Mathematical State Function Structure Matters in Metal Oxide Reduction Thermodynamic Modeling

Area of Science:

• Materials Science
• Thermodynamics
• Computational Modeling

Background:

• Thermodynamic modeling often assumes equivalent physical insight from mathematically identical state function formulations.
• The structural form of state functions can influence solution robustness, parameter identifiability, and physical interpretability.
• Compound Energy Formalism (CEF) provides rigor but faces challenges due to high-dimensional parameter spaces and finding unique global minima.

Purpose of the Study:

• To investigate how structurally distinct but mathematically equivalent state function formulations affect thermodynamic model robustness and extracted data.
• To identify formulation-dependent failure modes and establish criteria for robust, physically meaningful thermodynamic models.
• To evaluate the influence of different free energy expansions on enthalpy and entropy stability within the CrossFit CEF (CF-CEF) framework.

Main Methods:

• Systematic comparison of two distinct Gibbs free energy formulations under identical data, constraints, and optimization frameworks.
• Utilized the CrossFit CEF (CF-CEF) method, integrating experimental and first-principles data for the (Ba,Sr)FeO3-δ (BSF) perovskite system.
• Evaluated model performance across various optimizers, parameter initializations, and normalization strategies.

Main Results:

• The choice of state function form significantly impacts enthalpy and entropy stability.
• A simpler three-parameter expansion (ΔG = G° + BT - ATln(T)) exhibited high susceptibility to parameter compensation.
• The thermodynamically equivalent expansion (ΔG = H° + (A - S°)T - ATln(T)) consistently yielded more robust and physically intuitive results across different optimization methods.

Conclusions:

• The mathematical construction of state functions is as critical as data quality for reliable thermodynamic modeling.
• The formulation ΔG = H° + (A - S°)T - ATln(T) is recommended for future thermodynamic CF-CEF models due to its improved robustness and interpretability.
• This study provides criteria for developing thermodynamically meaningful and numerically robust models by carefully selecting state function structures.