Finite size corrections on the estimation of the effective diffusion coefficients through the dynamical behavior of the diffusion zone during gaseous nitriding of pure iron

Abstract

Effective diffusion coefficients in monolayer and bilayer growth experiments during gaseous nitriding of pure iron have been previously determined by assuming a diffusion zone of infinite size. In this work, finite size corrections to the effective diffusion coefficients are determined by imposing total mass balance of nitrogen in a sample with a diffusion zone of finite size. The proposed model incorporates an equation of motion for the diffusion zone thickness, which is consistent with total mass balance. The model does not have an exact analytical solution; therefore, semi-analytical methods are used to find approximate solutions to the problem. The effective diffusion coefficients are estimated through a double minimization process. Experimental data from other authors are used to define a least squares error function for the layer thicknesses and another error function for the total mass of nitrogen. The steepest descent method is used to determine a set of diffusion coefficients that minimize the error in the layer thicknesses. The effective diffusion coefficients that best approximate the total mass of nitrogen in the sample are estimated by solving the model for each of the local minima previously determined. The values of the effective diffusion coefficients are validated by comparing the numerical and semi-analytical solutions obtained from the proposed model, with the experimental values for the total nitrogen mass at different nitriding conditions. Finally, non-parabolic growth behavior is captured by the proposed model in experiments where the assumption of a diffusion zone of infinite size or saturated substrate is arguable.