A Defect Interaction Model: A Theoretical Approach to Proton Conductivity in K₃H(SeO₄)₂ from the Ferroelastic Phase to the Superprotonic Transition

In this work, we propose, to the best of our knowledge, the first model of interactions following a probability distribution that effectively fits the experimental conductivity data of a member of the superprotonic conductor family, Me₃H(AO₄)₂. This study provides critical insights into the temperature-dependent proton conductivity in the electrolyte K₃H(SeO₄)₂ (TKHSe), particularly in phase II below the transition temperature, T_t, and during the sharp conductivity surge at T_t. Proton conductivity was characterized using impedance spectroscopy, and a modified phenomenological model of cooperative defect interactions was applied to fit the data. This model employs a trial free energy density as a function of the η parameter, which relates to proton carrier density. By solving the transcendental equation for η, we determine a critical probability of site occupancy, p_c, interpreted as the threshold for the onset of proton conductivity. The observed conductivity behavior is attributed to the increase in Frenkel defects as p progresses from p_c to p = 1, explaining the abrupt conductivity transition. Our theoretical predictions align with experimental data from both heating and cooling runs, validating the model’s ability to capture the first-order transition and accurately fit conductivity as a function of temperature for Tt and at T_t. Based on Frenkel defect formation, this probabilistic approach provides novel insights into the conductivity mechanisms of solid-state proton conductors, such as the Me₃H(AO₄)₂ crystal family. The model’s success in fitting experimental data underscores its potential for advancing the understanding of proton conduction in solid-state materials. Furthermore, this approach offers valuable insight for designing and optimizing solid electrolytes in fuel cell applications, bridging fundamental physics with practical technological advances to address critical needs in energy technology.