Anisotropic Compositional Expansion and Chemical Potential of

Research Article Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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Anisotropic Compositional Expansion and Chemical Potential of Lithiated SiO2 Electrodes: Multiscale Mechanical Analysis Janghyuk Moon,† Min-Sik Park,*,‡ and Maenghyo Cho*,§ †

School of Energy Systems Engineering, Chung-Ang University, Heukseok-Ro, Dongjak-Gu, Seoul 06974, Republic of Korea Department of Advanced Materials Engineering for Information and Electronics, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin 17104, Republic of Korea § School of Mechanical and Aerospace Engineering, Seoul National University, 1 Gwanak-Ro, Gwanak-Gu, Seoul 08826, Republic of Korea Downloaded via UNIV AUTONOMA DE COAHUILA on May 14, 2019 at 22:09:41 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: The use of high-capacity electrode materials (i.e., Si) in Li-ion batteries is hindered by their mechanical degradation. Thus, oxides (i.e., SiO2) are commonly used to obtain high expected capacities and long-term cycle performances. Despite extensive studies of the electrochemical−mechanical behaviors of high-capacity energy storage materials, the mechanical behaviors of amorphous SiO2 during electrochemical reaction remain largely unknown. Here, we systematically investigate the stress evolution, electronic structure, and mechanical deformation of lithiated SiO2 through first-principles computation and the finite element method. The structural and thermodynamic role of O in the amorphous Li−O−Si system is reported and compared with that in Si. Strong Si−O bonds in SiO2 show high mechanical strength and brittle behavior, but as Li is inserted, the Li-rich SiO2 phases become mechanically softened. The relaxation kinetics of SiO2, inducing deviatoric inelastic strains under mechanical constraints, is also compared with that of Si. The finite element model including the kinetic model for anisotropic expansion demonstrates that the long-term cycling stability of core−shell Si−SiO2 nanoparticles mainly arises from the reaction kinetics and high mechanical strength of SiO2. These results provide fundamental insights into the chemomechanical behavior of SiO2 for practical use. KEYWORDS: silicon dioxide, Si/SiOx nanocomposites, anode, lithium-ion battery, multiscale analysis

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INTRODUCTION Performance requirements for high-energy Li-ion batteries (LIBs) are increasing more rapidly than ever.1 The rising demand for high-capacity LIBs necessitates the development of new electrode materials that can deliver very high specific capacities.2−5 Among the available options, Si is one of the most suitable alternative high-capacity anode materials compared to commercial carbonaceous anode materials (LiC6: 372 mA h g−1) because of the high theoretical capacities of Li−Si systems (3580 mA h g−1 for Li15Si4). Unlike commercial graphite anodes containing intercalated Li+, this alloy system undergoes significant volume expansion and contraction during Li+ alloying and dealloying.6 This volume change induces undesirable particle fracture, causing significant performance fading.7,8 To overcome such shortcomings, © XXXX American Chemical Society

nanostructured materials and active/inactive composite materials have been suggested.9−16 Si oxides as active and inactive nanocomposite materials have received significant attention because of their high storage capabilities and natural abundance, which is associated with low material cost.16−18 Nanocomposite Si oxides comprise Si nanocrystals dispersed in SiO2 matrices that exhibit improved cycling performance because the inactive SiO2 phase effectively buffers the strain induced by Li+ insertion and extraction in the embedded active Si nanocrystals. Oxides are often electronically insulating and typically brittle, fracturing easily under Received: March 11, 2019 Accepted: May 7, 2019

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DOI: 10.1021/acsami.9b04352 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

Research Article

ACS Applied Materials & Interfaces

in the Vienna Ab initio Simulation Package.42,43 For energy optimization, the atomic coordinates and the supercell shapes were fully relaxed, and the residual forces of each atom were 1). This indicates that Si−O bonds are stiffer than Si−Si bonds. Compared to that of aLi0.125SiO2, the stress−strain curve of a-Li2SiO2 shows much larger nonlinearity beyond the proportional limit. This contrast is caused by the increase in easily flowing components with increasing Li concentration, such as Li−O and Li−O−Si. The effect of the Li−O−Si phases also induces differences in yield points. Both the elastic modulus and strength are significantly decreased as the Li concentration increases. Lithiation-induced softening may enable atomic flow in the lithiation products. Figure 3b shows the calculated stress−strain responses of LixSiO2 under uniaxial compression by the same simulation procedure applied for the tensile simulation. As with uniaxial tension, all compositions of LixSiO2 experience initial elastic deformation under compression. The Young’s moduli of aLiSiO2 and a-Li2SiO2 in compression are consistent with those in tension. However, the Young’s moduli of a-Li0.125SiO2, a-

Figure 3. Stress−strain curves of lithiated a-SiO2 (LixSiO2, x = 0.0125, 0.25, 0.5, 1.0, and 2.0): (a) tensile and (b) compressive strain simulations.

Li0.25SiO2, and a-Li0.5SiO2 are decreased. These differ in that the pre-existing voids in SiO4 tetrahedral networks are more easily deformed under compression. The volume changes in compression testing are smaller than those in tensile, as shown in Figure S4. After inserted Li fills the voids, the elastic behavior under uniaxial compression is similar to that under tension. The yield strength magnitude under compression also decreases with increasing Li concentration. The yield strength of LixSiO2 is near the magnitude of the biaxial stress. The lithiated a-SiO2 shows higher mechanical strength than lithiated Si under both uniaxial tension/compression and biaxial compositional stresses (Figure S3). Furthermore, ductile behavior from lithiation and volume changes reaching 110% in Li-rich SiO2 can accommodate the mechanical stresses induced by Si expansion when SiO2 is used to coat Si-based materials. Electronic Structure Analysis. To understand the interaction among Si, O, and Li atoms in the a-SiO2 structure, we calculated the Bader charges of the atoms in all possible configurations. The net charge state of Si in the a-LixSiO2 structures depends strongly on the local O atomic network (Figure 4). In the a-Li0.125SiO2 matrices, the net charge states of Si are estimated as +2.5 and +4 depending on the number of neighboring O atoms. As the Li content is increased to 2, the corresponding net charge state of Si is also increased to −1.5, while that of the [SiO4] tetrahedron remains constant at +4. This indicates that each Si atom can accommodate additional electrons to fill the empty states in the outermost 3s and 3p D


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Figure 4. Net charge probability with respect to Li concentration using Bader charge analysis: (a) Si, (b) Li, and (c) O.

with further lithiation, the lattice structure is gradually rearranged. As a result, a-SiO2 shows much lower volume expansion (110%) than Si (380%). Volumetric Energy Density. To evaluate prospective SiOx anode materials, we predicted not only the voltages but also their volumetric energy densities (W·h cm−3). Using Obrovac’s methodology,3 the volumetric energy density (Uf) can be calculated according to eq 9

shells. Even if the Si charge in the [SiO4] tetrahedron remains constant during lithiation, the O atoms strongly interact with Li+ by forming Li−O−Si glasses. Similarly, the net charge state of O is calculated by Bader charge analysis. The greatest net charge on O induced by Li−O−Si formation in the a-SiO2 structure is −1.85 to −2.0, indicating that the formation of Li− O−Si glasses differs from that of lithium silicates such as Li2SiO3, Li2SiO3, and Li4SiO4. This indicates that the lithium silicates maintain their [SiO4] tetrahedral structures, while the a-SiO2 structure loses O connectivity during lithiation. The fraction of Si−O clusters with defects is higher than that of [SiO4] tetrahedral structures. The formation of Li−O−Si clusters is thermodynamically favored over the reduction of SiO2 to Si because of the formation of lithium silicate glasses and LixSi. Such electron transfer induces gradual weakening of the host matrix with a slight decrease in the bulk modulus from 45 to 42 GPa. Figure S6 compares the total density of states (DOS) of a-SiO2, LiSiO2, and Li2SiO2, indicating a clear insulator character of a-SiO2 with a large band gap of 3.5 eV.24 Upon lithiation, the band gap of a-LixSiO2 significantly decreases as a result of electron transfer from Li which is a clear evidence of the formation of Li−O−Si. To compare the quantitative electronic properties of Si and SiO2, we have also calculated the Bader charge to capture the electronic charge transfer from the interstitial Li atoms to the Si host matrix (Figure S5).50 A charge of 0.83e− is transferred from each Li atom. The transferred charges partially fill the anti-bonding sp3 orbital of Si and thus weaken the Si−Si bond. The mechanism of Li-assisted weakening of Si−Si bonds has been discussed previously.45 Increasing Li concentration causes significant elastic softening in an approximately linear manner. However, compared to Si, SiO2 shows more consistently brittle mechanical behavior and distinguishable phase transformations, despite the amorphous natures of the initial and formed structures. Stress relaxation behavior, such as in Si, is observed; a LixSi alloy that forms after 2 mol Li is incorporated in SiO2. The isolated O−Li local structure is also confirmed by the O net charge at Li 3.5SiO 2, as shown in the Supporting Information. These findings mean that partially reduced Si can promote local atomic rearrangement in highly lithiated SiO2, while the O content affects the mechanical stability of lithiated SiO2. Considering the volume change, the O−Li bond length is approximately 1.7 Å, while that of Si−Li reaches 3.3 Å depending on Li concentration. Thus, Li+ can be packed more effectively in the a-SiO2 structure than in LixSi. In the initial lithiation stage, most Li atoms are bonded to O, not Si. Thus, smaller dimensional change occurs in the a-SiO2 structure;

−∫ Uf =

0

y = yf

[V(+)(y) − V(−)(y)]F dy v (y )

(9)

where y and yf are the number of Li moles per mole of host alloy atoms. V(+) is the cathode voltage, V(−) is the anode voltage, v is the molar volume of the negative electrode, and F is Faraday’s number. Because recent studies have predicted volumetric energy densities versus a 3.75 V cathode, this value was selected for the reference cathodic state. Si shows volume expansion reaching 340% with a Li mole fraction of 4. However, the volume expansion ratio dramatically decreases as the O content increase. The a-SiO2 experiences less volume change of approximately 100%, as shown in Figure 5. The

Figure 5. Energy−expansion curves (vs 3.75 V cathode) for various aSiO2 (LixSiO2, 0 < x < 4) based on their voltage curves and volume expansion curves.

host-atom molar volume for SiOx changes linearly as a function of the Li content; the slope of the linear fit decreases as the O content increases. Figure 5 also shows the predicted volumetric energy densities as functions of the volume expansion ratio. Si provides the largest energy density (7.89 W·h cm−3) at ∼340% volume expansion; SiO2 provides 6.94 W·h cm−3 at ∼100%. By E


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ACS Applied Materials & Interfaces tailoring the O content, the anode material benefits from the change in volume and voltage. FEM Analysis. To model the lithiation-induced deformation, researchers often assume that purely volumetric transformation strain occurs in an amorphous reaction. The plastic flow that generates deviatoric inelastic strain is considered a separate process.36 However, under this assumption, the composition-dependent yield strength must be considered.35,36 To simplify the representation, Levitas and Attariani38 and Hong37 have suggested decomposing the transformation strain into volumetric and deviatoric components, in which the deviatoric strain rate is dependent on the deviatoric stress. For example, the reactive plastic flow is interpreted as the strain rate of the deviatoric parts induced by the deviatoric stress. Using Hong’s model, we performed finite element analysis using COMSOL (Multiphysic 5.2) for comparison with the atomistic simulations. Details of the model equation are summarized in the Experimental Details section. Our FEM model is well matched with Hong’s continuum model, as shown in Figure S7.37 At the atomistic scale, the solid-state reactions are slightly anisotropic in their calculation results, particularly for SiO2 materials. Assuming that the average properties are macroscopically isotropic, the atomicscale simulation results agree with the continuum model result. For Si, the stress-composition hysteresis loop in our FEM simulation shows satisfactory agreement with DFT measurements. This means that the spatial distribution of Si and Li atoms is significantly well rearranged by reaction-induced deformation. Otherwise, the FEM stress-composition curve of SiO2 would not fit the DFT results. This is because the reaction results between SiO2 and Li are seldom isotropic, or because atomic rearrangement is difficult in SiO2 systems. The small-sized model may cause anisotropic reactions showing large deviations in lateral stress. Lithiation has energetically favorable sites in SiO2, such as those next to oxygen in a distorted [SiO4] tetrahedron. Strongly bonded [SiO 4] tetrahedral networks maintain their structures with infrequent atomic rearrangement. However, for lithiation of 1 mol Li, the Si−O bonds disappear, and the material behaves like a lithiated Si matrix. The compositional stress curves intersect at 1 mol Li and remain well matched during delithiation. The elastic regime of SiO2 is longer than that of Si. By considering the value fitting parameter γ2/ξ of 0.8 GPa−1 in Si and 0.2 GPa−1 in SiO2 (Table S2), we achieve a good agreement with the above explanation, in which the deviatoric strain (γ) from atomic rearrangement in SiO2 is lower than that in Si. Figure 6a shows the simulated results of the Si@SiO2 core− shell nanoparticle by FEM. During Li insertion to 1.5 Li moles, the Si phase at the center experiences hydrostatic pressure (compressive stress) because the SiO2 shell prevents outward expansion. The different volumetric changes between Si and SiO2 with changing Li concentration contribute to the development of tensile stress on the SiO2 surface. The influence of the ratio between the core radius (R) and shell thickness (t) on the development of stress is shown in Figure 6b. The normalized hoop stresses of the core−shell nanoparticles with t/R ratios from 0.1 to 0.5 are calculated on the outer surface. The Li concentration-dependent yield stress σyield(x) is taken from Figure 3. The growth rate of the hoop stress is decreased as the ratio of t/R increases. The thicker SiO2 shell, which can expand, facilitates stress relief by expanding or shrinking the compositional volume change in the deviatoric direction. If the SiO2 shell were assumed as rigid

Figure 6. (a) FEM results showing the simulated Von Mises stresses in core−shell nanoparticles (R = 100 nm, t = 20 nm). (b) Normalized stress evolution of hoop stress at the surface region: t is the thickness of the SiO2 shell, and R is the radius of the Si core.

or elastic without reaction kinetics, the stress evolution of SiO2 would be stiffer or unsolvable by analytical or numerical methods. From the simulated results, we find that materials with reaction kinetics and high mechanical strength decrease the development of mechanical stress and increase mechanical stability during cycling.

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CONCLUSIONS We have demonstrated the high mechanical stability of electrochemically lithiated SiO2 electrodes using integrated modeling. The ab initio mechanical simulation showed a dramatic mechanical distinction between brittle behavior in nonlithiated SiO2 and ductile deformation in lithiated SiO2. Atomistic rearrangement during the anisotropic compositional expansion phenomenon occurred as the Li concentration increased (Li x SiO 2 : x > 0.5). Our DFT calculation demonstrated that the mechanistic transition from brittle to ductile arose from the [SiO4] tetrahedral networks which were distorted by the initial reaction with Li. This mechanistic understanding of SiO2 as an anode and coating material may facilitate the rational design of durable Si and SiOx nanoengineered electrodes for high-capacity LIBs. Our mechanical characterization using integrated simulations can be applied to many electrochemically active materials for energy storage applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.9b04352. F


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Calculated formation energies of interstitial Li, structural characterizations of bond length and angles in amorphous silicon dioxide, tensile/compressive stress profiles, volume change ratios, net charge probabilities of lithiated Si, and parameters for finite element analysis are provided (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.-S.P.). *E-mail: [email protected] (M.C.). ORCID

Min-Sik Park: 0000-0002-3490-2999 Maenghyo Cho: 0000-0003-3942-9261 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Technology Development Program to Solve Climate Changes through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT (NRF-2018M1A2A2063355) and also supported by the National Research Foundation (NRF2018R1A5A1025594) of the Ministry of Science and ICT of Korea.

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Anisotropic Compositional Expansion and Chemical Potential of

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