Analysis of experimental results by the Havriliak–Negami model in dielectric spectroscopy

The problem of identifying experimental results on studying frequency dependences of the real and imaginary parts of dielectric permittivity concerning the correspondence to one of accepted frequency dispersion models: Debye, Cole–Cole, Davidson–Cole, and Havriliak–Negami models is considered. Based on expressions for components of complex dielectric permittivity with the use of mathematical analysis, a sequence of steps for the determination of the following characteristic parameters of the generalized Havriliak–Negami model is developed: static $\varepsilon_ S$ and high-frequency $\varepsilon_\infty$ dielectric permittivity, frequency dispersion indices $\alpha$ and $\beta$, and relaxation time $\tau$. As an example, the parameters $\varepsilon_{S}$, $\varepsilon_\infty$, $\alpha$, $\beta$, and $\tau$ are calculated for a sample of a frozen disperse medium based on fine-grained quartz powder at a humidity of 13% in a temperature range from –140 to 0$^{\circ}$C.