Papers by Keyword: Darken Method

Abstract: Even though several methods of diffusion analysis avoid a necessity for the Matano plane determination, the Matano plane locations are of interest in the multicomponent couples and when tracer experiments are performed. The positions of the Matano plane calculated from the concentration profiles should be exactly the same. However, due to experimental errors, the results can differ significantly. In the paper we consider Matano plane for multi-component couples of conserved and non-conserved overall volumes. We use Darken method and Sauer-Freise scheme, respectively and show that looking for the Matano plane as an inverse problem leads to a system of linear algebraic equations which are over-determined. The relations for the Matano plane position are derived by virtue of the least-squares methodology. The exemplary computations shows that the method is particularly useful in analysis of experimental data and allows decreasing computing errors.

Abstract: This works presents new approach to model formation of expanded austenite (S-phase) during nitriding in plasma conditions. Diffusion saturation of the substrate (iron or austenite steel) is treated as interdiffusion of nitrogen and iron that involves stresses and plastic deformation and is based on the Darken scheme. It is argued that S-phase growing at nitriding behaves as elasto-viscous Maxwell solid. During the process, in the nitride zone, the dynamic pressure appears, which is related to Darken drift and depends on metal viscosity. Basic equations are formulated and discussed. The formula for drift is derived. Exemplary results, i.e. concentration profiles, dynamic pressure and dilatation of the sample during the process, are presented. Concentration profiles confirm existence of characteristic plateau like zone in the surface adjacent zone.

Abstract: The intrinsic diffusion coefficients in diffusion aluminide coatings based on Fe-30Cr were determined at 1000oC. The diffusion fluxes were given by the Nernst Planck formulae and the Darken method for multicomponent systems was applied. This paper summarizes some numerical results to determine the composition dependent diffusivities in Fe-Cr-Al systems. The method presented in this study to obtain average intrinsic diffusion coefficients is as an alternative to the Dayananda method. Our method based on empirical parameters allowed us to predict the concentration profile during the interdiffusion process.

Abstract: This paper presents a numerical method to determine the composition dependent diffusivities and to predict the concentration profile during the interdiffusion process. The intrinsic diffusion coefficients in diffusion aluminide coatings (Fe-Al) were determined at 1000oC. The obtained diffusion coefficient for iron in Fe3Al or FeAl is in the range 10-10 to 10-9 cm2.s-1. The aluminum diffusion coefficient varies from 10-11 to 10-7 cm2.s-1 in the same phases.The present approach also permits to model the reactive diffusion in the Fe-Al systems.

Abstract: In order to model the diffusion in multicomponent and multiphase systems we define and use the volume fixed frame of reference. In this unique frame all diffusion fluxes are expressed by the combined Darken-Nernst-Planck formulae. The components mobility is estimated using the NIST data and Calphad approach. The resulting CADiff method is used for the modeling (inter)diffusion process in the multicomponent diffusion multiple. We shows results for the IN718-Rene88 terminal compositions. Comparison of the simulation results with experimental data shows good agreement. The presented CADiff method allows to model interdiffusion in multicomponent non-ideal systems. When the thermodynamical data are available, the method allows to include reactions, variable partial molar volumes and effect of stress.

Abstract: We compare the experimental and computed results of the stress assisted interdiffusion. The Cu-Fe-Ni diffusion couples were investigated at 1273 K. The alloys in this system do not form ideal solid solutions and consequently the Calphad method was used to compute the elements activities. The method applied in this work base on the Darken’s drift velocity concept, Vegard law and Navier-Lamé equation. It allows computing the deformation field during the interdiffusion process. The driving force for diffusion in such a ternary system is the gradient of the chemical potential which can be calculated from the concentration profiles and using the known thermodynamical data of the system. Comparison between the Darken method without stress and the influence of stress on the interdiffusion in the Cu-Fe-Ni system is presented. Simulations that take into account the deformation field give better fit to the experimental results. Moreover we show qualitative and quantitative differences between the simulations of interdiffusion using the Calphad method and with the ideality sweeping statement.