Diffusing species into some host metals in spherical solids

Abstract

This study investigates the diffusion of various species into host metals in spherical solids. The time-dependent diffusion equation in radial spherical coordinates was transformed into a time-independent form, resulting in a Bessel differential equation of the zeroth kind. The concentration profile within the system was obtained using the Frobenius method. This solution, combined with the fractional Stokes-Einstein model, was used to plot graphs showing the effect of the fractional exponent and temperature on the diffusing species. The results indicate that a rise in temperature leads to early saturation or convergence, followed by divergence, reflecting an increase in the concentration of the diffusing species. Additionally, it was observed that as the fractional exponent increases, the concentration of the diffusing species is enhanced. A model for determining the diffusion coefficient of the host metals is also proposed. The characteristics of the host metals, as shown, significantly affect their diffusion rates. The experimental model is presented alongside the calculated concentration values. The unique approach and findings of this research offer a valuable contribution to diffusion analysis, with potential implications for a wide range of applications involving solid-state materials.