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Research Papers

# Concentration-Dependent Chemical Expansion in Lithium-Ion Battery Cathode Particles

[+] Author and Article Information
Veruska Malavé

Department of Mechanical Engineering,
Golden, CO 80401
e-mail: vmalaved@mines.edu

J. R. Berger

Department of Mechanical Engineering,
Golden, CO 80401
e-mail: jberger@mines.edu

P. A. Martin

Department of Applied Mathematics
and Statistics,
Golden, CO 80401
e-mail: pamartin@mines.edu

Crystal volumetric variations in other LIB electrode materials, such as LixM1∕6Mn2O4 derivative cathodes (M = Cr, Co, and Ni) and Li-alloy anodes, appear to experience linear volume changes with Li content [31,32].

The general spherically symmetric solution of Laplace's equation, ∇2Φ = 0, is Φ(r) = A + B/r.

For practical purposes, the saturation time is considered to be the time needed to lithiate the cathode particle until it reaches the maximum concentration of the compositional range studied (i.e., Li0.55CoO2).

Note that the terms $C∧$ and x in LixCoO2 are equivalent.

Maximum discharge (at $C∧=0.55$) or charge (at $C∧=0.37$) is reached at $t∧=0.5$.

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 13, 2014; final manuscript received June 5, 2014; accepted manuscript posted June 11, 2014; published online June 23, 2014. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 81(9), 091005 (Jun 23, 2014) (9 pages) Paper No: JAM-14-1212; doi: 10.1115/1.4027833 History: Received May 13, 2014; Revised June 05, 2014

## Abstract

In this work, the effect of the concentration-dependent chemical-expansion coefficient, β, on the chemo-elastic field in lithium-ion cathode particles is examined. To accomplish this, an isotropic linear-elastic model is developed for a single idealistic particle subjected to potentiostatic-discharge and charge conditions. It is shown that β can be a key parameter in demarcating the chemo-stress–strain state of the cathode material undergoing nonlinear volumetric strains. As an example, such strains develop in the hexagonal-to-monoclinic-phase region of LixCoO2 (0.37 ≤ x ≤ 0.55) and, subsequently, the corresponding β is a linear function of concentration. Previous studies have assumed a constant value for β. Findings suggest that the composition-generated chemo-elastic field that is based on a linear-β dramatically affects both the interdiffusion and the mechanical behavior of the LixCoO2 cathode particle. Because the chemo-elastic phenomena emanate in a reciprocal fashion, the resulting linear β-based hydrostatic-stress gradients significantly aid the diffusion of lithium. Thus, diffusion is accelerated in either electrochemical process that the cathode material undergoes.

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## Figures

Fig. 1

LixCoO2 crystal volume as a function of Li content (adapted from Reimers and Dahn [28]). The monoclinic phase is labeled as M1; two hexagonal phases are labeled as H1 and H2.

Fig. 2

Influence of hypothetical parameters of a linear β∧ on saturation time, t∧s, within the LixCoO2 cathode particle (0.37 ≤x≤ 0.55) at r∧ = 0.5: (a) ξ∧ effect at fixed η∧ = 1.0 and (b) η∧ effect at fixed ξ∧ = 1.0 during potentiostatic discharge conditions

Fig. 3

Influence of the β∧ parameter at r∧ = 0.5 for normalized values on the (a) Li diffusion and (b) hydrostatic stress during discharge-and-charge potentiostatic conditions (0.37 ≤x≤ 0.55)

Fig. 4

Evolution of the Li concentration profile across the LixCoO2 particle radius (a)–(d) and hydrostatic stress (e)–(f) under discharge potentiostatic conditions (0.37 ≤x≤ 0.55). Note that no steady state is reached by the reported t∧.

Fig. 5

Evolution of the Li concentration profile across the LixCoO2 particle radius (a)–(d) and hydrostatic stress (e)–(f) under charge potentiostatic conditions (0.55 ≥ x ≥ 0.37). Note that no steady state is reached by the reported t∧.

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