[论文解读] Thermodynamics and its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives

Zi‐Kui Liu|arXiv (Cornell University)|Jan 5, 2023

Advanced Thermodynamics and Statistical Mechanics被引用 4

一句话总结

本文提出了一种统一框架，通过‘zentropy理论’将密度泛函理论（DFT）与统计力学相结合，实现了对非平衡态以外热力学性质的预测性CALPHAD建模。通过用DFT计算的吉布斯自由能替代经典内能，并在非平衡系统中引入熵产生，该方法为相稳定性和动力学建模建立了热力学一致的基础，具有对角化的动力学系数和明确的昂萨格倒数关系。

ABSTRACT

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system. With the quantum mechanics (QM) developed, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau. The development of density function theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager and Prigogine and co-workers. The digitization of thermodynamics was developed by Kaufman in the framework of the CALPHAD modeling of individual phases. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. Furthermore, through the combined law of thermodynamics with the entropy production as a function of internal degrees of freedom, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena represented by the phenomenological Onsager reciprocal relationships are due to the dependence of the conjugate potential of the molar quantity in a flux on nonconjugate potentials.

研究动机与目标

• 将基于DFT的量子力学预测（通过DFT）与统计热力学统一，以改进相稳定性建模。
• 通过引入内部过程产生的熵产生，解决经典热力学在非平衡系统中的局限性。
• 开发一种预测性CALPHAD框架，通过整合DFT计算的吉布斯自由能，将模型扩展至非平衡状态。
• 通过动力学系数中的共轭与非共轭势的依赖关系，阐明昂萨格倒数关系的物理起源。
• 为材料中亚稳态和不稳定态的建模建立热力学一致的基础。

提出的方法

• 通过用各构型的DFT预测吉布斯自由能替代内能，提出‘zentropy理论’。
• 应用包含熵产生作为内自由度函数的热力学联合定律。
• 推导出动力学系数矩阵相对于共轭势为对角化，从而阐明交叉现象的起源。
• 利用共轭势对非共轭变量的依赖关系，解释昂萨格倒数关系。
• 通过统计力学建立从量子力学DFT计算到宏观热力学行为的联系。
• 通过引入不可逆过程，将经典吉布斯-杜海姆方程扩展至非平衡系统。

实验结果

研究问题

• RQ1 如何系统性地将DFT预测的吉布斯自由能整合到统计热力学中，以改进相稳定性预测？
• RQ2 熵产生在非平衡系统中的作用是什么？如何在热力学框架内一致地建模？
• RQ3 昂萨格倒数关系为何出现？它们与共轭势对非共轭变量的依赖关系有何关联？
• RQ4 在热力学力与通量的背景下，如何实现动力学系数矩阵的对角化？
• RQ5 将CALPHAD建模扩展至非平衡条件的理论基础是什么？

主要发现

• Zentropy理论通过用DFT计算的吉布斯自由能替代经典内能，成功将基于DFT的电子结构计算与统计热力学统一。
• 证明了动力学系数矩阵相对于共轭势是对角化的，表明交叉效应源于非共轭势的依赖关系。
• 昂萨格倒数关系被解释为共轭势对非共轭变量依赖的结果，而非源于内在对称性。
• 该框架通过引入非平衡热力学贡献，实现了对亚稳态和不稳定相的预测性建模。
• 该理论通过将熵产生作为内自由度的函数，一致地将热力学联合定律扩展至非平衡系统。
• 该方法为下一代包含动力学和非平衡效应的CALPHAD建模建立了严格的热力学基础。