相场模型及其在电化学储能材料中的应用

张更; 王巧; 沙立婷; 李亚捷; 王达; 施思齐

doi:10.7498/aps.69.20201411

摘要

随着计算机技术的快速发展, 计算研究在探究材料体系微结构演化方面展示出巨大的优势. 作为材料动力学的一种计算研究方法, 相场模型不仅可以避免复杂的界面追踪, 而且便于处理各类外场因素, 因而受到广泛关注. 藉此本文介绍了相场模型的理论框架以及目前主流的多元多相系相场模型: Carter模型, Steinbach模型和Chen模型, 并从相场变量的解释、耦合热力学数据库的方式、体系自由能密度的构建方式以及演化方程等方面对上述三个模型进行了系统地概括和比较. 进一步, 聚焦于相场模型在各向异性输运和相分离、弹性和塑性变形、裂纹扩展和断裂、枝晶生长机制等方面的应用, 系统展示了相场模型在描述电化学储能材料微结构演化以及改进其性能方面的巨大潜力. 最后, 从相场模型的理论改进和应用拓展两个方面, 讨论并展望了电化学储能材料相场模拟的未来发展方向和亟待解决的关键问题.

关键词:

Abstract

With the rapid progress of computer technology, computational research exhibits significant advantages in investigating microstructure evolution of material systems. As a computational research method of material dynamics, increasing attention has been paid to the phase-field model because of its avoidance of complicated interface tracking and convenience of dealing with applied fields. Theoretical framework of the phase-field model and three current phase-field models for multicomponent multiphase systems (the Carter, Steinbach, and Chen models) are introduced and reviewed in terms of interpretation of phase-field variables, way of coupling thermodynamic database, way of constructing the free energy density, and evolution equations. This review only focuses on the application of the phase-field model in electrochemical energy storage materials, and introduces its existing phase-field simulation results, which demonstrates that the phase-field model has tremendous potential in describing the microstructure evolution (anisotropic transport and phase separation, elastic and plastic deformation, crack propagation and fracture, dendrite growth, etc) and improving the performance of electrochemical energy storage materials. Finally, from two aspects of improving phase-field theory and extending application, future development trend and problems to be solved of phase-field simulations in electrochemical energy storage materials are discussed and looked ahead.

Keywords:

phase-field model /
electrochemical energy storage materials /
stress evolution /
plastic deformation /
dendrite growth

作者及机构信息

1.
阿卜杜拉国王科技大学物理科学与工程系, 图瓦, 沙特阿拉伯　23955-6900

2.
上海大学材料基因组工程研究院, 上海　200444

3.
上海大学材料科学与工程学院, 上海　200444

通信作者: 李亚捷, liyajiejuly@shu.edu.cn

基金项目: 国家自然科学基金(批准号: 11874254)和上海市浦江人才计划(批准号: 2019PJD016)资助的课题

Authors and contacts

1.
Physical Science and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia

2.
Materials Genome Institute, Shanghai University, Shanghai 200444, China

3.
School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China

Corresponding author: Li Ya-Jie, liyajiejuly@shu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874254) and Shanghai Pujiang Talents Program, China (Grant No. 2019PJD016)

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 相变界问题的尖锐界面和扩散界面的对比

Fig. 1. Comparison between sharp and diffusive interfaces for phase boundary problems.

下载: 全尺寸图片幻灯片

图 2 相场变量与Steinbach模型、Chen模型中的相权重函数的比较

Fig. 2. Comparison of phase field and phase-weight functions in Steinbach and Chen models.

下载: 全尺寸图片幻灯片

图 3 相场模型中研究电化学储能材料微结构演化的步骤

Fig. 3. Steps for investigating microstructure evolution of electrochemical energy storage materials in phase-field model.

下载: 全尺寸图片幻灯片

图 4 (a) 锂离子嵌入到FePO₄时活跃面(010)快速扩散(蓝色箭头)和相分离示意图^[43]; (b) LiFePO₄相变过程中的三种可能的扩散路径: 体扩散、表面扩散和电解液扩散^[45]

Fig. 4. (a) Schematic diagram of diffusion of active surface (010) (blue arrows) and phase separation when Li-ion intercalates FePO₄^[43]; (b) three potential migration paths in phase transition of LiFePO₄: bulk, surface, and electrolyte diffusions^[45].

下载: 全尺寸图片幻灯片

图 5 硅颗粒的弹性和塑性变形^[50-52]

Fig. 5. Elastic and plastic deformations of Si particles^[50-52].

下载: 全尺寸图片幻灯片

图 6 锂化过程中的裂纹扩展　(a)初始状态; (b)相偏析导致裂纹扩展; (c)相界面赶上裂纹尖端; (d)裂纹尖端在相界面处开始分叉; (e)相界面离开裂纹尖端向中心移动; (f)反应停止^[73]

Fig. 6. Crack propagation during lithiation process: (a) Initial state; (b) phase segregation generates crack propagation; (c) the phase interface catches up with the crack tip; (d) the crack tip starts to branch at the phase interphase; (e) phase interface leaves crack tip and moves towards center; (f) the reaction stops ^[73].

下载: 全尺寸图片幻灯片

图 7 相场模型模拟的Li枝晶生长　(a) 序参量, (b) Li⁺浓度和(c)电势的演化^[87]

Fig. 7. Dendrite growth of Li simulated by phase-field model: evolution of (a) order parameter, (b) concentration of Li⁺, and (c) electric potential ^[87].

下载: 全尺寸图片幻灯片

map

[1]	Gogotsi Y, Simon P 2011 Science 334 917 Google Scholar
[2]	Ceder G 2010 MRS Bull. 35 693 Google Scholar
[3]	Wang A P, Kadam S, Li H, Shi S Q, Qi Y 2018 NPJ Comput. Mater. 4 15 Google Scholar
[4]	Andersen H C 1980 J. Chem. Phys. 72 2384 Google Scholar
[5]	Stramer O 2001 J. Am. Stat. Assoc. 96 342
[6]	Shi S, Gao J, Liu Y, Zhao Y, Wu Q, Ju W, Ouyang C, Xiao R 2016 Chin. Phys. B 25 018212 Google Scholar
[7]	Zou Z Z, Li Y Y, Lu Z H, Wang D, Cui Y H, Guo B K, Li Y J, Liang X M, Feng J W, Li H, Nan C W, Armand M, Chen L Q, Xu K, Shi S Q 2020 Chem. Rev. 120 4169 Google Scholar
[8]	Biner S B 2017 Programming Phase-Field Modeling (Berlin: Springer)
[9]	Steinbach I, Pezzolla F, Nestler B, Sedklberg M, Ptieler R, Schmitz G J, Rezende J L L 1996 Physica D 94 135 Google Scholar
[10]	De Groot S R, Mazur P 2013 Non-Equilibrium Thermodynamics (Courier Corporation)
[11]	Wheeler A A, Boettinger W S, McFadden G B 1992 Phys. Rev. A 45 7424 Google Scholar
[12]	Kazaryan A, Wang Y, Dregia S A, Patton B R 2000 Phys. Rev. B 61 14275 Google Scholar
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[31]	Zhang L, Steinbach I 2012 Acta Mater. 60 2702 Google Scholar
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[33]	Cogswell D A, Carter W C 2011 Phys. Rev. E 83 061602
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[35]	Yu H C, Wang F, Amatucci G G, Thornton K 2016 J. Phase. Equilib. Diffus. 37 86 Google Scholar
[36]	Garcı́a R E, Bishop C M, Carter W C 2004 Acta Mater. 52 11 Google Scholar
[37]	Guyer J E, Boettinger W J, Warren J A, McFadden G B 2004 Phys. Rev. E 69 021603 Google Scholar
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[41]	Singh G K, Ceder G, Bazant M Z 2008 Electrochim. Acta 53 7599 Google Scholar
[42]	Bazant M Z 2012 arXiv preprint arXiv 1208 1587
[43]	Bai P, Cogswell D A, Bazant M Z 2011 Nano. Lett. 11 4890 Google Scholar
[44]	Hong L, Li L, Chen-Wiegart Y K, Wang J, Xiang K, Gan L, Li W, Meng F, Wang F, Wang J, Chiang Y M, Jin S, Tang M 2017 Nat. Commun. 8 1194 Google Scholar
[45]	Li Y Y, Chen H G, Lim K, Deng H D, Lim J, Fraggedakis D, Attia P M, Lee S C, Jin N, Moškon J, Guan Z, Gent W E, Hong J, Yu Y S, Gaberšček M, Islam M S, Bazant M Z, Chueh W C 2018 Nat. Mater. 17 915 Google Scholar
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[47]	Zhang X Y, Hao F, Chen H S, Fang D N 2015 Mech. Mater. 91 351 Google Scholar
[48]	Zuo P, Zhao Y P 2015 Phys. Chem. Chem. Phys. 17 287 Google Scholar
[49]	Lim C, Yan B, Yin L, Zhu L 2012 Electrochim. Acta 75 279 Google Scholar
[50]	Gao F, Hong W 2016 J. Mech. Phys. Solids 94 18 Google Scholar
[51]	Chen L, Fan F, Hong L, Chen J, Ji Y Z, Zhang S L, Zhu T, Chen L Q 2014 J. Electrochem. Soc. 161 F3164 Google Scholar
[52]	Zhang X, Krischok A, Linder C 2016 Comput. Method Appl. M. 312 51 Google Scholar
[53]	Zhao K, Pharr M, Vlassak J J, Suo Z 2011 J. Appl. Phys. 109 016110 Google Scholar
[54]	Zhao K, Pharr M, Cai S, Vlassak J J, Suo Z 2011 J. Am. Ceram. Soc. 94 S226 Google Scholar
[55]	Bower A F, Guduru P R, Sethuraman V A 2011 J. Mech. Phys. Solids. 59 804 Google Scholar
[56]	Walk A C, Huttin M, Kamlah M 2014 Eur. J. Mech. A.Solids 48 74 Google Scholar
[57]	Aranson I S, Kalatsky V A, Vinokur V M 2000 Phys. Rev. Lett. 85 118 Google Scholar
[58]	Marconi V I, Jagla E A 2005 Phys. Rev. E 71 036110 Google Scholar
[59]	Spatschek R, Muller-Gugenberger C, Brener E, Nestler B 2007 Phys. Rev. E 75 066111 Google Scholar
[60]	Miehe C, Hofacker M, Welschinger F 2010 Comput. Method Appl. M. 199 2765 Google Scholar
[61]	Miehe C, Welschinger F, Hofacker M 2010 Mech. Phys. Solids 58 1716 Google Scholar
[62]	Hofacker M, Miehe C 2013 Int. J. Numer. Meth. Eng. 93 276 Google Scholar
[63]	Bhandakkar T K, Gao H 2010 Int. J. Solids Struct. 47 1424 Google Scholar
[64]	Bhandakkar T K, Gao H 2011 Int. J. Solids Struct. 48 2304 Google Scholar
[65]	Woodford W H, Chiang Y M, Carter W C 2010 J. Electrochem. Soc. 157 A1052 Google Scholar
[66]	Zhu M, Park J, Sastry A M 2012 J. Electrochem. Soc. 159 A492 Google Scholar
[67]	Gao Y F, Zhou M 2013 J. Power Sources 230 176 Google Scholar
[68]	Klinsmann M, Rosato D, Kamlah M, McMeeking R M 2016 Mech. Phys. Solids 92 313 Google Scholar
[69]	Zhao K, Pharr M, Vlassak J J, Suo Z 2010 J. Appl. Phys. 108 073517 Google Scholar
[70]	Huttin M, Kamlah M 2012 J. Appl. Phys. 101 133902
[71]	Liang L, Chen L Q 2014 Appl. Phys. Lett. 105 263903 Google Scholar
[72]	Miehe C, Dal H, Schänzel L M, Raina A 2016 Int. J. Numer. Meth. Eng. 106 683 Google Scholar
[73]	Zhao Y, Xu B X, Stein P, Gross D 2016 Comput. Method. Appl. M. 312 428 Google Scholar
[74]	Zhuang Y, Zou Z Y, Lu B, Li Y J, Wang D, Avdeev M, Shi S Q 2020 Chin. Phys. B 29 068202 Google Scholar
[75]	Lu B, Ning C Q, Shi D X, Zhao Y F, Zhang J Q 2020 Chin. Phys. B 29 026201 Google Scholar
[76]	Hong Z J, Viswanathan V 2020 ACS Energy Lett. 5 3254 Google Scholar
[77]	Li Y, Hu S, Sun X, Stan M 2017 NPJ Comput. Mater. 3 1 Google Scholar
[78]	Yamaki J I, Tobishima S I, Hayashi K, Saito K, Nemoto Y, Arakawa M 1998 J. Power Sources 74 219 Google Scholar
[79]	Jana A, Woo S I, Vikrant K S N, García R E 2019 Energy Environ. Sci. 12 3595 Google Scholar
[80]	Li G, Liu Z, Huang Q, Gao Y, Regula M, Wang D, Chen L Q, Wang D 2018 Nat. Energy 3 1076 Google Scholar
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相场模型及其在电化学储能材料中的应用