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基于Butler方程Al-Mg-Er三元合金表面张力的计算 被引量:7
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作者 孙顺平 易丹青 臧冰 《中国有色金属学报》 EI CAS CSCD 北大核心 2010年第5期930-936,共7页
基于Butler方程,结合热动力学数据和CALPHAD优化的过剩吉布斯自由能参数,计算Al-Mg、Mg-Er和Al-Er二元合金的表面张力。结果表明:在镁熔体中加入元素铝和铒时,将增加该熔体的表面张力。通过计算Al-Mg、Mg-Er和Al-Er二元合金的过剩表面张... 基于Butler方程,结合热动力学数据和CALPHAD优化的过剩吉布斯自由能参数,计算Al-Mg、Mg-Er和Al-Er二元合金的表面张力。结果表明:在镁熔体中加入元素铝和铒时,将增加该熔体的表面张力。通过计算Al-Mg、Mg-Er和Al-Er二元合金的过剩表面张力,发现过剩表面张力与过剩吉布斯自由能之间相对理想溶液偏差性质相反。选择铒为非对称性组元,并在此基础上结合Toop模型计算Al-Mg-Er三元合金的表面张力。结果表明:Al-Mg-Er三元合金的表面张力值基本在0.356~0.783N/m之间,且随着铒含量的增加,表面张力呈增大的趋势。 展开更多
关键词 Al-Mg-Er三元合金 表面张力 butler方程 Toop模型
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Lu-Mg和Lu-Al合金热力学性质的理论分析
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作者 纪凡 何荧 +1 位作者 向金秋 罗立平 《世界有色金属》 2024年第6期20-23,共4页
文章利用Miedema生成热模型计算Lu-Mg和Lu-Al二元合金的混合焓、过剩熵、过剩吉布斯自由能以及各组元的活度。结合Butler方程,计算Lu-Mg和Lu-Al合金熔体的表面张力以及表面相中各元素含量。研究结果表明,Lu-Mg和Lu-Al合金熔体的混合焓... 文章利用Miedema生成热模型计算Lu-Mg和Lu-Al二元合金的混合焓、过剩熵、过剩吉布斯自由能以及各组元的活度。结合Butler方程,计算Lu-Mg和Lu-Al合金熔体的表面张力以及表面相中各元素含量。研究结果表明,Lu-Mg和Lu-Al合金熔体的混合焓、过剩熵以及过剩吉布斯自由能都为负值,同时各组分活度较理想熔体有着一定负偏差,说明Lu与Mg和Al原子之间存在显著的相互作用力。Lu-Mg和Lu-Al合金熔体表面张力随Mg和Al含量的增加而减小,Mg和Al元素均会向熔体表面富集。 展开更多
关键词 MIEDEMA模型 butler方程 活度 表面张力 Lu-Mg Lu-Al
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液态Ag-O系表面张力和表面过剩量的理论计算
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作者 李天骕 刘剑雄 +1 位作者 单显祥 李堪鹏 《过程工程学报》 CAS CSCD 北大核心 2024年第4期453-461,共9页
本工作利用表面能与内聚能的比例关系,计算了液态Ag的表面张力和表面过剩熵。结果显示,随着温度的升高,表面张力近似线性下降,表面过剩熵也逐渐减小,这表明液态Ag表面总是保持有序结构。在此基础上,证明了Ag-O系具有理想溶体性质,并简化... 本工作利用表面能与内聚能的比例关系,计算了液态Ag的表面张力和表面过剩熵。结果显示,随着温度的升高,表面张力近似线性下降,表面过剩熵也逐渐减小,这表明液态Ag表面总是保持有序结构。在此基础上,证明了Ag-O系具有理想溶体性质,并简化了Butler方程,修正了液态Ag-O系表面张力关于氧气压力和温度的预测模型。结果表明,当氧气压力低于10 kPa时,液态Ag-O系的表面张力与温度呈负相关;而当氧气压力高于10 kPa时,随着温度的升高,表面张力呈现先增大后减小的趋势。此外,还探究了O原子的表面偏析行为。研究发现,表面偏析因子与温度和氧气压力均呈负相关,在较低的温度和氧气压力下,O原子倾向富集于表面。 展开更多
关键词 Ag-O系 butler方程 理想溶体近似 表面张力 表面过剩
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Influences of Co-Flow and Counter-Flow Modes of Reactant Flow Arrangement on a PEMFC at Start-Up
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作者 Qianqian Shao Min Wang Nuo Xu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1337-1356,共20页
To investigate the influences of co-flowand counter-flowmodes of reactant flowarrangement on a proton exchange membrane fuel cell(PEMFC)during start-up,unsteady physical and mathematical models fully coupling the flow... To investigate the influences of co-flowand counter-flowmodes of reactant flowarrangement on a proton exchange membrane fuel cell(PEMFC)during start-up,unsteady physical and mathematical models fully coupling the flow,heat,and electrochemical reactions in a PEMFC are established.The continuity equation and momentum equation are solved by handling pressure-velocity coupling using the SIMPLE algorithm.The electrochemical reaction rates in the catalyst layers(CLs)of the cathode and anode are calculated using the Butler-Volmer equation.The multiphase mixture model describes the multiphase transport process of gas mixtures and liquid water in the fuel cell.After validation,the influences of co-flow and counter-flow modes on the PEMFC performance are investigated,including the evolution of the current density,flow field,temperature field,and reactant concentration field during start-up,as well as the steady distribution of the current density,reactant concentration,andmembrane water content when the start-up stabilizes.Co-flow and counter-flow modes influence the current density distribution and temperature distribution.On the one hand,the co-flow mode accelerates the start-up process of the PEMFC and leads to a more evenly distributed current density than the counter-flow mode.On the other hand,the temperature difference between the inlet and outlet sections of the cell is up to 10.1℃ under the co-flow mode,much larger than the 5.0℃ observed in the counter-flow mode.Accordingly,the counter-flowmode results in a more evenly distributed temperature and a lower maximum temperature than the co-flow case.Therefore,in the flow field design of a PEMFC,the reactant flow arrangements can be considered to weigh between better heat management and higher current density distribution of the cell. 展开更多
关键词 PEMFC full coupling model butler-Volmer equation multiphase mixture model co-flow mode counter-flow mode
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Surface tension of liquid Au-Bi-Sn alloys 被引量:2
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作者 Guo, Zhongnan Li, Shan +1 位作者 Mikula, Adolf Yuan, Wenxia 《Rare Metals》 SCIE EI CAS CSCD 2012年第3期250-254,共5页
The surface tension of a promising lead-free solder Au-Bi-Sn alloys was investigated both by the sessile-drop method and calculation. Experimental measurements were carried out for two cross-sections with the constant... The surface tension of a promising lead-free solder Au-Bi-Sn alloys was investigated both by the sessile-drop method and calculation. Experimental measurements were carried out for two cross-sections with the constant gold to bismuth ration of 1:1 and 1:2. For all the investigated compositions, decrease of the surface tension is observed with increasing temperature. Meanwhile, the surface tension values were also calculated based on Butler’s equation, with using the newest research on thermodynamics data of Au-Bi-Sn ternary system. Compared with the experimental results, a good agreement was obtained. 展开更多
关键词 sessile-drop method Au-Bi-Sn alloys density surface tension butler’s equation
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Surface Tension Calculation of Undercooled Alloys 被引量:2
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作者 Zhiyu Qiao, Lijun Yan, Zhanmin Cao, Guirong Liu (Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, China) 《Rare Metals》 SCIE EI CAS CSCD 2001年第1期58-61,共4页
Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensio... Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensions of liquid stable and undercooled Ni-Cu (x(Ni)=0.42) and Ni-Fe (x(Ni)=0.3 and 0.7) alloys are calculated using STCBE (Surface Tension Calculation based on Butler Equation) program. The agreement between calculated values and experimental data is good enough, and the temperature dependence of the surface tension can be reasonable down to 150-200 K under the liquid temperature of the alloys. 展开更多
关键词 undercooled alloy surface tension butler equation
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Calculating models on surface tension of RE_2O_3-Mg O-SiO_2(RE=La, Nd, Sm, Gd and Y) melts 被引量:2
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作者 吴铖川 成国光 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2014年第11期3696-3701,共6页
A thermodynamic model was developed for determining the surface tension of RE2O3-MgO-SiO2(RE=La, Nd, Sm, Gd and Y) melts considering the ionic radii of the components and Butler's equation. The temperature and com... A thermodynamic model was developed for determining the surface tension of RE2O3-MgO-SiO2(RE=La, Nd, Sm, Gd and Y) melts considering the ionic radii of the components and Butler's equation. The temperature and composition dependence of the surface tensions in molten RE2O3-MgO-SiO2 slag systems was reproduced by the present model using surface tensions and molar volumes of pure oxides, as well as the anionic and cationic radii of the melt components. The iso-surface tension lines of La2O3-MgO-SiO2 slag melt at 1873 K were calculated and the effects of slag composition on the surface tension were also investigated. The surface tensions of La2O3, Gd2O3, Nd2O3 and Y2O3 at 1873 K were evaluated as 686, 677, 664 and 541 m N/m, respectively. The surface tension of pure rare earth oxide melts linearly decreases with increasing cationic field strength, except for Y2O3 oxide, while Y2O3 has a much weaker surface tension. The evaluated results of the surface tension show good agreements with literature data, and the mean deviation of the present model is found to be 1.05% at 1873 K. 展开更多
关键词 rare-earth oxide surface tension ionic radius butler's equation calculating model
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混合熔融Li2CO3-Na2CO3-K2CO3体系表面张力计算 被引量:2
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作者 李建朝 齐素慈 +2 位作者 许继芳 王瞡 翁文凭 《无机盐工业》 CAS 北大核心 2016年第5期16-19,共4页
熔融碳酸盐是一种良好的热载体和反应介质,其表面张力直接影响反应体系中熔盐分布和界面反应。在熔融盐离子半径和Butler方程的基础上,建立了熔融混合碳酸盐Li_2CO_3-Na_2CO_3-K2CO3体系的表面张力计算模型,考察了温度和熔盐组分对表面... 熔融碳酸盐是一种良好的热载体和反应介质,其表面张力直接影响反应体系中熔盐分布和界面反应。在熔融盐离子半径和Butler方程的基础上,建立了熔融混合碳酸盐Li_2CO_3-Na_2CO_3-K2CO3体系的表面张力计算模型,考察了温度和熔盐组分对表面张力的影响。结果表明:模型计算的表面张力值与实际测量值比较吻合;熔融碳酸盐纯物质的表面张力随着阳离子的静电势(Z/r)的增大而逐渐减小;Li_2CO_3-Na_2CO_3-K2CO3体系中,熔盐的表面张力随着温度的升高而减小;混合熔融盐表面张力随着Li_2CO_3含量的增加而逐渐增大,随着K2CO3含量的增加而逐渐减小。 展开更多
关键词 熔融碳酸盐 表面张力 模型 butler方程
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Al-Mg-Li三元合金表面张力的估算 被引量:1
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作者 刘姗姗 王波 +2 位作者 周艾琳 张捷宇 周国治 《过程工程学报》 CAS CSCD 北大核心 2020年第1期59-66,共8页
运用表面张力计算公式Butler方程,与过剩吉布斯自由能结合,计算了973 K温度下Al-Mg, Al-Li和Mg-Li二元体系的表面张力。结果表明,在铝熔体中分别加入金属镁或锂,合金表面张力随其含量增加而降低;在镁熔体中加入金属锂,合金表面张力随锂... 运用表面张力计算公式Butler方程,与过剩吉布斯自由能结合,计算了973 K温度下Al-Mg, Al-Li和Mg-Li二元体系的表面张力。结果表明,在铝熔体中分别加入金属镁或锂,合金表面张力随其含量增加而降低;在镁熔体中加入金属锂,合金表面张力随锂含量增加而降低。以此为基础,利用Chou模型计算得Al-Mg-Li三元合金的表面张力为0.326~0.851 N/m,随铝或镁含量增加表面张力增大,随锂含量增加表面张力减小。 展开更多
关键词 Al-Mg-Li三元合金 butler方程 表面张力 Chou模型
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CaO-MnO-SiO_2渣系的表面张力计算模型 被引量:1
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作者 吴铖川 成国光 《热加工工艺》 CSCD 北大核心 2014年第19期58-62,共5页
基于熔渣结构离子与分子共存理论和Butler方程,建立了CaO-MnO-SiO2熔渣表面张力计算模型。模型利用纯组元的表面张力和摩尔体积以及熔渣中各组元表面相和体相中作用浓度(活度)可以计算出CaO-MnO-SiO2熔渣表面张力随熔渣成分、温度的变... 基于熔渣结构离子与分子共存理论和Butler方程,建立了CaO-MnO-SiO2熔渣表面张力计算模型。模型利用纯组元的表面张力和摩尔体积以及熔渣中各组元表面相和体相中作用浓度(活度)可以计算出CaO-MnO-SiO2熔渣表面张力随熔渣成分、温度的变化规律。表面张力的计算结果与文献介绍的值吻合很好。计算了1773 K下CaO-MnO-SiO2渣系的等表面张力线,并进一步考察了炉渣成分对表面张力的影响。 展开更多
关键词 CaO-MnO-SiO2 表面张力 离子与分子共存理论 butler方程 计算模型
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CaO-Al2O3-TiO2熔渣表面张力计算模型 被引量:1
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作者 吴铖川 成国光 《上海金属》 CAS 北大核心 2014年第2期35-39,共5页
基于熔渣结构离子与分子共存理论和Butler方程,建立了CaO-Al2O3-TiO2熔渣表面张力计算模型。本模型利用纯组元的表面张力和摩尔体积以及熔渣中各组元表面相和体相中作用浓度(活度)可以计算出CaO-Al2O3-TiO2熔渣表面张力随熔渣成分、温... 基于熔渣结构离子与分子共存理论和Butler方程,建立了CaO-Al2O3-TiO2熔渣表面张力计算模型。本模型利用纯组元的表面张力和摩尔体积以及熔渣中各组元表面相和体相中作用浓度(活度)可以计算出CaO-Al2O3-TiO2熔渣表面张力随熔渣成分、温度的变化规律。将计算得到的表面张力值与文献实测值进行对比,计算结果与文献实测值吻合较好。并进一步绘制了CaO-Al2O3-TiO2熔渣等表面张力线,考察了炉渣成分对表面张力的影响,以期为含TiO2渣系控制提供理论参考。 展开更多
关键词 CaO-Al2O3-TiO2熔渣 表面张力 计算模型 butler方程
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Calculating Models on the Surface Tension of CaO-FeO-SiO2 Molten Slags 被引量:2
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作者 Chengchuan Wu 《材料科学研究(中英文版)》 2014年第1期10-16,共7页
关键词 二氧化硅基 表面张力 计算模型 熔渣 炉渣结构 炉渣成分 热力学模型 共存理论
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Al-Mg-Zn三元合金表面张力的估算
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作者 周艾琳 杨志良 +4 位作者 史航 李竹 吴连得 吴广新 张捷宇 《上海大学学报(自然科学版)》 CAS CSCD 北大核心 2019年第4期462-471,共10页
运用Butler方程,结合CALPHAD优化后的过剩吉布斯自由能,计算了973 K温度下, Al-Mg, Mg-Zn, Al-Zn二元合金的表面张力.结果表明,在Al熔体中加入金属Mg和Zn,可降低该液态合金的表面张力.在此基础上,利用Chou模型计算了Al-Mg-Zn三元合金的... 运用Butler方程,结合CALPHAD优化后的过剩吉布斯自由能,计算了973 K温度下, Al-Mg, Mg-Zn, Al-Zn二元合金的表面张力.结果表明,在Al熔体中加入金属Mg和Zn,可降低该液态合金的表面张力.在此基础上,利用Chou模型计算了Al-Mg-Zn三元合金的表面张力.结果表明, Al-Mg-Zn三元合金表面张力计算值范围为0.575~0.864 N/m,且随着Mg含量的增加,表面张力减小.对比了二元及三元合金表面张力的计算值与实验值,误差在5%以内. 展开更多
关键词 Al-Mg-Zn三元合金 表面张力 Chou模型 butler方程
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ACl-CeCl_3(A=Li,Na,K,Cs)体系表面张力的计算
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作者 何茂刚 卢广轩 +1 位作者 康张阳 刘向阳 《工程热物理学报》 EI CAS CSCD 北大核心 2017年第1期1-5,共5页
对二元系NaCl-CeCl_3进行了热力学优化,得到一套能够合理描述该体系的热力学参数,计算出的相图及其他热力学数据与实验值吻合良好。由CALPHAD方法得到了热力学数据库,并结合Butler方程对含稀土金属氯化盐的熔盐体系表面张力的计算模型... 对二元系NaCl-CeCl_3进行了热力学优化,得到一套能够合理描述该体系的热力学参数,计算出的相图及其他热力学数据与实验值吻合良好。由CALPHAD方法得到了热力学数据库,并结合Butler方程对含稀土金属氯化盐的熔盐体系表面张力的计算模型进行了修正,计算了ACl-CeCl_3(A=Li,Na,K,Cs)体系的表面张力。结果显示,描述体系表面相和体相吉布斯能关系的模型参数β与体系类别密切相关,对于本文所计算的熔盐体系,β值随碱金属离子半径的增大而增大。本文还探讨了熔盐体系中表面相与体相组分之间的关系。 展开更多
关键词 CALPHAD方法 表面张力 butler方程 稀土金属氯化盐
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The influence of stress-dependent overpotential on dendrite growth in all-solid-state battery with cracks
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作者 ZHANG ZhenHua ZHANG Yong +2 位作者 LIU Chang HOU Xu WANG Jie 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2024年第8期2493-2504,共12页
Dendrite growth is one of the main challenges in maintaining the service life of all-solid-state lithium-ion batteries.Mechanical stress has been reported to significantly affect dendrite growth.In this study,to expla... Dendrite growth is one of the main challenges in maintaining the service life of all-solid-state lithium-ion batteries.Mechanical stress has been reported to significantly affect dendrite growth.In this study,to explain the effect of mechanical stress on electrochemical reactions in all-solid-state batteries,a modified phase-field model for dendrite growth is proposed by considering the stress-dependent overpotential.Dendrite growth under different mechanical loadings in an all-solid-state battery is investigated using the proposed model.Consistent with previous experimental results,the current result shows that compressive stress inhibits dendrite growth.Considering the stress concentration at the tips of processing-induced microcracks,the effects of the number and distribution of microcracks on dendrite growth are investigated.The results show that the stress-concentration field induced at the tips of cracks or voids can change the morphology of dendrites and decrease their growth rates.This study provides a new perspective for explaining Li dendrite growth under mechanical stress and offers inspiration for prolonging the service life of all-solid-state batteries based on defect and stress regulation,which may be further realized in experiments by filling solid electrolytes with different types of nanofillers. 展开更多
关键词 butler–Volmer equation stress-dependent overpotential MICROCRACKS all-solid-state battery phase-field simulation
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电池系统建模中Butler-Volmer方程的同伦分析求解 被引量:3
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作者 宋辉 李芬 徐献芝 《应用数学和力学》 CSCD 北大核心 2013年第4期373-382,共10页
Butler-Volmer方程是电化学系统中描述电极动力学过程的本构方程,具有强非线性.为了对这一方程(耦合两个Ohm方程)进行解析求解,在同伦分析方法的框架下,发展了满足简单条件的广义非线性算子的算法,以取代原同伦分析中的非线性算子.该广... Butler-Volmer方程是电化学系统中描述电极动力学过程的本构方程,具有强非线性.为了对这一方程(耦合两个Ohm方程)进行解析求解,在同伦分析方法的框架下,发展了满足简单条件的广义非线性算子的算法,以取代原同伦分析中的非线性算子.该广义非线性算子的构造保证了高阶形变方程的线性特征.这一方法的有效性通过一些算例得到了验证.最后通过同伦分析方法对Butler-Volmer方程进行了求解,结果显示过电位和电流密度的级数解析解与数值解吻合很好,并有很好的收敛效率. 展开更多
关键词 butler-Volmer方程 同伦分析方法 复合函数 强非线性项 广义非线性算子
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Observations on Arrhenius Degradation of Lithium-Ion Capacitors
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作者 Davis George Moye Pedro L. Moss +2 位作者 Xujie Chen Wanjun Cao Simon Foo 《Materials Sciences and Applications》 2020年第7期450-461,共12页
Earlier research determined that lithium-ion capacitor (LIC) cycle life degradation can be accelerated by elevated temperature. LIC cycle life degradation can be described by an Arrhenius equation. This study performe... Earlier research determined that lithium-ion capacitor (LIC) cycle life degradation can be accelerated by elevated temperature. LIC cycle life degradation can be described by an Arrhenius equation. This study performed cycle life testing at a constant temperature but varied cycle current. The results were described by an Arrhenius equation relying upon the number of cycles and a constant, which was determined by cycle current. Using mathematical derivations and experimental results, the researchers quantified the effects of activation energy and temperature upon this constant. Because cell temperature is nearly constant during cycles, it was deduced that elevated cycle current decreases activation energy. This lower activation energy then accelerates degradation. Thus this research demonstrates that cycle current ages LICs through its effects on their activation energies. 展开更多
关键词 Arrhenius equation Cycle Life Cycle Life Degradation Lithium-Ion Capacitor butler-Volmer equation Activation Energy
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多元电解质溶液表面张力的新型预测方程 被引量:1
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作者 彭效明 胡玉峰 +1 位作者 凌山 张金柱 《中国科学:化学》 CSCD 北大核心 2010年第9期1324-1331,共8页
将半理想溶液理论和Butler方程相结合建立了预测多元电解质溶液表面张力的新型线性预测方程.新方程可由二元系数据预测多元系的表面张力数据,而不涉及任何多元交互作用参数.利用不同温度下24个混合电解质溶液的表面张力数据对新方程进... 将半理想溶液理论和Butler方程相结合建立了预测多元电解质溶液表面张力的新型线性预测方程.新方程可由二元系数据预测多元系的表面张力数据,而不涉及任何多元交互作用参数.利用不同温度下24个混合电解质溶液的表面张力数据对新方程进行了系统检验.结果表明新方程可利用298.15K时二元系的渗透压系数和不同温度下二元系的表面张力数据预测不同温度下高浓度的多元系的表面张力数据,且预测结果与实验数据符合得很好,并且预测结果普遍优于基于Pitzer方程的表面张力模型. 展开更多
关键词 表面张力 半理想溶液理论 butler方程 新型线性预测方程
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Improvements to Temperature, Warburg Impedance, and Voltage Computations for a Design-Based Predictive Model for Lithium-Ion Capacitors
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作者 Davis George Moye Pedro L. Moss +4 位作者 Dhevathi Rajan Rajagopalan Kannan Xujie Chen Omonayo Bolufawi Wanjun Cao Simon Y. Foo 《Materials Sciences and Applications》 2020年第6期347-369,共23页
An earlier study manipulated the Butler-Volmer equation to effectively model a lithium-ion capacitor’s (LIC) energy storage as a function of its constituent components and charge current. However, this model had seve... An earlier study manipulated the Butler-Volmer equation to effectively model a lithium-ion capacitor’s (LIC) energy storage as a function of its constituent components and charge current. However, this model had several shortcomings: computed temperature values were too low, voltage was inaccurate, and the model required Warburg impedance values that were two orders of magnitude higher than experimental results. This study began by analyzing the model’s temperature and voltage computations in order to justify output values. Ultimately, these justifications failed. Therefore, in situ temperature rise was measured during charge cycles. Experimental results indicated that temperature increases minimally during a charge cycle (<1%). At high current densities (≥150 A<span style="white-space:nowrap;">·</span>kg<sup>-1</sup>) temperature increase is negligible. After it was found that LIC temperature change is minimal during a charge cycle, the model accurately computed LIC voltage during the charge cycle and computed Warburg impedance that agreed with values derived from earlier experimental studies, even falling within the measurements’ precision error. 展开更多
关键词 Lithium-Ion Capacitor Randles Equivalent Circuit Model butler-Volmer equation
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