Error Propagation in the Estimate of Surface Free Energy Components by Nonlinear Best Fitting

The problem of error propagation in the estimate of material components for quadratic multicomponent surface free energy theories is addressed. It is shown that invariance properties of the model equations, through an appropriate group of linear transformations, imply a very peculiar structure of any merit function used for general best-fit estimates of surface free energy components in quadratic multicomponent models. Such a structure is reflected in the distribution of merit-function minima, involved in the calculation of best fit estimates to surface free energy components, according to the nonlinear method. A simple and reasonable stategy allows to describe the displacement of minima due to uncertainties on experimental data, and therefore to evaluate the consequent error propagation on the final results.