Papers by Author: Marek Danielewski

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: Low-temperature nitriding of austenitic stainless steels or chromium containing alloys can produce expanded austenite, known as S-phase, with combined improvement in wear and corrosion resistance. In the paper a critical review of various models for nitrogen diffusion during nitriding is presented. A special attention is paid to the expanded austenite growth. A new model based on bi-velocity method and including stresses is presented. Basic equations and boundary conditions are discussed. Composition dependent nitrogen diffusion coefficient is assumed. Numerical solutions are obtained for the growth of the S-phase layer in steel. The results are compared with previous experiment and calculations.

Abstract: Interdiffusion in two-phase Ni-Cr-Al diffusion couple was studied experimentally and simulated numerically. The diffusion multiples were prepared by hot isostatic pressing, HIP and post-annealing at 1200°C. The concentration profiles were measured with wide line EDS technique – a method suitable to study multiphases. Hence the diffusion paths were determined. The experimental profiles and diffusion paths were compared with numerical results simulated with application of the Darken bi-velocity method implemented to describe interdiffusion in a two-phase zone.

Abstract: A consistency between the Darken method and the Onsager representation for cross diffusion in multicomponent system is shown. The justification is made by defining new sets of forces and fluxes linearly interrelated by a symmetric matrix of phenomenological coefficients. For the first time, the system of the components having various molar volumes is treated in this way. It is shown that the transformation leaves the entropy production unchanged. As an example, the entropy production for interdiffusion in the ternary Co-Fe-Ni diffusion couple is calculated and compared with mixing entropy.

Abstract: The Nernst-Planck flux formula is used in Darken's method to obtain the interdiffusion fluxes. The effective interdiffusion potentials, derived for the independent components in the system, allow obtaining the symmetrical matrix of the interdiffusion coefficients. The transport coefficients for 2, 3 and r-component system are presented. Interpretation of obtained matrixes in the light of Onsager's theory of irreversible thermodynamics is shown. Equation for the entropy production in the interdiffusion process is displayed. The presented approach allows calculation of entropy production during interdiffusion, as well as formulating Onsager's phenomenological coefficients for the interdiffusion in an explicit form, a form which is directly correlated with the mobilities of the atoms present in the system.

Abstract: The paper provides a physical description of ionic transport through the rigid symmetrical channel. A three-dimensional mathematical model, in which the ionic transport is treated as the electrodiffusion of ions, is presented. The model bases on the solution of the 3D Nernst-Planck-Poisson system for cylindrical geometry. The total flux includes drift (convection) and diffusion terms. It allows simulating the transport characteristics at the steady-state and time evolution of the system. The numerical solutions of the coupled differential diffusion equation system are obtained by finite element method. Examples are presented in which the flow characteristics at the stationary state and during time evolution are compared. It is shown that the stationary state is achieved after about 2×10 ^-8 s since the process beginning. Various initial conditions (channel charging and dimensions) are considered as the key parameters controlling the selectivity of the channel. The model allows determining the flow characteristic, calculating the local concentration and potential across the channel. The model can be extended to simulate transport in polymer membranes and nanopores which might be useful in designing biosensors and nanodevices.

Abstract: The Kirkendall effect appears due to the unbalanced diffusion fluxes causing the vacancy flux. There are several numerical methods that allow to predict the position of Kirkendall plane after the diffusion couple annealing. In this work for the first time the entropy density distribution is used to estimate the trajectory of the Kirkendall plane. The entropy density distribution is calculated with use of the bi-velocity method, which combines: (1) the volume continuity, (2) the conservation of mass, (3) momentum and (4) entropy-density. The method is applied to simulate the diffusion in Ni-Pd diffusion couple.

Abstract: Gas carburizing is a widely used heat treatment process in which carbon is transferred into steel. The hardening reliability involves an active control of mass transfer during the process and this is why understanding diffusion in solids is so essential to model the process. The currently used models are often based on the simplest, one-dimensional form of the diffusion equation in which diffusivity depends on composition. The objective of this work is to develop a model of carbon diffusion in multicomponent alloy subjected to pulse carburizing. The model is based on the Darken method (bi-velocity method) in which the diffusion velocity depends on the diffusion potential gradient and is independent of the choice of the reference frame while the drift velocity is common for the carbon and steel components. Our model allows predicting the kinetics of carbon transfer at various treatment conditions and is applied to the pulse carburizing process at constant temperature. The process is carried out by repeating consecutively a carburization stage, when the carburizing gas is supplied into a carburizing chamber, and a diffusion stage at vacuum conditions, when the carburizing gas is exhausted and only the diffusion of carbon takes place. The numerical calculations are made for varying carburization and diffusion periods and are confirmed by the experimental results. On the basis of the series of computer experiments some findings that are important in designing the carburizing technology are formulated.

Abstract: Interdiffusion plays a significant role in the formation and stability of metallic joints and coatings. It is also of critical importance in designing advanced materials. Because commercial alloys are usually multicomponent, the key target is prediction of a complex morphology of the diffusion zone which grows between the alloys, alloy-coating, etc. In a two-component system, the diffusion zone can be composed of single-phase layers of the intermetallic compounds and solid solutions. The evolution of the composition and thicknesses of such layers are fairly well understood and consistent with the phase diagrams. The situation is qualitatively different in multicomponent systems. For example, the diffusion zone in a ternary system can be composed of single-and two-phase sublayers. Their number and thicknesses depend on the initial conditions, i.e. composition, component diffusivities and geometry of the system. The usual way of presenting the sequence of the layers and their compositions is by drawing a diffusion path which is, by definition, a mapping of the stationary concentrations onto the isothermal section of the equilibrium phase diagram. The diffusion path connects initial compositions of the diffusion couple and can go across the single-, two-and three-phase fields. It starts at the composition of one alloy and ends at the other. The possibility of mapping the concentration profiles onto the ternary isotherm has been postulated in one from the seventeen theorems by Kirkaldy and Brown [] for the diffusion path. The detailed presentation of all theorems was recently done by Morral []. Here we remind the reader only of the chosen ones (shown in italics).