An efficient method of calculating composition-dependent inter-diffusion coefficients based on compressed sensing method

Composition-dependent inter-diffusion coefficients are key parameters in many physical processes. Due to the under-determinedness of the governing diffusion equations, numerical methods either impose strict physical conditions on the samples or require a computationally onerous amount of data. To address such problems, we propose a novel inverse framework to recover the diffusion coefficients using a compressed sensing method, which in principle can be extended to alloy systems with arbitrary number of species. Comparing to conventional methods, the new approach does not impose any priori assumptions on the functional relationship between diffusion coefficients and concentrations, nor any preference on the locations of the samples, as long as it is in the diffused zone. It also requires much less data compared to least-squares approaches. Through a few numerical examples of ternary and quandary systems, we demonstrate the accuracy and robustness of the new method.