A First-Principles Study of Lithium Intercalation and Diffusion in

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C: Energy Conversion and Storage; Energy and Charge Transport

A First-Principles Study of Lithium Intercalation and Diffusion in Oxygen-Defective Titanium Dioxide Hsiu-Liang Yeh, Shih-Hsuan Tai, Chieh-Ming Hsieh, and Bor Kae Chang J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 31 Jul 2018 Downloaded from http://pubs.acs.org on July 31, 2018

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The Journal of Physical Chemistry

A First-Principles Study of Lithium Intercalation and Diffusion in Oxygen-Defective Titanium Dioxide Hsiu-Liang Yeh, Shih-Hsuan Tai, Chieh-Ming Hsieh*, and Bor Kae Chang* Department of Chemical and Materials Engineering, National Central University, Taoyuan City 32001, Taiwan

ABSTRACT: Titanium dioxide has attracted considerable attention as a potential alternative anode material in lithium-ion rechargeable batteries (LiBs). In recent years, the incorporation of oxygen vacancy into such anode materials has been demonstrated to improve electrical conductivity, cycling stability, and rate performance through experimental studies. In this work, lithium intercalation and diffusion behavior in pristine and oxygen-defective TiO2 were studied by first-principles based on density functional theory (DFT) calculations. Total energies of possible intercalation sites were first calculated to find the most favorable site in the three commonly used polymorphs: anatase, rutile, and TiO2(B). Furthermore, the energy barriers of possible paths for lithium diffusion from one stable site to another have been calculated by climbing image nudged elastic band (CI-NEB) method. The electronic structures are also presented to compare conductivity of pristine and oxygen-defective TiO2. Our results indicate that although all three phases show enhanced conductivity via oxygen defect introduction, TiO2(B) is the best choice for lithium intercalation and diffusion as potential anode materials, having the lowest intercalation energy and lithium diffusion barrier, both of which are expected to result in better battery performance.

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1. INTRODUCTION Rechargeable lithium batteries have attracted considerable attention due to the growing demand for large-scale energy storage devices and green vehicles.1-5 In a conventional construction using graphite anodes, the formation of solid electrolyte interface (SEI) leads to an irreversible capacity loss and limited battery performance.6 Furthermore, lithium dendrites readily penetrate the SEI layer and lead to a short circuit in the battery, resulting in poor cycle lifetime and safety issues.7 One possible candidate anode material for lithium batteries is titanium dioxide-based materials due to associated lower cost, abundant source, light weight, safety, and high theoretical capacity.6, 8-11 In recent years, hydrogenation process is used as a strategy to create oxygen vacancies in TiO2 as anode for high-performance lithium batteries.12-16 Anatase, rutile, and TiO2(B) are the three most common TiO2 polymorphs, and have been investigated experimentally and theoretically as anode material for lithium batteries. Rutile is the most thermodynamically stable polymorph and the most commonly available form. Particle size effect has been demonstrated for lithium insertion with better electrochemical performance and capacity found in nanometer-sized rutile than in micrometer-sized particles.17 Anatase is more stable in the form of nanoparticles and is generally considered as a better electroactive host for lithium insertion than rutile.18 Furthermore, nanocrystalline anatase has shown better lithium storage capacity and rate performance attributed to the stability of surface lithium storage.8 TiO2(B) has a favorable structure containing open channels and an interesting pseudocapacitive electrochemical storage for lithium, which are good characteristics for host materials to accommodate lithium.19-21 Armstrong et al. demonstrated that lithium intercalation in TiO2(B) nanowires results in superior capacity of 305 mAhg-1, close to the theoretical capacity.22


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Among the three phases, anatase and TiO2(B) are more interesting anode materials than rutile due to their high theoretical capacity (335 mAhg-1) and better cycle lifetime,23 while rutile has a lower theoretical capacity (168 mAhg-1).24 Moreover, these two phases have been experimentally confirmed as excellent host materials for lithium incorporation.22, 25-26 However, poor electronic conductivity and inefficient lithium diffusion within the structure are the main drawbacks of TiO2-based anode electrodes for lithium batteries.27-30 Recently, further strategies have been proposed to improve performance and capacity, including size reduction as an efficient method for better energy storage due to increased surface area and reduced ionic/electronic diffusion lengths;30-31 coating active materials such as carbon on the surface to improve electrochemical properties as high power anode materials;3 and applying hydrogenation process to remove oxygen atoms from TiO2 and create oxygen vacancies to improve electronic conductivity and facilitate lithium diffusion.12-16 With increased computing power more readily available, first-principles calculations have been applied to investigate experimentally observed phenomena and to explain underlying mechanisms. The insertion energies of lithium within anatase, rutile, and TiO2(B) were first systematically calculated and compared at the same level of theory (GGA-PBE) by Legrain et al.32 The results indicated all three TiO2 polymorphs are thermodynamically favorable for lithium insertion and TiO2(B) provides the most favorable insertion sites for lithium. Dawson and Robertson employed both GGA and sX hybrid functional, the latter requiring intensive computational efforts, to study intercalation voltages of lithium in anatase, rutile, and TiO2(B), and confirmed that all three are good candidates for lithium intercalation but anatase is the most thermodynamically favorable for intercalation process.33


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Furthermore, the energy barrier of lithium diffusion in the c-direction within rutile was estimated with GGA functional by Koudiachova et al.34 The energy barrier in anatase was determined with GGA+U functional and showed good agreement with experimental value.35 In the case of TiO2(B), the energy barriers along all three possible pathways were calculated with GGA-PW91 by Arrouvel et al.21 and the diffusion pathway along b-axis channel was the most favorable. Although TiO2 with oxygen vacancy has shown potential as anode material for lithium batteries, few studies based on first-principles calculations have been conducted to investigate possible reasons. Kong et al. showed that oxygen vacancies were favorable for lithium insertion and diffusion, and thus was beneficial for charge process for TiO2(B) through GGA-PW91 with DFT+U calculations.36 Furthermore, Qiu et al. suggested with their GGA-PBE with DFT+U work that hydrogenation process for rutile to create oxygen vacancies not only improves electronic conductivity, but also enhanced lithium mass transport.12 However, Sushko et al. found that oxygen vacancy can significantly slow down the diffusion of lithium ions along cdirection channel in rutile by an embedded cluster (QM cluster) method.37 In this study, we use density functional theory to model lithium intercalation and diffusion in anatase, rutile, and TiO2(B) with/without oxygen vacancy as well as their electronic structures. Although a few computational studies have been carried out for lithium intercalation and diffusion in oxygen-defective rutile37 and TiO2(B),36 there lacks a systematic investigation with the same computational setup and scale-similar models. The calculation results of density functional theory were analyzed and compared to understand the merits of these three TiO2 polymorphs with oxygen vacancy as host materials for lithium intercalation and transportation. This can contribute to the understanding of how oxygen vacancy affect the lithium intercalation and diffusion paths in TiO2 systems. In addition, we also present GGA+U calculations on the


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electronic properties of all structures, elucidating the reason oxygen vacancy can improve TiO2 performance as anode material for lithium batteries.

2. METHODS All calculations were performed using the generalized gradient approximation (GGA) Perdew-Burke-Ernzerhof (PBE) density functional38 with ultrasoft pseudopotentials from standard database as implemented in the CASTEP plane-wave code.39 A plane-wave cutoff energy of 620 eV was chosen after convergence testing to ensure a good description of the system. For k-space sampling, we used the Γ–point scheme, which is suitable for the large supercells investigated here. U = 9.0 eV was applied to the Ti 3d states for electronic structure calculations, supported by a satisfactory match with the experimental band gap value of 3.2 eV for anatase. The total electronic density of states (DOS) and partial density of states (PDOS) were calculated using 2x2x2 k-point grid. Full geometry optimization calculations were performed until total energy change was less than 10-5 eV/atom, the forces on each atom were smaller than 0.03 eV/Å, final stress in the unit cell was less than 0.05 GPa, and atomic displacements were smaller than 0.001 Å. To investigate the lithium diffusion mechanism, activation barriers were calculated using the climbing image nudged elastic band (CI-NEB) method.40 Structures of initial and final configurations along the diffusion pathway were first fully geometry optimized. Then, five intermediate images of lithium fixed within the structure obtained by linearly interpolating between initial and final points were used to determine the minimum energy pathway and saddle points of reactions. If the local energy maximum was not located by these five images, the


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energy of an additional interpolated image with fixed lithium between the two points was calculated. To model TiO2, we considered a 216-atom (Ti72O144) supercell consisting of 3x3x2 unit cells for anatase, a 216-atom (Ti72O144) supercell consisting of 3x3x4 unit cells for rutile, and a 192-atom (Ti64O128) supercell consisting of 1x4x2 unit cells for TiO2(B), ensuring distances of approximately 10Å between any lithium atom and its self-image included in the structure at later stages. In this study, our aim is to investigate the mechanism of lithium insertion and transport in oxygen-defective TiO2, therefore the dilute concentration case was considered because lithium intercalation and diffusion at this limit is expected to yield only a small change in the lattice parameter.41 One lithium atom was added for each model, resulting in a concentration of [Li]/[Ti] = 0.014 for anatase and rutile, and 0.016 for TiO2(B). Lithium intercalation sites are shown as purple spheres in Figure 1, corresponding to octahedral sites occupied by lithium atoms demonstrated in anatase and rutile phase33-35,

42-43

and three possible sites: A1, A2, C in

TiO2(B).21, 33, 41, 44 The C site is in the middle of the cavity of the b-axis channel, while the A1 site is 5-fold coordinated to oxygen atoms and the A2 site is also 5-fold coordinated and lies between bridging oxygen atoms. Oxygen vacancies were included in TiO2 models to systematically investigate the resulting effect. Possible oxygen vacancy sites are shown as orange spheres in Figure 1. There is only one type of oxygen vacancy site possible for anatase and rutile, denoted by Ov in this work, whereas TiO2(B) has four types of sites possible: Obr, O3f1, O3f2, and O4f.36 Obr is located in the bridging location between two Ti atoms, O3f1 and O3f2 are two types of threefold coordinated oxygen vacancy sites, and O4f is the fourfold coordinated vacancy site.45


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Figures 2 and S1 show all possible lithium pathways in the three TiO2 polymorphs. Previous studies have shown possible lithium diffusion pathways, where lithium follows a zigzag path from one octahedral hole to the next, crossing a saddle point halfway in the anatase phase.35 Diffusion can also occur between the octahedral sites within the open channels in the c-direction in the rutile structure.34 Although it has been shown that lithium diffusion from one C site along the b-axis to another adjacent C site is the most possible pathway in TiO2(B),21, 36, 41 in this study all three diffusion pathways were still considered in TiO2(B) for a comprehensive investigation. As a result, pathways that from A1 site to another A1 site and from A2 site to another A2 site were also calculated using the same examination method. To compare the effect of the presence of oxygen vacancy, we calculated the same diffusion pathways with the addition of vacancy sites described above for oxygen-defective TiO2.

3. RESULTS AND DISCUSSION The crystal structure of anatase is tetragonal (space group I41/amd), as is rutile (space group P42/mnm), while TiO2(B) is monoclinic (space group C2/m). Unit cells of the polymorphs are shown in Figure 3. Calculated lattice parameter of TiO2 unit cells listed in Table 1 are in good agreement with the experimental values46-47 to within 3%. Table 2 lists the calculated formation energy of oxygen vacancy in all possible sites for the three polymorphs. The magnitude of oxygen vacancy formation energy of TiO2 increases in the order of anatase-Ov (4.46 eV), rutile-Ov (4.60 eV), TiO2(B)-Obr (5.34 eV), TiO2(B)-O3f1 (5.48 eV), TiO2(B)-O4f (5.73 eV), TiO2(B)-O3f2 (5.98 eV). As a result, it seems oxygen vacancy is more easily created in anatase than rutile and TiO2(B). Here, the formation energy (EOv) was calculated using the equation EOv = ETiO2-Ov – ETiO2 + EO, where ETiO2-Ov, ETiO2, and EO are the


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total energies from DFT calculations of oxygen-defective TiO2, pristine TiO2, and oxygen atom, respectively. When modeling lithium intercalation sites, lithium atoms were placed in octahedral sites in anatase33, 35, 42 and rutile models,33-34, 43 and in A1, A2, or C sites in TiO2(B) model21, 33, 36, 41, 44, 48-49

in accordance to previous computational and experimental studies. Models were then fully

geometry optimized. Here, intercalation energy (Eintercalated) represents the stability of such lithium intercalated system, and was calculated using the equation Eintercalated = Elithiated – ETiO2 – ELi , where Elithiated, ETiO2, and ELi are the total energies of TiO2 intercalated with a lithium atom, pristine TiO2, and lithium atom, respectively. The energy of lithium metal was obtained by optimization of body-centered lithium metal using 25x25x25 k-points mesh, commonly seen in literature21, 36 and 620 eV cutoff. ELi is then taken as half the value of this two-atom structure. Table 3 summarizes the lithium intercalation energy for all TiO2 polymorphs. The calculation results indicate that the C site of TiO2(B) is the most favorable site for lithium intercalation in dilute limit among the four sites of TiO2(B)21, 33, 41, 44 and also the other two TiO2 polymorphs. The lithium intercalation energy of rutile is an order of magnitude smaller than those of anatase and TiO2(B). This confirms that rutile is not a good candidate as lithium intercalation materials from experimental observation.50 The lithium intercalated TiO2 polymorphs with an oxygen vacancy were fully optimized and their structures are summarized in Fig. S2 and S3. The lithium atom moved slightly along the c-axis channel in the anatase polymorph, and stayed in the same position in rutile. In the case of TiO2(B), the lithium atom at C site stayed nearly in the same position and the lithium atom at A1 and A2 sites shifted slightly in all oxygen-defective TiO2(B). Lithium intercalation energy was calculated for oxygendefective structures using the following equation: Eintercalated-Ov = Elithiated-Ov – ETiO2-Ov – ELi, where


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Elithiated-Ov is the total energy of oxygen-defective TiO2 after lithiation. Table 4 lists the lithium intercalation energies for all combinations of TiO2 polymorphs with possible oxygen vacancy sites. In general, lithium intercalated in TiO2(B) C site is the most stable site for pristine TiO2, whereas TiO2(B)-O4f C site is the most stable site for the oxygen-defective case. Furthermore, TiO2(B) is more favorable than the other two polymorphs of TiO2 with oxygen vacancy no matter which oxygen vacancy site is considered in TiO2(B), with the exception of O3f2 A1. It is interesting to find that lithium atom placed at A2 site in TiO2(B)-O4f moved towards the C site after structure relaxation, which may indicate that A2 is not stable within TiO2(B)-O4f. To further confirm this, we also performed single point energy calculations to obtain the intercalation energies for A2 and C site in this oxygen-defective structure, and found that the intercalation energy of lithium in A2 site was 0.2411 eV higher than that in C site. The energy profiles for lithium diffusion from one stable site to adjacent stable site in pristine and defective TiO2 are shown in Figure 4, and their energy barriers are summarized in Table 5. For pristine TiO2 structure, the calculated energy barriers for lithium diffusion in anatase and rutile are 0.5056 and 0.0254 eV, respectively, whereas the energy barrier in TiO2(B) from one C site to another C site is 0.3894 eV. Our results are of the same order of magnitude compared to previous computational studies of anatase (0.51 eV),35 rutile (0.04 eV),43 and TiO2(B) (0.3eV).21 In the case of TiO2(B), literature mostly reported C-C as the favorable lithium diffusion pathway.21,

36, 41, 44

To warrant a systematic investigation of the minimum

energy path in TiO2(B), it is necessary to also take account of A1-A1 and A2-A2 paths for overall consideration. The resulting energy barrier was lowest for A1-A1 (0.3037 eV), similar to C-C (0.3894 eV) and much lower than A2-A2 (0.9381 eV). The increased diffusion energy barriers of oxygen-defective anatase and rutile TiO2 compared to those of pristine TiO2 indicate


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that oxygen vacancy may hinder lithium diffusion in these polymorphs. However, in the case of TiO2(B), lithium A1-A1 diffusion energy barrier decreased in the case of TiO2(B)-O3f1 and TiO2(B)-O4f, which means that lithium can diffuse more efficiently in the presence of these two types of vacancies. It is worth noting that the final position of lithium in the original A2-A2 diffusion pathway in TiO2(B)-Obr moved to an adjacent C site after full relaxation of the structure, implying that such diffusion mechanism may not exist in the presence of Obr vacancy. TiO2(B) is the only polymorph to exhibit lowering of energy barrier upon introduction of oxygen vacancy configurations, specifically O3f1 and O4f which have resulting activation energies of 0.2973 and 0.2547 eV along the A1-A1 pathway, respectively. This pathway already has a low activation energy of 0.3037 eV in the pristine material, with only pristine rutile having a lower barrier of all structures studied here. However, as mentioned above, the lithium intercalation energy for rutile is lower by an order of magnitude, confirming it as a poor material for lithium ion battery application. This means that TiO2(B) may be a better choice for manufacturing oxygen-defective materials among these three polymorphs. It is well known that GGA underestimates the absolute value of the band gap and performs poorly in calculating electronic properties of transition metal compounds like Ti. Therefore, DFT+U method was used to correct the self-intercalation error.33, 51-55 U = 9.0 eV was imposed on Ti d orbital of anatase, where the calculated band gap for bulk anatase (3.18 eV) was close to the experimental value (3.20 eV). The band structure and density of states (DOS) calculations for the three phases and their respective oxygen defective models are shown in Fig. S4-S6. Figure 5 shows the partial density of states (PDOS) results for anatase, rutile, and TiO2(B) with and without oxygen vacancy. In cases of pristine TiO2, the valence bands (VB) were mostly made up of O 2p states and the conduction bands (CB) were mostly made up of Ti 3d states. The


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calculated band gaps for pristine anatase, rutile, and TiO2(B) are 3.18, 2.52, and 3.28 eV, respectively. Both PDOS contribution and band gap values are in agreement with previous study.33 In the case of TiO2 with oxygen vacancy, the shape of PDOS is similar to those of pristine TiO2, but the Fermi level is shifted toward the conduction band and the band gap is reduced by 0.66, 0.55, and 0.22~0.65 eV for oxygen-defective anatase, rutile, and TiO2(B), respectively. These two phenomena imply an enhancement in electronic conductivity after introducing oxygen vacancy into TiO2 models. As a result, the performance of oxygen-defective TiO2 as an anode material for lithium rechargeable batteries is expected to be enhanced when compared to that of pristine TiO2.

4. CONCLUSION Density functional theory calculations were performed to investigate the intercalation sites and diffusion paths of lithium in three common TiO2 polymorphs (anatase, rutile, and TiO2(B)) with and without oxygen vacancy using the same computational methodology and scale-similar models. Results showed that intercalation energy of lithium is less stable in rutile both with and without oxygen vacancy, suggesting that this phase may not be a good choice for using hydrogenation process as host materials for lithium intercalation process. Lithium in the C site of TiO2(B), on the other hand, is the most favorable among all pristine TiO2 sites. In general, TiO2(B) still has sites that are more stable after introduction of oxygen vacancy, especially for C site in TiO2(B)-O4f, which is the most favorable. Furthermore, the energy barrier for lithium diffusion in anatase, rutile, and TiO2(B) mostly increased after introduction of oxygen vacancy, except for the A1 to A1 site diffusion in


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TiO2(B)-O3f1 and TiO2(B)-O4f which showed a slight decrease. As a result, it seems that oxygen vacancy may hinder the lithium diffusion in TiO2 polymorphs. Lithium diffusion from one A1 site to another in TiO2(B)-O4f is the pathway with the lowest energy barrier of 0.2547 eV. In general, presence of oxygen vacancy in TiO2(B) results in a relatively small energy barrier increase compared to that found in oxygen-defective rutile and anatase, no matter which oxygen vacancy site is considered, which can be attributed to the unique channel structure of TiO2(B). In addition, the narrowed band gaps and shifted Fermi level for all three phases indicate an enhanced electronic conductivity after introduction of oxygen vacancy. It can be concluded that TiO2(B) may be the best candidate for hydrogenation process to create oxygen vacancy to obtain anode materials of rechargeable lithium ion batteries with enhanced performance.


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ASSOCIATED CONTENT Supporting Information Models of fully geometry optimized structures of lithium intercalated in oxygen-defective TiO2 polymorphs at initial and final positions in respective diffusion paths, and band structure and DOS analysis for pristine and oxygen-defective TiO2 polymorphs. (PDF)

AUTHOR INFORMATION Corresponding Author E-mail: [email protected] E-mail: [email protected] ORCID Chieh-Ming Hsieh: 0000-0002-3063-2135 Bor Kae Chang: 0000-0002-7039-9729

ACKNOWLEDGMENTS This work was supported by the Ministry of Science and Technology of Taiwan (MOST 1062221-E-008-088-MY3). The authors are grateful to National Center for High-Performance Computing (NCHC).


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FIGURES

Figure 1. Models of all possible lithium intercalation sites and oxygen vacancy sites in (a) anatase, (b) rutile, and (c) TiO2(B). Red, gray, and purple spheres represent O, Ti, and Li atoms, respectively. Orange spheres represent possible vacancy sites.

Figure 2. Lithium diffusion pathways for (a) anatase, (b) rutile, and (c) TiO2(B).


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Figure 3. Unit cells of crystal structures of (a) anatase, (b) rutile, and (c) TiO2(B). Red and gray spheres represent O and Ti atoms, respectively.

Figure 4. Calculated energy profiles for lithium diffusion pathways in pristine and oxygendefective models of (a) anatase, (b) rutile, and TiO2(B): (c) C-C, (d) A1-A1, (e) A2-A2.


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Figure 5. PDOS of anatase, rutile, TiO2(B) and the oxygen-defective models. The red line represents

O

2p

states

and

gray

line

represents

Ti

3d

states.


20

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TABLES. Table 1. Calculated and experimental structural parameters of bulk anatase, rutile, and TiO2(B). Experiment46-47

This work

Difference

a

b

c

V

a

b

c

V

a

b

c

V

Anatase

3.79

3.79

9.77

140.11

3.79

3.79

9.51

136.30

-0.10%

-0.10%

2.77%

2.79%

Rutile

4.64

4.64

2.97

63.91

4.59

4.59

2.96

62.40

1.09%

1.09%

0.28%

2.42%

TiO2(B)

12.28

3.76

6.62

292.12

12.18

3.74

6.52

284.22

0.82%

0.45%

1.54%

2.78%

All lattice parameters are given in angstroms.


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Table 2. The oxygen vacancy formation energy of oxygen-defective TiO2 Oxygen-defective TiO2

Formation energy (eV)

Anatase-Ov

4.46

Rutile-Ov

4.60

TiO2(B)-Obr

5.34

TiO2(B)-O3f1

5.48

TiO2(B)-O3f2

5.98

TiO2(B)-O4f

5.73

Table 3. Lithium intercalation energies (Eintercalated) for three TiO2 polymorphs. Polymorph Intercalated Site

Eintercalated (eV)

Rutile

octahedral site

-0.1531

Anatase

octahedral site

-1.3616

TiO2(B)

C

-1.4079

A1

-1.2644

A2

-1.3901


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Table 4. Lithium intercalation energies for three TiO2 polymorphs with an oxygen vacancy. Polymorph

Intercalated Site

Eintercalated-Ov (eV)

Rutile-Ov

octahedral site

-0.1064

Anatase-Ov

octahedral site

-0.8620

TiO2(B)-Ov

Obr

O3f1

O3f2

O4f

C

-1.1484

-1.3467

-1.2901

-1.5187

A1

-1.2256

-0.9464

-0.7897

-1.1645

A2

-0.9960

-1.1498

-1.3110

-- a

a

The lithium atom at A2 site in TiO2(B)-O4f structure was unstable and lithium moved from A2 site to C site after fully geometric optimization.


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Table 5. Activation energies of lithium migration in pristine and oxygen-defective models of three TiO2 polymorphs.

Polymorph Anatase Rutile TiO2(B)

Migration Pathway O–O

Energy difference (eV)

pristine

Activation energy (eV) 0.5056 1.0406 0.0254

0.5350

O–O

Ov pristine

0.4434 0.3037

0.4180

A1 – A1

Ov pristine Obr

0.3052

0.0015

O3f1

0.2973

-0.0064

O3f2

0.5244

0.2207

O4f pristine

0.2547 0.9381

-0.049

Obr

--a

O3f1

0.9807

0.0426

O3f2

0.9928

0.0547

A2 – A2

C–C

a

Structure

a

O4f

--

pristine

0.3894

Obr

0.4276

0.0382

O3f1

0.4054

0.0160

O3f2

0.5700

0.1806

O4f 0.4605 0.0711 The final position moved from A2 site to adjacent C site after fully geometry optimization,

resulting in a different diffusion path than the original.


24

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Table of Contents Graphic


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A First-Principles Study of Lithium Intercalation and Diffusion in

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