Article pubs.acs.org/JPCC
Atomistic Mechanisms of Phase Boundary Evolution during Initial Lithiation of Crystalline Silicon Sang-Pil Kim,† Dibakar Datta,‡ and Vivek B. Shenoy*,§,∥ †
Samsung SDI R&D Center, 130 Samsung-ro, Suwon, Gyunggi 443-803, South Korea School of Engineering, Brown University, 184 Hope Street, Providence, Rhode Island 02912, United States § Department of Materials Science and Engineering and ∥Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States ‡
S Supporting Information *
ABSTRACT: In lithium-ion batteries, the electrochemical reaction between Li and Si causes structural changes in the negative electrode. The dynamics of lithiation of Si can be further complicated by the crystalline-to-amorphous phase transition. In situ TEM experiments show that a sharp interface, known as phase boundary, is formed in between c-Si and a-LixSi during initial lithiation. Despite intensive study of the mixing mechanism during lithiation of Si negative electrode, the atomistic investigation of the formation and propagation of phase boundary for different orientation of Si remains unclear. We, therefore, performed molecular dynamics simulations to characterize the structural evolution of the phase boundary with a newly developed reactive force field (ReaxFF) potential for Li−Si. Our results confirm the phase boundary formation in between c-Si and a-LixSi. Structure and dynamics of the phase boundary depend on the crystalline phase of the Si. In particular, the location of the (111) plane plays a key role in crystal-to-amorphous phase transformation. A relatively thick phase boundary is developed at the (100) surface, while an atomically sharp interface of negligible thickness is formed at the (111) surface. An amorphous phase of lithiated Si is developed beyond the phase boundary, in which the ratio of lithium to silicon atoms is steady at 0.8. Partial RDF studies revealed that the structures of the phase boundary and the lithiated Si region are c-LiSi and a-Li15Si4, respectively.
■
INTRODUCTION Rechargeable lithium-ion batteries (LIBs) have been extensively used in portable electronics, light vehicles, and miscellaneous power devices over the past decades because of their high gravimetric energy storage and are currently being considered for use in critical applications such as heavy automotives and medical devices.1 In terms of energy density, the seemingly ubiquitous LIBs exhibit superb performance as compared to other types of rechargeable batteries.2 In most Li-ion batteries, the negative electrode (anode) material is graphite, which forms lithium−graphite intercalation compounds (Li-GICs).3 However, silicon can store approximately 10 times more Li than graphite (the gravimetric energy densities of silicon and graphite are 3579 and 372 mAh/g, respectively).4 In addition, silicon and silicon-composite materials are cheap, readily available, and possess high charge capacity and low discharge potential. Thus, silicon-based materials are strong potential candidates for anode materials in LIBs.5,6 However, the high charge capacity is associated with excessive volume swelling (∼370%) and structural changes during the charging/ discharging process, leading to mechanical fracture, interparticle disconnection, irreversible capacity loss, and limited electrode cycle life.7−9 Despite the advantages of Si electrodes in LIBs, mechanical damages induced by large volumetric strain during cycling present a major challenge in optimizing the microstructure of composite electrodes. To overcome these problems, various nanostructured architectures of Si electrodes © 2014 American Chemical Society
have been proposed, with proven improvements in the mechanical durability of Si-electrode batteries.10−13 The dynamics of Li in Si anodes have been investigated experimentally and theoretically.14−35 Using transmission electron microscopy (TEM), Liu et al. directly observed the crystal-to-amorphous phase transformation (CAPT) of Si during lithiation resulting from anisotropic swelling as tensile hoop stress accumulated in the lithiated shell.29 Anomalous shape changes during the lithiation of single crystal Si nanopillars have been shown to depend on the orientation of the Si structure.30 The composition of the lithiated region and its CAPT has been revealed by nuclear magnetic resonance and by analyzing the Li−Si interphase structures.27,28 The phase boundary formation and the stress associated with damage evolution have been characterized by real-time measurement during the initial lithiation/delithiation cycle.32 Liu et al. observed a sharp interface between the c-Si and an a-LixSi alloy.36 The observed phase boundary32 between the c-Si and the lithiated Si region is expected to be pivotal in understanding the plastic deformation of electrodes. In contrast to the experimental studies, theoretical approaches to date have been hindered by our limited ability to interpret the experimental observations or to find physical Received: March 13, 2014 Revised: July 7, 2014 Published: July 8, 2014 17247
dx.doi.org/10.1021/jp502523t | J. Phys. Chem. C 2014, 118, 17247−17253
The Journal of Physical Chemistry C
Article
enforced along both off-axial directions. A virtual flat wall, erected at the far axial boundary, generated a perpendicular force to prevent atoms from escaping the simulation box. Motivated by the experimental42,43 and theoretical26 work at high temperatures, the MD calculations were performed at temperatures ranging from 600 to 1500 K in order to reduce the simulation time by accelerating the reactions. This approach has been employed in several previous studies for simulating chemical reactions on time scales relevant for MD simulations. For example, Johari et al.26 studied different stages of lithiation of crystalline as well as a-Si anodes at 1200 K and have successfully examined the diffusion kinetics of Li and Si atoms in both crystalline and amorphous Si. The temperature was controlled by a Berendsen thermostat, which rescaled atom velocities at each step (one MD time step Δt = 0.2 fs).44 The charge transfer was performed by the charge equilibrium (QEq) method45 at each step.
parameters that can be integrated into large-scale simulations. Lithiation-induced shape changes and evolution of stress during the volumetric expansion of plastically deformed lithiated silicon have been investigated using continuum models.14,17,19,22,37,38 Atomic-scale theoretical studies, however, have not progressed beyond the density functional theory (DFT), which characterizes diffusion energy barriers, elastic properties, and formation energies.10,16,19−21,23−26,31,37 The ab initio molecular dynamics method is a useful for exploring the dynamics during lithiation16,21,24,26,35,36 but is restricted to lengths and time scales of nanometers and picoseconds, respectively. An alternative (and more promising) method is classical molecular dynamics (MD), which yields information on structural and thermodynamic evolutions under various conditions. MD operates over tens of nanometers and a few nanoseconds of simulation time. However, MD requires knowledge of the interatomic potentials that accurately describe chemical reactions. Such knowledge is limited for the specific case of Li-ion batteries to the formation of the solid electrolyte interphase (SEI).39 Because of lack of suitable potentials, MD simulations have not yet been implemented to investigate phase boundary motion in Li−Si systems, despite the importance of this process to the performance of the anode. However, Fan et al.40 recently have employed a newly developed reactive force field (ReaxFF) to study the mechanical properties of a-LixSi alloys using MD simulations. This ReaxFF potential provides accurate predictions of a set of fundamental properties for LixSi alloys, such as Li composition dependent elastic modulus, open-cell voltage, and volume expansion. In addition, ReaxFF is capable of describing various bonding environments, essential for improving the chemical accuracy of simulated structures and properties spanning a wide range of Li compositions. The optimized force field parameters, used to predict lattice parameters and the heat of formation of selected condensed phases, closely match those of the previous DFT calculations and experiments. In this work, we have studied the dynamic evolution of the first lithiation cycle into various Si structures (a-Si and c-Si with (100)-, (110)-, and (111)-oriented structures). In addition, the structural evolution of the phase boundary formation between the crystalline and lithiated silicon is systematically investigated.
■
RESULTS AND DISCUSSION During initial lithiation, distinct structural evolutions are observed in the lithiated Si region of different Si structures (Figure 1). The reaction is most active in a-Si (Figure 1a). As
Figure 1. Atom and charge configurations during initial lithiation of (a) a-Si, and (b−d) c-Si. The snapshots of c-Si are viewed along the [110] direction, and a set of bonds connecting two (111) planes are highlighted by red lines. The atom colors denote the charge state. Green indicates neutral atoms, blue indicates Si atoms q < −0.5e, and red indicates Li atoms q > +0.5e. All snapshots are taken after a reaction time of 200 ps at 1200 K.
■
SIMULATION METHODS To obtain the a-Si structure, a diamond cubic crystal was melted followed by quenching of liquid by an NPT MD calculation.41 The c-Si structures of different orientations were created by rotating the Si(100) structure considering the periodicity at the boundary. We focused solely on lithiation behavior, ignoring the effects of electric current density, electrolyte, and cathode materials. The sample size extended sufficiently along the axial direction for formation and evolution of lithiation to be observed during the simulation time but was restricted to slightly longer than the cutoff radius of the interatomic potential (here, 10 Å) in order to maximize the computational efficiency. Given the above considerations, the size of the simulation domain was approximately 300 Å × 17 Å (where the lengths denote the axial and off-axial directions, respectively). The axial direction was occupied by Si atoms up to approximately 110 Å; the remaining space contained a sufficient number of Li atoms (Li:Si ratio = 12:7 in all cases). In total, the systems were composed of about 3908 and 6253 atoms, respectively. Periodic boundary conditions were
Li reacts with c-Si, different interface structures are formed. The thickness of the lithiated Si region depends on the direction of the crystal orientations. The unique interphase, the so-called “phase boundary”, is formed between the regions of c-Si and lithiated Si and can be easily distinguished by the atom colors representing the charge states (Figure 1b−d). Since the atoms at the phase boundary are well ordered and evenly distributed, we infer that this region is crystalline. As described by the Supporting Information movies (LiSi100.avi and LiSi110.avi), which are taken from the simulations at 1200 K, the lithiation behavior at the phase boundary is governed by hopping diffusion between the tetrahedral sites (the most stable positions in the Si crystal for Li insertion19,20). The energy barrier of a Li atom hopping between two tetrahedral sites in the Si crystal structure is computed by a nudged elastic band (NEB) calculation.46 Multiple NEB simulations established an energy barrier of 0.52 eV for Li diffusion, which is in good agreement with previous results calculated by DFT.20 17248
dx.doi.org/10.1021/jp502523t | J. Phys. Chem. C 2014, 118, 17247−17253
The Journal of Physical Chemistry C
Article
growth mechanism, once the a-Li−Si alloy begins to expand, it is pushed away from the interface between the crystalline and amorphous phase because the yield strength of the c-Si greatly exceeds that of the a-LixSi alloy.30 To investigate atomic diffusion during lithiation, we compute the concentration profile from the results of Figure 1 (see Figure 2). The Si and Li concentrations are observed to be
Lithiation behavior at the phase boundary (both direction of Li diffusion and propagation of Si−Si bond fracture) depends heavily on crystalline orientation. Previous studies have reported that Li preferentially diffuses along the [110] direction (as demonstrated in Figure 1) and tends to accumulate at tetrahedral sites,30 causing Si−Si bond breakage between (111) planes. This mechanism is similar to that of “half-stacking fault” exhibited by H atoms.47 Furthermore, breaking is developed by the chemical change known as “charge-induced Si-bond weakening”, rather than by mechanical swelling caused by the Li insertions.19 Therefore, the thickness of the phase boundary is strongly related to the Si−Si bond locations between the (111) planes (highlighted in red in Figure 1b−d). In Si(100), these bonds are oblique to the normal surface, which increases the time required for Li atoms to occupy all tetrahedral sites in a particular plane. Therefore, compared with the other states, the phase boundary structure of Si(100) shows a longer region of phase evolution from crystalline to amorphous structures. Conversely, the bonds of Si(111) are normal to the surface, enabling CAPT to develop by “layer-by-layer cleavage”. Consequently, formation of a phase boundary at the Si(111) surface would be unlikely. This behavior, demonstrated in the Supporting Information movie (LiSi111.avi), has also been recently observed by in situ TEM.36 We now attempt to quantify the physical properties associated with phase boundary motion. Propagation velocities are calculated from the final thickness of the remaining Si after 300 ps MD simulation at 1200 K. The phase transition occurs in a region less than 2 nm wide. The smallest phase boundary appears in the [111] crystal, where the transformation from aLixSi to c-Si is abrupt. The phase boundary thicknesses obtained from our MD simulations and the HR TEM by Chon et al.32 are listed in Table 1, together with the simulated phase
Figure 2. Relative concentration profiles based on the results of Figure 1. Concentration is regarded as the ratio of the number of Li (or Si) atoms to the total number of atoms in the given space. The first point of intersection from the Li side is taken as the interface (CSi = CLi = 0.5).
almost equal around the interface region. Although a long, clearly defined region of 1:1 Li:Si composition is developed in the a-Si sample, this region cannot be regarded as the phase boundary because the concentration of both Si and Li gradually decreases or increases outward from the interface, signifying normal diffusion. By contrast, the phase boundary is characterized by drastic changes in concentration, as observed in the c-Si cases. The Si(100) sample develops the thickest and most obvious phase boundary, while those of Si(110) and Si(111) are relatively vague. The concentration profile remains at approximately 0.8 Li atoms per Si atom beyond the phase boundary (in the amorphous lithiated Si region). In the a-Si sample, Li (Si) concentration monotonically increases (decreases) up to the pure Li region. On the basis of the concentration and the phase boundary thickness, we hypothesize that the amorphous lithiated Si region is a-Li15Si4 (in which the atomic ratio of Li to Si is 0.79). To investigate the breakage of Si−Si network bonds across the lithiated Si region, the partial coordination number of Si−Si pairs (CNSi−Si) is computed. As shown in Figure 3a, the initial CNSi−Si is 4.0 (indicating a perfect diamond structure) and declines to zero (an isolated Si atom or pure Li region). The CNSi−Si in the c-Si structures changes suddenly around the interface, indicating the presence of the phase boundary. The lack of a phase boundary in the a-Si structure is also verified, since the CNSi−Si decays monotonically with constant slope. According to Figure 2, the phase boundaries develop at −10.0− 0.0 Å from the interface, where the CNSi−Si remains approximately 4.0. This implies that the Si−Si bond network at the phase boundary sustains its lattice structure by allowing the diffusion of Li atoms into the tetrahedral. Once the relative
Table 1. Summary of Physical Properties Pertaining to the Phase Boundary Evolution during the Lithiation of a-Si and c-Si thickness of phase boundary [nm] samples
MD simulation
experiment
velocity [nm/ps] at 1200 K
a-Si Si(100) Si(110) Si(111)
N/A 1.61 1.23 0.59
N/A ∼1.5 ∼1
