Abstract A new thermodynamic model based on the Einstein function with more physical significance is used to describe the hcp, bcc, fcc, ω, liquid and amorphous phases for Ti and V from above the melting point down to 0 K by the CALPHAD (CALculation of PHAse Diagrams) approach for the third generation thermodynamic databases. The liquid and amorphous phases are treated as one phase using the generalized two-state model. The Debye temperatures and the enthalpy differences at 0 K for different allotropes of Ti and V have been computed by ab initio calculations. The Ti–V system has been reassessed based on the new Gibbs energy functions for Ti and V obtained in the present work and experimental data available in the literature. The martensitic transformation and metastable ω phase formation in the Ti–V system at low temperature are thermodynamically described. The new description can better represent both the phase equilibria data and the temperatures of martensitic transformation and ω formation. The metastable phase diagram of the Ti–V system as well as the T0(β/α) and T0(β/ω) curves have been calculated using the obtained thermodynamic parameters. The calculated results indicate that most of the reliable experimental data are satisfactorily reproduced in the present modeling.

中文翻译：

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包括亚稳态 ω 相的 Ti-V 系统的新热力学模型

摘要 基于具有更多物理意义的爱因斯坦函数的新热力学模型被用来描述 Ti 和 V 从熔点以上到 0 K 的 hcp、bcc、fcc、ω、液相和非晶相通过 CALPHAD（计算PHAse Diagrams）方法用于第三代热力学数据库。使用广义二态模型将液相和非晶相视为一相。Ti 和 V 的不同同素异形体的德拜温度和 0 K 时的焓差已通过从头计算计算得出。基于当前工作中获得的 Ti 和 V 的新 Gibbs 能量函数和文献中可用的实验数据，对 Ti-V 系统进行了重新评估。热力学描述了低温下 Ti-V 系统中的马氏体转变和亚稳态 ω 相的形成。新的描述可以更好地表示相平衡数据以及马氏体转变和 ω 形成的温度。使用获得的热力学参数计算了 Ti-V 系统的亚稳态相图以及 T0(β/α) 和 T0(β/ω) 曲线。计算结果表明，大多数可靠的实验数据在目前的建模中得到了令人满意的再现。使用获得的热力学参数计算了 Ti-V 系统的亚稳态相图以及 T0(β/α) 和 T0(β/ω) 曲线。计算结果表明，大多数可靠的实验数据在目前的建模中得到了令人满意的再现。使用获得的热力学参数计算了 Ti-V 系统的亚稳态相图以及 T0(β/α) 和 T0(β/ω) 曲线。计算结果表明，大多数可靠的实验数据在目前的建模中得到了令人满意的再现。