Evaluating Interdiffusion Matrices in High Temperature Ternary Alloys
Extracting ternary interdiffusion matrices requires intersecting diffusion paths, rigorous molar volume corrections, and thermodynamic constraints.
Boltzmann-Matano Method
Meaning
Mathematical procedure for calculating the diffusion coefficient from the concentration profile of a diffusion couple. The boltzmann-matano method relies on the transformation of the partial differential equation of Fick’s second law into an ordinary differential equation. It assumes that the interdiffusion coefficient is a function of concentration only and that the molar volume remains constant during the process.
Calculation Sequence
Integration of the concentration distance curve provides the necessary data for determining the matano plane. Finding this neutral plane requires a balance of areas on either side of the concentration profile. The boltzmann-matano method then applies a gradient analysis at specific concentration points to solve for the diffusion variable.
This involves taking the derivative of the concentration with respect to distance and multiplying it by the integral of the distance from the matano plane.
Integration Limit
Boundary conditions must be satisfied at both ends of the sample where concentration remains constant. Errors arise if the sample is too short to maintain these semi-infinite conditions. The boltzmann-matano method becomes difficult to apply at extreme concentrations where the slope of the profile approaches zero.
Physical Constraint
Validity of the result depends on the absence of porosity or major volume changes. Total volume contraction during the mixing process can shift the experimental results away from theoretical predictions. The boltzmann-matano method represents a standard for analyzing binary metallic systems.