Diffusion–reaction of aluminum and oxygen in thermally grown Al2O3 oxide layers

The diffusion–reaction of aluminum (Al) and oxygen (O), to form thermally grown oxide (TGO) layers in thermal barrier coatings (TBCs), is studied through an analytical model. A nonsymmetrical radial basis function approach is used to numerically solve the mass balance equations that predict the TGO growth. Correct boundary conditions for the Al and O reactions are laid out using scaling arguments. The Damkohler number shows that the O–Al reaction is several orders of magnitude faster than diffusion. In addition, a comparison between aluminum and oxygen diffusivities indicates that TGO growth is governed by aluminum diffusion. The results are compared with experimental measurements on air plasma spray-deposited TBCs treated at 1,373 K with exposure times ranging from 1 to 1700 hours. We found that, for several time decades, the thickness of the thermally grown layer has power law dependence of time with an exponent of ½, following the diffusion control mechanism. At later times, however, the presence of other oxides and additional kinetics modify the diffusive exponent.