The linear diffusion equation was proposed to provide a macroscopic description of ionic mobility in nanostructures. This approach was shown to account for diffusion processes in nanostructured titania-based films. The formulation of a classical diffusion inverse problem and the experimental determination of concentration profiles by Rutherford back-scattering spectrometry were used for this purpose. The model allowed the measurement of the diffusion coefficient of W and Mo impurities in titania.

Diffusion-Equation Approach to Describe Ionic Mobility in Nanostructured Titania. Guidi, V., Martinelli, G., Schiffrer, G., Vomiero, A., Della Mea, G., Comini, E., Ferroni, M., Sberveglieri, G.: Physical Review B, 2005, 72[15], 155401