Analysis of oxygen-18 tracer profiles in two-stage oxidation experiments (I): predominant oxygen diffusion in the growing scale

Abstract

Typical two-stage oxidation experiments in high-temperature oxidation studies on metals are analyzed. Two cases of predominant oxygen diffusion in the scale are studied: pure volume diffusion and simultaneous transport via grain boundaries and via the bulk. An analytical expression for the growth of the oxide layer is given for the assumption that the chemical potential of the oxygen varies linearly over the oxide layer. The numerical treatment of the differential equation is improved so that the calculation is possibly faster and/ or more accurate compared to a method given in the literature. The experimental profiles are described by four parameters, the grain boundary width, the grain radius, and the volume and grain boundary diffusivities. Two equations correlating these parameters can be extracted from the profiles. Two benchmark tests are described for testing the program. An analytical solution is presented which approximately describes the distribution of O-18 in the oxide layer for pure volume diffusion. Experimental SIMS profiles on Fe-Cr-Al alloys are explored on the basis of our calculation.