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Theory of structural transformation in lithiated amorphous silicon Ekin Dogus Cubuk, and Efthimios Kaxiras Nano Lett., Just Accepted Manuscript • Publication Date (Web): 09 Jun 2014 Downloaded from http://pubs.acs.org on June 10, 2014
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Nano Letters
Theory of structural transformation in lithiated amorphous silicon Ekin D. Cubuk and Efthimios Kaxiras∗ Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge MA 02138 E-mail:
[email protected] Abstract Determining structural transformations in amorphous solids is challenging due to the paucity of structural signatures. The effect of the transitions on the properties of the solid can be significant and important for applications. Moreover, such transitions may not be discernible in the behavior of the total-energy or the volume of the solid as a function of the variables that identify its phases. These issues arise in the context of lithiation of amorphous silicon (a-Si), a promising anode material for high-energy-density batteries based on lithium ions. Recent experiments suggest the surprising result that the lithiation of a-Si is a two-phase process. Here, we present first-principles calculations of the structure of a-Si at different lithiation levels. Through a detailed analysis of the short and medium-range properties of the amorphous network, using Voronoi-Delaunay methods and ring statistics, we show that a-Lix Si has a fundamentally different structure below and above a lithiation level corresponding to x ∼ 2.
Keywords: Li-ion batteries, silicon, amorphous solids, first-principles Materials are slated to play a key role in addressing future challenges in energy use. As a case in point, high-energy density batteries, often based on Li-ion technology, are important for ∗ To
whom correspondence should be addressed
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many mobile applications. Increasing the capacity and durability of Li-ion batteries is necessary for enabling solutions in various energy sectors, such as transportation. 1,2 Silicon is a promising anode material for Li-ion batteries with a high theoretical capacity, because it can absorb more than 4 Li atoms per Si atom, as compared to the capacity of graphite, a common anode material, which absorbs up to 1 Li atom per 6 C atoms. 3,4 This has fueled an intense research effort for integrating Si in Li-ion battery design. 3–7 Understanding the lithiation/delithiation process of Si anodes is very important for designing the next-generation Li-ion batteries, because at the high lithiation limit the material expands by up to 400% and the anode fractures and cannot sustain many charging cycles. The fracture behavior depends sensitively on the lithiation/delithiation process. 8 The lithiation reaction of crystalline Si (c-Si) has been studied extensively and has been described in detail, both theoretically and experimentally. 9–18 c-Si becomes amorphous after the first cycle of lithiation and delithiation. Much less is known about these processes in amorphous Si (a-Si), which has better lithiation characteristics than c-Si. 8 Lithiation of c-Si is a two-phase reaction, in which c-Si is lithiated layer by layer. 9,10,15,19 Lithiated Si is separated from pristine c-Si by a sharp (∼ 1 nm thickness) reaction front, which moves into c-Si as the reaction progresses. Recent experiments suggest that the lithiation of a-Si is also a two-phase mechanism, contrary to previous understanding. 8,20 These experiments indicate a clear boundary between lithiated and pristine a-Si as the reaction progresses. This is quite surprising given the lack of crystalline order in a-Si, although the thickness of the reaction front may not be as sharp as in c-Si. In addition, one experimental study has proposed that as the reaction front progresses into pure a-Si, the lithiated Si has relatively constant Li concentration of x ≈ 2.5. 20 After most of the a-Si is lithiated to the concentration of x ≈ 2.5, a second step of the reaction occurs, where the concentration of the aLix Si increases from x ≈ 2.5 to x = 3.75. The experimental results are not conclusive on whether this second step is a single-phase or two-phase reaction. 20
In order to resolve these issues, and to provide a comprehensive picture of the a-Si lithiation processes, it is necessary to describe the relevant atomistic features with an unbiased and reliable theoretical model. It is also important to include in the model enough degrees of freedom to
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Nano Letters
capture the complexity of the amorphous network and the changes it undergoes during the lithiation/delithiation process. Previously reported atomistic models of a-Lix Si with first-principles calculations used small unit cells with periodic boundary conditions to describe the structures at different Li content (x values). 21–23 The relatively small size of the unit cells imposes severe limitations on how well the model captures the nature of the amorphous solid. Large unit cells of a-Lix Si have recently been studied using empirical potentials of the type second nearest neighbor modified embedded atom method (2NN MEAM) 24 and reactive force field (ReaxFF). 25 We present detailed structural and geometric analysis of a-Lix Si for a very wide range of concentrations, x = 0 − 4.25. To improve the statistics, for each x value, we have investigated 10 different structures. Each one of our structures has 64 Si atoms, and a corresponding number of Li atoms for different x values. The largest unit cell, corresponding to x = 4.25, contains 336 atoms. To achieve a detailed understanding of the effect of varying x on medium-range order, we analyzed ring statistics and the geometric properties of the Delaunay triangulation. Our results suggest that a-Lix Si goes through a structural transformation during lithiation until about x ≈ 2, after which the short-range and medium-range order stays relatively constant in several important aspects. We discuss how this analysis can help explain the lithiation reaction and crystallization of a-Si observed in experiments. We also offer some predictions on why limiting the range of lithiation in batteries with a-Si anodes could significantly reduce the structural degradation of the electrodes. To obtain reliable structural models, we used first-principles calculations within density functional theory with the SIESTA code 26 and the PBE exchange-correlation functional. 27 The KohnSham orbitals are represented by a double-ζ plus polarization basis set, with an energy cutoff of 70 Ry. Structural relaxations were considered converged when the magnitude of the force on each atom was smaller than 0.04 eV/Å. Our starting point was an amorphous bulk structure consisting of 64 Si atoms with no coordination defects to model the a-Si electrode before lithiation. 28,29 To model the lithiation of a-Si, we inserted Li atoms in selected positions of the a-Si structure, and relaxed the structure in terms of both atomic positions and lattice vectors. At each step, Li atoms were placed in tetrahedral-like (“Td-like”) positions in a-Si. To find these positions, we identify
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