*Article* **Third-Generation Thermodynamic Descriptions for Ta-Cr and Ta-V Binary Systems**

**Enkuan Zhang <sup>1</sup> , Xinpei Xu <sup>1</sup> , Yun Chen <sup>2</sup> and Ying Tang 1,\***


**Abstract:** The third-generation thermodynamic descriptions for Ta-Cr and Ta-V binary systems were performed to construct the reliable thermodynamic database for refractory high-entropy alloys (RHEAs) containing Laves phase. The third-generation Gibbs energy expressions of pure Cr and V in both solid and liquid phases were established, from which the thermodynamic properties and thermal vacancy can be well described. The thermodynamic descriptions of Ta-Cr and Ta-V over the whole composition and temperature regions were carried out based on the reviewed phase equilibria and thermodynamic data with the CALPHAD (CALculation of PHAse Diagrams) approach. Specifically, the thermodynamic parameters of C14 and C15 Laves phases were evaluated by combining the theoretically computed and experimentally measured thermodynamic properties as well as the semiempirical relations. The calculated phase diagrams and thermodynamic properties in Ta-Cr and Ta-V systems according to the present thermodynamic parameters had a nice agreement with the experimental data even down to 0 K, indicating the reliability of the present modeling.

**Keywords:** third-generation thermodynamic description; Ta-Cr system; Ta-V system; CALPHAD; Laves phase
