The Impact of Variable Measurement Spacing in Concentration Profiles Used in Diffusion Experiments

In diffusion experiments, concentration profiles are typically measured by using regularly-spaced sampling locations along the diffusion penetration direction. This paper proposes an approach and justification for optimizing the sampling location plan so that uncertainties and errors in the measured diffusion coefficients are minimized. This method can also reduce the number of experiments necessary to determine the diffusion coefficient, proposing a new distribution in terms of the relevance that they have. This relevance is quantified using the covariance matrix for the concentration in terms of the diffusivity, which can also be related to the flux gradient in each point. Two cases of study were developed, for a constant and an instant source. Deviation coefficients for the determination of the diffusivity decreased from 18% (uniform distribution) to 14% (optimized distribution). This shows that the new distribution lowers the error in the determination of the diffusivity, using a procedure that is neither complex nor tedious. The methods and results presented can help researchers improve diffusion experiment design, and better quantify the quality of their data.