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A bi?velocity method is used to simulate the element?concentration evolution in the diffusion zone during the aluminization of a Rene?80 nickel?based superalloy. The basis of the method and the detailed calculations are presented. The model enables the prediction of the formation of intermetallic phases and multi?phase layers. The entropy?production rate can also be calculated, and it is shown that it might serve as a basis to indicate the interphases. The proposed model is applied to model the diffusion in a ternary Al?Cr?Ni system. The results of the calculations are compared with experimental element?concentration profiles, measured for the Rene?80 alloy subjected to aluminization by CVD. [ABSTRACT FROM AUTHOR]

Bi-velocity (Darken) method, which includes material drift and diffusion fluxes, is for the first time applied to describe mass transport in multiphase materials. The respective model is formulated in details and then applied for a ternary diffusion couple in which a two-phase zone can grow during isothermal diffusion. Thanks to the use of a phase-field order parameter, identified here with volume fraction of a chosen phase, the mass transport throughout both phases within a two-phase zone can be considered. The model allows smooth crossing of the type 1 boundary, which makes the mass transport equations valid in both single- and two-phase regions. The solution obtained for 1D geometry provides: (1) a diffusion path in the concentration triangle, (2) element-concentration profiles, (3) volume fractions of the phases in the two-phase zone and (4) drift-velocity distribution along x axis parallel to the mass transport. As an example, the interdiffusion in thediffusion couple of Type 0 boundary is modelled. The zigzag diffusion path is predicted and the profiles of the element concentrations are simulated. For the first time, the drift velocity for the diffusion in two-phase system is determined and correlated with the changes in volume fractions of the phases. [ABSTRACT FROM AUTHOR]

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]

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: A thermodynamically consistent framework is developed to combine the convection and dissipative contributions with the mass and energy fluxes in multicomponent materials. The method, which is known as bi-velocity or Darken method, is based on the postulate of the unique (independent on the frame of reference) transport of the mass due to diffusion. In this work we merge: (i) the combined statements of the first and second laws of thermodynamics (linear irreversible thermodynamics) and (ii) the Euler and Liouville theorems. We derive an expression for the rate of the entropy production that does not depend on the frame of reference and is always positive. We show that the derived set of partial differential equations describing the mechanochemical mass transport is thermodynamically consistent and can be used in advanced modeling. [ABSTRACT FROM AUTHOR]