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Phase transition and hysteresis in a rechargeable lithium battery

Abstract

We develop a model which describes the evolution of a phase transition that occurs in some part of a rechargeable lithium battery during the process of charging/discharging. The model is capable to simulate hysteretic behavior of the voltage - charge characteristics. During discharging of the battery, the interstitial lattice sites of a small crystalline host system are filled up with lithium atoms and these are released again during charging. We show within the context of a sharp interface model that two mechanical phenomena go along with a phase transition that appears in the host system during supply and removal of lithium. At first the lithium atoms need more space than it is available by the interstitial lattice sites, which leads to a maximal relative change of the crystal volume of about 6%. Furthermore there is an interface between two adjacent phases that has very large curvature of the order of magnitude 100 m, which evoke here a discontinuity of the normal component of the stress. In order to simulate the dynamics of the phase transitions and in particular the observed hysteresis we establish a new initial and boundary value problem for a nonlinear PDE system that can be reduced in  More>>
Authors:
Dreyer, Wolfgang; [1]  Gaberscek, Miran; Jamnik, Janko [2] 
  1. Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany)
  2. Kemijski Institut Ljubljana Slovenija (Slovenia). L10 Lab. for Materials Electrochemistry
Publication Date:
Jul 01, 2007
Product Type:
Miscellaneous
Report Number:
WIAS-1284(prepr.)
Subject:
25 ENERGY STORAGE; HYSTERESIS; LITHIUM; INTERSTITIALS; INTERFACES; STRESSES; BOUNDARY-VALUE PROBLEMS; CRYSTAL-PHASE TRANSFORMATIONS; METAL-NONMETAL BATTERIES; MATHEMATICAL MODELS; CONTINUITY EQUATIONS; CONSERVATION LAWS; THERMODYNAMICS; ENERGY DENSITY; DIFFUSION; SIMULATION; FREE ENERGY; THERMAL EQUILIBRIUM; KINETIC EQUATIONS; IRON PHOSPHATES; SURFACE TENSION; BATTERY CHARGE STATE
OSTI ID:
21092185
Research Organizations:
Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany)
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Other: ISSN 0946-8633; TRN: DE08GB108
Availability:
Commercial reproduction prohibited; OSTI as DE21092185
Submitting Site:
DE
Size:
32 pages
Announcement Date:
Nov 06, 2008

Citation Formats

Dreyer, Wolfgang, Gaberscek, Miran, and Jamnik, Janko. Phase transition and hysteresis in a rechargeable lithium battery. Germany: N. p., 2007. Web.
Dreyer, Wolfgang, Gaberscek, Miran, & Jamnik, Janko. Phase transition and hysteresis in a rechargeable lithium battery. Germany.
Dreyer, Wolfgang, Gaberscek, Miran, and Jamnik, Janko. 2007. "Phase transition and hysteresis in a rechargeable lithium battery." Germany.
@misc{etde_21092185,
title = {Phase transition and hysteresis in a rechargeable lithium battery}
author = {Dreyer, Wolfgang, Gaberscek, Miran, and Jamnik, Janko}
abstractNote = {We develop a model which describes the evolution of a phase transition that occurs in some part of a rechargeable lithium battery during the process of charging/discharging. The model is capable to simulate hysteretic behavior of the voltage - charge characteristics. During discharging of the battery, the interstitial lattice sites of a small crystalline host system are filled up with lithium atoms and these are released again during charging. We show within the context of a sharp interface model that two mechanical phenomena go along with a phase transition that appears in the host system during supply and removal of lithium. At first the lithium atoms need more space than it is available by the interstitial lattice sites, which leads to a maximal relative change of the crystal volume of about 6%. Furthermore there is an interface between two adjacent phases that has very large curvature of the order of magnitude 100 m, which evoke here a discontinuity of the normal component of the stress. In order to simulate the dynamics of the phase transitions and in particular the observed hysteresis we establish a new initial and boundary value problem for a nonlinear PDE system that can be reduced in some limiting case to an ODE system. (orig.)}
place = {Germany}
year = {2007}
month = {Jul}
}