Papers by Author: Marek Danielewski

Abstract: In this paper we couple the bi-velocity with the phase field method. It deals with: (1) the different mobility of the components in the two-phase zone; (2) nonzero steps of molar volumes for each component from phase to phase and (3) the composition dependent interdiffusion coefficients. The method allows to determine the average stress field during the diffusion process, the kinetics of the reactions and estimate the entropy production. The paper presents the numerical computations of diffusion in th eNiAlCr system. The results can serve as a basis in designing gradient coatings of extended life time.

Abstract: A general, consistent with linear irreversible thermodynamics, theory of stress and elastic deformation during interdiffusion is shown. Special consideration is given to the entropy balance and its production rate during diffusion in Cu-Fe-Ni alloys. The entropy produced during diffusion does not depend on the reference frame and is always positive. The paper spans the gap between the Darken method, linear irreversible thermodynamics and treatments by Stephenson and Svoboda.

Abstract: The formation of intermetallic compounds (IMC) at the solder-substrate interface is required to initiate the metallurgical bond. However, rapid growth of IMCs may degrade joint strength through i) the increased presence of a low toughness phase, ii) the consumption of the solderable surface (void formation) and iii) generation of primary and secondary stresses. Knowledge of mass transport and reaction processes during joint formation and service life are essential for solder system design. The mathematical description of inter-and reactive diffusion in open system presented here is based on Darken method (bi-velocity), involving the different molar volumes in the system and Wagner boundary conditions. It combines the interdiffusion, reactive diffusion and the effective flux constraints to couple processes occurring at different time scales. The rCADiff software serves as a tool to simulate simultaneous growth of the two Cu-Sn IMCs.

Abstract: The modified Redlich-Kister approximation of the composition dependent intrinsic diffusivities in the multicomponent solid solution is presented. The effective computation method (the inverse problem) combines the Hierarchical Genetic Strategy with real number encoding (HGS-FP) with the modified Redlich-Kister approximation. The Cu–Ni–Fe alloys at 1271 K are analyzed. We show that the measured intrinsic diffusivities, the estimated from available diffusivity data and calculated by inverse method are in agreement. The presented method may become a very effective tool when the diffusion multiple technique is considered.

Abstract: We propose a theoretical framework to derive a consistent set of equations describing sedimentation, i.e. diffusion induced by the gravity (centrifugal) field, in a multi component system. This procedure starts from the combined 1) mass conservation law, 2) equation of motion, 3) volume continuity equation and 4) Nernst-Planck flux formulae. The method known as bi-velocity or Darken model is based on the postulate of a unique transport mechanism for volume and mass. The concentration profile in the equilibrium state is found by solving the nonlinear set of equations. Example applications of this theory applied to Bi-Sb system is evidence of sedimentation of substitutional atoms in condensed matter via diffusion mechanisms.

Abstract: Ion transport across the membrane of the living cell (molecular ion channels) is a critical process, e.g., the triggering of nerve cells and heart muscle cells is coupled with mechanisms controlled by ion diffusion (electrodiffusion). Although the process is described by the century old Nernst- Planck-Poisson system of equations, it is not well understood and a clear understanding of how the interaction between channel and ions affects the flow is still missing. We present a three-dimensional model of the molecular channel. An appropriate quantitative description of the ion transport process allows proper explanation of molecule channel interactions (e.g. the ions flow for a given concentration gradient should depend on the potential and other parameters describing the interaction, i.e. asymmetric transport). We show the simulation of the stationary electrodiffusion in the ion channel showing radial symmetry.

Abstract: Kirkendall and Darken findings of the drift velocity since 1948 have stimulated progress in transport phenomenological models. The convection velocity (the Darken drift in solids), , and velocity of diffusion, , require definition and the method how the diffusion displacement is defined, computed and measured. The equation of volume continuity allowed the extension of the Darken method and avoids the rigid assumption of the constant molar concentration. In this work, we use the bi-velocity approach, i.e., the generalized Darken method, to model interdiffusion in two-dimensional diffusion multiple. We show the convergence of one- and two-dimensional models in the case of the process at the constant volume and perfect agreement between R1 and R2 simulations. We impose modifications in the foundations of mechanics of solids namely, the Navier-Lamé-Fourier equations. We show that the method can be used in the mechano-chemistry of solids and is self-consistent with linear irreversible thermodynamics.

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: The kinetics and mechanism of metal dusting corrosion of 9Cr-1Mo steel, commonly used in CCR platforming units, have been studied as a function of temperature (773 – 1173 K) in propane-butane atmosphere, being the mixture of 70 vol. % of propane and 30 vol. % of butane with the total pressure equal 105 Pa. The kinetics of corrosion have been studied thermogravimetrically in the apparatus enabling the mass changes of corroded sample to be followed continuously with the accuracy of the order of 10-6 g. It has been found that metal dusting corrosion in this atmosphere, modeling in some way industrial environments in petrochemical industry, is complex and two-stages of linear kinetics may be distinguished. In the first stage, which may be considered as an incubation period, the reaction proceeds with rather low rate, which increases dramatically in the second stage, the beginning of which depends strongly on temperature. Linear course of reaction indicates that chemical reactions and not diffusion processes determine the rate of corrosion. This conclusion is confirmed by the fact, that the layer of corrosion products is not compact but considerably porous.

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.