From heat capacity to Gibbs energy: An experimental thermodynamic route for single-phase high-entropy alloys

A comprehensive experimental methodology was developed to determine the thermodynamic functions of single-phase Al_xCoCrFeNi high-entropy alloys (HEAs). The approach integrates calorimetric measurements, thermophysical characterization, and physically based entropy models. Low-temperature heat capacities, C_p(T), were measured between 4 and 473 K, while high-temperature C_p(T) values were determined near the solidus temperature. Controlled interpolation across decomposition regions enabled the construction of metastable C_p(T) functions over the entire temperature range. The enthalpy of formation at 298 K, H_f,elem⁰(298K), was determined by high-temperature oxide melt solution calorimetry and combined with the measured C_p(T) data to derive temperature-dependent enthalpy functions, ΔH_T(T). The configurational entropy, S_conf, was calculated using the ideal solid-solution model for the FCC alloys, whereas for the B2 alloys it was estimated from CALPHAD-predicted sublattice occupancies (TCHEA8 database) due to the absence of experimental methods capable of directly determining site-specific compositions. The thermal entropy contribution, ΔS_thermal(T), was obtained by integrating C _p( T )/ T , and combined with S_conf to generate Gibbs energy functions, ΔG_T(T), for each single-phase alloy. For the FCC alloy, the experimentally derived ΔG_T(T) values are in good agreement with the TCHEA8 predictions. In contrast, the B2 alloys exhibit significant deviations from the CALPHAD description, reflecting discrepancies in both C _p( T ) and entropy. Nevertheless, the overall temperature dependence and magnitude of ΔG_T(T) are reproduced reasonably well. This work establishes an experimentally grounded framework for determining Gibbs energy functions in complex alloys and provides valuable benchmarks for the development and validation of CALPHAD databases.