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In this paper the Diffusion Path (DP) method is presented. The method allows for the determination of the diffusion path during a reactive diffusion process. The initial conditions of the method are the phase diagram, diffusion coefficients in the phases and initial composition of the diffusion couple. The method allows for the determination of the diffusion path—the intermetallic phases generated during the diffusion process and the order of their generation. The results of the DP method are compared with the experimental results obtained for the Ti-NiCu diffusion couples with various Ni to Cu content ratio. [ABSTRACT FROM AUTHOR]

In this paper the vacancies formation and agglomeration under centrifugal force — sedimentation will be analyzed. The evolutionary algorithm for diffusion and vacancy evolution will be shown. The model predicts the location of vacancies agglomeration during the sedimentation process — the most probably place of voids formation. The computed results will be compared with experiments in Cu–brass diffusion couple. The influence of the centrifugal force on the vacancies migration will be presented. [ABSTRACT FROM AUTHOR]

The complete understanding of the phenomenological process related to the position of the Matano and Kirkendall plane in multicomponent system is still lacking. In this paper some aspects of Matano and lattice plane migration are studied by means of numerical simulations. New approach to calculate intrinsic diffusion coefficients in binary Ni–Au system and ternary Cu–Fe–Ni and Co–Fe–Ni is presented. Diffusivities were calculated using modified Boltzmann–Matano method. Self diffusion coefficients of the elements in diffusion couple must be known as well as position of the Kirkendall plane after the experiment to use this method. Diffusion profile was calculated using presented equations. Calculations compared with experimental data prove validity of the presented approach. This work proves that intrinsic diffusion coefficients should be given by the concentration function, not the exact value. [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: 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]

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]