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An Octave based script for solving defect thermodynamic model to generate Brouwer diagram of triple conducting perovskite as a function of temperature, P(O2)/P(H2O), or P(H2)/P(H2O) based on nonstoichiometry dependent defect formation energies and entropies.
Distinct from the proton defect, the hydride defect species may be present in certain perovskite materials in reducing environments such as in fuel electrodes of solid oxide cells (SOCs) or on the reducing side of ceramic membranes. A generalized defect thermodynamic model was developed for the triple-conducting perovskites (La,Ba)Fe 1-x M x O 3-δ (M = Y and Zr) to allow inclusion of the hydride defect formation reaction in addition to the other three main defect reactions, namely, the oxygen vacancy formation, hydration, and charge disproportionation reactions. This comprehensive defect model also allows the incorporation of polynomial functional forms of oxygen nonstoichiometry δ to describe the defect reaction energies and entropies and to enable refinements of the defect reaction equilibrium constants in the defect thermodynamic analysis. As a first step, the developed model is applied to the Ba 0.95 La 0.05 FeO 3-δ material as an illustrative system to obtain its Brouwer diagrams with both the proton and hydride defects in relevant SOC conditions, particularly for more reducing environments. In conclusion, the results provide direct guidance on the influence of electronic and ionic defect concentrations upon thermodynamic properties and ultimately on the performance of Ba 0.95 La 0.05 FeO 3-δ and potentially other (La,Ba)Fe 1-x M x O 3-δ perovskite materials involved in SOC applications.
A modeling tool of the defect thermodynamics of (La,Ba)Fe1-xMxO3-δ perovskites which includes energetic information about oxygen vacancy formation, hydration, hydride formation, and charge disproportionation reactions has been developed1. This tool incorporates defect energies and entropies expressed as sixth order polynomial functions to allow refinements of the defect reaction equilibrium constants in the thermodynamic analysis. Calculation of (La,Ba)Fe1-xMxO3-δ Brouwer diagrams as a function of pO2/pH2O and pH2/H2O in a range of temperatures of interest is facilitated by this modeling tool. The results obtained can provide direct guidance how the electronic and ionic defect concentrations of the triple conducting perovskite materials can be used to optimize performance of solid oxide cells for energy applications. The impact of magnetic and electronic structures of the perovskites on the defect reaction energies and entropies as obtained from density function theory modeling and the role played by hydride defect species will also be discussed.
Both electron-rich and electron-poor perovskite oxides have been used in solid oxide cell applications as electrode and electrolyte materials. The rich oxygen defect chemistry and its coupling to temperature, hydrogen-steam or oxygen-steam gas pressure, or to the applied potentials creates enormous complexities for modeling performance and degradation of the materials. Herein, density functional theory-based thermodynamic modeling was carried out to describe the defect chemistry and transport properties of the proton-conducting electrolyte BaZr1-xYxO3-δ (x≤0.1) and of the triple-conducting perovskite (La,Ba)(Fe,M)O3-δ (M=Y and Zr). The defect thermodynamics of intrinsic point defects and the hydrogen-related defect reactions were solved in integrated defect models and further used to predict the Brouwer diagram and the transport properties of the functional perovskites. For the electron-poor electrolytes BaZr0.9Y0.1O3-δ, the developed model has been used to describe the experimental transport properties in the SOC operating conditions. Specifically, the roles played by the acceptor-bound holes and the intrinsic and hydrogen point defects upon the conductivities of holes, protons, and oxygen vacancies under the hydrogen-rich and oxygen-rich conditions at various humidity levels were demonstrated. A defect modeling tool was also developed for the triple-conducting perovskite (La,Ba)(Fe,M)O3-δ (M=Y and Zr) to examine magnetic effects and hydride defects in defect equilibria.