标题： 电极的化学和电化学热力学的统一 显示英文标题

标题： Unifying Chemical and Electrochemical Thermodynamics of Electrodes

摘要： 电池对于电动交通和航空至关重要，但电极材料的热力学理解仍然不足，这从开路电压（OCV）模型经常违反热力学第二定律的现象中可以看出。 另一方面，热力学建模很少利用电化学数据，如OCV、熵热（dOCV/dT），这些数据包含丰富的热力学信息。 本工作引入了一种用于电化学能量存储材料的热力学建模框架，使用可微编程和热力学参数的基于梯度的优化。 使用一种考虑声子态密度的改进的德拜模型，从实验测量的比热（$c_p$）以及声子态密度$g(\omega)$对纯物质的热力学进行建模。 混合的热力学通过测量的熵热和OCV数据进行建模。 我们通过正问题和反问题展示了可微分的热力学建模框架。 在正问题中，即给定热化学和电化学数据确定石墨负极的相图，我们表明除了准确再现LixC6的相图外，拟合的温度依赖性OCV在10$^\circ$C下测试集数据的平均绝对误差（MAE）达到3.8 mV，与在25$^\circ$C - 57$^\circ$C下测量的训练集数据的2.9-3.6 mV MAE相比。在反问题中，即从由热化学和电化学数据约束的相图中确定锂铁磷酸盐（LFP）正极的OCV，我们展示了LFP OCV以及相图的准确再现。 该框架为电极材料的化学和电化学热力学数据提供了统一的处理方式。 显示英文摘要

摘要： Batteries are critical for electrified transportation and aviation, yet thermodynamic understanding of electrode materials remains lacking, as indicated by the often-seen violation of the second law of thermodynamics of open-circuit voltage (OCV) models. On the other hand, thermodynamic modeling rarely utilizes electrochemical data such as OCV, entropic heat (dOCV/dT), which contains rich thermodynamic information. This work introduces a framework of thermodynamic modeling of materials for electrochemical energy storage, using differentiable programming and gradient-based optimization of thermodynamic parameters. Using a modified Debye model that accounts for the phonon density of states, the thermodynamics of pure substances is modeled from experimental measurements of specific heat ($c_p$) as well as the phonon density of states $g(\omega)$. Thermodynamics of mixing is modeled with measured entropic heat and OCV data. We demonstrate the differentiable thermodynamic modeling framework with forward and inverse problems. In the forward problem, i.e. determining phase diagram of graphite anode given thermochemical and electrochemical data, we show that in addition to accurate reproduction of phase diagram of LixC6, the fitted temperature-dependent OCV of graphite reaches 3.8 mV mean absolute error (MAE) for test set data measured at 10$^\circ$C, compared with 2.9-3.6 mV MAE for training set data measured at 25$^\circ$C - 57$^\circ$C. In the inverse problem, i.e. determining OCV of lithium iron phosphate (LFP) cathode from phase diagram constrained by thermochemical and electrochemical data, we demonstrate accurate reproduction of LFP OCV as well as phase diagram. This framework offers a unified treatment of chemical and electrochemical thermodynamic data for electrode materials.