Application of numerical inverse method in calculation of composition-dependent interdiffusion coefficients in finite diffusion couples

The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples.

Computation of Trajectories and Displacement Fields in a Three-Dimensional Ternary Diffusion Couple: Parabolic Transform Method

The problem of Kirkendall’s trajectories in finite, three- and one-dimensional ternary diffusion couples is studied. By means of the parabolic transformation method, we calculate the solute field, the Kirkendall marker velocity, and displacement fields. The velocity field is generally continuous and can be integrated to obtain a displacement field that is continuous everywhere. Special features observed experimentally and reported in the literature are also studied: (i) multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple evolve into two locations as a result of the initial distribution, (ii) multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple move into two locations due to composition dependent mobilities, and (iii) a Kirkendall plane that coincides with the interphase interface. The details of the deformation (material trajectories) in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect. Our nonlinear transform generalizes the diagonalization method by Krishtal, Mokrov, Akimov, and Zakharov, whose transform of diffusivities was linear.

Calculating of Diffusion Profiles in Ternary Systems Using Effective Interdiffusion Coefficients of Components

A method has been developed for calculating diffusion profiles in ternary systems by using effective interdiffusion coefficients of components and Boltzmanns solution for diffusion equation with variable diffusion coefficient. Using this method the concentration profiles for several diffusion couples in the systems Fe-Co-Ni and Cu-Fe-Ni are calculated as examples and some peculiarities of these calculations are discussed, particularly, how to solve some possible difficulties, which may sometimes arise at calculation procedures. It is shown that having the data on effective interdiffusion coefficients and their concentration dependence for at least two components in a ternary diffusion couple, the concentration profiles for all three components can be calculated with good accuracy.

The Effective Interdiffusion Coefficients in Experimental Investigations of Interdiffusion in Ternary Systems

The application of the effective interdiffusion coefficients for describing the interdiffusion process in ternary systems is discussed. It is shown that the relative values of effective interdiffusion coefficients, which are directly related to the diffusion path developed in a given diffusion couple, are responsible for deviation of the diffusion paths from linearity. The relationship between effective interdiffusion coefficients and partial (intrinsic) coefficients in ternary systems is analysed. It is shown that Boltzmann’s solution for diffusion equation with variable diffusion coefficient by means of relatively easy calculation procedure gives reliable results for the calculation concentration distributions in a ternary diffusion couple.

Inverse T-Sample Method of Determination of the Interdiffusion Coefficients in the Cu-Ni-Sn System

A method of the determining of the mutual diffusion coefficients in ternary intermediate phases is suggested. Methodology for determination of the interdiffusion coefficients of phases formed in a ternary diffusion couple in T-sample configuration is presented. The method requires only one annealing of the T-sample and makes it possible to calculate the matrix of the diffusion coefficients in the (CuNi)6Sn5 and Cu3Sn ternary intermediate phases under low temperature. The concentration profiles and electron micrograph of the diffusion zone was obtained in the ternary Cu-Ni-Sn system annealed for 64 hours under 200°C. Phase competition in this ternary system with special configuration of T-sample leads to lateral diffusion of Cu, to formation (CuNi)6Sn5 compound between Ni-Sn side and to suppression of other NixSny intermediate phases.