919 and 1040 K using semi-infinite diffusion couples consisting of pure copper and Cu–Sb alloys with the Kirkendall markers. From the interdiffusion coefficient and the marker shift, the intrinsic diffusion coefficients have been determined at the marker positions, 1.0 and 1.7 at%Sb. Using thin plate couples, the intrinsic diffusion coefficients in Cu-0.6 at%Sb alloy at 1005 K have been determined by Heumann’s method. From the value of the intrinsic diffusion coefficient of copper in the infinite dilution of Sb and the tracer diffusion coefficients of Sb and Cu in pure Cu, the vacancy flow factor for the interdiffusion in Cu–Sb alloys at 1005 K has been calculated to be −1.20−0.28+0.22, which suggests a strong interaction between an antimony atom and a vacancy. Combining the present result on the vacancy flow factor with the previous experimental data on the enhancement factor of solvent diffusivity by the addition of solute atoms, the correlation factor and the jump frequency ratios in the five-frequency model have been estimated. The correlation factor for the impurity diffusion of Sb in Cu thus obtained is about 0.1 at 1005 K, which indicates highly correlated jumps of an antimony atom to a vacancy.

Diffusion in the Ag-Cd system was investigated at 600°C with vapor-solid and solid-solid diffusion couples in the α-phase for the determination of intrinsic diffusion coefficients, atomic mobilities and interdiffus ion coefficients. Intrinsic diffusion coefficients, DCd and DAg, determined experimentally, were compared with those predicted from the models of Darken, Manning, and Dayananda with the aid of tracer diffusion and thermodynamic data. The experimental coefficients for various alpha alloys were found to be higher than those evaluated from each of the three models. On the other hand, the experimental values of the ratio, DCd/DAg were found to be in good agreement with the models of Manning and Dayananda where the vacancy wind effects on intrinsic diffusion are taken into account. Darken’s relations are considered inadequate to interrelate tracer and intrinsic diffusion coefficients in the Ag-Cd system, since vacancy wind effects are found to be appreciable in this system.

On the determination of diffusion coefficients in multi-phase ternary couples

Study of diffusion and atomic mobilities for fcc Ag–Cd and Ag–Sn solder alloys

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

Diffusion studies were made in the alpha and beta phases of the silver-zinc system at 600°C with vapor-solid and solid-solid diffusion couples in order to determine intrinsic diffusion coefficients and interdiffusion coefficients. Intrinsic diffusion coefficients, DZn and DAg, determined experimentally for bothα andβ alloys, were compared with those predicted from the models of Darken, Manning, and Dayananda with the aid of thermodynamic and single crystal tracer diffusion data. The experimental values of Dzn were close to those predicted by the models of Darken and Manning, while the experimental DAg values were higher than those determined by both models. The experimental values of the ratio, DZn/DAg, were found to be lower than those predicted by either Darken’s or Manning’s relations. Also, Dayananda’s model was found to be inapplicable with the available tracer diffusion data. This disagreement is considered to reflect the inadequacy of the single crystal tracer diffusivities in the analysis of intrinsic diffusion in polycrystalline Ag-Zn alloys.

As energy demand increases and global warming progresses, expectations for fuel cells, which generate electricity through chemical reactions between hydrogen and oxygen, are rising. There are various types of fuel cells, which are classified according to the electrolyte. Polymer electrolyte fuel cells (PEFCs) are expected to be used in stationary power sources for home use and fuel cell vehicles because of their low operating temperature, short start-up time, and ease of miniaturization. The cost has been an issue in the widespread use of fuel cells. The amount of platinum used in the catalyst layer (CL) must be reduced to reduce costs. However, it increases the current density per unit area of platinum. There are three factors that contribute to voltage drop: ohmic polarization, activation polarization, and diffusion polarization. At high current densities, the voltage drop due to diffusion polarization is dominant. The main cause of diffusion polarization is the transport resistance of oxygen molecules in the CL, and improving the oxygen transport properties in the CL will lead to lower cost PEFCs. In this study, we analyzed the transport properties of oxygen molecules in the CLs of PEFCs using the Monte Carlo (MC) method. The effect of oxygen scattering on the overall oxygen transport properties was investigated by considering the behavior on the surface of the ionomer film (surface diffusion) into the MC method, which simulates the overall transport in the PEFC CL. The objective of this study is to reproduce accurate oxygen transport by comparing the results of MC and molecular dynamics (MD) methods. First, we used the MC method to analyze oxygen scattering phenomena. In this study, we used the 3D structure data of CL in the MC simulations. The three-dimensional structure of the sample was reconstructed from sequential slice images. Molecules were assumed to reflect specularly on the boundaries of the simulation domain. Oxygen molecules were randomly placed in the simulation system. The time step was set at 5 ps and the simulation time was set at 4 μs. In order to examine the effect of surface diffusion on the transport properties of oxygen molecules, the simulation was performed using various conditions of surface diffusion. We calculated the effective diffusion coefficient of oxygen in the CL as the transport property of oxygen molecules in the MC method. As the surface diffusion coefficient increases, the effective diffusion coefficient of oxygen increases. When the surface diffusion coefficient is small, the effective diffusion coefficient of oxygen increases due to a decrease in the time constant, which determines the probability distribution of the surface residence time. However, when the surface diffusion coefficient is large, a different trend emerges. As the time constant increases, the effective diffusion coefficient has a peak value and then decreases. Next, to verify the model of surface diffusion in the MC method, we analyzed the scattering phenomenon of oxygen molecules in a simulation system that simulates the pores in the CL using the MD method. We modeled the nano pores in the CL as a slit between the ionomer walls in the MD method. Nafion with the equivalent weight (EW) of 1146 was used as polymer model. The number of Nafion chains is set at 4, and the water content λ is set at 7. Three-dimensional periodic boundary conditions were applied to the simulation domain. After the system was equilibrated, 1 ns of NVT simulation was performed for production. The temperature was set at 297 K. The behavior of oxygen molecules impacting on the ionomer wall was analyzed. We analyzed the behavior of oxygen molecules colliding with the ionomer membrane using the MD method. The average residence time of surface diffusion on the ionomer thin film was of the order of 10-10s. When the calculation results were compared with the MC results, it was found that the average residence time obtained by the MD method was the value where the surface diffusion coefficient affects much on the effective diffusion coefficient. Comparing the results of the MD method with the surface diffusion model used in the MC method, there are some discrepancies between the results and the model. For example, the MC method used a model in which oxygen molecules reflect diffusively on the ionomer surface. However, in the MD method, it was found that oxygen molecules tend to reflect in the direction of travel (Fig. 1). Therefore, a more accurate model of the MC method needs to be developed in the future. Figure 1

The dependences of intrinsic diffusion coefficients (DSb, DAg) and interdiffusion coefficients (D) upon temperature and composition in dilute AgSb alloys have been measured. The interdiffusion coefficients D(0) obtained with infinitely dilute solutions agree well with tracer data for D*Sb(0) from the literature. The ratio of the intrinsic diffusion coefficients was determined by applying the thin plate method. Within the error margins the ratio DSb/DAg can be regarded as independent of concentration up to 3 at.% Sb. The values of DSb/DAg(0) with infinitely dilute solutions decrease linearly with increasing temperature. The jump frequency ratios w4/w0, w2/w1 and w3/w1 were calculated according to the five-frequency model on the basis of the vacancy flow factor LAB/LBB(0), the ratio of tracer diffusion coefficients D*Sb/D*Ag(0) and the linear enhancement factor b1. From these the correlation factor fSb of impurity diffusion is obtained, which increases with temperature from 0.30 at 890 K to 0.49 at 1048 K, as expected. The binding Gibbs free energy delta g1 of a vacancy-antimony pair has been estimated using four different methods of evaluation using the values measured in the present paper and diffusion data from the literature. The temperature dependence of delta g1 is critically discussed.

New method for measurement of interdiffusion coefficient in high temperature solutions based on Fick's first law

Diffusion simulation based on atomistic model and mobility determination via Kirkendall experiment for multi-component systems

Intrinsic diffusion coefficients have been calculated for a solid solution binary fcc metal alloy with vacancies using grand canonical and kinetic Monte Carlo (MC) methods for a variety of model Hamiltonians. Model Hamiltonians include a kinetically and thermodynamically ideal case, solute-vacancy attraction and repulsion, and solute-solute attraction and repulsion. These model Hamiltonians are chosen to have constant average activation energies in order to focus on contributions from other thermodynamic and kinetic factors. The thermodynamic factor calculated using MC is compared to a mean-field regular solution model. It is shown that the mean-field model accurately predicts the thermodynamic factors for each model alloy Hamiltonian except for the alloys with a solute-solute interaction and concentration that are in the spinodal region (as predicted by the regular solution model). The MC determined concentration-dependent intrinsic diffusion coefficients are compared to values determined from the dilute five-frequency model and Darken and Manning analytical approximations. The results indicate that for a solid solution with known average barriers and vacancy concentration, Darken and Manning approximation-based analytic expressions and mean-field theory can be used to predict concentration-dependent diffusion coefficients within a factor of approximately three, provided the system is outside of the spinodal region. The good accuracy of this approximate approach follows from the fact that the thermodynamic factor is the main contribution to the concentration dependence of the diffusion constants, and that this thermodynamic factor is well described by mean-field theory.

ABSTRACTThe benefits of using the pseudo-binary and pseudo-ternary diffusion couple methods in multicomponent inhomogeneous systems are demonstrated by estimating different types of composition-dependent diffusion coefficients. These are important for understanding the basic atomic mechanism of diffusion and complex compositional evolutions. These were otherwise considered impossible during the last many decades. Without any options previously, sometimes the average values over a composition range of random choice were estimated, which are not the material constants but depend on the composition range and also the end member compositions. The steps and analyses for utilising the pseudo-binary and pseudo-ternary methods are first described in the Ni-Co-Fe-Mo system by producing the ideal diffusion profiles fulfilling the concepts behind these methods. Following, the discussion is extended to the systems related to medium (Ni-Co-Cr) and high (Ni-Co-Fe-Mn-Al) entropy alloys. In fact, this is the first report showing a correct experimental method that should be followed for the estimation of the interdiffusion and intrinsic diffusion coefficients in inhomogeneous high entropy alloys. In the end, the limitations of following these methods because of the generation of non-ideal diffusion profiles are discussed based on experimental results. The steps are also suggested to avoid such complications. These methods are easy to adopt for research engineers. Most importantly, these give an opportunity to validate the data estimated following newly proposed numerical methods by different groups with experimentally estimated diffusion coefficients, which were not possible earlier.

The paper gives a brief overview of our recent work on atomistic computer modeling of ordered intermetallic compounds of the Ni-Al and Ti-Al systems. Atomic interactions in these systems are modeled by semi-empirical potentials fit to experimental and first-principles data. The methodology includes a large variety of techniques ranging from harmonic lattice dynamics to molecular dynamics and Monte Carlo simulations. The properties studied include lattice characteristics (elastic constants, phonons, thermal expansion), point-defect properties, atomic diffusion, generalized stacking faults, dislocations, surfaces, grain boundaries, interphase boundaries, and phase diagrams. We especially emphasize the recent progress in the understanding of diffusion mechanisms in NiAl and TiAl, calculation of stacking fault energies in Ni3Al in relation to dislocation behavior, and calculations of / 0 interface boundaries in Ni-Al alloys.

Intermetallic formation and interdiffusion in diffusion couples made of uranium and single crystal iron