Charge carrier relaxation in YSZ and CaSZ single crystals: In search of the analytic representation of DRT

Abstract The Python applications using the least-square solver for a non-negative solution and Tikhonov regularization were applied for finding the distribution function of relaxation (DRT) times. The impedance data which represent the process of charge carrier relaxation in the bulk of 10 mol%Y2O3–90 mol%ZrO2 and 15 mol%CaO– 85 mol%ZrO2 single crystals herewith the minor influence of the interfacial polarization was separated from experimental data sets and distribution function of relaxation times (eDRT) were found. The obtained eDRT was used to fit parameters of skewed normal, Weibull, and Johnson SU continuous probability density functions (PDFs). The experimental datasets were also used to fit parameters of two equivalent circuits, which allowed to derive the distribution function of relaxation times (cDRT) from noiseless data. Noteworthy that obtained cDRT showed a significant difference from eDRT. The spectra of various electrical properties were reconstructed from both kinds of DRTs as well as from PDFs and were compared. The Johnson SU function stood out by describing the electrical response of charge carrier relaxation very well. It reproduced not only the impedance spectra but also all peculiarities of spectra of various electrical parameters: the dependence of AC conductivity close to the power-law, a linear relationship between the real and the imaginary parts of electric modulus in the high-frequency range, and the bend of dielectric permittivity in the middle frequencies.