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The solid-state diffusion in binary and ternary systems is overall treated and modeled using the bi-velocity method. The mathematical formulation is given, and the boundary conditions discussed. The model allows the calculation of concentration profiles, spatial distribution of the entropy production rate, and diffusion path. The last two can be used to identify the phases present in the diffusion zone of the ternary system, and determine the thicknesses of the respective layers. The model is applied for the first time to simulate diffusion during aluminization of nickel and its super-alloys, MAR-M200+Hf and CMSX-4, and the predictions are compared with the results of the experiments performed by the authors. The results give a new quantitative explanation of the high-active and low-active regimes of aluminization. It is, in particular, confirmed that the high-active and low-active regimes of nickel aluminization can be carried out by a variation of the HCl/H2 flow ratio. The most important, and a brand new, result concerns the entropy production rate. It is shown that its maxima coincidence with the two-phase zone boundaries in real space, which gives new insight into the modeling of the diffusion in ternary systems. [ABSTRACT FROM AUTHOR]

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]

In this work we solve the problem of the simultaneous growth and competition of intermediate phases. The crystal lattice as the frame of reference for diffusion is defined, based on the volume continuity equation. It permits the computation of the material velocity in a system in which reactions at several moving interfaces occur. All reactions lead to the lattice shift due to the difference of diffusivities and molar volumes. We simulate the CVD process followed by annealing in a non-oxidizing atmosphere. The computed kinetics and concentration profiles are compared with experimental results. [ABSTRACT FROM AUTHOR]