A constructive approach to the theory of diffusion processes was proposed which was based upon the application of both symmetry analysis and the method of modelling functions. An algorithm was suggested, for the construction of the modelling functions, which was based upon the error function expansion of experimental concentration profiles. The highly accurate analytical description of the profiles, provided by error function expansion approximation, permitted a convenient extraction of the concentration dependence of the diffusivity, from the experimental data, and a prediction of the diffusion process. The analysis was demonstrated via its use in treating experimental results which had been obtained for the surface diffusion of lithium on the molybdenum (112) surface pre-covered with dysprosium. The error function expansion approximation could be directly extended to many other diffusion systems.

Symmetries and Modelling Functions for Diffusion Processes. A.G.Nikitin, S.V.Spichak, Y.S.Vedula, A.G.Naumovets: Journal of Physics D, 2009, 42[5], 055301