Publication date: 10th April 2024
Since 2014, we have suggested a superior description of the impedance of the polycrystalline solid electrolytes [1-4] compared to the brick-layer model heavily stained by constant-phase-elements (CPEs) in most applications. Time- and painstaking parameter determination from the individual fitting analysis hindered further progress. The recent dissemination of Python-based data science tools and AI assistance like ChatGPT allowed the layman to code the algorithms that fit up to hundreds of spectra or thousands of impedance data labeled with temperature values. We applied the techniques to various Li7La3Zr2O12 (LLZ) samples. In essence, the AC response of the polycrystalline electrolytes can be described by the additive electric polarization relaxations, which can be represented by Havriliak-Negami (HN) capacitance functions or generalized Debye models, originating from the mobile charge carriers by the current constriction effects at the grain boundaries and also in bulk. The capacitance magnitude is inversely proportional to the temperature, and the time constants are activated similarly to the ionic conductivity. All the data are thus collapsed to the single trace of the complex capacitance. The overall sample resistance of the grain and grain boundaries is connected in parallel. Temperature-independent geometric capacitance with nearly constant loss (NCL) can be identified only at cryostatic temperature. Low-frequency blocking effects by the inert metal electrodes can be best described by the transmission line model (TLM) with the longitudinal resistance and the Warburg-interfacial impedance parameter activated by higher activation energy alike than the bulk one. While the interfacial and transverse shunt capacitance is inversely proportional to the temperature, as for the polarizations in the sample, the presence of the temperature-independent double-layer capacitance is also noted, which can be put at the other terminal of the TLM for the electrode response. The exponents of the Havriliak-Negami capacitance functions, similar to the power exponents of CPEs, can be and need to be fixed, unlike the conventional CPE modeling, the physics of which is related to the universal dielectric relaxation phenomena or Kohlraush-Williams-Watt stretched exponential functions. It has been found the low-frequency and high-frequency limiting exponents of one or half can be widely applied [5], which corresponds to the ideal relaxation and the diffusion-related relaxations, respectively. Havriliak-Negami capacitance functions (DE31) and the transmission line models with the generalized Havariliak-Negami capacitance elements (DX26) have been implemented in ZView® for the convenient preliminary analysis of the individual spectra. The models are directly indicated in the raw data presented in AC conductivity Arrhenius plots and capacitance and admittance Bode plots, and hence, are physics-based. The models can be successfully applied to the extremely nontrivial individual impedance of the composite solid electrolytes with the percolating conducting components for the battery electrode applications. Surface or near-surface conduction often leads to flattened activation at lower temperatures. The short-circuit paths as parallel resistance hardly affect the capacitance relaxations in the present modeling, so the original AC response and the surface conduction can be determined and separated.
This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Ministry of Science and ICT (MSIT) (grant no. NRF-2018R1A5A1025224).