Interdiffusion and phase formation in the Fe–TiO$_2$ thin-film system

The interaction of magnetron-sputtered metal iron with titanium–oxide films upon isothermal vacuum annealing is studied by X-ray phase analysis, secondary-ion mass spectrometry, atomic-force microscopy, and mathematical simulation. A mechanism for the formation of complex oxides at grain boundaries is suggested. The mechanism is based on the reaction diffusion of metal iron into titanium oxide. A quantitative model of reaction interdiffusion in two-layer polycrystalline metal–oxide film systems with limited component solubility is developed. From numerical analysis of the experimental distributions of the metal concentrations in the Fe–TiO$_2$ film system, the individual diffusion coefficients are determined. It is found that, under the conditions of vacuum annealing at 1073 K, the diffusion coefficients of iron and titanium are 8.0 $\times$ 10$^{-13}$ and 3.0 $\times$ 10$^{-15}$ cm$^2$ s$^{-1}$, respectively.