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Cahn-Hilliard Reaction Model for Isotropic Li-ion Battery Particles

  • Yi Zeng (a1) and Martin Z. Bazant (a1) (a2)

Abstract

Using the recently developed Cahn-Hilliard reaction (CHR) theory, we present a simple mathematical model of the transition from solid-solution radial diffusion to two-phase shrinking-core dynamics during ion intercalation in a spherical solid particle. This general approach extends previous Li-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary under all conditions, by predicting phase separation only under appropriate circumstances. The effect of the applied current is captured by generalized Butler-Volmer kinetics, formulated in terms of the diffusional chemical potential in the CHR theory. We also consider the effect of surface wetting or de-wetting by intercalated ions, which can lead to shrinking core phenomena with three distinct phase regions. The basic physics are illustrated by different cases, including a simple model of lithium iron phosphate (neglecting crystal anisotropy and coherency strain).

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[1] Allen, JL, Jow, TR, and Wolfenstine, J. Analysis of the FePO4 to LiFePO4 phase transition. Journal of Solid State Electrochemistry, 12(7-8):10311033, 2008.
[2] Bai, Peng, Cogswell, Daniel, and Bazant, Martin Z.. Suppression of phase separation in LiFePO4 nanoparticles during battery discharge. Nano Letters, 11(11):48904896, 2011.
[3] Bazant, M. Z.. Theory of chemical kinetics and charge transfer based on non-equilibrium thermodynamics. Accounts of Chemical Research, 46:11441160, 2013.
[4] Burch, Damian and Bazant, Martin Z.. Size-dependent spinodal and miscibility gaps for intercalation in nanoparticles. Nano Letters, 9(11):37953800, 2009.
[5] Cahn, J. W.. Critical point wetting. J. Chem. Phys., 66:36673672, 1977.
[6] Chen, Guoying, Song, Xiangyun, and Richardson, Thomas. Electron microscopy study of the LiFePO4 to FePO4 phase transition. Electrochemical and Solid State Letters, 9(6):A295A298, 2006.
[7] Chueh, William C, Gabaly, Farid El, Sugar, Josh D, Bartelt, Norman C., McDaniel, Anthony H., Fenton, Kyle R, Zavadil, Kevin R., Tyliszczak, Tolek, Lai, Wei, and McCarty, Kevin F.. Intercalation pathway in many-particle LiFePO4 electrode revealed by nanoscale state-of-charge mapping. Nano Letters, 13:866872, 2013.
[8] Cogswell, D. A. and Bazant, M. Z.. Theory of coherent nucleation in phase-separating nanoparticles. Nano Letters, Article ASAP, 2013.
[9] Cogswell, Daniel A. and Bazant, Martin Z.. Coherency strain and the kinetics of phase separation in LiFePO4 nanoparticles. ACS Nano, 6:22152225, 2012.
[10] Dargaville, S. and Farrell, T.W.. Predicting active material utilization in LiFePO4 electrodes using a multiscale mathematical model. Journal of the Electrochemical Society, 157(7):A830A840, 2010.
[11] Delacourt, Charles, Poizot, Philippe, Tarascon, Jean-Marie, and Masquelier, Christian. The existence of a temperature-driven solid solution in LixFePO4 for 0 ≤ x ≤ 1. Nature materials, 4(3):254260, 2005.
[12] Delmas, C., Maccario, M., Croguennec, L., Le Cras, F., and Weill, F.. Lithium deintercalation of LiFePO4 nanoparticles via a domino-cascade model. Nature Materials, 7:665671, 2008.
[13] Doyle, Marc, Fuller, Thomas F., and Newman, John. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. Journal of the Electrochemical Society, 140(6):15261533, 1993.
[14] Ferguson, T. R. and Bazant, M. Z.. Non-equilibrium thermodynamics of porous electrodes. J. Electrochem. Soc., 159:A1967A1985, 2012.
[15] Kang, Byoungwoo and Ceder, Gerbrand. Battery materials for ultrafast charging and discharging. Nature, 458:190193, 2009.
[16] Laffont, L., Delacourt, C., Gibot, P., Yue Wu, M., Kooyman, P., Masquelier, C., and Marie Tarascon, J.. Study of the LiFePO4/FePO4 two-phase system by high-resolution electron energy loss spectroscopy. Chem. Mater., 18:55205529, 2006.
[17] Malik, Rahul, Burch, Damian, Bazant, Martin, and Ceder, Gerbrand. Particle size dependence of the ionic diffusivity. Nano Letters, 10:41234127, 2010.
[18] Newman, John and Thomas-Alyea, Karen E.. Electrochemical Systems. Prentice-Hall, Inc., Englewood Cliffs, NJ, third edition, 2004.
[19] Oyama, Gosuke, Yamada, Yuki, Natsui, Ryuichi, Nishimura, Shinichi, and Yamada, Atsuo. Kinetics of nucleation and growth in two-phase electrochemical reaction of LiFePO4 . J. Phys. Chem. C, 116:73067311, 2012.
[20] Padhi, A.K., Nanjundaswamy, K.S., and Goodenough, J.B.. Phospho-olivines as positiveelectrode materials for rechargeable lithium batteries. Journal of the Electrochemical Society, 144(4):11881194, 1997.
[21] Ritchie, Andrew and Howard, Wilmont. Recent developments and likely advances in lithiumion batteries. Journal of Power Sources, 162(2):809812, 2006.
[22] Singh, Gogi, Burch, Damian, and Bazant, Martin Z.. Intercalation dynamics in rechargeable battery materials: General theory and phase-transformation waves in LiFePO4 . Electrochimica Acta, 53:75997613, 2008. arXiv:0707.1858v1 [cond-mat.mtrl-sci] (2007).
[23] Srinivasan, Venkat and Newman, John. Discharge model for the lithium iron-phosphate electrode. Journal of the Electrochemical Society, 151(101):A1517A1529, 2004.
[24] Tang, Ming, Belak, James F., and Dorr, Milo R.. Anisotropic phase boundary morphology in nanoscale olivine electrode particles. The Journal of Physical Chemistry C, 115:49224926, 2011.
[25] Tang, Ming, Craig Carter, W., and Chiang, Yet-Ming. Electrochemically driven phase transitions in insertion electrodes for lithium-ion batteries: Examples in lithium metal phosphate olivines. Annual Review of Materials Research, 40:501529, 2010.
[26] Tarascon, J.M. and Armand, M.. Issues and challenges facing rechargeable lithium batteries. Nature, 414:359367, 2001.
[27] Yamada, Atsuo, Koizumi, Hiroshi, Sonoyama, Noriyuki, and Kanno, Ryoji. Phase change in LixFePO4 . Electrochemical and Solid-State Letters, 8(8):A409A413, 2005.
[28] Zackrisson, Mats, Avellán, Lars, and Orlenius, Jessica. Life cycle assessment of lithium-ion batteries for plug-in hybrid electric vehicles–critical issues. Journal of Cleaner Production, 18(15):15191529, 2010.
[29] Zeng, Yi and Bazant, Martin Z.. Phase separation dynamics in isotropic ion-intercalation nanoparticles. in preparation, 2013.

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