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In this paper, some aspects of the determination of the concentration profile during diffusion in NiAl- Ti and CMSX4 systems are shown by means of numerical simulations. The results are compared with experiments. The bivelocity method is used to show the evolution of the three-component multiphase system. The simulations present that the local entropy production allows for determination of the profiles in complicated systems. [ABSTRACT FROM AUTHOR]

The Poisson equation is used to calculate the drift velocity in the two-dimensional diffusion couple. This approach is based on the bi-velocity (Darken) method which combines the Darken and Brenner concepts that the volume velocity is essential in defining the local material velocity in multicomponent mixture at non-equilibrium. As an example the arbitrary binary system is considered. It is shown that (1) the two dimensional calculations should be applied with the stochastization method and (2) the drift term in mass conservation law does not affect the calculations. [ABSTRACT FROM AUTHOR]

Abstract: In this work the competition between Kirkendall effect caused by intrinsic diffusion coefficients and vacancy generation and evolution is discussed. The proposed approach is based on the bi-velocity (Darken) approach which combines the Darken and Brenner concepts that the volume velocity is essential in defining the local material velocity at non-equilibrium. The model is formulated for arbitrary systems however for discussion only the binary system is presented. The distributions of (1) components, (2) vacancy and (3) voids radius over the distance are presented. [Copyright &y& Elsevier]

Abstract: The phenomenological Boltzmann–Matano (B–M) analysis allows approximating the concentration dependent interdiffusion coefficients related to infinite binary diffusion couple experiments. However, the complete understanding of the phenomenological process related to the Kirkendall plane position coupled with the B–M method is still lacking. A purpose of the present study is to generalize the Boltzmann–Matano analysis and propose a method of estimating the unique intrinsic diffusion coefficients of components from the experimental concentration profile and the positions of Matano and Kirkendall planes in multicomponent systems. The proposed physico-chemical approach is used to approximate the intrinsic diffusivities in a single phase of Ni–Pd binary and Cu–Fe–Ni ternary diffusion couples. [Copyright &y& Elsevier]

Abstract: The understanding of the phenomenological process related to the position of the Kirkendall plane is still lacking. In this study some aspects of Kirkendall and lattice plane migration in binary diffusion couples are studied by means of numerical simulations by the bi-velocity method. The simulations are performed using constant and composition dependent intrinsic diffusion coefficients. The results show that the position and stability of the Kirkendall plane as well as a number of other interesting features can be predicted using the entropy–density curve calculated by the bi-velocity method. [Copyright &y& Elsevier]

Abstract: The Bi-velocity Phase Field Method (BPFM), which allows a quantitative description of diffusion mass transport in multi-phase materials, is presented and applied to simulate formation of a diffusion zone in aluminized MAR-247. The method links the bi-velocity Darken approach with the phase-field model in which the diffusion zone is quantitatively characterized by phase volume fractions. Accordingly, composition dependent diffusivities in a two-phase region are defined. The present method allows calculation of element-distribution profiles and volume fractions of the phases across a diffusion couple. Hence, a diffusion path can be determined for three component systems and, besides, the average stress field and entropy production during diffusion can be calculated. An example of the application of BPFM in the modeling of high-temperature reactive diffusion in an AlCrNi ternary system is presented. The simulated results are compared with experimental data obtained in aluminization of MAR-247 by the chemical vapor deposition process. [Copyright &y& Elsevier]

Abstract: An approach to the problem of interdiffusion in multicomponent–multiphase system is presented. It couples bi-velocity (Darken) method, in which the mass conservation and volume continuity laws are considered, with the phase field model and is a generalization of the model based on the diffusion equation implemented in Dictra. The proposed bi-velocity phase field method allows computing the kinetics of the process, diffusive mass transport in every phase, concentration profiles, diffusion paths, and Kirkendall effect. The example problem presented here is a fundamental problem concerning the reactive diffusion at high temperatures in Al–Cr–Ni ternary system. It is a starting point that will allow modeling the coating composition to reduce interdiffusion and stabilize a desired microstructure, i.e., to extend coating life time. [Copyright &y& Elsevier]

In the paper the mathematical model describing the gravity induced sedimentation process in multicomponent system is presented. The model is based on the generalized interdiffusion method (bi-velocity method): (1) the volume continuity equation, (2) equation of motion, (3) Cauchy stress tensor and (4) Nernst Planck flux formulae. The method is applied to simulate the sedimentation processes of the selenium isotopes and the ternary InSbGe system. [ABSTRACT FROM AUTHOR]

Abstract: The bi-velocity method allows quantitative description of the complex diffusion mass transport process for an unlimited number of elements. The method deals with (1) composition dependent diffusivities, (2) different partial molar volumes of components, (3) the stress field during the diffusion process and (4) entropy production. It allows for calculation of the time evolution of the components’ concentration profiles for non-ideal systems when thermodynamic activity data is available. Applications of the model describing interdiffusion in a ternary Cu–Fe–Ni system under the stress field is presented. [Copyright &y& Elsevier]

A theory of stress and elastic deformation during interdiffusion is presented. It is shown that it is consistent with the general Darken analysis and linear irreversible thermodynamics. Special consideration is given to local entropy production. An expression is derived for the rate of entropy production during interdiffusion and practical computations presented of the internal energy and entropy densities and the entropy production. It is shown that the entropy produced by the diffusion of mass is positive, [image omitted], and it does not depend on the frame of reference. The results span the gap between the Darken method, linear irreversible thermodynamics and treatments by Larche, Cahn and Stephenson. [ABSTRACT FROM AUTHOR]

Abstract: The bi-velocity concept of separation of diffusion and drift flows allows one to combine the convection and dissipative contributions to the mass and energy fluxes. It is shown that the bi-velocity method combined with statements of the first law of thermodynamics and the Euler’s and Liouville theorems is consistent with linear irreversible thermodynamics. We apply the derived formalism in modeling the two-dimensional sedimentation between Bi and Sb and demonstrate the satisfactory agreement with experimental data. The method allows modeling the sedimentation of isotopes in solids. [Copyright &y& Elsevier]