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Phase transition in a rechargeable lithium battery

Published online by Cambridge University Press:  17 February 2011

W. DREYER ,
M. GABERŠČEK ,
C. GUHLKE ,
R. HUTH  and
J. JAMNIK
W. DREYER
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr 39, 10117 Berlin, Germany email: guhlke@wias-berlin.de
M. GABERŠČEK
Affiliation:
Kemijski Inštitut Ljubljana Slovenija, L10 Laboratory for Materials Electrochemistry, SI-1001 Ljubljana, Hajdrihova 19, Slovenia
C. GUHLKE
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr 39, 10117 Berlin, Germany email: guhlke@wias-berlin.de
R. HUTH
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr 39, 10117 Berlin, Germany email: guhlke@wias-berlin.de
J. JAMNIK
Affiliation:
Kemijski Inštitut Ljubljana Slovenija, L10 Laboratory for Materials Electrochemistry, SI-1001 Ljubljana, Hajdrihova 19, Slovenia
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Abstract

We discuss the lithium storage process within a single-particle cathode of a lithium-ion battery. The single storage particle consists of a crystal lattice whose interstitial lattice sites may be empty or reversibly filled with lithium atoms. The resulting evolution equations describe diffusion with mechanical coupling and incorporate volume changes, phase transitions and surface tension. In order to simulate the dynamics, we assume spherical symmetry and fast bulk diffusion of the lithium atoms, which lead to a core shell model. We verify the common assumption of phase nucleation at the external boundary of the particle. This model is capable to predict voltage–capacity behaviour. For slow charging rates, we compare the results with experimental voltage–capacity plots exhibiting hysteretic behaviour. We observe that hysteresis cannot be described within the setting of a single-particle cathode. The origin of this fact is discussed in detail. The result is of enormous importance because single-particle models, in particular core shell models, up to now are very popular in the chemical literature.

Keywords

lithium-ion-batteryphase transitionthermodynamic
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 3 , June 2011 , pp. 267 - 290
Copyright
Copyright © Cambridge University Press 2011

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References

[1]Allen, J. L., Jow, T. R. & Wolfenstine, J. (2004) Kinetic study of the electrochemical FePO4 to LiFePO4 phase transition. Chem. Mater. 19, 2108–2111.Google Scholar
[2]Delmas, C., Maccario, M., Croguennec, L., Le Cras, F. & Weill, F. (2008) Lithium deintercalation in LiFePO4 nanoparticles via a domino-cascade model. Nature Mater. 7, 665–671.Google Scholar
[3]Dreyer, W. (2003) Jump conditions at phase boundaries for ordered and disordered phases. (WIAS preprint No. 869).Google Scholar
[4]Dreyer, W. & Duderstadt, F. (2008) On the modelling of semi-insulating GaAs, including surface tension and bulk stresses. Proc. R. Soc. Lond., Ser. A Math. Phys. Eng. Sci. 464, 2693–2720.Google Scholar
[5]Dreyer, W., Jamnik, J., Guhlke, C., Huth, R., Moškon, J. & Gaberšček, M. (2010) The thermodynamic origin of hysteresis in insertion batteries. Nature Mater. 9, 448–453.Google Scholar
[6]Dreyer, W., Guhlke, C. & Herrmann, M. (to appear) Hysteresis and phase transition in many-particle storage systems. Contin. Mech. Thermodyn. (WIAS preprint 1481).Google Scholar
[7]Dreyer, W., Guhlke, C. & Huth, R. (2009) The behavior of a many particle cathode in a lithium-ion battery. Physica D. (WIAS preprint No. 1423).Google Scholar
[8]Gaberšček, M., Dominko, R., Bele, M., Remškar, M., Hanzel, D. & Jamnik, J. (2005) Porous, carbon-decorated LiFePO4 prepared by sol-gel method based on citric acid. Solid State Ion. 176, 1801–1805.Google Scholar
[9]Han, B. C., Van der Ven, A., Morgan, D. & Ceder, G. (2004) Electrochemical modeling of intercalation processes with phase field models. Electrochim. Acta. 49, 4691–4699.Google Scholar
[10]Maxisch, T. & Ceder, G. (2006) Elastic properties of olivine LixFePO4 from first principles. Phys. Rev. B. 73, 174112-1–174112-4.CrossRefGoogle Scholar
[11]Padhi, A. K., Nanjundaswamy, K. S. & Goodenough, J. B. (1997) Phospho-olivines as positive-electrode materials for rechargeable lithium batteries. J. Electrochem. Soc. 144, 1188–1194.CrossRefGoogle Scholar
[12]Srinivasan, V. & Newman, J. (2004) Discharge model for the lithium iron-phosphate electrode. J. Electrochem. Soc. 151 (10), A1517–A1529.CrossRefGoogle Scholar
[13]Wagemaker, M., Borghols, W. J. H. & Mulder, F. M. (2007) Large impact of particle size on insertion reaction. A case for anatase LixTiO2. J. Am. Chem. Soc. 129 (14), 4323–4327.Google Scholar
[14]Yamada, A., Koizumi, H., Nishimura, S. I., Sonoyama, N., Kanno, R., Yonemura, M., Nakamura, T. & Kobayashi, Y. (2006) Room-temperature miscibility gap in LixFePO4. Nature Mater. Lett. 5, 357–360.Google Scholar