Mathematical modeling of internal oxidation

Internal oxidation is a process in which oxygen diffuses into an alloy and reacts with solute to form oxide precipitates internally. Although mathematical modeling of internal oxidation has been performed for decades, most models followed the classic work of Carl Wagner. His model assumes that the dissolved solute concentration is zero at the moving boundary between the internal oxidation zone and the unoxidized zone, an assumption that leads to the enrichment of solute in the internal oxidation zone. However recent work on local equilibrium at moving boundaries suggests that this assumption is in error for all cases. It follows that new models for internal oxidation are needed, ones that make use of different conditions at the moving interface, that provide a different explanation for enrichment, and that can explain other experimental results found in the literature, as well. The goal of this project is to create such mathematical models. ^ An Error Function Model (EFM) was derived first and used to simulate internal oxidation in the limit of small volume fractions of oxide and for cases when the initial alloy is unsaturated with oxygen. Then a more general finite difference model was created using DICTRA, a commercial finite difference software designed to simulate phase transformation, for cases when the initial alloy is saturated with oxygen. Although both models assume local equilibrium conditions, this is a reasonable assumption for internal oxidation at high temperature where there is sufficient thermal energy for rapid nucleation and growth. ^ Both models can predict concentration profiles, diffusion paths, and oxide volume fraction profiles that result from internal oxidation. The simulation results show that when oxide fraction decreases to zero near the moving boundary, the dissolved solute concentration is equal to the average concentration rather than zero as suggested by the classic model. These simulation results are supported with the experimental NiO volume fraction profiles measured in internally oxidized Cu-Ni alloys. The enrichment of Ni in internal oxidation zone is explained with the outward diffusion of Cu from internal oxidation zone to surface rather than the diffusion of Ni from unoxidized zone to internal oxidation zone as suggested by the classic model.