A Bayesian approach to electrical conductivity relaxation and isotope exchange/secondary ion mass spectrometry

• Bayesian analysis of electrical conductivity relaxation
• Bayesian analysis of isotope exchange depth profiling
• Software is available; please contact the author.

A Bayesian method for interpretation of electrical conductivity relaxation and isotope exchange/secondary ion mass spectrometry data is presented and demonstrated on data appearing in the literature. The new method enables quantification of uncertainty due to data fitting in estimates for the effective surface exchange coefficient k* and the effective diffusion coefficient D*. The standard infinite series solutions to the semi-infinite diffusion problem with linearized chemical kinetics at the boundary are utilized, although the Bayesian technique does not depend on the existence of analytical solutions. The methodology is demonstrated in the analysis of data appearing in the literature, both for isotope exchange/secondary ion mass spectrometry and electrical conductivity relaxation. In particular, the utility of the technique in definitively resolving questions of parameter identifiability is demonstrated in a comparison of two literature studies on the same bulk material that lead to widely different estimated parameters using the standard nonlinear least squares fit.