Modeling of the impedance data of gadolinia doped ceria based actuators: a distribution function of relaxation times and machine learning approach

Abstract

Gadolinia-doped ceria is one of the most extensively examined oxide ion conductors to exhibit large nonclassical electrostriction. The electromechanical response depends on the grain and grain boundaries which can be probed using electrochemical impedance spectroscopy. In this study, we have modeled the impedance spectra from buckled and free standing gadolinia doped ceria (Gd0.2Ce0.8O1.9) membrane in Al/Ti/Gd0.2Ce0.8O1.9/Ti/Al electromechanical device, at different AC excitation voltages (2, 4, 6, 8 and 10 V), and starting from room temperature to 100 °C. The analysis of impedance spectrum is commonly done by equivalent circuit modeling to obtain the resistors () and capacitors (). However, to overcome the inherent problems like non-uniqueness, over fitting, presently different approaches have been chosen such as impedance spectroscopy genetic programming (ISGP) and artificial neural networks (ANNs). ISGP finds an analytic form of the distribution function of relaxation times (DFRTs) using impedance spectra. The DFRT analysis reveals that the grain boundary capacitance for the membrane ∼10−8–10−9 F decreases with increasing temperature and excitation voltages. Besides, neural networks, which are optimized by Bayesian regularization, simulate both the real and imaginary parts of impedance following the pattern of experimental data up to several Hz. The DFRT analysis on this simulated impedance data shows an effect of grain boundaries. Indeed, ANNs as optimized by Levenberg-Marquardt method, can estimate the and ’s for present system with maximum relative errors of 24% and 22%, respectively.