In the present work, the Al–Nb–V ternary system was thermodynamically modeled using the compound energy formalism (CEF) within the framework of the CALPHAD method and supported by ab initio calculations, which we report here for the first time. The thermodynamic descriptions of the Al–Nb, Al–V and Nb–V binary systems were taken from literature. Since it is not clear which is the best Al–V assessment available in the literature, three sets of thermodynamic parameters with three different thermodynamic descriptions of the Al–V system are proposed. End-member energies of Nb₃Al and Nb₂Al were obtained from first-principles electronic-structure calculations following the density functional theory (DFT). The optimized ternary parameters were based on experimental isothermal sections and liquidus projections data. The three sets of thermodynamic parameters show good agreement with experimental data. The new assessments successfully describe the miscibility gap between NbAl₃ and VAl₃ close to the Al–Nb system, the V solubility in Nb₃Al, the tie-triangles Nb₂Al-NbAl₃-BCC and NbAl₃-BCC-V₅Al₈, and the tie-lines between Nb₃Al and BCC. In this sense, our work provides self-consistent thermodynamic descriptions of the Al–Nb–V system which can be used for the development of thermodynamic databases of higher order systems for refractory high-entropy alloys (RHEAs).

在目前的工作中，Al-Nb-V 三元系统在 CALPHAD 方法的框架内使用复合能量形式化 (CEF) 进行热力学建模，并得到 ab initio 计算的支持，这是我们首次在此报告。Al-Nb、Al-V 和 Nb-V 二元系统的热力学描述取自文献。由于尚不清楚文献中可用的最佳 Al-V 评估方法，因此提出了三组热力学参数，其中包含对 Al-V 系统的三种不同热力学描述。Nb ₃ Al 和 Nb _{2 的}端元能量Al 是根据密度泛函理论 (DFT) 从第一性原理电子结构计算中获得的。优化的三元参数基于实验等温截面和液相线投影数据。三组热力学参数与实验数据显示出良好的一致性。新的评估成功地描述了接近 Al-Nb 系统的NbAl ₃和 VAl ₃之间的混溶性差距、V 在 Nb ₃ Al 中的溶解度、连接三角形 Nb ₂ Al-NbAl ₃ -BCC 和 NbAl ₃ -BCC-V ₅ Al ₈和 Nb ₃之间的连接线艾尔和密件抄送。从这个意义上说，我们的工作提供了 Al-Nb-V 系统的自洽热力学描述，可用于开发高阶耐火合金 (RHEA) 系统的热力学数据库。