Diffusion in a semi-infinite system with a moving interface at constant temperature for application to α-zirconium oxidation at high temperature

Abstract

Many gas-metal reactions are closely related to gas migration through several solid phases generated during the reaction. Apart from the gaseous phase, which is invariant with time, a semi-infinite solid-subsystem is considered. This subsystem is formed by two phases separated by an interface parallel to the specimen surface (gas-metal interface). It is the first interface displacement which defines the features of the gas-solid reaction studied. The literature reports exact analytical solutions for the simplest initial and boundary conditions of the system. A numerical method is presented applicable to all diffusion equations of practical interest. The finite-difference method together with “parabolic interpolation” (FIDIP) are used to calculate simultaneously the gas concentration profile and the relative position of the above-mentioned interface as a function of time, and also to compute the different parameters of the system. The finite-solid case is later given as a particular example of the semi-infinite solid. An excellent agreement is found between the concentration profiles computed from analytical solutions and those derived from the finite-difference method with parabolic interpolation for isothermal reactions. It is encouraging enough and suggests that the numerical method could be particularly useful in studying similar systems in temperature transients, of more practical interest today.