Matlab implementation of inverse diffusion methods Afina LUPULESCU, Christopher O BRIEN, Martin GLICKSMAN, Wei YANG,

One of the authors (CJO) developed a MATLAB code called Inversemethods to determine concentration'dependent diffusivities from experimental data. This software allows comparison between the diffusivities calculated with four numerical methods: a) Boltzmann-Matano (BM), b) Sauer-Freise-den Broeder (SFB), c) Fictitious image'source method (error function approximation), and d) Fourier series image'source solutions. The choice of writing this code in MATLAB was meeting the requirements for portability, as MATLAB runs on various platforms and enables users to perform subsequent analyses on the data produced by this program. The BM and SFB methods are implemented following Simpson's rule to calculate the integrals, and employs a simple finite'difference method to calculate the derivatives. The software also implements a Savizky-Golay filtering algorithm that smoothes noisy penetration data by locally fitting a 3rd-order polynomial to 201 points. Such parameters were found to be most effective for noisy experimental data obtained using electron microprobe, proton-induced X-ray emission (PIXE), and Rutherford Back Scattering (RBS).