A238 Journal of The Electrochemical Society, 159 (3) A238-A243 (2012) 0013-4651/2012/159(3)/A238/6/$28.00 © The Electrochemical Society Concurrent Reaction and Plasticity during Initial Lithiation of Crystalline Silicon in Lithium-Ion Batteries Kejie Zhao, a, * Matt Pharr, a Qiang Wan, a,b, ** Wei L. Wang, a,c Efthimios Kaxiras, a,c Joost J. Vlassak, a and Zhigang Suo a, z a School of Engineering and Applied Sciences and c Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA b Institute of Structural Mechanics, China Academy of Engineering Physics, Mianyang 621900, China In an electrochemical cell, crystalline silicon and lithium react at room temperature, forming an amorphous phase of lithiated silicon. The reaction front—the phase boundary between the crystalline silicon and the lithiated silicon—is atomically sharp. Evidence has accumulated recently that the velocity of the reaction front is limited by the rate of the reaction at the front, rather than by the diffusion of lithium through the amorphous phase. This paper presents a model of concurrent reaction and plasticity. We identify the driving force for the movement of the reaction front, and accommodate the reaction-induced volumetric expansion by plastic deformation of the lithiated silicon. The model is illustrated by an analytical solution of the co-evolving reaction and plasticity in a spherical particle. We derive the conditions under which the lithiation-induced stress stalls the reaction. We show that fracture is averted if the particle is small and the yield strength of lithiated silicon is low. Furthermore, we show that the model accounts for recently observed lithiated silicon of anisotropic morphologies. © 2011 The Electrochemical Society. [DOI: 10.1149/2.020203jes] All rights reserved. Manuscript submitted July 22, 2011; revised manuscript received October 4, 2011. Published December 30, 2011. Lithium-ion batteries dominate the market of power sources for wireless electronics, and are being implemented in electric vehicles. 1, 2 Intense efforts are dedicated to developing next-generation lithium- ion batteries with high energy density, long cycle life, and safe operation. 3, 4 Silicon can host a large amount of lithium, making it one of the most promising materials for anodes. 5 Lithiation of silicon, however, causes large volumetric expansion and mechanical stress, often leading to the shedding of active materials and rapid decay of capacity. 6 This mode of failure can be mitigated in nanostructured sil- icon anodes. Examples include nanowires, 7 thin films, 8 nanoporous structures, 9 hollow nano-particles, 10 and carbon-silicon composites. 11 Specifically, recent experiments and theories show that nanostructured silicon may avert fracture when the lithiation-induced expansion is accommodated by plasticity. 12 –18 To develop such nanostructured an- odes, it is urgent to understand lithiation-induced stress, deformation, and fracture. Nanostructured electrodes of silicon are often fabricated with crystalline silicon. In an electrochemical cell, crystalline silicon and lithium react at room temperature, forming an amorphous phase of lithiated silicon [Fig. 1]. 7, 19–23 The reaction front is atomically sharp— the phase boundary between the crystalline silicon and the lithiated silicon has a thickness of ∼1 nm. 24 Evidence has accumulated recently that, in the nanostructured electrodes, the velocity of the reaction front is not limited by the diffusion of lithium through the amorphous phase, but by the reaction of lithium and silicon at the front. For example, it has been observed that under a constant voltage the displacement of the reaction front is linear in time. 25 This observation indicates that the rate of lithiation is limited by short-range processes at the reaction front, such as breaking and forming atomic bonds. That the reaction is the rate-limiting step is perhaps most dramat- ically demonstrated by lithiated silicon of anisotropic morphologies. Recent experiments have shown that lithiated silicon grows preferen- tially in a direction perpendicular to the (110) planes of crystalline silicon. 25 –27 It has been suggested that the anisotropic morphologies are due to the difference in diffusivities along various crystalline ori- entations of silicon. However, it is well established that the tensor of diffusivity of a species in a cubic crystal is isotropic. 28 We propose that the observed anisotropic morphologies are due to the variation in the short-range atomic processes at the reaction fronts in different crystallographic orientations. ∗ Electrochemical Society Student Member. ∗∗ Electrochemical Society Active Member. z E-mail: suo@seas.harvard.edu We further note that, to accommodate the large volumetric expan- sion associated with the phase transition, the lithiated silicon must deform plastically. It is instructive to compare a flat reaction front with a curved one. When the reaction front is flat [Fig. 2a], the large volumetric expansion associated with the reaction is accommodated by elongating the lithiated silicon in the direction normal to the re- action front, while maintaining the geometric compatibility between the two phases in the directions tangential to the reaction front. As the reaction front advances, freshly lithiated silicon is added at the front, and previously lithiated silicon recedes by rigid-body transla- tion, with no deformation. The biaxial stresses in the lithiated silicon remain at the compressive yield strength. When the reaction front is flat, reaction and plasticity are concurrent and co-locate—right at the reaction front. Indeed, the two processes may not be differentiated without ambiguity. When the reaction front is curved, the crystalline silicon and the lithiated silicon form a core-shell structure [Fig. 2b]. As the reaction front advances, freshly lithiated silicon is added at the front, previously lithiated silicon recedes, and the shell enlarges. An element of lithiated silicon at the curved front initially undergoes compressive plastic deformation in the hoop directions. Upon subsequent lithiation of the core, the element is pushed away from the front, unloads elastically, and then deforms plastically in tension in the hoop directions. This process results in tensile hoop stress at the surface of the particle, possibly causing fracture. When the reaction front is curved, reaction and plasticity are concurrent, but can occur at different places. There is no ambiguity in differentiating processes at the reaction front and plastic deformation inside the lithiated silicon. We present a model of concurrent reaction and plasticity. Existing analyzes of lithiation-induced deformation and fracture have assumed diffusion-limited lithiation. 15–17, 29–36 Liu et. al. described a two-phase model with diffusivities dependence on local lithium concentration, giving an evolving core-shell structure with a sharp interface separat- ing Li-deficient core and Li-rich shell. 31 In this paper, motivated by experimental observations, we assume that the velocity of the reac- tion front is limited by the rate of the reaction of lithium and silicon at the front, rather than by the diffusion of lithium through the amor- phous phase. We identify the driving force for the movement of the phase boundary, and accommodate the reaction-induced volumetric expansion by plastic deformation of lithiated silicon. The model is illustrated by an analytical solution of the co-evolving reaction and plasticity in a spherical particle. We show that lithiation may induce high enough stress to stall the reaction, and that fracture is averted if the particle is small and the yield strength of lithiated silicon is low. Downloaded 30 Dec 2011 to 129.10.107.106. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp