Iterative approaches describing atomic diffusion in finite single‐ and two‐phase systems
Iterative solutions are given for planar one‐dimensional atomic diffusion in finite single‐ and two‐phase systems. They are usable for any continuous variation of the interdiffusion coefficient D (C) within each phase, and need not be fitted to special functions such as a power series or an exponential function. Modified integral functions similar to one first proposed by Boltzmann are used along with a conservation criterion to locate the interface position ξ. Computer time for the iterative solutions is about two to three magnitudes shorter than finite‐difference (F‐D) calculations because of the rapid convergence of the integral equations. The accuracy of these approximate forms is considered. Excellent agreement was obtained between F‐D calculations and the iterative approach for semi‐infinite single‐phase systems. Good agreement is also found for two‐phase systems; however, the accuracy varies with the solubility gap size C βα−Cαβ. The best results are obtained for gaps larger than 0.7 which includes most eutectic systems. Calculations of composition profiles which are based upon the maximum solid solubilities for the Cu‐Ag system are within 1% of the F‐D calculations.