Atomic Insight into the Lithium Storage and Diffusion Mechanism of

Article pubs.acs.org/JPCA

Atomic Insight into the Lithium Storage and Diffusion Mechanism of SiO2/Al2O3 Electrodes of Lithium Ion Batteries: ReaxFF Reactive Force Field Modeling Alireza Ostadhossein,† Sung-Yup Kim,‡ Ekin D. Cubuk,§ Yue Qi,‡ and Adri C. T. van Duin*,∥ †

Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824-1226, United States § Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States ∥ Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: Atomically deposited layers of SiO2 and Al2O3 have been recognized as promising coating materials to buffer the volumetric expansion and capacity retention upon the chemomechanical cycling of the nanostructured silicon- (Si-) based electrodes. Furthermore, silica (SiO2) is known as a promising candidate for the anode of next-generation lithium ion batteries (LIBs) due to its superior specific charge capacity and low discharge potential similar to Si anodes. In order to describe Li-transport in mixed silica/alumina/silicon systems we developed a ReaxFF potential for Li−Si−O−Al interactions. Using this potential, a series of hybrid grand canonical Monte Carlo (GCMC) and molecular dynamic (MD) simulations were carried out to probe the lithiation behavior of silica structures. The Li transport through both crystalline and amorphous silica was evaluated using the newly optimized force field. The anisotropic diffusivity of Li in crystalline silica cases is demonstrated. The ReaxFF diffusion study also verifies the transferability of the new force field from crystalline to amorphous phases. Our simulation results indicates the capability of the developed force field to examine the energetics and kinetics of lithiation as well as Li transportation within the crystalline/amorphous silica and alumina phases and provide a fundamental understanding on the lithiation reactions involved in the Si electrodes covered by silica/alumina coating layers.

1. INTRODUCTION To meet the ever-increasing energy and power demands for portable electronics, electric vehicles and large-scale energy storage devices, high-energy-density lithium (Li) ion batteries (LIBs) have been identified as one of the most promising sources.1 Tremendous research efforts have been carried out to develop new materials with superior specific charge capacity, power and stable cycle performance for electrodes of LIBs.2,3 Silicon (Si) has shown a great promise to be employed as anode of next-generation LIBs due to its high storage capacity, ∼3579 mAh/gr, almost ten times higher than that of conventional graphitic-based anodes.4−6 However, associated with such a high capacity, chemo-electromechanical degradation of Si upon lithiation as a result of its severe volumetric strain up to 300% has so far impeded the commercial application of this material. High resolution transmission electron microscopy (HRTEM) revealed that first-cycle lithiation in crystalline Si nanowire (c© 2016 American Chemical Society

SiNW) electrodes involves structural transformation from c-Si into amorphous lithiated silicon (a-LixSi) alloy with x as high as 3.75.7 The amorphization of Si causes the fracture and pulverization of Li-active materials followed by loss of the electrical contact resulting in the rapid capacity retention. Several volume buffering matrices, which can effectively passivate the surface of nanoelectrodes, have been proposed to minimize the lithiation-induced mechanical strains. Among them, carbon nanostructures and composites have been widely utilized to encapsulate Si-based electrodes owing to their low cost and high conductivity and mechanical stability.8−11 The mechanical and electronic properties of carbon-based coating layers have been extensively studied experimentally and computationally.12−19 Received: December 5, 2015 Revised: March 15, 2016 Published: March 15, 2016 2114

DOI: 10.1021/acs.jpca.5b11908 J. Phys. Chem. A 2016, 120, 2114−2127

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The Journal of Physical Chemistry A

against a wide range of new quantum mechanical calculations. Consecutively, we have carried out a series of reactive molecular dynamics (MD) simulations combining with the grand canonical Monte Carlo (GCMC)42,43 study to model the lithiation of amorphous and crystalline silica (a- and c-SiO2). The stability of reaction product has been then examined by uniaxial tensile loading tests. The diffusion mechanisms of Li through silica layer has been explored.

Recently, atomic layer deposition (ALD) of oxide coating layers, such as SiO2 and Al2O3, has attracted considerable attention as an effective solution to accommodate the large volume expansion and enhance the cyclability of Si electrodes apart from their higher columbic efficiency.20−22 Contrary to the naturally formed oxide layer on SiNWs, artificial ALD coatings demonstrated a great resistance against the fracture of Si-based electrodes during Li loading and unloading. Also, ALD coatings can serve as an artificial solid electrolyte interface (SEI) supporting the underlying Si layers when they are tailored to gain better cyclic performance. While the crucial effects of native oxide layer on Si surface are often ignored,23 considerable experimental studies have been carried out to design various types of artificial oxide coatings on Si surfaces.24,25 Although SiO2 and Al2O3 layers are relatively robust to withstand the volume expansion of Si electrodes upon lithiation, because of their brittleness in their pristine state, they are not capable of sustaining large plastic deformations. In addition, it is reported that undesirable lithiation reactions occurring at the interface of the Si electrode and intrinsic existing oxides leads to incomplete lithiation and large capacity loss after the first cycle.23,26,27 However, the details of these reactions at the atomic scale has not yet been understood. The morphology of the coated Si electrodes and their lithiation reaction-rates alter due to the variation of the ionic conductivity and evolution of the mechanical properties of these coating layers under lithiation.28 From a theoretical standpoint, the chemical potential of Li atoms decreases as a result of the oxide-induced compressive stress at the interface of oxide-layer and the covered Si negative electrode. Hence, finding the optimal thickness of the ALD coatings seems to be critical to attain the simultaneous fast Li diffusion and effective control of the volume expansion. MC Dowel et al.27 showed that 2−5 nm thin layer of SiO2 can limit the volume expansion of Si nanowires within a radius of 25 nm. Xiao et al.29 and Sim et al.30 identified that Si with a coating thickness of 7 nm leads to the best electrochemical performance. However, the underlying mechanism of Li insertion into these oxide layers still remained elusive. Furthermore, Si suboxides (SiOx with x < 2), with a high specific charge capacity and limited lithiation induced volume expansions, have been suggested as a viable material for negative electrode of LIBs.31−34 More recently, new designed nanostructures of silica in the form of hallow nanotubes,35 thin films,36 and nanospheres37 exhibited Li reactivity in the amorphous SiO2 (aSiO2) phases.32 Because of its abundance and environmental friendliness, silica could become an alternative anode for the next generation of LIBs. However, reaction pathways and final products of lithiation of silica has been subject of debate. Using nuclear magnetic resonance (NMR) Kim and co-workers38 predicted that SiO2 irreversibly reacts with Li ions to produce lithium silicates and Li2O during the first discharging process. Meanwhile, Li atoms reversibly participate to make LixSi alloys.38 On the basis of these experiments, lithiation reaction of SiO2 results in formation of lithiated silica compounds such as Li2Si2O5 and Li4SiO4, in agreement with the more recent HRTEM studies.32 However, earlier experiments39 indicated that silica is a completely inert material when it is exposed to Li. In the current paper, a new ReaxFF potential for Li−Si−O−Al has been developed to examine the lithiation kinetics, diffusion and mechanical properties evolution of SiO2 electrodes. This force field, which is built upon an existing potential by Narayanet al.40 and the Li/Si ReaxFF description by Ostadhosseinet al.,41 was tuned to model the batteries interfaces by further training

2. COMPUTATIONAL METHODS 2.1. Ab Initio Calculations. Periodic-DFT calculations were performed using the VASP code. For the exchange-correlation functional approximation we chose the generalized gradient approximation proposed by Perdew−Burke−Ernzerhof (GGAPBE). The projector augmented wave (PAW) pseudopotential was used for describing the core electrons interactions. The surface Brillouin-zone integration was performed using the γcentered Monkhorst−Pack mesh. The plane wave energy cutoff was set to 400 eV. In all of simulations, the atom coordinates were relaxed using a conjugate gradient algorithm until the force components on any atom were smaller than 0.02 eV/Å. To compute diffusion barriers, the nudged elastic band method (NEB) is selected to search for the transition state along the diffusion pathway. 2.2. ReaxFF Reactive Potential. ReaxFF is a highly transferable empirical reactive potential, constructed based on bond-order/bond distance notion,44,45 which allows for bond formation and bond dissociation during molecular statics/ dynamics (MS/D) simulation. It is capable of describing a smooth transition between the nonbonded states and single, double or triple bonded systems. The total interaction energy in ReaxFF is divided in to several energy contributions given by Esystem = Ebond + Eval + Etor + Eover + Eunder + Elp + Evdw + Ecoulombic

(1)

The energy terms in eq 1 comprise the bond energy (Ebond), valence-angle (Eval), torsion-angle energy (Etor) and lone pair (Elp), overcoordinate (Eover) and under coordinate (Eunder) energy penalty terms as well as nonbonded interactions i.e. van der Waals (Evdw) and coloumbic energy (Ecoulomb). All the connectivity dependent energy terms (e.g., valence and torsionangles) are bond-order dependent and updated at every MD or energy minimization step. Thus, the energy and forces pertinent to these components approaches to zero upon bonddissociation. Furthermore, nonbonded interactions such as van der Waals and Columbic terms are calculated for the entire system between each pair of atoms. ReaxFF is a polarizable force field in which electronegativity equalization method (EEM)46 and47 is employed to account for the charge distribution based on the geometry changes of atoms. All the aforementioned features enable ReaxFF to simulate the chemical reactions occur between elements at extreme dynamic environment with a comparable accuracy of DFT simulations. More explanation about the ReaxFF model was presented in the earlier works by Chenoweth et al. and van Duin et al.48,49 ReaxFF potential has been successfully used to model the materials behavior under extreme conditions of loading, temperature and pressure.50,51 It has also been recently applied to identify the reactive properties for complex battery materials and interfaces such as SiNW anode electrodes,41 lithiated sulfur cathode electrodes,52,53 and carbonbased anodes.54 2115


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The Journal of Physical Chemistry A Table 1. Structural Properties of Crystalline Lithium Silica (LixSiO2) with Various Ratios of Li2O versus SiO2

Table 2. Cohesive Energies and Material Properties of Lithium-Silicate and Aluminate Obtained from ReaxFF, DFT, and Experiments phase

property

DFT

SiO2

Young’s modulus (GPa) Poisson ratio density (g/cm3)

Li2Si2O5

Ecohesive (eV) Ecohesive(stable) − Ecohesive (metastable) (kcal/mol) density (g/cm3) Ecohesive (eV) density (g/cm3) Ecohesive (eV) density (g/cm3) Ecohesive (eV) density (g/cm3) Ecohesive (eV) density (g/cm3)

Li4SiO4 Li2Si3O7 Li2SiO3 α-LiAlO2

2.3. Fitting the ReaxFF Parameters for Li/Si/O/Al Systems. In the current paper, by adding a collection of DFT derived data, such as geometries, lithiation energies and diffusion barriers, to the existing ReaxFF Li/Si/Al/O parametrization by Narayanan and co-workers,40 a ReaxFF optimized parameters for Li−Si−Al−O are developed. The parameters for Li/Si were previously employed by Ostadhosseinet al.41 to study the influence of the lithiation-induced stress on the initial discharge of SiNW electrodes. We calculated the equations of states (EOSs), reaction energies and energy barriers of Li in silica and alumina crystals using periodic DFT calculations within a plane wave basis sets. To ensure proper transferability of the resulting Li/Al/Si/O parameters, we added the following sets of DFTcalculated data for a wide range of condensed phases to the previous force field: (1) cohesive energy (based on calculations

−62.6 0.05 2.353 −54.23 −86.12 2.335 −39.05 2.438 −12.46 3.412

reaxFF

experiment

70.15 0.23 2.18 (α-quartz) 2.34 (a-SiO2) −53.5 0.26 2.410 −47.12 2.07 −73.40 2.339 −33.86 2.433 −13.09 3.395

76.6 ± 7.2 0.17 2.2 2.360

of ref 55), heat of formation, and equation of states associated with lithium silicate and aluminates. These data are based upon the open circuit voltages computations of ref 56. The structural properties of these compounds are listed in Table 1. The other three are (2) the Li interstitial diffusion in the pristine α-quartz (SiO2), (3) Li ion diffusion energy barriers in Al2O3 and AlO2, and (4) the long-range diffusion of lithium atom through c-SiO2 (α-quartz). The new sets of data were chosen such that they can represent the compositional dependent mechanical evolution of silica and alumina upon Li cycling. The positive heat of formation calculated using ReaxFF, +0.016 eV/Si atom, in agreement with the DFT results, +0.027 eV/Si-atom, indicates that insertion of a single Li atom into the interstitial site of c-SiO2 lattice is thermodynamically unfavorable.57,58 However, we will show in 2116


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Figure 1. Equation of states (EOS) of (a) Li2Si2O5 and Li2SiO3 and (b) LiO, Li2O, and LiAlO2.

less importance in our current work, we assigned a lower weight comparing to Li2O crystal on this data point during the force field optimization. In addition, the heat of formations of these crystals were computed using ReaxFF and DFT and displayed in Figure 2. The formation energies of these crystals calculated using ReaxFF are in reasonable agreement with the values obtained from DFT, indicating that that the new developed force field can

section 3.1 that, by increasing the Li concentration, the lithiation of c-SiO2 becomes favorable. The structural properties associated with various crystal structures of lithium silicate/aluminate, and the open circuit voltage (OCV) of lithiation reactions are listed in Table 2 and compared with their DFT counterparts. To explore the relative stability of lithiated compounds, we calculated the equation of states (EOS) pertaining to the crystal structures listed in Table 1. These volume−energy relations in Figure 1, represent the strainenergies stored in lithium silicate and aluminate phases at different levels of compression and tension and thus can play an important role in the calculations related to the elastic constants and the lithiation induced volumetric expansion of lithiated produces. The heat of formation associated with these compounds are calculated based on the following equation: t H f (V ) = E(LixAl ySizOt ) − xE Li − yEAl − zESi − EO2 2 (2)

Here E(LixAlySizOt) is the total energy of a given lithium silicate/ aluminate compounds with volume V. The energy of Lifcc, Alfcc, Sidiamond crystals and O2 molecules in the gas phase are the elemental ground-state phases which are used as the reference for the calculation for the heat of formation energies in eq 2. As depicted in Figure 1, overall ReaxFF can successfully reproduce the EOSs obtained from DFT computations. On the basis of this figure, ReaxFF predicts that the LiO crystal is ∼1.6 eV more stable than that of DFT. However, since this species has

Figure 2. Heat of formation (Hf) of lithium aluminate and silicates selected phases using ReaxFF at 0 K. 2117


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(i.e., when a = b = c = d). In this position, Li−O bond lengths are ranging from 1.956 to 2.024 Å. The barrier which has to be overcome by Li atom to hop between two of these sites is calculated as 3.2 and 3.1 kcal/mol in DFT and ReaxFF simulations, respectively. It should be noted that Li atom bonds with two neighboring O(b) atoms at the transition state of diffusion in c-SiO2. Furthermore, the energy profile for Li diffusion between two local minima of alumina, Al2O and Al2O3 phases, are displayed in Figure 3, parts a, b, and c. Contrary to the fast Li diffusion in silica, parts b and c of Figure 3 indicate that diffusion of Li in Al2O and Al2O3 is too slow with a barrier heights of ∼0.8 and 1 eV, respectively. Force Field Optimization. We modified the Li−O and Si− O and Al−O bonds as well as Li−O−Si/Al angle parameters in the new force field optimization steps. A successive oneparameter search method is used to minimize the sum-of-square error function given as

provide reliable thermodynamic behavior for the Li−Si−Al−O systems. A recent study by Kim et al.56 provided a series of interstitial and vacancy diffusion barriers based on which we retrained our Li/Si/Al/O force field and validated our force field for Li diffusion behavior in both silica and alumina phases. This study, in line with the reported results on the lithiation kinetics of SiO2 by Zhang et al.,25 confirms that Li diffusion in c-SiO2 and a-SiO2 is relatively fast. While the old version of the force field (Narayanet al.40) produced a tightly bound state of Li to the bridging O atoms in SiO2 crystal, resulting in a very high diffusion barrier for Li jumping, the modified force field predicts very small Li migration barrier in consistence with DFT and experiments (Figure 3a). According to the DFT calculations the lowest potential energy of Li in c-SiO2 lattice occurs when Li atom is located in the same distance from four bridging oxygen atoms

2 ⎡ (χ − χi ,ReaxFF ⎤ i ,QM ⎢ ⎥ error = ∑ ⎢ ⎥⎦ σi i ⎣

(3)

where, χi,QM and χi,ReaxFF are DFT and ReaxFF computed values respectively and σi is the assigned weight in the ith data point. The fitted Si−O and Li−O bond and off-diagonal parameters are listed in Table 3. Fully optimized parameters ReaxFF for Li− Si−Al−O systems can be found in the Supporting Information. Force Field Validation. To validate the developed ReaxFF description, a series of molecular dynamics simulations were performed and compared with DFT and experiments. The results from these validation simulations are described in the following sections. Structural and Mechanical Properties of Pristine Amorphous Silica. Even though previous studies have successfully implemented ReaxFF for characterization of Si−O systems;59 here, to assess the stability of the new fitted Si−O parameters, the structural and mechanical properties of amorphous silica are examined using the newly developed force field. The amorphous structures were prepared by annealing of crystalline 10 × 10 × 10 supercell of α-quartz comprising 3000 atoms. The unit cell of α-quartz, the first structure listed in Table 1, consists of two silicon and four oxygen atoms. The optimized lattice parameters calculated using ReaxFF are specified in Table 1. The system is heated up from 300 K to 3500K for 1 ns and subsequently quenched with a relatively low cooling rate of 1.024 K/ps. The low quenching rate ensures that the strong Si−O covalent bonds form such that the final structure becomes less defective. Figure 4a displays the amorphous silica structure and the inset shows the 4-fold coordinated Si atoms connected to the vicinal O atoms. Radial pair distribution function (RDF), g(r), is calculated based on 250 ps NVT simulation at finite temperature (300 K) for Si−Si, Si−O, and O−O pairs. The broad peaks of Si− O bonds and absence of sharp peaks at long-range clearly corroborates the structural transformation through the amorphization. The density of the amorphous structure after NPT simulation (with P = 0 and T = 300 K) is measured as 2.17 g/cm3, which is in agreement with 2.2 g/cm3 reported for fused quartz reported by experiments. The uniaxial stiffness and the mechanical strength associated with a-SiO2 is also determined based on the stress−strain analysis from a nonequilibrium MD (NEMD) simulation under standard conditions at constant pressure of 0 atm and finite temperature of 300 K. Following the NPT steps at 300 K, the prepared

Figure 3. Li diffusion barriers in (a) α-quartz and (b) Al2O and (c) Al2O3 calculated based on ReaxFF and DFT. 2118


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The Journal of Physical Chemistry A Table 3. Optimized Parameters for Si−O and Li−O and Al−O Bonds Bond Parameters for Li−O σ-bond dissociation energy (Deσ)

Pbe,1

76.3539

−0.4239

Pbe,2

σ bond order (pbo,1)

σ bond order (pbo2)

−0.2142

6.5996

0.4308 Off-Diagonal Parameters for Li−O

Ediss

Rvdw

Alfa

cov,r

0.1154

1.7012

11.0486

1.5265

Bond Parameters for Si−O σ-bond dissociation energy (Deσ)

Pbe,1

266.5680

−0.3834

Pbe,2



π bond order (pbo3)

8.1149

−0.2163

10.2370 −0.1450 Off-Diagonal Parameters for Si−O

Ediss

Rvdw

Alfa

cov,r

0.1541

1.9059

10.7397

1.6504

Bond Parameters for Al−O σ-bond dissociation energy (Deσ)

Pbe,1

181.1998

−0.2276

Pbe,2



−

6.1462

0.2086 Off-Diagonal Parameters for Al−O

Ediss

Rvdw

Alfa

cov,r

0.2017

1.8458

11.0700

1.6009

Figure 4. Structural and mechanical properties of amorphous silica before lithiation (a) Structure of amorphous silica, due to slow quenching process generates the a-SiO2 structure free of coordination defects. Radial distribution function of Si−O bond in a-SiO2, the first coordination shell and the second peak is in agreement with experiments. (b) Stress−strain curve for amorphous silica under uniaxial tensile loading at 109 s−1.

discuss the adsorption energies and energetics of Li atom diffusion in both crystalline and amorphous silica. Li Insertion into the c/a-SiO2: Voltage Profiles. A hybrid grand canonical Monte Carlo/molecular dynamics (GCMC/ MD) sampling based on the Metropolis algorithm is employed to obtain the formation energies (Ef) per Si atom at various Li concentrations. The potential energy of one Li atom in the bulk body centered cubic (bcc) crystal is used as a reference chemical potential of Li atoms to be placed in the system. The implementation of the hybrid GCMC/MD scheme in ReaxFF is a recently developed tool which is described in detail in Senftle et al.42,43 This method has been lately employed by Raju and his co-workers to calculate the voltage profiles of pristine and defected graphene based anodes when they are intercalated by Li-ion.54 Evolution of Structural Properties during Li Discharge of SiO2. In order to gain atomistic insight into the structural

amorphous sample model has been subjected by uniaxial tensile loading and the stress−strain curve was obtained. We considered different uniaxial strain rates of 108, 109, and 1010 s−1 to probe strain-rate effects on the mechanical properties. Young’s modulus of glassy silica, computed based on the curve fitting to the initial linear part of the stress−strain profile, is obtained as 71.2 GPa, in reasonable agreement with the experimental reported values,60 76.6 ± 7 GPa, as well as the previous MD-simulations using BKS potential, 73.5 GPa.61 Figure 4b shows the stress−strain relation in silica under 109s−1applied strain-rate. The ultimate fracture strength (σu) and strain (εu) were calculated as 20.6 GPa and 0.30, respectively.

3. RESULTS AND DISCUSSION 3.1. Thermodynamics of Li Incorporation and Diffusion in α-Quartz and Amorphous Silica. In this section, we 2119


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Figure 5. Results of the calculated radial/angle distribution functions of glassy SiO2 and fully lithiated silica: (a) RDF shows a first sharp peak position at 1.56 Å reflecting the presence of well-defined Si(O4) tetrahedral units in the glass. The second RDF peak represents the interaction of O(b) atoms locating on the vertices of neighboring tetrahedrons. Also, RDF of Si−O bond indicates bond weakening since to the first coordination shell shifted to the higher bond distances. Also, in the fully lithiated state, stronger Si−Si bonding is confirmed by the merge of the second peaks of Si−Si. (b) Angle distribution functions obtained for Si−O−Si and O−Si−O angle during the lithiation of SiO2 glasses showed that the Si−O−Si units are fragmented into the smaller angles as a result of Li loading, while the stiffer O−Si−O angles are retained.

complexes stopped to grow at x ≈ 2.5. This coincides with the consumption of Si−O(3) to form the Si−O(1) smaller component. Simultaneously, the population of Li2O starts to increase dramatically. To the best of our knowledge, the intrinsic Li-to-Si ratio of 2.5 reflecting the two step lithiation of silica has not yet been reported neither by theoretical models nor by experimental studies. In this concentration, the rate of decay of Si−O(4) tetrahedron-units starts to decrease as indicated by the inflection point of the blue curve in Figure 6a. Looking at the average CN numbers indicates that CNSi−Si and CNO−Si drop from 3.2 and 2.0 (at x = 0) to 0.7 and 0.1 in the fully lithiated state, respectively, because of disintegration of the initial a-SiO2 host network. The CNSi−Si plot is indicative of stable bonding before x ≈ 2.5. However, the fragmentation of the strong tetrahedron units and isolation of O atoms surrounded by Li ions becomes more prominent after x ≈ 2.5. Also, according to the RDF for Si−Si/O and Si−Li/O bonds, as the Li content increases, the first coordination shell of Si−O measured as 1.64 in the pristine and 1.93 in the fully lithiated state, is shifted to higher distances, see Figure 7a. The calculated peaks in the RDF of Figure 7a are verified by the XRD calculated peaks in Figure 7b. When the ReaxFF computed XRD pattern of quartz, Figure 7c, showed sharp peaks around 21° and 27°, the multiple broadened and weaker peaks of amorphous lithiated silica compared with those of pure a-SiO2 confirms the distortion of silica structure after introduction of Li atoms. Our structural evolution analysis and visualization of lithiation products supports that the lithiation reaction in silica consists of two consecutive steps. First, the partial reduction of glassy silica with Li through the conversion of SiO2 into Si and Li2Si2O5 and reduction of Si reacted with Li through a subsequent reversible reaction of

changes during the lithiation of silica, herein we focus our attention to the angle/radial distribution function (A/RDF) and X-ray diffraction patterns (XRD) to characterize the lithiated products, a-LixSiO2.The A/RDF with respect to the Li chemical composition are shown in Figure 5a and b, respectively. According to Figure 5, increasing the Li content results in the structural transformation initiated by Si−O bond breakage and Si−O−Si angles disintegration to smaller fragments in which Li atoms surround the O atoms in the lithiation products. The broadened and smoother peaks of RDF signifies the amorphous nature of lithiated compounds. Also, the lack of long-range interaction in lithium-rich-silica represents the loss of structural order. Looking at the first peak intensities, we find that by increasing the Li-to-Si ratio, Li−O peaks become more pronounced, while the Si−O and Si−Si peaks diminish. The lower Si−Si peak intensity is indicative of breaking the Si matrix through a reversible lithiation scheme. The reduction of the intensity in Si−O peak is also attributed to disintegration of the SiO(4) tetrahedron units through the breakage of Si−O−Si angle units. The bridging O atoms in the silicates and lithiated silicates (expressed by by O(b)) has been shown to play a crucial role in the flexibility of Si−O−Si units. Therefore, they are vulnerable sites to break in the presence of Li atoms. Moreover, our structural evolution study, shown in Figure 6, indicates the cleavage of the tetrahedron units into SiO(3) smaller fragments coincides with the formation of Li−O(b) bonds when more Li atoms incorporate in the mixture. The increase of Li concentration leads to the formation of bigger LixO complexes, which based on our average coordination number (CN) analysis x can be as high as 4 when silica gets fully lithiated. It should be noted that the formation of Li6O units upon Li insertion into Si rich suboxides (SiO1/3) has been reported by Huang and co-workers.31 In addition, the number of Si−O(3)

Si + x Li → LixSi 2120


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performing annealing steps followed by enough NPT equilibration at 300 K. In Figure 8a, we compared the formation energies of these components, indicated by green triangular markers, with the results of GCMC-MD simulations. It is noted that more negative formation energies of amorphous silica, compared to crystalline silica, demonstrate that the Li insertion into c-SiO2 is less energetic favorable. Also, a comparison between open circuit voltages (OCV) from lithiation of a-SiO2 and amorphous silicon (a-Si reveals that the Li incorporation in the silica samples thermodynamically more favors than that in the LixSi alloys. The lithiation open circuit voltage (OCV) profile, shown in Figure 8b, is computed based on the following equation. V (x) = −dEf (x)/dx

where Ef is the formation energy and x represents the Li concentration. The initial OCV for lithiation of silica is ∼3.9 V and the slope voltages from 2 to 0.10 is observed within the first discharge process. The higher voltage of LixSiO2, as well as its lower formation energy, could be ascribed to the strong Li−O bonding in the lithiated alloys relative to the weaker Li−Si interactions in the a-LixSi. Diffusion Behavior of Li Atoms in the Bulk Crystalline and Amorphous Silica. As mentioned in the force field optimization section, both DFT and ReaxFF results confirm that the Li migration barrier for hopping between two adjacent interstitials sites of α-quartz is quite low (∼0.2 eV). According to Figure 3, the crystal structure of α-quartz facilitates the motion of Li guest atoms by providing an open channels along direction through which Li can readily diffuse. However, to fully understand the diffusion mechanisms, long-range Li transport within c-/a-SiO2 must be taken in to account. As seen in Figure 9, in its minimum energy configuration, Li bonds with four nearest O(b) neighbors, i.e. a 4-fold coordinated state. We considered here two different paths for motion of Li. Path 1, Figure 9a, corresponds to the motion of Li perpendicular to the c-axis of the crystal, when path 2 is chosen parallel to the c-axis, Figure 9b. On the basis of our comparison from the energetics of Li motion along these two paths, ReaxFF successfully reproduces the DFT local minima and diffusion barriers; see Figure 10, parts a and b. In contrast with the fast diffusion along path 1, barrier energy of 0.12 eV, Li motion along the perpendicular direction is markedly slower by overcoming the barrier heights of ∼0.9 eV. Such a strong anisotropic diffusion behavior, attributed to different orientation of O atoms along the Li atom paths, has also been reported by DFT calculations about the motion of H atoms within quartz lattice.62 To probe the transferability of the developed force field to the amorphous phase, Li diffusion is studied along three minimum energy pathways (MEPs) adopted from our DFT simulations. The minimum energy configurations, namely sites I, II and III (shown in Figure S2), are determined through a cooperative search using GCMC under isothermal isobaric conditions based on a constant external chemical potential of Li (ELi = −1.56 eV). The GCMC sampling steps followed by equilibration at low temperature, ∼1 K, facilitates the finding of energy minima in the host lattice. Coordinates of inserted Li atoms were chosen randomly such that any unoccupied sites in the amorphous structure could be selected with an equal probability. Consequently, the diffusion paths and the transition states are determined via climbing image nudge elastic band (CINEB) 41,63−65 method between each pairs of minimum configurations (see Figure 11a,b). The obtained initial and

Figure 6. Structural evolution and coordination number changes during the lithiation of a-SiO2. (a) Lithium insertion breaks the Si−O(4) tetrahedron units by cleavage of strong Si−O covalent bonds. (b) The probability of the Li−O bond formation increases when the Li loading proceeds. The number of Si−O and Li−O bonds are normalized with respect to the number of existing Si atoms in the supercell.

The reaction energies and theoretical discharge voltages pertinent to these two steps are summarized in Table 4 for both ReaxFF and DFT. Energetics of Lithiated Products. The formation energy of c/a-LixSiO2 as a function of x, with respect to the a-SiO2 host and body centered-cubic Li (bcc-Li) is calculated. The formation energy per Si atom (Ef) is given by Ef (x) = E(LixSiO2 ) − E(SiO2 ) − xE(Libcc)

where x = nLi/nSi represents the concentration of Li in the lithiated compounds. In Figure 8a, the solid symbols represent the formation energy of LixSiO2 alloys as a function of Li-to-Si ratio (x). The negative formation energy values indicate that the lithiation of a-SiO2 is thermodynamically favorable. The formation energy decreases monotonically when the lithiation progresses. However, it becomes plateau when the system reaches fully lithiated state at x ∼ 4.4 corresponding to the theoretical capacity of 2200 mA h g−1. This concentration in which the lithiation of silica stops corresponds to the moment that silica will no longer accept new Li atoms and it is consistent with the theoretical specific capacity of milled SiO232. Thus, the potential energy starts to increase beyond x ∼ 4.5. In order to verify our GCMC/MD simulations, equilibrium molecular dynamics simulation was utilized to equilibrate the lithiated silica compounds. This time, we generated the lithaited structures by randomly dispersing Li atoms in a-SiO2 up to certain concentrations of x = 1, 2.0, 2.5, 3.75, 4.4, and 4.7 and 2121


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Figure 7. (a) Radial distribution function of Si−O/Si/Li and O−Li during the Li insertion in the a-SiO2. The top left figure is the RDF for the unlithiated SiO2 (x = 0). The middle left figure is plotted for (x = 2.5) and the bottom left is related to the fully lithiated silica at x = 4.4 concentration level. (b) Top right figure: XRD pattern for a-SiO2 (pristine silica) and fully lithiated silica (x = 4.4). The intensity of peaks decrease due to the lithiation. Also, the major peak is shifted from 1.56 to 1.90 Å in the fully lithiated state. Bottom right figure: XRD of α-quartz phase computed by ReaxFF optimization. The peaks coincide with the reported experimental data in ref 32.

Table 4. ReaxFF and DFT Calculated Reaction Energy and Li Discharge Potential of α-SiO2 no. R1 R2 R3 no.

reactions

DFT

0.8 Li + SiO2 → 0.4 Li2Si2O5 + 0.2 Si 0.4 Li2Si2O5 + 0.533 Li → 0.133 Si + 0.667 Li2SiO3 0.667 Li2SiO3 + 0.667Li → 0.167 Si + 0.5 Li4SiO4 reactions

1.38 1.32 0.68

1.5 Li + Al2O3 → 1.5 LiAlO2 + 0.5 Al

R1

final configurations are used to examine the diffusion barriers in the ReaxFF level. Figure 11 clearly indicates that new ReaxFF is capable of reproducing the diffusion behavior of Li within a-SiO2 as well. Subsequently, MD simulation at elevated temperatures was utilized to investigate the kinetics of Li mobility within the lithiated silica bulks. Since the diffusivity of Li at room temperature is too slow for ReaxFF-based MD-sampling, motivated by recent first principle simulations for Li diffusivity through amorphous silicon (a-Si),66 lithiated silica samples with various Li contents were equilibrated at high temperatures of 1000, 1500, 2000, and 2500 K. The motion of Li atoms is traced by their mean square displacement (MSD) throughout a 1.0 ns NVT simulation. MSD is calculated based on following equation:

1 N

DFT

1.21 1.40 0.57 reaxFF

0.93

0.82

affect the Li diffusion coefficients, we eliminate the stress effects by relaxing the pressure of simulation box to 0 atm through a NPT simulations at 300 K for 250 ps prior to increasing the temperature to the target values. The computed MSD values were plotted as a function of time in Figure S1 and the diffusion constants are extracted at various Li concentration levels ranging from 0 to 3.5. Then, the linear interpolation of diffusion coefficients of Li is obtained. Arrhenius equation, D = D0 exp(−ΔEa/KBT), is used to estimate the activation barriers, ΔEa and the pre-exponential Li diffusion factor, D0 at 300 K (see Figure S1). Comparing the ReaxFF computed diffusion barriers, ΔEa, with their corresponding values from ab initio MD (AIMD) simulations, reported by the Supporting Information of ref 25 (0.1< ΔEa < 0.3), shows that ReaxFF allows a reasonable evaluation of the lithiation kinetics and diffusion behavior of Li atoms for dilute systems (x < 2.0). We will denote the ratio of the mole concentration of Li2O to the mole concentration of SiO2, [Li2O]/[SiO2] as R. The room temperature diffusion constants, D300Li, associated with various Li compositions, shown in Figure 12, demonstrates that lithiation kinetics is promoted by increasing the Li/Si ratio.

MSD(t ) = ⟨Δri(t )2 ⟩ = ⟨(ri(t ) − ri(0))2 ⟩ MSD(t ) =

reaxFF

N

∑ ((Δxi(t ))2 + (Δyi (t ))2 + (Δzi(t ))2 ) i=1

Since, residual stresses essentially generated by Li insertion and bond association/cleavage of the host lattice significantly 2122


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Figure 8. (a) Formation energy per Li atom in LixSiO2, the red dashed line is added as a guide for the eyes. (b) Comparison between open circuit voltages of a-LixSi and a-LixSiO2.

Figure 10. Long range diffusion of Li in α-quartz (a) motion parallel to c-axis and (b) moving along the perpendicular to c-axis of the crystal.

Figure 9. Li migration pathways within c-SiO2: (a) Path 1 corresponds to the direction perpendicular to the c-axis of the α-quartz crystal while (b) path 2 is parallel to the c-axis of the crystal.

Higher conductivity of lithium silicate compounds with higher Rratios has been demonstrated by DFT results of Kim et al.56 as well. On the basis of this study, when the vacancy diffusion barrier of Li2Si2O5 (with R = 1) is a round 2.41 eV, it is significantly lowered by increase of the Li contents in Li2SiO3 (ΔEa = 1.19 eV) and Li4SiO4 (ΔEa = 0.91 eV). Further, Li and Garofalini67 showed that the diffusivity of Li in the aluminum

Figure 11. Li diffusion in amorphous silica. Comparison between the diffusion barriers and configurational paths (Figure S2): (a) path 1; (b) path 2 for Li migration within a-SiO2 in two representative cases, DFT results (black lines) vs ReaxFF results (red lines).

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with the increase of the Li content, the diffusivity of Li ions is facilitated. Impact of Lithiation on the Mechanical Properties of SiO2. Finally, the evolution of the mechanical properties of aSiO2 upon lithiation has been studied by conducting NEMD simulations of uniaxial deformation on a-LixSiO2 alloys. The displacement was applied at constant strain-rate of 109 s−1 along x-direction under both NVT and NPT ensemble at 300 K and 0 atm lateral pressure. Parts a and b of Figure 13 show the tensile stress−strain curves for a pristine and lithiated silica for the NVT and NPT conditions, respectively. The maximum fracture strengths of lithiated compounds at various Li concentration are plotted in Figure 13c. Evidently, increasing the Li-to-Si ratio results in the elastic softening of lithiated compounds and the ductility enhancement. This behavior is also reflected by the progression of strainhardening region of the stress−strain curves in the NPT simulations. While the oxide layers are typically brittle, the increase in the ductility due to the lithiation can assist the SiO2 passivation-layer to sustain the mechanical deformations of protected active electrodes. Weakening of pristine silica under lithiation implies that the strong Si−O bonds and Si−O−Si angles in tetrahedron SiO(4) units are gradually fragmented and displaced by weaker Li−O bonds and Si−Li−O angles, respectively. Characterization of structural properties using Si−O bond length distribution indicates that lithiation of silica shifted the main peaks of Dij to the longer distances (see Figure 13d). In the pristine silica (x = 0), the main peak at 1.59 Å agrees well with the equilibrium Si−O bond length computed by ReaxFF, while the second peak corresponds to the long-range interaction of O atom

Figure 12. Activation energy (blue curve) and Li diffusion constants (red curve) at room temperature for Li migration in amorphous silica. By increasing the Li content, the diffusion becomes faster until x ≈ 2.5.

lithium silicate (ALS) glasses depends strongly on the Li2O− Al2O3−SiO2 compositions. On the basis of our ReaxFF diffusion analysis, shown in Figure 12, the energy barrier of Li transport in Li/SiO2 alloy with Li/Si ratio of 2 is approximately 0.72 eV which is in reasonable agreement with the activation energies about the Li2SiO3 glasses presented by Li et al.67 (0.75 eV) and Beier and Frischat68 experimental result of 0.78 eV. In general, Li ions diffusion occurs when Li−O(b) bonds are broken and Li ions can jump between two adjacent minimum sites in the lattice. The lithium ions are predominantly bonded to O(b) when x < 2.5. Therefore, the diffusion barrier is high for compositions with x < 2.50 since it is difficult to break the Li−O(b) bonds. However,

Figure 13. Uniaxial tensile stress−strain curve for lithiated silica under (a) NVT at T = 300 K and (b) NPT ensemble at T = 300 K and 0 pressure. (c) Fracture strength of silica under lithiation. (d) Bond-length distribution before and after Li insertion. 2124


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from one tetrahedron unit with a Si atom from the vicinal tetrahedron unit. The Si−O bonds are clearly split into a trimodal distribution spread around wide range of Si−O bonding after Li incorporation. Such a wide range of bonding indicate the structural disorder after Li insertion. It should be mentioned that, the local clusters of Li2Si2O5 start to appear in the middle of simulation-cell when silica is fully lithiated. This is in good agreement with the experimental data from selected area electron diffraction pattern (SAED) reported by Chang et al.32

4. SUMMARY AND CONCLUSIONS We have developed a ReaxFF description of the Li−Si−O−Al interaction. We found that structural properties and heats of formation for selected condensed phases of lithium silicates and aluminates agree well with the results of DFT calculations and with experimental reported values. The combined GCMC and MD modeling of lithiation in silica layers indicated that Li insertion into amorphous silica is more thermodynamically favorable. Li transport in crystalline case is strongly anisotropic. Our results successfully demonstrated that the newly developed force field can successfully describe the energetics and kinetics of Li insertion into silica and alumina. Therefore, it can be employed in large scale atomistic simulations to examine the mechanisms involved in the lithium insertion into Si anodes covered by silica/alumina coating layers in addition to its application in the modeling of (de)lithiation processes in the newly emerged silicon oxide negative electrodes.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b11908. Figures showing the diffusion coefficient of Li, representative structure of a-SiO2 and diffusion of Li, and lithiation and dilithiation of a-Si, and a table for the newly parametrized ReaxFF potential (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*(A.C.T.v.D.) E-mail: [email protected]. Telephone: +1-814863-6277. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS A.C.T.v.D. and A.O. acknowledge funding from a grant from the U.S. Army Research Laboratory through the Collaborative Research Alliance (CRA) for Multi Scale Multidisciplinary Modeling of Electronic Materials (MSME).

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REFERENCES

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