First-Principles Calculations of Lithiation of a Hydroxylated Surface of

Article pubs.acs.org/JPCC

First-Principles Calculations of Lithiation of a Hydroxylated Surface of Amorphous Silicon Dioxide Saul Perez-Beltran,†,‡ Gustavo E. Ramírez-Caballero,‡ and Perla B. Balbuena*,† †

Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States Departamento de Ingeniería Química, Universidad Industrial de Santander, Bucaramanga, Colombia

‡

ABSTRACT: Amorphous silicon dioxide films arise naturally by exposure of silicon surfaces to atmospheric environments. When used as electrodes in Li-ion batteries, the characterization of surface lithiation is relevant to the understanding of the performance of Si anodes. In this work, density functional theory analyses of the lithiation of an amorphous silicon dioxide film reveal the lithiation mechanisms and the role of the surface functional groups on the lithiation reactions and on the structure of the lithiated film. The surface concentration of silanol groups and structure of the optimized model of amorphous hydroxylated silicon dioxide film agree with those observed experimentally. It is found that Li is incorporated via breaking of Si−O bonds and partial reduction of the Si atoms. Evaluation of the formation energy for lithiation of the film indicates that the film would saturate at a Li/Si ratio of 3.48. Analyses of radial distribution functions and coordination numbers show the evolution of the structure upon lithiation, indicating the presence of Li6O complexes stabilized by the surrounding Si atoms. irreversible capacity lost at the first cycle has been also attributed to formation of lithium silicates during lithiation of SiO2.9 There are many experimental and theoretical studies focused on the lithiation of silicon nanoparticles, most of them oriented to understand the lithiation/delithiation mechanism of crystalline and/or amorphous Si in bulk phases.12−14 Periodic density functional theory (periodic-DFT) studies have analyzed dilute Li incorporation and diffusion in crystalline Si, thin films and nanowires, and crystalline LixSi phases. Lithiation of bulk amorphous Si to form amorphous lithium silicides has been also studied.4 However, none of these studies have tried to describe at the atomistic level the lithiation of the outermost surface layer on silicon nanoparticles which may have a very different chemistry because of being exposed to environmental conditions. Thus, to the best of our knowledge, there is a lack in understanding the lithiation of silicon nanoparticle surfaces during the first cycle. This is crucial because there is a lot of experimental evidence that silicon nanoparticles are always covered by a naturally formed layer of hydroxylated silicon dioxide,3,15−17 whose composition may affect both the electrochemical lithiation process and the interfacial interaction with the electrolyte.3,9 In this work we address the lithiation of a hydroxylated amorphous silicon dioxide surface using theoretical modeling via periodic-DFT calculations. We expect that these results will

1. INTRODUCTION Li-ion batteries are the preferred source of portable energy in electronic devices and an attractive option for a wider range of applications.1,2 However, their use in highly demanding power applications like commercial transportation is still limited. Among other reasons, this is due to the current Li storage capacity at the anode,3,4 which is usually composed by graphite.5,6 In that sense, research efforts are directed to find new anode materials with better volumetric and gravimetric capabilities for Li incorporation.7 Si-based anodes are one of the most promising materials to replace graphitic anodes. Besides the natural abundance of silicon,3 silicon nanoparticles possess gravimetric and volumetric capacities almost 10 and 3 times higher than that of graphite, respectively.4,8 However, commercial use of Si-based Li-ion batteries is still not massively implemented because silicon nanoparticles suffer from a poor cyclability. During lithiation/ delithiation cycles there is a volumetric expansion/contraction up to 300%, leading to structural pulverization, formation of cracks, and damage of the SEI (solid electrolyte interphase) layer, which induce continuous exposing of the surface of silicon nanoparticles to the liquid electrolyte.4,9,10 There is not general agreement about the effects of the presence of an amorphous silicon dioxide film on silicon surfaces on the Si anode performance for Li-ion batteries. Recent work addressed the effects of surface functional groups on electrolyte degradation and cyclability on Si anodes. It was found that possible formation of covalent bonds between surface silanol groups and the binder can minimize the electrolyte decomposition11 and enhance the cyclability.3 However, the © 2015 American Chemical Society

Received: March 28, 2015 Revised: June 26, 2015 Published: June 26, 2015 16424

DOI: 10.1021/acs.jpcc.5b02992 J. Phys. Chem. C 2015, 119, 16424−16431

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reproduced. The model with a silanol number of 5.8 OH/nm2 was considered representative for temperatures up to 673 K.21 Based on the aforementioned model with periodic boundary conditions,17 here we reproduce a hydroxylated amorphous silicon dioxide film representative of the outermost external layer of silicon nanoparticles.3 The atomic coordinates were approximately extracted, and a MD relaxation using the universal force field (UFF) potential was applied on a 3 × 3 supercell.27 A second relaxation was performed on the unit cell using periodicDFT.23 The resulting slab of approximately 9 Å thickness was characterized in its ring size distribution, its bond angle distribution, and its silanol number. A radial distribution function (DFT) analysis was also applied. The RDF analysis provides an important criterion by which the validity of the proposed model can be tested. It is defined as the number of neighbors of a given species per unit volume evaluated as a radial function of distance.4,28,29 2.2. Lithiation Protocol. The study of lithiation of hydroxylated amorphous silicon dioxide films by experimental or computational methods is still scarce. The available literature is mainly devoted to lithiation of silicon dioxides, where it is reported that Li incorporation occurs through breaking of Si−O bonds to form lithium silicate like structures and Si−Si bonds.30 For hydroxylated amorphous silicon dioxide films on silicon surfaces it is required to perform the identification of favorable mechanisms for Li incorporation. The presence of both surface functional groups, as well as the solid-vacuum interphase, may influence the lithiation reactions and also the structure of the lithiated film. Here we test three lithiation mechanisms for the early stages of lithiation at the first lithiation cycle:30 first, direct incorporation of Li atoms into the interstitial sites; second, formation of Li2O-like clusters and Si−Si bonds through the attack of two Li atoms to an oxygen atom belonging to a siloxane bridge (Si−O−Si); third, formation of Li2SiO4-like structures by breaking of Si−O bonds by two Li atoms. Once a favorable Li insertion mechanism was identified, simulations of lithiation until saturation are performed by a step-by-step computational procedure. While avoids the simulation of Li diffusion, this procedure has been successfully employed for lithiation of amorphous silicon.12 Li atoms are incorporated by testing all possible energetically favorable sites in a configurational sampling at each composition, selecting only the lowest energetically configuration for further Li incorporation.4 Potential−composition curves comparable to experiment have been obtained. Analysis of structural changes as a function of Li content can also be performed. Selected lithiated films were also subject to a Bader charge analysis in order to examine the electronic transfer between atoms. Bader charge analysis is defined as the quantification of the total electronic charge associated with an atom through definition of a sphere surrounding the atom whose volume is defined by zero flux surfaces.31 2.3. Computational Methods. Surface relaxation was done using first classical MD and then periodic-DFT. Lithiation calculations were performed using periodic-DFT. MD calculations were done using the full periodic table force field model UFF as implemented in AVOGADRO code.27 For the UFF the force field parameters are estimated using general rules based only on the element, its hybridization, and its connectivity. Since its publication in 1992, the UFF model has been successfully applied in several types of systems for structural relaxations.32−35

2. SYSTEM AND COMPUTATIONAL DETAILS 2.1. Hydroxylated Amorphous Silicon Dioxide Film. The amorphous nature of hydroxylated silicon dioxide surfaces makes difficult its study by both experimental and theoretical methods. For example, conventional use of X-ray scattering to obtain surfaces via cleavage of crystalline materials is prohibited because of the absence of long-range order.17 This lack of long-range ordering also hinders the use of computational modeling.18−20 However, recent published works17,21 have opened the way to the use of periodic-DFT methods as implemented in VASP (Vienna Ab-initio Simulation Package)22,23 for modeling amorphous surfaces like hydroxylated amorphous silicon dioxide. A computational model representative of a hydroxylated silicon dioxide surface must reproduce structural properties as the Si ring size distribution, the silanol type distribution, and the silanol number. The silanol number is defined as the total number of silanol groups per unit surface area.24 The ring size distribution varies from 4 to 10 Si atoms per ring, with a majority of 5 and 6 Si atoms per ring.17,20 The silanol number varies with temperature and synthesis method in a complex way. For a completely hydroxylated surface the silanol number can vary from 4.2 to 5.7 OH/nm2, with an average value of 4.9 OH/nm2.3,18 Surface silanols can be classified according to their bonding interactions, being called single or terminal silanols when there is a single hydroxyl group bonded to the Si atom and geminal when there are two hydroxyl groups attached to the Si atom. If two silanols are bonded to Si atoms connected by a siloxane bridge, they are called vicinal, or if they are bonded to Si atoms separated by an O−Si−O bridge, they are called adjacent. Through-space interactions between silanols are possible, too. If a silanol has hydrogen bond interactions with other silanols, it is called associated; if not, it is called isolated.17,25 Several models aiming to reproduce the main characteristics of a hydroxylated silicon dioxide surface have been proposed. Using cluster-DFT calculations, the ring size distribution for hydroxylated amorphous silica was reproduced, and the following ordering was found: 6-membered ring > 5-membered ring > 7-membered ring > 8-membered ring > 4-membered ring.20 However, for this model, because of the border effects produced by saturation with hydrogen atoms, the silanol number of the surface deviates from a physically acceptable representation. In other work, the surface of amorphous silica was modeled with facets (100), (101), and (111) of crystalline β-cristobalite saturated with hydroxyl groups.26 The silanol number vs temperature dependence was reproduced by applying a dehydroxylation process originally developed for alumina surfaces. A linear combination of each facet using adjustable parameters for weighting was used. However, because of the crystallinity of the facets, this model does not reproduce the actual structure of amorphous silica surface.26 In a recent work, a model of an amorphous hydroxylated silica surface was proposed using periodic boundary conditions.17 The surface was created by cutting a slab from a bulk model of silica generated using classical molecular dynamics (MD). The dangling bonds were saturated with hydroxyl groups, and then a geometric optimization using periodic-DFT was performed. The ring size distribution, the Si−O−Si angle distribution, and the silanol type distribution were fairly well 16425

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Figure 1. Periodic model of a hydroxylated amorphous silicon dioxide film: (a) top view, (b) side view, and (c) orthographic view.

Table 1. Computed Structural Properties Compared to Reported Experimental Data this work (av values)

std dev (σ)

exptl value

Si−O [Å]

1.639

0.01

O−Si−O angle [deg]

109.48

2.68

Si−O−Si angle [deg]

143.51

9.29

1.6141 1.6242 109.443 109.542 14342 15342

Periodic-DFT calculations were performed using the VASP code.19,22,23 For the exchange-correlation functional approximation we chose the generalized gradient approximation proposed by Perdew−Burke−Ernzerhof (GGA-PBE).36 The projector augmented wave (PAW) pseudopotential was used for describing the core electrons interactions.37,38 Because of the large size of the hydroxylated silicon dioxide system, the surface Brillouin zone integration was performed using the gamma point Monkhorst−Pack mesh.39 The ionic relaxation loop was performed until total energy differences were below to 10−3 eV and electronic self-consistent iteration was set to 10−4 eV. Surface relaxation by using DFT was implemented following a two steps approach while all atoms were enabled to move in both cases. The first relaxation was done using a plane-wave expansion up to 230 eV. The second more refined relaxation used a plane wave expansion up to 400 eV. DFT parameters for surface lithiation are the same used for surface relaxation, using an energy cutoff of 400 eV in all cases. 2.4. Formation Energy Calculations. The formation energy was calculated from the total energy of each configuration after the DFT relaxation:

Figure 2. Calculated Si−O−Si angle distribution for the computed hydroxylated amorphous silicon dioxide film.

Figure 3. Si−O pair RDFs for the computed hydroxylated amorphous silicon dioxide film (blue) and experimental RDF obtained for silica glass (red).

ΔE(x) = [E(LixSurface) − xE(Li metallic) − E(Surface)]/N

total energy per atom of Li in a metallic body-centeredcubic (BCC) phase, and E(Surface) is the total energy of the hydroxylated silicon dioxide surface without Li atoms. The formation energy is normalized with respect to the total number of

(1)

In this case, E(LixSurface) is referring to the total energy of the lithiated surface with x Li atoms, E(Limetallic) corresponds to the 16426

DOI: 10.1021/acs.jpcc.5b02992 J. Phys. Chem. C 2015, 119, 16424−16431

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Figure 4. Direct incorporation of Li atoms at different interstitial sites over the film before DFT optimization.

Figure 5. Li incorporation through breaking of a siloxane bridge.

Figure 6. Li incorporation through breaking a Si−O bond before structural DFT relaxation.

density of approximately 1.9 g/cm3. Figure 1a−c shows the top, side, and orthographic views of the film illustrating the presence of different ring sizes ranging from 4 Si membered rings up to 10 Si membered rings, which is in agreement with experimental measurements.17,20 The surface silanol number of 5.9 OH/nm2 on the top surface is slightly above than the average experimental value of 4.9 OH/nm2. However, it is still representative for completely hydroxylated silica surfaces as reported in earlier work where atomistic models of silica surfaces with a silanol number of 5.8 OH/nm2 were considered valid for temperatures up to 673 K.18,21 The dangling bonds on the bottom surface are

Si atoms in the unit cell N, giving the formation energy per Si atom ΔE(x). A negative value for the formation energy indicates a thermodynamically favorable process.4,40

3. RESULTS AND DISCUSSION 3.1. Structural Properties of the Hydroxylated Amorphous Silicon Dioxide Film. The relaxed film geometry obtained after DFT optimization has a thickness of approximately 9 Å. The unit cell size contains 120 atoms (Si27O67H26) with a volume of 17.6 × 12.5 × 25.2 Å and film 16427

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groups involved in strong H bond interactions. The differences between the structures at higher Si−O distances indicates that the modeled film reproduces the amorphous nature of the hydroxylated silicon dioxide layer.3 3.2. Energetically Favorable Li Incorporation on the Hydroxylated Amorphous Silicon Dioxide Film. Each lithiation mechanism was tested on several points on the surface in order to find thermodynamically favorable sites for Li incorporation. Figure 4 shows selected geometries before structural optimization with Li atoms disposed for incorporation into the interstitial sites. The most favorable case has a positive value for the formation energy of 0.0406 eV per Si atom. None of the calculated sites have a negative value for the formation energy. Direct incorporation of Li atoms seems to be unfavorable for the initial stages of lithiation of the hydroxylated amorphous film of silicon dioxide. This behavior differs from the lithiation of crystalline or amorphous silicon, where Li incorporation is done through the interstitial sites.4,10 The simultaneous incorporation of two Li atoms through the attack of an O atom belonging to a siloxane bridge is shown in Figure 5 for a selected geometry before and after DFT optimization. After optimization, the Li atoms are displaced far away from their initial positions. After optimization, the Li atoms are displaced far away from their initial positions and the siloxane bridge remains unchanged. The average formation energy for all the studied sites is 0.037 eV per Si atom. This lithiation mechanism also seems energetically unfavorable for the initial stages of lithiation of the hydroxylated amorphous silicon dioxide film.30 Figure 6 shows before and after DFT optimization the simultaneous incorporation of two Li atoms through breaking of a Si−O bond. All tested Si−O bonds were thermodynamically favorable with an average value of −0.0419 eV per Si atom for the formation energy. After structural optimization the Si−O

Table 2. Bader Electronic Charge (Li/Si = 0.074) atom

before Li insertion |e|

after Li insertion |e|

Si1 Si2 O1 Li1 Li2

3.15 3.17 −1.58

1.72 3.13 −1.56 0.86 0.88

also saturated to form hydroxyl groups. It is worth to mention that although this model does not reproduce the transition between the hydroxylated surface of amorphous silica and the bulk phase of amorphous SiO2, it is still representative for studying the lithiation mechanism of the most external layer arising on silicon surfaces exposed to atmospheric environments. The slab thickness of 9 Å is not thick enough to address the lithiation of the whole SiO2 layer on Si surfaces. Only the most external hydroxylated layer is addressed here. Table 1 shows the average values for the bond length and the bond angles compared with experimental data.18,41−43 The Si−O−Si angle distribution is also shown in Figure 2. The broad distribution ranging from 125° to 165° is representative of the low bending barrier for the Si−O−Si angle which has been used for explaining the large number of structural arrangements in which silicon dioxide can be found.44,45 Comparison of standard deviations between the O−Si−O angle and Si−O−Si angle reinforces the notion that amorphous nature comes from the flexibility of the O−Si−O angle. The SiO4 tetrahedra remain almost undistorted.17 Figure 3 compares the RDFs for the studied hydroxylated silicon dioxide film and an optimized α-SiO2 crystalline structure using the same level theory. The peak around 1.63 Å indicates agreement in short-range order in both structures. The small peak around 1.85 Å corresponds to some silanol

Figure 7. Detailed view of Li incorporation by a step-by-step procedure. 16428

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Figure 8. Formation energy profile. The red lines are guide for the eyes.

bond is broken, the Si atom is displaced from its tetrahedral position and both the Si and O atoms become 3-fold coordinated. The electronic charge associated with each atom in Figure 6 after structural optimization is shown in Table 2. Each value of charge corresponds to the missing valence electrons of an atom, so a reduction in its value corresponds to electron gain or an atomic reduction. As can be seen, the displaced Si atom changes its electronic charge from 3.15 to 1.72, which indicates a partial reduction through electronic charge transfer from Li atoms. 3.3. Lithiation until Saturation of the Hydroxylated Silicon Dioxide Film. Figure 7 shows in a schematic view the applied lithiation protocol starting from the relaxed film of the hydroxylated amorphous silicon dioxide film. Two Li atoms are added at each step by testing its incorporation in all available Si−O bonds. Then, the lowest energy relaxed configuration is for further Li incorporation. The same procedure is performed several times until surface saturation. Figure 8 shows the formation energy computed as a function of Li content. All tested configurations are shown. The lithiation is favorable until a Li content of Li/Si = 3.48. Any additional Li incorporation was thermodynamically unfavorable. The lithium storage capacity of the hydroxylated silicon dioxide film at the first cycle is similar to Li15Si4 at room temperature with a Li/Si ratio of 3.75.4,9 The structural evolution as a function of Li content is shown in Figure 9. At low Li content the Si atoms are displaced from their tetrahedral positions, and formation of Li4SiO4-like structures is predominant. At high Li content formation of Si−Si bonds is observed. This is confirmed in Figure 10 showing the RDF analysis of the Si−Si interaction for several Li contents. The non-lithiated film has a peak around 3 Å for the Si−Si interaction, which indicates the presence of siloxane bridges. However, at elevated Li contents most of siloxane bridges tend to disappear and a Si−Si interaction at 2.29 Å becomes predominant, which is indicative of possible formation of Li2O-like structures because of the interaction of Li atoms with free O atoms. The presence of surface hydroxyl groups seems to favor the structural reconstruction implied by the displacement of Si atoms. The average coordination number is used to study the bonding mechanism as a function of Li content in Si and O atoms, as is shown in Figure 11. Formation of Si−Si bonds is

Figure 9. Structural evolution as a function of Li/Si content.

assumed for distances of 2.50 Å ± 15%. A distance between 2.57−3.09 Å is chosen as a representative bond length for Si−Li atoms, as has been measured in Li−Si alloys.46 Si−O atoms are defined to be bonded if the distance between them is less than 1.88 Å, which is 15% above the average Si−O bond distance calculated for the studied hydroxylated silicon dioxide film. O atoms are defined to be bonded to Li atoms if they are located at less than 2.15 Å between them, as has been measured in lithium silicates of Li2Si2O5 and Li4SiO4.14 The average coordination of ⟨Si−Si⟩, ⟨Si−Li⟩, ⟨Si−O⟩, and ⟨O−Li⟩ is shown in Figure 11 (vertical left axis). A quasilinear decrease of the ⟨Si−O⟩ coordination number from 4 (Li/Si = 0) to 1.78 (Li/Si = 3.48) confirms the disappearance of the Si−O bonds. The increase in ⟨Si−Si⟩ linked to the increase in ⟨O−Li⟩ as the Li content rises indicates that formation of Li2O-like structures is possibly favored at Li contents near to the saturation point. 16429

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4. CONCLUSIONS Density functional theory studies of an amorphous silicon dioxide film with hydroxylated surfaces provide new insights into the lithiation of the most probable surface chemistries exposed by silicon anodes of Li-ion batteries. A model amorphous silicon dioxide film is built that reproduces the main surface properties: Si ring size distribution, silanol type distribution, and total number of silanol groups per unit surface area, in comparison with experimental values. The lithiation mechanism is identified by testing all possible sites, and it is found that the most favorable pathway involves breaking of the SiO bond by simultaneous reaction with two Li atoms causing partial reduction of the involved Si atoms. Once the most favorable lithiation mechanism is detected, a lithiation protocol is followed to characterize lithiation at each step by computing the formation energies. It is found that the film becomes saturated at a Li/Si ratio of 3.48. Interestingly, it is found that the lowest energy configuration usually corresponds to a displaced Si atom bonded to at least one hydroxyl group, thus revealing the role of the hydroxyl groups on lithiation. Hydroxyl groups favor surface lithiation because a structural reconstruction is more favorable when the Si atoms are not fully linked by siloxane bridges. The structural evolution during lithiation shows that Si atoms are displaced from their tetrahedral positions as they are partially reduced, and starting from a Li/Si ratio of ∼1.85, some Si atoms lose all the Si−O bonds and form Si−Si bonds. The average coordination number is used as an indicator of changes in the bonding mechanism for the Si and the O atoms as a function of Li content. The analysis indicates that breaking of the SiO bonds becomes less favorable at high degrees of lithiation and is accompanied by Si−Si bond formation and nucleation of Li6O complexes stabilized by Si atoms.

Figure 10. Calculated Si−Si RDF for the hydroxylated amorphous silica surface at several degrees of lithiation.

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Figure 11. Average coordination number for Si and O atoms as a function of Li content.

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph 979 845 3375 (P.B.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy under Contract DE-AC0205CH11231, Subcontract 7060634 under the Advanced Batteries Materials Research (BMR) Program. Computational resources from Texas A&M Supercomputing Center, Brazos Supercomputing Cluster at Texas A&M University, and Texas Advanced Computing Center at UT Austin are gratefully acknowledged.

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REFERENCES

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Figure 12. Formation of Li6O complex at Li/Si = 3.48.

The data labeled as “frac. Li6O” (vertical right axis) show the fraction of O atoms involved in formation of Li6O complexes. Detailed view of Li6O complexes over the surface at the saturation point (Li/Si = 3.48) can be seen in Figure 12. As the Li content increases, more O atoms are involved in formation of Li6O complexes. Stable formation of Li6O at high Li content in silicon suboxides has been attributed to the presence of surrounding Si atoms.46 16430

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DOI: 10.1021/acs.jpcc.5b02992 J. Phys. Chem. C 2015, 119, 16424−16431