Abstract
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.
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