Symmetries and modelling functions for diffusion processes

Details Symmetries and modelling functions for diffusion processes Symmetries and modelling functions for diffusion processes

2008-08-15

arxiv.org/abs/0808.2177v2

Journal of Physics D: Applied Physics (2009) Volume 42, Number 5 055301

Physics

Data Analysis, Statistics and Probability

19 pages, 8 figures

Scientific paper

10.1088/0022-3727/42/5/055301

A constructive approach to theory of diffusion processes is proposed, which is based on application of both the symmetry analysis and method of modelling functions. An algorithm for construction of the modelling functions is suggested. This algorithm is based on the error functions expansion (ERFEX) of experimental concentration profiles. The high-accuracy analytical description of the profiles provided by ERFEX approximation allows a convenient extraction of the concentration dependence of diffusivity from experimental data and prediction of the diffusion process. Our analysis is exemplified by its employment to experimental results obtained for surface diffusion of lithium on the molybdenum (112) surface pre-covered with dysprosium. The ERFEX approximation can be directly extended to many other diffusion systems.

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