1、材料热力学作业论文翻译材料热力学作业材料与能源学院材料工程xxx学号xxx文章来源：ElectrochimicaActa 214 (2016) 56-67A Combined Thermodynamics & Computational Method to Assess Lithium Composition in Anode and Cathode of Lithium Ion Batteries锂离子电池正极与负极锂成分的热力学计算方法Wenyu Zhang, Lianlian Jiang, Pauline Van Durmen, SomayeSaadat, RachidYazamiEne
2、rgy Research lnstituteNTU (ERIAN), Nanyang Technological University, 1 Cleantech Loop, CleanTech One, #06-04, Singapore 637141, SingaporeABSTRACTWith aim to address the open question of accurate determination of lithium composition in anode andcathode at a defined state of charge (SOC) of lithium io
3、n batteries (LIB), we developed a methodcombining electrochemical thermodynamic measurements (ETM) and computational data fittingprotocol. It is a common knowledge that in a lithium ion battery the SOC of anode and cathodediffer fromthe SOC of the full-cell. Differences are in large part due to irre
4、versible lithium losses within cell and to electrode mass unbalance. This implies that the lithium composition range in anode and in cathode during full charge and discharge cycle in full-cell is different from the composition range achieved in lithium half-cells of anode and cathode over their resp
5、ective full SOC ranges. To the authors knowledge there is no unequivocal and practical method to determine the actual lithium composition of electrodes in a LIB, hence their SOC. Yet, accurate lithium composition assessment is fundamental not only for understanding the physics of electrodes but also
6、 for optimizing cell performances, particularly energy density and cycle life.摘要这个开放性的课题旨在解决在给定的锂离子电池（LIB）的充电状态（SOC）下准确测定阳极和阴极的锂化合物组成的。我们开发了一种电化学热力学测量（ETM）与计算数据拟合相结合的方法。众所周知，半锂离子电池中的阳极和阴极的与锂电池不同。这种差异在很大程度上是由于电池内不可逆的锂损失和电极质量的不平衡。这意味着，在电池的充放电循环期间，在阳极和阴极中的锂化合物的组成与半电池的阳极和阴极锂化合物的组成是不同的。据作者所知，还没有有效的方法来确定半
7、电池的实际锂化合物的组成。然而，测量准确的锂电极的成分的对于了解电极的物理变化、优化电池的性能（特别是能量密度和循环寿命）是十分重要的。In this study thermodynamics data, including open-circuit potential (OCP), entropy (S) and enthalpy (H) are collected on full-cells and on their derived lithium half-cells. Fundamentally, the thermodynamics data of a full-cell is th
8、e arithmetic difference between the corresponding data of cathode and anode achieved in half-cells. However, as we show here misfits exist between experimental data and the arithmetic difference indicating cells data depart from theory. Misfits were significantly reduced by applying linear transform
9、s to the half-cells data and by iterative computational method. The fitting parameters are adjusted independently for anode and cathode to minimize differences between experimental and computed thermodynamics data. This method enables accurate Li composition in anode and cathode over the full SOC ra
10、nge of the full-cell to be assessed. It is found that both anode and cathode in the full-cell operate under lower Li composition ranges than those achieved in half-cells, which significantly reduces the full-cell energy density. Moreover, the effect of full-cell cycle ageing at the ambient and high
11、temperatures on electrodes composition is investigated independently for anode and cathode so as to understand their respective contribution to l capacity losses.在这项研究中要收集的热力学数据包括锂电池和半锂电池的开路电位（OCP），熵（S）和焓（H）。一般来说，锂电池的热力学数据就是充电中的电池的阴极和阳极的相应数据间的算术差。然而，我们在这里展示的实验数据和理论数据存在差异。通过线性变换在半电池数据中的应用和迭代计算方法，异常数据
12、显著降低。阳极和阴极的拟合参数被独立调整，目的是尽量减少实验和计算热力学数据之间的差异。这种方法可以准确的测出在阳极和阴极的锂化合物在充电和放电过程中的成分。据发现，锂电池的阳极和阴极比半锂电池的电池Li化合物的含量更低，这显着降低了电池的能量密度。此外，为了找出锂电池能量密度降低的原因，研究人员调查了阳极和阴极老化和高温造成的影响。1. IntroductionLithium ion batteries (LIB) are currently the main power source in a wide range of applications including mobile elec
13、tronics, electric vehicles and in stationary energy storage 1,2. During charge and discharge lithium ions are shuttled between anode and cathode through the electrolyte owing to lithium intercalation/de- intercalation and/or alloying/de-alloying electrode processes. Accordingly, lithium composition
14、in anode and cathode varies with cells SOC In an ideal cell design the SOC of anode, cathode and full-cell should be equal to maximize energy storage performances. In practical cells, however, the SOC matching is hard to achieve mainly because of: 1) electrode processes causing irreversible active l
15、ithium losses such as formation (and reformation) of a solid interphase electrolyte (SEI) on the surfaces of anode and following thermal ageing, trapped lithium, active material electrical disconnection, and 2) unbalanced anode and cathode active masses in cell starting from inception. Irreversible
16、lithium losses cause the full-cell, hence anode and cathode to become lithium deficient. Therefore, lithium composition range in anode and cathode in the full-cell departs from the one achieved in halfcells.1引言锂离子电池（LIB）目前被广泛应用于移动电子产品、电动汽车和能源存储1,2。锂离子充放电过程就是电子在阴极与阳极之间穿梭的过程。因此，在理想电池设计中，阳极和阴极中的锂化合物的成分
17、随电池充电状态的变化而变化，半锂电池的阳极、阴极和锂电池的最大化的储能性能应该匹配。然而在实际的操作中，充电状态匹配很难实现，主要是因为：1）电化学过程中的不可逆损失，比如在阳极表面的固体电解质界面（SEI）发生老化后，锂失活、活性材料电气断开，2）阳极和阴极反应的不平衡。电池产生了不可逆的锂损失，导致阳极和阴极都失去了锂。因此，锂电池中阳极和阴极的锂成分范围与理论值偏离。Typically, lithium half-cells contain excess metallic lithium so as to fully charge and discharge the working el
18、ectrode (anode or cathode). Excess lithium also compensates for lithium lossesduring cycling and ageing. In half-cells the SOC of the working electrode is usually determined by Coulomb counting and voltage measurements the lithium being used as a counter and a reference electrode. Commercial full-ce
19、lls, however, are two-electrode cells which voltage is the difference between cathode and anode voltages. Full-cells voltage reading doesnt teach on individual electrode voltages therefore, not on their composition. Should a reference electrode be used, the voltage-composition relationship is not un
20、equivocal since for example electrodes such as the graphite anode and the lithium iron phosphate cathode show voltage plateaus over a wide range of lithium composition.通常情况下，锂电池含有多余的金属锂，以便工作电极（阳极或阴极）的完全充电和放电。过量锂也补偿循环和老化过程中锂的损失。在电池的充电过程中，工作电极通常是用计数器和参考电极确定库仑计数和电压测量。商业化的电池有两个电极，电池的电压是阴极和阳极电压之间的差异。正确的电
21、池的电压读数并不是两个电极的电压之差。电压关系是不明确的，例如石墨正极和磷酸铁锂正极正极材料，所以应该使用参比电极。Electrochemical thermodynamics measurements technique (ETM) was introduced by us over a decade ago and has since cells 3-6. In ETM the temperature is used as additional parameter enabling entropy and enthalpy profiles to be achieved.我们在十多年前介绍
22、过电化学热力学测量技术（ETM）3-6。在ETM中，温度作为额外的参数使熵和焓分布实现。A new combined ETM and computational technique will be introduced in this work with aim to determine the actual lithium composition in anode and cathode at any SOC of the full-cell. Thermodynamics data are collected on anode and cathode half-cells and then
23、 data are processed in order to best fit the experimental data on full-cell. ETM data including open-circuit potential (OCP), entropy (S) and enthalpy (H) are processed independently with same fitting parameters so as to minimize differences between experimental and computed data, thus accurately re
24、vealing lithium composition in anode and cathode.一种新的ETM组合和计算技术将引入这项工作，旨在确定在任何状态下的电池阳极和阴极的锂的组成。对半锂电池阳极和阴极的热力学数据进行收集，然后进行数据处理，目的是找出满足电池使用的最适合的实验数据。ETM数据包括都经过独立处理和参数拟合的开路电位（OCP），熵（S）和焓（H），以减少实验数据和计算数据之间的差异，从而准确地揭示在阳极和阴极的锂化合物组成。2. Principles of the combined ETM-computational method2.1. The linear trans
25、form (ushift and stretchn)2 结合ETM的计算方法原理2.1线性变换（ushift和stretchn）At a defined SOC of a full-cell，Xcf，cells OCP,，equals the difference between the cathode (ca）and anode (an）potentials at their respective SOC, XcaandXan:定义：锂电池为xcf，电池的OCP为，阴极和阳极在各自的充电潜力，使用Xca和Xan表示：In half-cell OCP relates to free energ
26、y G of cell reaction according to:半锂电池的OCP涉及自由能G电池反应where n = number of exchanged electron per mole (n = l for lithium).The SOC of an optimized full-cell should be equal to the SOC of each electrode:其中n =每摩尔的交换电子数（锂）。一个完整的电池的SOC应等于每个电极的SOC：(“100-Xan” formula applies because anodeand cathode havecomp
27、lementary SOC in the full-cell.)The free energy relates to enthalpy () and entropy S(X) according to:Deriving Eq. (5) vs. T yields S and according to:By combination of the above equations, one gets:通过上述方程的组合，得到：Practical full-cells most of the times depart from optimized electrode mass balance and i
28、ncur lithium losses; therefore, Eqn. (4) doesnt apply. In order to determine the actual SOC of anode and cathode at a well-defined SOC of the full-cell, our approach here consists of fitting OCP, S and H data of full-cells and half-cells by applying a linear transform ofXcaandXan vs. Xfc, process ca
29、lled shift and stretch according to:实用的完整的锂电池大多数时候偏离电极的质量平衡，招致锂的损失；因此，Eqn（4）不适用。为了确定一个明确的全电池的阳极和阴极的实际SOC，我们这里的做法是由拟合锂电池OCP，S和H的数据，运用xCa、Xan和Xfc线性变换，一个称为“移动”和“拉伸”的过程。Let H1 be a lithium host electrode structure. The electrode reaction can be schematized as:The electrode theoretical specific capacity
30、(mAh/g), qth is given by Eq. (13):电极的理论比容量（mAh/g），qth是由Eq.给出（13）：where F = Faraday constant (96500 C) and M(H) = molecular mass of H (g/mole).AssumingXmaxandXmincorrespond respectively to 100% and 0%SOC of electrode H the relationship between SOC X and Li composition X is given by:F =法拉第常数（96500 C）和
31、M（H）= 氢的分子质量（克/摩尔）。假设Xmax、Xmin分别对应于锂含量为100%和0%的电极：Should 100% and 0% SOC correspond toXminandXmax, respectively, Eq. (14) becomes:充电状态下锂含量为100%和0%的Xmin和xmax，分别为式（14）：Eq. (14) and (14) will be used to convert SOC to lithium composition in anode and cathode, respectively.Eq.（14）和（14）将被用来分别计算充电状态下阳极和阴极
32、的锂组成。2.2. Fitting parameters assessmentIn order to verify the effectiveness of the proposed shift and stretch method, five sets of data OCP vs. SOC, S vs. SOC, S vs. OCP, H VS. SOC and H vs. OCP are used to compute the four parametersof Eqns. (10) and (11). The purpose of the curve fitting is to find the optimal values of these four parameters by shifting and stretching the curve of cathode and anode so that the reformed curves in full cell can match with its measured values for entropy, entha
