Atomic-Level Understanding toward a High-Capacity and High-Power

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Atomic-Level Understanding Toward a HighCapacity and High-Power Silicon Oxide (SiO) Material Sung Chul Jung, Hyung-Jin Kim, Jae-Hun Kim, and Young-Kyu Han J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10589 • Publication Date (Web): 18 Dec 2015 Downloaded from http://pubs.acs.org on December 20, 2015

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The Journal of Physical Chemistry

Atomic-Level Understanding toward a HighCapacity and High-Power Silicon Oxide (SiO) Material Sung Chul Jung †,§, Hyung-Jin Kim†,§, Jae-Hun Kim‡, and Young-Kyu Han*,† †

Department of Energy and Materials Engineering and Advanced Energy and Electronic

Materials Research Center, Dongguk University-Seoul, Seoul 100-715, Republic of Korea ‡

School of Advanced Materials Engineering, Kookmin University, Seoul 136-702, Republic of

Korea Corresponding Author *E-mail: [email protected]; Phone: +82 2 2260 4975. Author Contributions §

S.C.J. and H.J.K. contributed equally.

ACS Paragon Plus Environment

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ABSTRACT Silicon oxide (SiO) has attracted much attention as a promising anode material for Li-ion batteries. The lithiation of SiO results in the formation of active Li–Si alloy cores embedded in an inactive matrix consisting of Li-silicates (Li2Si2O5, Li6Si2O7, and Li4SiO4) and Li2O. The maximum Li content in lithiated SiO (LixSiO) is known to be x = 4.4 based on experiments. Our calculations reveal that Li-silicates are dominant over Li2O among matrix components of the experimental Li4.4SiO phase. We show that LixSiO can become thermodynamically more stable and thus accommodate more Li ions up to x = 5.2 when Li2O dominates over Li-silicates. The minor portion of Li2O in the experimental phase is attributed to kinetically difficult transformations of Li-silicates into Li2O during electrochemical lithiation. The Li2O subphase can act as a major transport channel for Li ions because the Li diffusivity in Li2O is calculated to be faster by at least two orders of magnitude than in Li-silicates. We suggest that Li2O is a critical matrix component of lithiated SiO because it maximizes the performance of SiO in terms of both capacity and rate capability.


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INTRODUCTION High capacity and high power are ultimate goals for modern electrochemical energy storage devices. Li-ion batteries (LIBs) have played a leading role in realizing advanced energy technologies and are currently the most commonly utilized power sources for everyday electronic consumer products such as cell phones, laptop computers, portable music players, and digital cameras. Now applied in the transportation industry as well, LIBs are used in electric vehicles, hybrid electric vehicles, and plug-in hybrid electric vehicles, which demand much higher capacity and power than portable electronic devices. Si has been the subject of intensive research as a next-generation anode material for LIBs because of its appealing high-energy density. The outstanding capacity of Si (3579 mAh g–1 for Li15Si4) is much higher than that of conventional graphite (372 mAh g–1 for LiC6), and on this basis Si is expected to meet the rapidly increasing demands for portable electronic devices and electric vehicles. The lithiation of Si results in the formation of an amorphous LixSi phase, followed by the crystallization of Li15Si4 from amorphous Li3.75Si at the end of lithiation. However, the huge volume expansion (300%) for Li15Si4 is a major obstacle to the use of Si in LIBs, because this deteriorates the mechanical stability and electrical conductivity of the electrode and, in turn, leads to rapid capacity fading. These problems derived from the volume expansion have been overcome to some degree by using strategies such as nanostructure fabrication1–5 and coating,6–10 but the practical implementation of Si anodes in LIBs has yet to be realized. The oxidation of Si is one of the most widely employed approaches for practical applications of Si-based materials in LIBs. In particular, SiO has attracted a great deal of attention as a


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promising anode material for LIBs owing to its significantly high capacity and long cycle life compared with graphite and Si, respectively.11–29 The structure of SiO is inhomogeneous and consists of amorphous Si and SiO2 clusters surrounded by a Si-suboxide matrix.18,19 The lithiation of SiO in the first cycle results in the formation of a reversible Li–Si alloy and irreversible Li-silicate and Li2O phases.20–25 The Li-silicates (Li2Si2O5, Li6Si2O7, and Li4SiO4) and Li2O are known to act as buffering phases against the volume expansion during cycling, thereby enhancing the cycle performance of SiO.20,21,24–26 It is important to understand how the Li-silicates and Li2O phases are formed during lithiation and how these irreversible phases affect the reversible capacity and rate capability of SiO. Contrary to many experimental studies,12–29 to the best of our knowledge, there are no theoretical studies to interpret accumulated experimental data for the lithiation of SiO, likely because it is difficult to simulate the complicated structure of lithiated SiO with multiple subphases. A fascinating first-principles study was reported, but it investigated the lithiation behavior of a Si-rich oxide (SiO1/3).30 Herein, we explore the lithiation process of SiO using first-principles molecular dynamics simulations. We suggest that the experimental LixSiO (x = 3.64–4.39) phases22,23,27,28 observed at the end of lithiation contain Li-silicates and Li2O as major and minor components of an inactive matrix of LixSiO, respectively. Our calculations show that the thermodynamically most stable Li5.22SiO phase can be formed when Li2O becomes dominant over Li-silicates. The minor Li2O subphases in the experimental samples are interpreted to be due to the kinetically limited evolution of Li-silicates into Li2O during electrochemical lithiation. The Li ions in Li2O are found to diffuse faster by at least two orders of magnitude than those in Li-silicates, revealing that the Li2O subphase can act as a fast Li diffusion channel. This study suggests that the


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formation of a Li2O-rich matrix in lithiated SiO can maximize the performance of SiO in terms of both capacity and rate capability.

COMPUTATIONAL DETAILS Density functional theory (DFT) calculations were carried out using the Vienna ab initio simulation package (VASP).31 The Perdew−Burke−Ernzerhof (PBE) exchange and correlation functionals32 and the projector-augmented wave (PAW) method33 were employed. The electronic wave functions were expanded in a plane-wave basis set of 400 eV. We treated 1s22s1, 3s23p2, and 2s22p4 as the valence electron configurations for Li, Si, and O, respectively. The amorphous LixSiO bulk structures were simulated by a periodic cubic supercell containing 30 × x Li atoms, 30 Si atoms, and 30 O atoms. The calculated mass density of amorphous SiO is 2.22 g cm–3, which is in good agreement with the theoretical value34 of 2.21 g cm–3 and compares well with the experimental value19 of 2.13 g cm–3. A 2 × 2 × 2 k-point mesh was used for Brillouin zone integrations. For the calculations of vacancy formation energies and Li diffusion barriers in Li15Si4, Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O crystals, the numbers of atoms and k-point meshes used are presented in Table S1. We performed ab initio molecular dynamics simulations in the course of generating the amorphous structures. The equations of motion were integrated with the Verlet algorithm using a time step of 1 fs, and the temperature was controlled by velocity rescaling and a canonical ensemble (NVT) using a Nosé-Hoover thermostat. The amorphous structures were constructed by rapidly cooling the liquid phase. This approach, called the liquidquench method, is a successive process of heating, equilibration, and cooling. The heating temperature for creating amorphous LixSiO structures is 2500 K, sufficiently higher than the


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melting temperature (1975 K) of SiO. The total simulation time required to create the amorphous LixSiO phase is at least 30 ps for each x. The structure of the created amorphous SiO is inhomogeneous, as observed in previous theoretical studies.35,36 A 1 × 1 × 1 k-point mesh was used to save an enormous amount of computational time during the ab initio molecular dynamics simulations. More details of the simulation schemes can be found in our previous studies.37–39

RESULTS AND DISCUSSION Figure 1a shows the calculated formation energies of amorphous LixSi and LixSiO alloys. The formation energies of LixSiO are significantly lower for all ranges of x than those of LixSi, indicating that oxidized Si is much more reactive toward lithiation than pristine Si. The most energetically stable LixSi phase is calculated to be Li3.78Si,39 which is very similar in composition to the Li15Si4 crystal (x = 3.75) observed at the end of lithiation.40–42 This implies that the lithiation proceeds until the thermodynamically most stable phase is formed in the anode material. Notably, our calculations reveal that the most stable composition for LixSiO is x = 5.22, corresponding to the theoretical specific capacity of 3172 mAh g–1. As far as we know, this is the first report of the theoretical capacity of SiO. The theoretical capacity of 3172 mAh g–1 for Li5.22SiO is higher than the experimental values, which range from 2216 to 2667 mAh g–1 (from Li3.64SiO to Li4.39SiO) in the first cycle.22,23,27,28 To interpret this discrepancy between theory and experiment, we simplify the lithiated SiO structure by assuming that fully lithiated SiO phases have only two subphases,20–25 i.e., the reversible Li15Si4 phase and one of the irreversible Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O phases (see Figure 2). Based on this assumption, we can imagine four fully lithiated SiO phases that


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have hypothetical compositions of Li2.65SiO, Li3.54SiO, Li3.81SiO, and Li5.75SiO (see Table 1). For instance, Li3.81SiO is composed of 3/16(Li15Si4) and 1/4(Li4SiO4), where 3/16 and 1/4 are coefficients to preserve the stoichiometry. The hypothetical Li3.81SiO phase exhibits initial and reversible capacities of 2316 and 1710 mAh g–1, respectively, which arise from both the 3/16(Li15Si4) and 1/4(Li4SiO4) subphases and only the 3/16(Li15Si4) subphase, respectively. The compositions and capacities of the hypothetical LixSiO phases are illustrated in Figure 3, revealing that the capacities can vary significantly depending on the irreversible subphase. In particular, when the irreversible subphase is Li2O, the resulting hypothetical Li5.75SiO phase exhibits considerably high capacities. The experimental Li4.39SiO phase23 is closer in capacity to the hypothetical Li3.81SiO phase with the Li4SiO4 subphase than the hypothetical Li5.75SiO phase with the Li2O subphase (see Figure 3), implying that the experimental Li4.39SiO phase contains Li-silicates more dominantly than Li2O. On the other hand, the thermodynamically most stable Li5.22SiO phase is closer in capacity to the hypothetical Li5.75SiO phase and thus possesses more structural characteristics of Li2O than of Li-silicates. This suggests that the formation of Li2O-rich lithiated SiO anodes is thermodynamically favorable. The major and minor portions of Li-silicates and Li2O, respectively, in the experimental Li4.39SiO phase are associated with the irreversible formation of Li-silicates and Li2O. The irreversibility has been reported by transmission electron microscopy (TEM) studies.23–25 Because Li-silicates and Li2O, once formed, persist over cycles, the SiO anodes after the first lithiation will contain various ratios of Li-silicates and Li2O depending on experimental conditions. In fact, experimental studies22,23,27,28 have reported a range of capacities from 2216 to 2667 mAh g–1 for the first lithiation of SiO anodes. We speculate that Li-silicates rather than Li2O were predominantly formed during the lithiation of experimental SiO anodes


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and that, in particular, the formed Li-silicates did not transform into Li2O under electrochemical conditions. The foregoing could explain the minor portions of Li2O in experimental LixSiO (x = 3.64–4.39) anodes and the resulting lower capacities than that of the thermodynamically most stable Li5.22SiO structure. It is intriguing that the electrochemical transformations of Li-silicates into Li2O during lithiation are limited whereas the predominant formation of Li2O over Li-silicates is thermodynamically much favored in our calculations. The evolution of Li-silicates into Li2O demands their structural disintegration. Our calculations show that the vacancy formation energies required to remove single atoms from Li2Si2O5, Li6Si2O7, and Li4SiO4 crystals are far larger than those required to remove them from the Li15Si4 crystal (see Table 2). In particular, the Si atoms in Li-silicates should be removed for the transformation of Li-silicates into Li2O, but they are not readily extracted from Li-silicates. The Si vacancy formation energies in Li2Si2O5, Li6Si2O7, and Li4SiO4 are 11.58–16.30 eV, which are much larger than the value (0.98 eV) in Li15Si4 (Table 2). Considering these vacancy formation energy values, we predict that there will be large activation barriers that should be overcome to decompose the SiO4 tetrahedral units in Li-silicates (see Figure 2). Thus, we conclude that the evolution of Li2Si2O5, Li6Si2O7, and Li4SiO4 into Li2O will be kinetically difficult under electrochemical conditions. For this kinetic reason, the experimental maximum Li content in LixSiO is only x = 4.39, which is 16% smaller than the thermodynamically favorable value of x = 5.22. If kinetically controlled transformations of Li-silicates into Li2O become possible during electrochemical lithiation, the capacity of SiO could increase up to 3172 mAh g–1 (see Figure 3). Figure 1b shows the calculated average voltages during lithiation of SiO. Overall, the voltage curve lies between the experimental charge–discharge profiles, verifying that our calculations


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reasonably describe the alloying reaction of SiO with Li ions. The volume of LixSiO increases linearly with the Li content x, as shown in Figure 1c. The theoretical maximum volume expansion ratio for Li5.22SiO is 191%, but the ratio for Li4.39SiO that is currently known as the highest Li composition is 160%. The 160% volume expansion ratio for Li4.39SiO is much smaller than the value (298%) for Li3.78Si,39 indicating that the SiO anode can exhibit better capacity retention than the Si anode. The mitigated volume expansion of SiO compared with Si can be understood in terms of the atomic volume. The volume occupied by one Li ion in LixSiO is calculated to be 12.4 Å3, which is much smaller than that (15.1 Å3) in LixSi, showing that the O atoms in LixSiO reduce the space occupied by Li ions by tightly holding their adjacent Li ions. In LixSiO, in fact, the Li–O bond length of 1.9 Å is significantly shorter than the Li–Li and Li–Si bond lengths of 2.8 and 2.7 Å, respectively (see the radial distribution functions in Figure S1). The effect of oxygen atoms is also evidenced by denser O-containing regions compared with O-free regions. The calculated densities of 2.36, 2.33, 2.32, and 1.97 g cm–3 for Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O crystals, respectively, are significantly higher than the density of 1.20 g cm–3 for the Li15Si4 crystal. Our analyses support the experimental reports20,21,24–26 that Li-silicates and Li2O can act as buffers against large volume expansion during lithiation. The charge states of Si clearly reflect all the structural characteristics of LixSiO. Figure 4 shows the distribution histograms of the Bader populations of Si in LixSiO. The charge states of Si in unlithiated SiO (x = 0) range from –0.09 to +3.17 e, which are assigned as Si atoms with 0– 4 nearest neighbor O atoms. For instance, the charge stages of +0.01 and +3.15 e (see green circles) originate from the central Si atoms in Si12O2 and Si5O13 local structures, respectively, as shown in Figure 4. These Si atoms (Si0 and Si4+) with +0.01 and +3.15 e have four Si and O


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nearest neighbors, respectively, corresponding to Si5 and SiO4 tetrahedral configurations in amorphous Si and SiO2 bulks, respectively. Our charge analyses demonstrate that the internal structure of SiO is highly inhomogeneous. This finding is in complete agreement with X-ray photoelectron spectroscopy (XPS) spectra20,23,24,27 showing various oxidation states of Si (Si0, Si1+, Si2+, Si3+, and Si4+), which reflect neutral and oxidized Si atoms in the Si and SiOy (0 < y ≤ 2) regions of SiO, respectively. As lithiation proceeds, the charge states of Si shift toward negative values, indicating the reduction of Si atoms. The disappearance of positive charge states indicates that the Si atoms in the SiOy region are replaced by Li ions during lithiation (see the coordination numbers of O atoms in Figure S2). The growth of negative charge states indicates the formation of a Li–Si alloy. During lithiation, the Li–Si alloy undergoes a structural evolution from Li-poor to Li-rich states, eventually leading to an isolation of Si atoms (see a Li12Si cluster at x = 4 in Figure 4). Notably, the charge states of about +3.2 e in Figure 4, stemming from the Si atoms in SiO4 tetrahedral configurations, are closely associated with the formation of Li-silicates that are threedimensional networks of corner-sharing SiO4 tetrahedra with interstitial Li ions. During lithiation, the network of SiO4 tetrahedra disintegrates and evolves into isolated Si4O8, Si2O7, and SiO4 clusters at x = 1, 2, and 3, respectively (see Figure 4). In the clusters, the SiO4 tetrahedron that includes the Si atom indicated by the arrow shares its corner oxygen atoms with other SiO4 tetrahedra (or their fragments). The number of shared oxygen atoms of each SiO4 tetrahedron is three in Si4O8, one in Si2O7, and zero in SiO4, and these figures are in excellent agreement with those in experimentally observed Li-silicates,20–25 i.e., three in Li2Si2O5, one in Li6Si2O7, and zero in Li4SiO4, respectively (see Figure 2). These results verify that our ab initio molecular


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dynamics simulations successfully capture the structural motifs of Li-silicates observed during the lithiation of SiO. We note that the commonly prepared SiO anode, which is created by a disproportionation reaction during heat treatment, consists of nano-crystalline Si cores surrounded by a Si-suboxide matrix.23–25,27,29 The Si cores and Si-suboxide matrix evolve into the Li–Si alloy and Lisilicates/Li2O, respectively, during lithiation (see Scheme 1).22–25,27 Experimental studies23–25 have reported that whereas the Li–Si alloy is reversible during cycling, the Li-silicates and Li2O are irreversible. The Li ions pass through the matrix when they shuttle between the LixSi cores and electrolyte during repeated lithiation–delithiation cycles. An understanding of Li transport in the polycrystalline matrix consisting of Li-silicates and Li2O is thus integral to enhancing the rate capability of the SiO anode. It should be mentioned that among Li-silicates, Li2Si2O5 has been reported to be reversible.23,25 However, we believe that Li2Si2O5 survives for a long period in a cycle because it appears at the initial stages of lithiation and disappears at the final stages of delithiation.23,25 We explored the Li diffusion in Li15Si4, Li-silicate (Li6Si2O7, Li2Si2O5, and Li4SiO4), and Li2O crystals. The migration of intrinsic Li vacancies in these crystals is regarded as the diffusion mechanism.43,44 The Li diffusion barriers are calculated by using the climbing-image nudged elastic band (CI-NEB) method,45 and the calculated barriers are used to determine the Li diffusivities at T = 300 K (see detailed procedures in the Supporting Information). The Li diffusivities in Table 3 reveal that the diffusivity increases in the following order: Li6Si2O7 < Li2Si2O5 < Li4SiO4 < Li2O < Li15Si4. The Li diffusivity in Li15Si4 is calculated to be 8.8 × 10–6 cm2 s–1, which is faster by at least two orders of magnitude than that in Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O, showing that the Li ions diffuse faster in active LixSi cores than in an inactive


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matrix. Intriguingly, inside the matrix, the Li diffusivity (1.8 × 10–8 cm2 s–1) in Li2O is faster by at least two orders of magnitude than that in Li-silicates. It is worth noting that Li2O can play a role as a main channel for diffusion of Li ions in the matrix. Thus, it is obvious that Li2O is superior to Li-silicates as an inactive matrix component because it can boost not only the capacity but also the rate capability of SiO. The Li2O-rich lithiated SiO anode can afford a high capacity, but its initial Coulombic efficiency may be relatively low due to an increased portion of the irreversibly formed Li2O subphase. We calculated the first-cycle Coulombic efficiency as 67% for the Li5.22SiO phase from the initial and reversible capacities in Figure 3, which is slightly lower than that (70%) for the Li4.39SiO phase. However, there is room for doubt as to whether the Li2O phase is totally irreversibly formed and thus whether its electrochemical decomposition is forbidden. Recently, it was experimentally reported that the Li2O phase formed in the lithiation of SnO and SnO2 can be partially decomposed during the subsequent delithiaion.46,47 We expect that the achievement of kinetically controlled transformation of Li-silicates into Li2O in the matrix will lead to great improvements in both the capacity and rate capability of SiO. As an alternative to the phase transformation, the fabrication of a SiO anode with a preexisting Li2O-rich matrix may be possible. Yoon et al.48,49 reported that a prelithiated SiO anode contains both Li-silicates and Li2O. We suggest that high-performance Li–Si–O anode materials consisting of Si cores embedded in a Li2O-rich matrix could be developed by a combined technique of prelithiation and heat treatment.

CONCLUSIONS


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The present first-principles study offers in-depth insights into the structures of lithiated SiO phases observed in experimental studies. Our interpretation suggests that Li-silicates are dominant over Li2O as irreversible subphases of the experimental Li4.39SiO phase that exhibits a capacity of 2667 mAh g–1. The formation energy calculations show that LixSiO can thermodynamically store up to x = 5.22, corresponding to higher capacity of 3172 mAh g–1, when Li2O becomes dominant over Li-silicates. The predominance of Li-silicates in the experimental phase results from the kinetic limitations of the electrochemical transformations of Li-silicates into Li2O during lithiation. The oxygen atoms in LixSiO reduce the space occupied by Li ions, resulting in a considerably alleviated volume expansion (298% → 160%) of SiO compared with Si. The molecular dynamics simulations clearly trace the structural evolution of the network of SiO4 tetrahedra in Li-silicates. The Li2O subphase serves as a fast Li diffusion channel of the matrix surrounding the LixSi cores, because the Li ions in Li2O diffuse faster by at least two orders of magnitude than those in Li-silicates. We suggest that the formation of a Li2Orich matrix in lithiated SiO can maximize the performance of SiO in terms of both capacity and rate capability. This finding reveals that the control of inactive matrix components can have a powerful influence on the electrochemical performance of a composite anode material. The present study provides an atomic-level understanding for the design of high-capacity and highpower SiO anode materials, which may represent a breakthrough for practical applications in the rapidly expanding market for LIBs.

ASSOCIATED CONTENT Supporting Information


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Calculation parameters for vacancy formation energies and Li diffusion barriers, radial distribution functions, coordination numbers, detailed procedure for Li diffusion barrier calculations, and full list of references 2, 12, and 36. This information is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]; Phone: +82 2 2260 4975. Author Contributions §

S.C.J. and H.J.K. contributed equally.

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS The authors acknowledge the financial support by the National Research Foundation of Korea Grant funded by the Korean Government (MEST, NRF-2010-C1AAA001-0029018). This work was also supported by the Energy Efficiency & Resources Core Technology Program of the KETEP granted financial resource from the Ministry of Trade, Industry & Energy (No. 20132020000260).


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Scheme 1. Schematic illustration of SiO anode during repeated lithiation–delithiation cycles. The LixSi cores (yellow) are embedded in a matrix (orange) consisting of Li-silicates and Li2O.


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Figure 1. (a) Formation energies of LixM (M = Si and SiO), defined as Ef(x) = Etot(LixM) – xEtot(Li) – Etot(M) where Etot(LixM) is the total energy per amorphous LixM formula unit, Etot(Li) is the total energy per atom of bcc Li crystal, and Etot(M) is the total energy per amorphous M formula unit. (b) Average voltages of LixSiO, defined as V(x) = –[Etot(Lix+∆xSiO) – Etot(LixSiO)]/∆x + Etot(Li). The experimental charge–discharge profiles were measured in the first cycle.23 (c) Volume expansion ratios of LixM. V0 and V represent the volumes of M and LixM, respectively. In (a) and (c), data for M = Si were taken from our previous study.39


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Figure 2. Crystal structures of Li15Si4, Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O. The yellow, blue, and red balls represent the Li, Si, and O atoms, respectively. The atomic bonds are connected when the Li–Si, Li–O, Si–Si, and Si–O distances are within 3.3, 2.5, 2.8, and 2.0 Å, respectively. For Li2Si2O5, Li6Si2O7, and Li4SiO4, only the Si–O bonds are shown for clarity.


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Figure 3. Initial and reversible capacities of hypothetical Li2.65SiO, Li3.54SiO, Li3.81SiO, and Li5.75SiO phases with irreversible Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O subphases, respectively (see Table 1). The experimental capacity 2667 mAh g–1 for the Li4.39SiO phase23 and higher theoretical capacity 3172 mAh g–1 for the most stable Li5.22SiO phase are indicated by black and red squares, respectively.


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Figure 4. Distribution histograms of the Bader populations of Si in LixSiO and local structures for the charge states enclosed with green circles.


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Table 1. Hypothetical Compositions and Capacities of Fully Lithiated SiO Phasesa capacity (mAh g–1) composition

a

initial

reversible

Li2.65SiO = 3/20(Li15Si4) + 1/5(Li2Si2O5)

1611

1368

Li3.54SiO = 5/28(Li15Si4) + 1/7(Li6Si2O7)

2152

1628

Li3.81SiO = 3/16(Li15Si4) + 1/4(Li4SiO4)

2316

1710

Li5.75SiO = 1/4(Li15Si4) + Li2O

3496

2280

The LixSiO phases are assumed to consist of only two simple subphases, i.e., the reversible

Li15Si4 crystal and one of the irreversible Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O crystals.


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Table 2. Vacancy Formation Energies in Li15Si4, Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O Crystalsa

a

crystal

Evac(Li)

Evac(Si)

Evac(O)

Li15Si4

1.28

0.98

Li2Si2O5

5.29

16.30

5.30

Li6Si2O7

3.94

12.88

5.67

Li4SiO4

3.62

11.58

5.85

Li2O

3.44

6.62

The vacancy formation energy (eV) is defined as Evac(j) = Etot(Nj – 1) – Etot(N) + Etot(j), where

Etot(Nj – 1) is the total energy of the supercell with a species j vacancy, Etot(N) is the total energy of the supercell for a perfect crystal, Etot(j) is the total energy per atom of elemental j (bcc Li crystal, diamond Si crystal, and O2 molecule for j = Li, Si, and O, respectively), and N is the number of species in the supercell.


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Table 3. Li Diffusion Properties in Li15Si4, Li2Si2O5, Li6Si2O7, Li4SiO4, and Li2O Crystalsa

a

crystal

ED

a

D

Li15Si4

0.11

2.5

8.8 × 10–6

Li2Si2O5

0.47

3.4

1.3 × 10–11

Li6Si2O7

0.54

5.0

1.8 × 10–12

Li4SiO4

0.45

6.7

1.1 × 10–10

Li2O

0.26

2.1

1.8 × 10–8

ED (eV) is the activation energy for diffusion and D (cm2 s–1) is the diffusivity at T = 300 K.

The diffusivity is defined as D = a2υexp(–ED/kBT), where a (Å) is the diffusion distance, υ is the attempt frequency (1012 Hz), and kB is the Boltzmann constant.


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TOC GRAPHICS


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Atomic-Level Understanding toward a High-Capacity and High-Power

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