Susceptibility functions for disordered materials: the full width at half maximum for different frequency and time representations

We here propose relations that provide a convenient way to obtain, from curve-fit parameters, the full width at half maximum (FWHM), which is one of the fundamental parameters in the scaling procedure for relaxations in disordered materials proposed by Dixon et al. We derive an analytical expression for the FWHM for symmetric loss peaks using a newly proposed response function. Since the response function contains e.g. the Cole–Cole and the Fouss–Kirkwood expressions as special cases, exact analytical expressions of the FWHM is also obtained for these functions. For asymmetric loss peaks, approximations are introduced and we show that the errors for the obtained functions are less than 6%. Furthermore, we propose an approximate relation between the stretching parameter, β, of the Kohlrausch–Williams–Watts function and the FWHM.