Open Access

ARTICLE

A Hybrid Quantum-Classical Simulation Study on Stress-Dependence of Li Diffusivity in Graphite

by N. Ohba¹, S. Ogata², T. Tamura², S. Yamakawa¹, R. Asahi¹

1 Toyota Central Research & Development Laboratories, Inc., Nagakute, Aichi 480-1192, Japan
2 Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-Cho, Showa-ku, Nagoya 466-8555, Japan

Computer Modeling in Engineering & Sciences 2011, 75(3&4), 247-266. https://doi.org/10.3970/cmes.2011.075.247

Abstract

Understanding the stress dependence of Li diffusivity in the Li-graphite intercalation compound (Li-GIC) that has been used in the Li-ion rechargeable battery as a negative electrode, is important to search for better conditions to improve the power performance of the battery. In the Li-GIC, the Li ion creates a long-ranged stress field around itself by expanding the inter-layer distance of the graphite. To take into account such a long-ranged stress field in the first-principles simulation of the Li diffusion, we develop the hybrid quantum (QM)-classical (CL) simulation code. In the hybrid code, the QM region selected adaptively around the Li ion following its motion is treated with the real-space density-functional theory. The rest of the total system is described with an empirical inter-atomic potential that includes a novel formula for the dispersion force between the C atoms that belong to different layers. A series of the hybrid QM-CL simulation runs for the dynamics of a single Li-ion in the graphite are performed at temperature 423 K for various values of the averaged inter-layer distance. We thereby find that the Li diffusivity is suppressed substantially when the inter-layer distance is compressed by a few percent from the equilibrium value. On the other hand, the Li diffusivity is unaffected by the stretching of the inter-layer distance up to a few percent. In the equilibrium and stretched cases, the diffusive motion of the Li ion is composed of ballistic and hopping modes. In the compressed case, the Li ion diffuses in the hopping mode only and is confined in a small area at long times. Separately the activation energy for the hopping diffusion is calculated at zero temperature to find that it is as small as 0.1 eV and that the substantial contribution comes from the deformation energy of the whole system. Based on the findings we propose a mechanism to explain the unique Li-density dependence of the Li diffusivity observed experimentally in the Li-GIC.

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