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Multiscale Science and Engineering

, Volume 1, Issue 2, pp 87–107 | Cite as

Recent Developments in Using Computational Materials Design for High-Performance Li4Ti5O12 Anode Material for Lithium-Ion Batteries

  • Ralph Nicolai Nasara
  • Shih-kang LinEmail author
Review
  • 189 Downloads

Abstract

By using knowledge of the fundamental laws of physics, we can determine multiple structural, and electronic property relationships that can be used as complementary guides in obtaining improved experimental information. Computational materials design allows us to fabricate optimized materials based on the understanding of key atomistic processes. In this review, we present an up to date summary of the computational approaches using first principles (ab initio) aimed at designing better lithium titanate oxide Li4Ti5O12 as anode material for lithium-ion batteries, and some key challenges and opportunities that lie ahead.

Keywords

Lithium titanate oxide Computation materials design Ab initio Density function theory (DFT) Anode material Lithium-ion batteries 

Introduction

Considerable research has been done in using Li4Ti5O12 (LTO) as a potential anode material for Lithium-ion batteries (LIBs). Despite LTO owning a negligible 1% in the anode material market share in 2013, companies like Altairnano (Nano-LTO technology) [1], Mircovast (LpTO™ technology) [2], Saft batteries (Evolion®™ and USABC 12 V Start-stop batteries) [3] and Toshiba (SCiB™) [4] still have active production and development for commercial solutions which they market towards heavy and high-power applications such as transportation systems (electric vehicles such as the Honda Fit EV), battery-driven industrial equipment and emergency back up power sources and supplies, and large-scale stationary battery energy storage systems (BESS) for frequency regulation and peak shaving [5].

Figure 1 shows the LTO-related published works in the Web of Science Core collection from 2002 to 2016 [6]. 2018 marks a ten-year anniversary since the rapid interest in LTO took off. Exploration peaked around 2014 when there were over 160 LTO-related published works. However, recently there has been diminishing output because of growing interests from higher capacity anode materials. However, in search of higher capacity anode materials, researchers also need to consider that almost all insertion compounds exhibit significant changes in the crystal structure as the concentration of the Li ion varies. The conventional graphite anode material with a theoretical capacity of 372 mAh g−1 shows as much as 10% volume increase when Li ion intercalates in between layers [7]. Extensive research has been done to explore and develop non-graphitized material with extremely high capacity. Group IV elements which form an alloying–dealloying reaction with Li were also promising alternatives with their relatively high theoretical specific capacity. Besenhard et al. [8] reported Si-based lithiated alloy Li4.4Si with a theoretical capacity of 4212 mAh g−1 or 3600 mAh g−1 for Li3.75Si at room temperature [9, 10]. Ge-based lithiated alloys have also been explored due to its high electronic conductivity (Eg = 0.66 eV vs. Eg = 1.12 eV for Si) [11] and high Li diffusivity (about two orders of magnitude lower than Si) [12] but even such promising high capacity material with differently developed nano-architectures are also plagued with substantial volume changes of up to 400% [13, 14, 15], and prone to pulverization and mechanical degradation. Conversion compounds such as α-Fe2O3 [16], and Co3O4 [17] offered twice as much specific capacity over the conventional graphite anode but also suffers drastic volume changes of up to 100%. A volume mismatch is then created which can induce some phase transformation, and if in excess, can significantly impede electronic conduction and increase electronic and ohmic resistances. This mechanical deformation also affects the integrity of the solid electrolyte interface (SEI) which affects the cycling efficiency and may even incur safety hazards [18].
Fig. 1

Li4Ti5O12-related published for each year from Web of Science.

Adapted from Ref. [6]

Among the anode materials, the LTO exhibits outstanding structural stability with its “zero-strain” character, which means that multiple cycles of Li ion and electron insertion/extraction from the solid matrix do not display relevant changes in the lattice dimensions [19]. LTO has a theoretical capacity of 175 mAh g−1 when discharged to 1.0 V. Coupled with a ~ 0.1% volume expansion Table 1 shows a figure of merit for this zero-strain property; factoring the amount of stored energy per unit volume change, LTO has the highest theoretical capacity among all anode materials. Another understated advantage of LTO is that it operates in a potential range where Aluminum is stable allowing the use of a much cheaper (66% cost reduction compared to Copper) current collector [20]. It also operates at a potential (1.55 V) where it is highlighted as an “Interphase-free” system because the organic electrolytes do not decompose and solid-electrolyte interphase (SEI) does not deposit on the surface and has been used a model system to calculate the Li+ desolvation activation energies [21, 22]. Aside from its promising cyclability, it has excellent chemical and thermal stability [23], but, LTO has been suffering poor high rate-capability, which has been attributed to its intrinsic low electronic conductivity (< 10−13 S cm−1), sluggish ionic transport [24], and interfacial kinetics [25]. Multiple approaches have been implemented such as doping [24, 26, 27], nanonization [28], compositing of conductive materials [29, 30] in an attempt to improve the rate performance of LTO. However, these approaches either involve considering different synthesis routes, multiple experimental conditions, and potential chemistries. With multiple experimental variables in consideration, these approaches are time/labor consuming. For example, even with the fundamental understanding that doping can generally enhance material properties; Fig. 2 shows that there is still uncertainty as to how and why certain transition metal dopants improve the rate-capability of LTO and their corresponding mechanisms, and all the reports are almost impossible to consolidate due to the multiple experimental variables involved. Despite LTO being a relatively mature, well-studied and with multiple published reports, the doping induced effect in the rate-capability is still under discussion.
Table 1

Selection of anode materials, their structure and, lithiation reactions, their theoretical capacities, their volume change during lithiation, and their normalized capacity per volume change

 

Structure and involved reaction

Theoretical capacity (mAh g−1)

Volume change (%)

Energy stored per volume change

LTO

Spinel/intercalation

175

0.1

1750

C

Layered/intercalation

372

9–14

31

Ge

Crystal/alloying

800–1300

400

2–3.25

Si

Crystal/alloying

4200

300

14

Sn

Crystal/alloying

660

250

2.64

α-Fe2O3

Cubic/conversion

500–1200

100

5–12

Co3O4

Cubic/conversion

890

100

8.90

Fig. 2

A collection of a few LTO doping-related published works up to 2018 from Web of Science

First principles (Ab initio) refers to knowledge of quantum mechanics to determine the structure–property relationship of a system. Ab initio calculations based on the density functional theory (DFT) is a necessary tool for modern materials design and the explanation of atomistic mechanisms. It provides insights into a specific system before synthesis. Researchers can complement the ability and accuracy of computational processes and supplant the traditional trial-and-error way. The gathered experimental information is also improved, and the whole nexus of materials design, experimentation and characterization are made much more efficient. There has been no review that only focuses on the use of ab initio on designing LTO-based anode materials for LIBs. Herein, we present recent developments in computational materials design using ab initio based on the density functional theory (DFT) for designing high-performance LTO anode material for rechargeable LIBs. In this review paper, we present a comprehensive overview of works aimed at the computational challenges of building the LTO host structure, thermodynamics and phase stability evaluation of the lithiated phases, enhancement of the electrochemical performance by doping, modeling of LTO at the macroscale and some supplementary information and critical challenges faced.

Building the Initial Host Structure

An ideal electrode material should display reversible Li intercalation, which means very conservative volume changes and stable phase transformations. An initial host structure is typically a starting point for more systematic analysis regarding different atomic compositions. A good example would be an analytical study on composition variations on the transition metal ion in olivine-LiMPO4 [31, 32]. Again, these computations are complementary and should guide the experiments, not supplant or replace them. For building the atomistic model, the only input required is the crystal structure and the atomic composition of the material. The LTO defect spinel structure belongs to the Fd3m space group (No. 227). Each formula unit is composed of three sub-lattices: the tetrahedral 8a sites, the octahedral 16d sites, and the octahedral 32e sites. Eight formula units form the unit cell which is expressed as \(\left( {Li^{ + } } \right)_{8a} \left[ {Li^{ + }_{{\frac{1}{3}}} Ti^{4}_{{\frac{5}{3}}} } \right]_{16d} \left( {O_{4} } \right)_{32e}\). Li and Ti atoms randomly occupy the 16d sites in a ratio of 1:5, respectively. O atoms are located at 32e octahedral sites. The challenge with the LTO defect spinel structure is that the 16d sites are randomly occupied by \(\frac{1}{3}\) Li atoms and \(\frac{5}{3}\) Ti atoms. Since the unit cell is expressed in terms of thirds, we need to construct unit cells by a factor of 3 to satisfy each atom being an integer. This is addressed by constructing a supercell, which is a term which often appears when dealing with ab initio calculations. The atomic arrangement in perfect crystals is described by a periodically repeating unit cell. However, ideal periodicity is not always present in some physical systems. For convenience, we simulate the system using periodically repeated fictitious supercells. The form and size (usually based on the number of atoms) depend on the physical system under investigation [33]. For a case of 3 unit cells forming a 1 × 1 × 3 supercell, the 16d sites are now randomly occupied by 8 Li and 40 titanium atoms. A computational barrier stems from the numerous possible atomistic arrangements; The random distribution of the Li and Ti ions at the 16d sites would lead to almost 377 million permutations.

Incorrect Stoichiometry

Lippens et al. [34] addressed the computational barrier due to random chemical disorder at the 16d sites by considering an ordered Li4.5Ti4.5O12 structure which has arguably similar Li and Ti local environments as compared to the correct stoichiometry of Li4Ti5O12. With only four Li atoms in the 16d sites, the multiple permutations are just simplified to four possible arrangements in the structure. The most abundant arrangements: LiT–O–3Ti and LiT–O–(2Ti, 1LiO), labeled O(1) and O(2), respectively were chosen for further analysis to distinguish the two Li sites (8a and 16d) by X-ray absorption spectroscopy. Kataoka et al. [35] used their previously reported single-crystal X-ray diffraction data for LTO [36] and built the atomic models for Li4+xTi5O12 (x = 0, 1.5 and 3.0). They also assumed postulated ordered compounds similar to Lippens et al. [34] such as “Li4.5Ti4.5O12” as Li4Ti5O12, “Li7.5Ti4.5O12” as Li7Ti5O12 and “Li6Ti4.5O12” as Li5.35Ti5O12. They calculated the theoretical electron density distributions and total energies using the Full-potential Linearized Augmented-plane-wave (FLAPW) [37] for the whole composition range, and based on the Li5.35Ti5O12 electron density distribution identified the location of intercalated Li ions to be in the 8a and 16c site. Liu et al. [27] adopted a 2 × 1 × 1 supercell, in which two unit cells are arranged along the a direction leading to a nominal composition of Li21.33Ti26O64 to avoid the complexity of building the necessary 1 × 1 × 3 supercell of 168 atoms. However, similar to previous models, they also concluded a Li27Ti26O64 structure with an incorrect stoichiometry. They justified the use of a simplified structural model since the random distribution at the 16d sites would result in a similar Li and Ti local environment with the structure with correct stoichiometry. Their Li27Ti26O64 structure also had an extra valence electron as compared to their intended LTO structure, and the final number was set to 512 valence electrons for the calculations by removing an electron. As for the random distribution of Li atoms at the 16d sites, they only considered the arrangements with the furthest Li–Li distance and finalized the structure with the lowest total energy. One of the problems with this approach is that given that the 16d is a boxed space with periodic boundary conditions (PBC), and the Li atoms are randomly distributed, increasing the Li–Li distance of one pair means also pushing those two Li atoms closer to the remaining Li atoms and creating repulsion at that end. For the longest Li–Li pair distance, there exists a multiplicity of configurations, and there were no physical reasons why the authors chose only some. Researches above have been using only one or two unit cells to address the computational barrier in modeling the complex LTO host structure. Despite justifying that the random distribution of Li and Ti atoms at the 16d sites will lead to a similar local environment, these have resulted in wrong stoichiometries of Li4.5Ti4.5O12 and Li3.94Ti5.06O12.

Computational Issues with a Three-Fold Supercell

As previously stated a three-fold unit cell is required to achieve the correct stoichiometry. Such an extensive system with 168 atoms will lead to more permutations in the 16d sites and yet presents another computational challenge. Ziebarth et al. [38] constructed a hexagonal supercell with two formula units of LTO to achieve the correct stoichiometry and keep the number of atoms as small as possible (42 atoms). Ouyang et al. [39] constructed the necessary 1 × 1 × 3 supercell by considering the random arrangement of the Li and Ti atoms at the 16d sites. To achieve this, they placed two or three Li atoms in the 16d sites and optimized the Li and Ti atom distribution. Considering the PBC, with two Li atoms they reported three different configurations (O2-1, O2-2, and O2-3) and four different configurations using three Li atoms (O2-1, O2-2, O3-3, and O3-4). The lowest energy configurations O2-2 and O3-3 were then used to construct the supercell. However, it was also reported the O2-2 is a non-stoichiometric model, and the reported electronic structures are erroneous. It is because the O2-2 configuration has two more excess electrons in the unit cell, which was verified by the removal of electrons and the appearance of the insulating property. However, the addition and removal of electrons to reproduce the experimentally observed electronic structure has no physical meaning and satisfying the correct stoichiometry is still necessary. Tanaka et al. [40] adapted the configurations made by Ouyang et al. [39] for their O-K edge ELNES/XANES spectra studies for LTO. The O2 configurations with two Li atoms were built as Li10Ti14O32 for Li4Ti5O12, and the O3 configurations with three Li atoms were built as Li11Ti13O32 for Li4Ti5O12 and were independently optimized. Their 1 × 1 × 3 supercell was constructed by using one O2-2 model and two O3-4 models to form the correct stoichiometry of Li32Ti40O96 for Li4Ti5O12. Chen et al. [41] also adapted the configurations made by Ouyang et al. [39] and reported that the slightly Li-rich unit cells (O3 configurations—Li11Ti13O32) are reasonable since during battery operation LTO can always be Li-rich after Li intercalates into the lattice. Zhong et al. [42] proposed that there be two kinds of the unit cell for LTO: first is with two Li ions in the 16d site and is metallic by electron called n-type, another with three Li ions in the 16d site and is metallic by hole called p-type. They constructed a 1 × 1 × 3 supercell by integrating a p-n-p arrangement of three individually optimized cells. Yi et al. [23] constructed a 1 × 1 × 3 supercell model of the Li8Ti10O24 by creating two LiTi2O4 units as the primitive cell and substituting two Ti atoms in the 16d sites with two Li atoms. They also compared the formation enthalpy of an ideal spinel LiTi2O4 (− 2070.723 ± 1.6 kJ mol−1) [43]. The substitution of the Ti atoms at the 16d site by Li resulted in a more positive formation enthalpy (− 2020.48 ± 1.33 kJ mol−1) suggesting the stability of the system is weakened during the replacement. It was still concluded that all phases have very high thermodynamic stability (Li4+xTi5O12; x = 0, 3 and 4.5). Weber et al. [44] used a 3 × 1 × 1 supercell as initial structure for their investigation for LTO as an electrode material for Li–S batteries. However, for such a large supercell there exist multiple possible configurations which are too computationally demanding to assess. Their strategy was to test four random configurations and optimize the distribution of the Li and Ti atoms at the 16d site using molecular dynamics (MD). The four different configurations gave lattice parameters that were within 0.04 Å, and the one with the lowest energy, Li4-4, was used for further investigation. Despite creating necessary 1 × 1 × 3 supercell setup for building the LTO, the interplay of the 168 atoms remains computationally intensive, and researchers have tried to simplify by making structural and electronic assumptions, and random selection of the substitution pattern. The studies which have composited different individually optimized unit cells such as the p-n-p and O3–O2–O3 supercell resulted in the correct stoichiometry but neglected interface energies by individually optimizing the unit cell. This lead to the supercell not being fully optimized and therefore with wrong atomic arrangements.

Assessing the Li–Li Pair Distribution at the 16d Site

Tsai et al. [45] constructed a 1 × 1 × 3 supercell of Li32Ti40O96 (168 atoms) for the correct stoichiometry of the LTO structure compound. To correctly have the proper 16d substitution arrangement, the Li–Li binding energy was evaluated for the cubic Li10Ti14O32 supercell. There are eight Li atoms which equate to eight Li–Li bonding lengths. By considering the PBC and crystal symmetry, the eight Li–Li bonding lengths are grouped into three types of pair distances: short (2.983 Å), medium (5.156 Å) and long (5.969 Å). With the stable medium pair Li–Li distances (the second stable, long pair distances are also considered), the random configuration of the Li and Ti atoms were arranged, and the same 16d Wyckoff positions were applied to the Li32Ti40O96 supercell. However, the initial Li–Li pair analysis was performed on the stoichiometry of Li10Ti14O32 and there exist entirely different Li arrangements that result in a much lower LTO energy. The total energy obtained from this work was reported to be lower by 2.97 eV among all other structures modeled for the LTO at the time of publication. There is no physical cause to the preferred structure, and therefore the 16d occupancy in LTO remains to be a systematic ansatz. Zahn et al. [46] agreed that an agglomeration of Li (short Li–Li pair distance) must be avoided as it will lead to strong repulsive-attractive forces within the plane. To have the ideal distribution, they proposed a rule that there must be only one Li atom residing on each plane and they must be homogeneously distributed over all planes of the system. By considering the 16d Wyckoff positions along the [100] lattice vector as planes with horizontal, vertical and their connecting diagonal lines, they identified the possible Li substitution sites. Also, they hypothesized that the energy difference of the Li substitution must be larger in Li4Ti5O12 than the Li7Ti5O12 structure, and used this as another consideration for choosing the possible substitution sites. They have validated their assumptions by starting with up to two substituted Li. Finally, they constructed the 1 × 1 × 3 supercell with eight substituted Li and reported a stable structure which is lower by 4.5 eV compared to previous works. In the most recent study, Ganapathy et al. [47] constructed a supercell Li8Ti10O24 with correct stoichiometry and predicted the distribution of the two electrochemically inactive Li ions in the Ti 16d sublattice. They calculated all the 19 symmetrically distinct Li–Ti configurations in the 16d sites and chose the arrangement with the lowest energy. Their analysis for the Li–Ti configurations reveals that the energy systematically increases with decreasing Li–Li pair distance. The shorter Li–Li pair (2.974 Å) introduces repulsive energy, and the longest Li–Li pairs (5.146 Å and 6.642 Å) resulted in the lowest energy configuration. The Li–Li pair distances previously reported by Tsai et al. [45] were in agreement although the different conclusion about the optimal Li–Li pair distance. Both reports ended up using the medium and long Li–Li pair distances since the energy differences are minimal. The difference might be attributed to the size of the supercell used to assess the Li–Li pair distance. Using the lowest energy Li–Ti configuration, the energetics of electrochemically active Li in the 8a and 16c sites were calculated using the cluster expansion which was developed by Van der ven’s group [48, 49]. Zhang et al. [50] also considered the furthest Li–Li pair distance in the 16d sites when constructing the initial host structure. The lowest energy structure was when the Li ions in the 16d sites were separated by four cation layers along the c-axis.

A compilation of all atomistic models that have been used is shown in Fig. 3, and a compilation of all the reported structures for LTO are summarized in Table 2. To further lower the energy for theoretical models of LTO, we can make the supercells even bigger by using larger factors of 3 (6, 9, or 12) but this will be more computationally intensive. Also, assessing the arrangement of the 16d site remains a challenge. A general agreement is that there exist attractive-repulsive forces found for short Li–Li pair distances in the 16d. In general, considering the furthest Li–Li pair distances lead to very stable structures with low total energies.
Fig. 3

Compiled atomistic models of the supercells used by various studies: a crystal structure from the structural refinement taken from Ref. [35, 36]; b hexagonal supercell of LTO, red spheres are oxygen ions at 32e sites, blue spheres at Ti atoms at 16d sites, green spheres are Li-ions. Li-ions on the 16d sites are encircled. Taken from Ref. [38]; c Crystal structure of the supercell taken from Ref. [23] Oxygen occupies 32e sites; Lithium occupies the 8a sites while the 16d sites are occupied by Li and Ti with a ratio of 5:1; d crystal structure of the cubic unit cell of [Li3]8a[Li1Ti5]16d[O12]32e taken from Ref. [46]. Purple spheres are the 8a sites, gray spheres are the 16d sites, red spheres are the 32e sites; e crystal structure of the unit cell of the LTO phase taken from Ref. [45]. Green tetrahedrons Li 8a sites, green octahedrons are Li in the 16c sites, blue octahedrons Li and Ti in 16d sites, Red spheres are O at the 32e sites; f crystal structure of the lowest energy configuration LTO taken from Ref. [47] where red spheres are O, gray spheres are Ti, cyan spheres are Li in the 16d sites, and violet spheres are Li in the 8a sites; g crystal structure of the model systems of the LTO lattice taken from Ref. [50] where green tetrahedrons represent Li at the 8a site, green octahedrons represent Li at the 16d sites, blue octahedron represent Ti at the 16d sites, and red spheres are oxygen (color figure online)

Table 2

Compilation of built atomistic structures for LTO

Author

References

Stoichiometry

Remarks

Atomistic models provided

Lippens et al.

[34]

Li4.5Ti4.5O12

Limit the computational effort

None

Kataoka et al.

[35, 36]

Li4.5Ti4.5O12

Limit the computational effort, reported the Li intercalation sites from the electron density distribution

Figure 3a

Liu et al.

[27]

Li21Ti27O64

Only used two unit cells since 168 atoms are computationally-intensive. There are excess valence electron for constructed model

None

Ziebarth et al.

[38]

Li8Ti10O24

Used two unit cells using forming a hexagonal supercell requiring fewer atoms (42 atoms)

Figure 3b

Ouyang et al.

[39]

Li30Ti42O96

Li33Ti39O46

Constructed a supercell from O2-2 and O3-3 unit cells. O2 models have two excess electrons

None

Tanaka et al.

[40]

Li32Ti40O96

Constructed a supercell from two O3 and one O2 cubic cells

None

Chen et al.

[41]

Li33Ti39O96

Slightly Li-rich model is valid and helps with the construction of other intermediate compositions

None

Zhong et al.

[42]

Li32Ti40O96

Constructed a supercell with one n-type unit cell in between by two p-types. Both n-type and p-type are conductors, but LTO is insulating. Removing and adding electrons to match experimental observations has no physical meaning

None

Yi et al.

[23]

Li8Ti10O24

Constructed a Li2Ti4O8 which was used that to make the necessary 1 × 1 × 3 supercell without a systematic analysis of the selection of the two Ti 16d sites chosen

Figure 3c

Weber et al.

[44]

Li32Ti40O96

Random selection of substitution pattern and optimization by molecular dynamics (MD)

None

Tsai et al.

[45]

Li32Ti40O96

Considered the Li–Li pair distance of the Li10Ti14O32 structure and then applied to the supercell. Medium and long pair Li–Li distances lead to structures with low total energies

Figure 3d

Zahn et al.

[46]

Li32Ti40O96

The proposed rule for homogenous distribution was applied only for the Li4Ti5O12 phase, but not for the Li7Ti5O12 phase. Other works have been straightforward to obtain the lithiated phases. There exist attractive-repulsive forces for short Li–Li pair distances

Figure 3e

Ganapathy et al.

[47]

Li32Ti40O96

Since there are two types of ions in the 16d sites (Li and Ti) considering the arrangement, the Li–Ti pair distance leads to the lowest structural configuration. A relationship between the Li–Ti and Li–Li pair distance was established an in agreement with previous researches

Figure 3f

Zhang et al.

[50]

Li8Ti10O24

Longest Li–Li pair distance lead to lowest energy configurations

Figure 3g

Lithiated and Overlithiated Structures

For virtually all intercalation compounds, there are noticeable, if not severe, lattice expansion/shrinking and structural rearrangements during intercalation/deintercalation. Ab initio calculations by DFT provide us critical insights during what occurs during these processes. With an initial host structure and information about the possible insertion sites, we can build the corresponding structures with the additionally intercalated Li atoms. Ab initio can often predict variations in the lattice parameters and unit cell volume which can provide atomistic information about phase transformation and structural integrity. As demonstrated for Li[Mn2]O4 and Li2[Mn2]O4 which had a well-studied volume variation of 5.8%, in-depth ab initio investigations allowed researchers to decouple volume variations to specific contributions such as Li intercalation, Jahn–teller distortion and electron effects in different orbitals to accurately identify the electron effect as the dominant contributor. [51].

During intercalation in LTO, Li atoms originally from the 8a sites along with the Li atoms from the anode/cathode would occupy the 16c sites and form the rocksalt structure Li7Ti5O12 which is referred to a lithiated structure, as given by Eq. 1:
$$\left( {Li^{ + } } \right)_{8a} \left( {null} \right)_{16c} \left[ {Li^{ + }_{{\frac{1}{3}}} Ti^{4 + }_{{\frac{5}{3}}} } \right]_{16d} \left( {O_{4} } \right)_{32e} + Li^{ + } + e^{ - } \mathop \leftrightarrow \limits^{ } \left( {null} \right)_{8a} \left( {Li_{2}^{ + } } \right)_{16c} \left[ {Li^{ + }_{{\frac{1}{3}}} Ti^{3 + }_{{\frac{3}{3}}} Ti^{4 + }_{{\frac{2}{3}}} } \right]_{16d} \left( {O_{4} } \right)_{32e} .$$
(1)

Because the Li atoms in the 16d sites do not participate in the intercalation/deintercalation reaction, their configurations were fixed during the construction of the lithiated structures. The same applies to the oxygen atoms at the 32e sites [47]. Previous researchers demonstrated that building the Li7Ti5O12 structure involved removing all Li atoms in the 8a sites and adding the removed Li atoms in the 16c sites together with the newly intercalated Li atoms. Building the Li7Ti5O12 has been as a more straightforward task once the starting Li7Ti5O12 has been modeled correctly. The Li+ ion is larger than the available space at the 8a site of the Li4Ti5O12 but smaller than the space at the 16c sites of the Li7Ti5O12 causing a structural relaxation during intercalation. [45] This results in a slight shrinkage in volume which is the opposite phenomenon observed for most electrode materials.

The Li7Ti5O12 lithiated structure was studied and paved the way for LTO’s stable cycling performance with its “zero-strain” character. Additionally, with a negligible volume change and still a relatively high cut-off potential at 1.0 V it was only intuitive to further discharge at lower potential to address the low working voltage and low reversible capacity of LTO. Based on Eq. (1), Ge et al. [52] challenged the classical viewpoint on the theoretical capacity of LTO. They reported that it can be extended to 293 mAh g−1 if there are enough interstitial sites to accommodate another two moles of Li ions because there are still 40% of tetravalent Ti ions to accept electrons as shown in Eq. 2. The limiting factor is the number of tetravalent Ti ions and not the octahedral or tetrahedral sites in the structure. Therefore, the LTO structure can theoretically accommodate five moles Li ions between 2.5 and 0.01 V and is referred to be at an overlithiated state forming a Li9Ti5O12 phase.
$$\left( {null} \right)_{8a} \left( {Li_{2}^{ + } } \right)_{16c} \left[ {Li^{ + }_{{\frac{1}{3}}} Ti^{3 + }_{{\frac{3}{3}}} Ti^{4 + }_{{\frac{2}{3}}} } \right]_{16d} \left( {O_{4} } \right)_{32e} + 2Li^{ + } + 2e^{ - } \mathop \leftrightarrow \limits^{ } \left( {Li_{2}^{ + } } \right)_{8a} \left( {Li_{2}^{ + } } \right)_{16c} \left[ {Li^{ + }_{{\frac{1}{3}}} Ti^{3 + }_{{\frac{5}{3}}} } \right]_{16d} \left( {O_{4} } \right)_{32e} .$$
(2)
This intercalation reaction does not change the structure of LTO significantly. Shu et al. reported that the thermodynamic stability of LTO could be improved after intercalation to Li7Ti5O12, but slightly diminished with more Li inserted into the structure forming a Li8.5Ti5O12 (both structures are still thermodynamically stable). It is amazing that the total volume change from 2.0 to 0 V is less than 1% [53], attesting to the extremely high structural stability of LTO. Figure 4 shows a schematic diagram of lithiation [6], and Table 3 shows a compiled calculation of lattice constants and intercalation for various lithiated structures [54].
Fig. 4

Atomistic structures of Li4Ti5O12, Li7Ti5O12, and Li9Ti5O12.

Taken from Ref. [6]

Table 3

Constructed lithiated structures, calculated lattice constant and average intercalation potential.

Taken from Ref. [54]

Structure

Lattice constant (Å)

Volume change from initial LTO (%)

Intercalation potential (V)

Li4Ti5O12

8.315

Li7Ti5O12

8.259

0.678 (shrinkage)

1.48

Li8.5Ti5O12

8.346

0.373 (expansion)

0.05

Li10Ti5O12

8.454

1.672 (expansion)

Negative value

Ab initio calculations validated that the LTO initial host compound can accommodate more Li leading to overlithiated phases with negligible volume changes [54]. The overlithitaed phase Li8.5Ti5O12 is experimentally obtainable and validates earlier studies that LTO can be discharged near 0 V [52]. At the overlithiated phase Li8.5Ti5O12, the 16c sites are fully occupied, and about half of the 8a sites are occupied by excess Li-ions. However, further Li insertion to occupy the vacant 8a sites is not thermodynamically stable because the predicted intercalation potential become negative. A negative intercalation potential indicates that the free energy of the system is lower than that of metallic Li, which results in Li deposition and formation at the electrode surface.

From the compiled reports, LTO is validated as a zero-strain material which is reflected in its cycling stability. A simple two-point calculation of the initial host compound and lithiated/overlithiated phases provide in-depth information, not just about the crystal structure, but also the electronic properties and activation barriers and help us understand and design higher performance LTO anode materials. Extra discharge capacity and higher nominal voltage can be achieved with LTO as anode material when using the overlithiated phase. However, previous studies show that optimum utilization of this extra capacity still needs more mechanistic studies and large irreversible capacities have previously been attributed to the large polarization caused by substantial activation energy [55], the stability of the overlithiated phase [23, 43] and SEI formation.

Assessing the Reliability of the Structure

A primary output of ab initio calculations, aside from the optimized model and information about its structural, and electronic properties is the total Energy E or E0; and is referred to as the energy of the system of the at 0 K. Finding the most thermodynamically stable structure is often done by comparing the calculated total energies of candidate structures. Researches above building the initial LTO host compound have been trying to build on top of each other, and the total energy for the LTO supercell has been vaguely used to compare if which model is the most thermodynamically stable, therefore striving for lower total energies. When building the LTO host structure, Tanaka et al. [40] despite using the same models with a previous study [39] have arrived at contrasting conclusions such as O2-1 and O3-3 energies and that the most stable configuration is O3-4. The possible origins of the discrepancy are from the use of pseudopotential (ultrasoft versus PAW), the difference in cut-off energy (40 Ryd versus 25 Ryd) or the difference in the exchange–correlation functional (PBE96 versus PW91). Because the LTO structure is quite complicated due to the random distribution at the 16d sites, along with the critical selection of exchange–correlation, multiple variables from the INCAR parameters, selection of pseudopotentials [56], initial host structure (supercell size) will lead to different total energies. Therefore, it almost impossible to consolidate and assess all reported structures for LTO and compare just based on the total energy. Not to mention that all computational details are not entirely disclosed by some researches.

Selection of Pseudopotential Materials Project, a large computational database for accelerated materials discovery, have implemented the projector augmented wave (PAW) pseudopotentials and have been a reference for total energy comparisons [56]. However, even for a given element, say Sodium, the choice of pseudopotential will have a further selection which is provided in the Vienna Ab initio Simulation Package (VASP) library [57, 58, 59, 60]. For most elements, there usually exists a standard, a soft and hard pseudopotential (e.g., Na has Na, Na_sv, and Na_pv). A recommended selection of the pseudopotential is usually based on the highest electron (sv), but the VASP manual and Materials Project have documentation on their selection and some useful remarks [61]. Zhong et al. [54] reported the intercalation potential of LTO to be 1.48 V which is slightly lower than the experimentally verified 1.55 V. The discrepancy has been attributed to the use of pseudopotential (PAW versus ultra-soft) [39] Taking the energies reported by Tsai et al. [45] using various pseudopotential for Li, Ti, and O, the energy can vary as much as 2 eV per formula unit which is significant for phase stability studies.

Selection of exchangecorrelation functional If we consider a simple system such as a free electron gas, then the exchange and correlation can be dealt with analytically. However, for more complex and real systems, exchange and correlation are not known but can be approximated quite accurately [62]. The oldest and most famous of the exchange–correlation functional, Local density approximation (LDA) assumes a simple linear functional of the density. To the surprise of the scientific community, LDA has been a massive success despite its very crude approximations. This is because of cancellation of errors derived from an overestimation of Ex (the exchange energy) while underestimating Ec (the correlation energy). Therefore, LDA satisfies one of the restrictions: the sum rule of the exchange–correlation holes. But not the exchange and correlations if individually considered. LDA also does not meet the one-electron limit but can be corrected with a self-interaction correction (SIC). LDA also treats all systems as homogenous, but real systems are inhomogeneous [63, 64]. Over the years, approximations attempted to satisfy the shortcomings of the LDA so it can be applied to real systems. Most researchers refer to following functionals: the generalized gradient approximation (GGA) potentials proposed by Perdew et al. [65], Wu and Cohen (GGWC) [66], Perdew and Wang (PW91) [66], Perdew (GGA-PRBE), GGA parameterized by Perdew-Burke and Ernzerhof (PBE) [67], and local density approximation (LDA) potential by Ceperley-Alder and Perdew-Zunger (CA-PZ) [68].

Asadikiya et al. [69] compared the choice of functionals based on LDA, GGA-PBE, and PW91 to calculate the phase stability by constructing the ab initio convex hulls of Li2O–TiO2 and Li2TiO3–TiO2 shown in Fig. 5. For the Li2O–TiO2 convex hull, they concluded that at 0 K LTO is a stable phase. To further study the phase stability, the TiO2-rich portion was re-drawn, and Li2TiO3–TiO2 phases were the reference states and a unanimous trend for selection the functional was not found as the LTO phase is not stable (energy above hull) when using the LDA functional. There exists some level of uncertainty arising from the LDA functional where the bond length is underestimated, but overestimated with the GGA. From here a selection of the reference or competing compounds is crucial for the proper analysis of the phase stability (more discussion in the section below). When constructing the LTO supercell, Yi et al. [23] compared the lattice parameters derived from using different exchange electron exchange–correlation functionals and chose GGA-WC because it showed the lowest error when compared with the experimental lattice parameter of LTO and are presented in Table 4.
Fig. 5

Ab initio convex hulls of the a Li2O–TiO2 and b Li2TiO3–TiO2 pseudo-binary systems based on LDA, GGA-PW91, and GGA-PBE functionals.

Taken from Ref. [69]

Table 4

Calculated and experimental lattice parameters of LiTi2O4.

Taken from Ref. [23]

Functional

LDA CA–PZ

GGA-PW91

GGA-PBE

GGA-RPBE

GGA-WC

Expt. [70]

Lattice parameters (Å)

8.259

8.457

8.457

8.528

8.386

8.405

Error (%)

1.74

0.619

0.619

1.46

0.226

Therefore, researchers tend to compare the reliability of their structure by comparing with experimental values obtained from the literature [23]. Ouyang et al. [39] reported a 1.09% error, while Tsai et al. [45] reported a 0.79% error in their lattice parameters and suggested that their structure showed slightly less discrepancy indicating the stable arrangement can be assessed by their relative error, along with the relative lattice shrinkage during phase transformation from the Li4Ti5O12 to the Li7Ti5O12 phase. However, the lattice parameter is independent and not sensitive to the stability of the constructed cell. In conjunction with the lattice parameter, researchers have also presented the electronic structures for assessing the reliability of constructed LTO structures. Comparing the width of the bandgap is a more appropriate analysis because it directly correlates the stable arrangements of the Li and Ti atoms at the 16d site. Table 5 shows how the reported experimentally obtained band gaps and how they compare to theoretical calculations. The experimentally obtained wide bandgap for LTO is generally accepted and ranges from 1.8 to 3.8 eV. The larger initial band gap is an indication of the poor electronic conductivity of LTO. There is a large discrepancy between experimental and ab initio since DFT has been notoriously known to underestimate bandgaps significantly, but has been continually studied for their ability to show trends for electrode materials design. [71] Since the lithiated/overlithiated phases are reported to be metallic conductors, no band gaps have been reported.
Table 5

The reported band gap of the Li4Ti5O12 [45]

 

Band gap (eV)

References

Optical spectra

1.8

[72]

3.1

[73]

3.8

[74, 75]

Theoretical value from ab initio

1.7

[76]

2.0

[39, 50]

2.3

[27, 45]

Thermodynamics and Phase Stability Evaluation

The total energy of a system is not a valid measure of its phase stability. However, it can be used to in conjunction with the energetics of the competing phases which participate during the thermodynamic cycle to perform phase stability evaluation. Building a convex hull and checking whether the energetics of an intended phase is above or below the convex hull concerning the reference states is an analogous approach to identifying reference states and drawing a tie-line in a phase diagram. Stability of the phase is usually evaluated using the molar formation enthalpy or the reaction energy, Er. Yi et al. [23] compared the phase stabilities of the Li4Ti5O12, Li7Ti5O12 and Li8.5Ti5O12 phases by calculating the molar formation enthalpy. The molar reaction enthalpy was derived from the formation energies of the phases participating in the thermodynamic cycle and is described below:
$$2Li_{2} O_{(s)} + 2TiO_{2(s)} \mathop \to \limits^{ } Li_{4} Ti_{5} O_{12(s)} .$$
(3)
Tsai et al. [45] calculated the reaction energy of LTO using competing binary phases given in Eq. 3:
$$E_{r} \left( {Li_{4} Ti_{5} O_{12} } \right) = E_{form} \left[ {Li_{4} Ti_{5} O_{12} } \right] - 2E_{form} \left[ {Li_{2} O} \right] - 5E_{form} \left[ {TiO_{2} } \right].$$
(4)
One of the prerequisites of using the reaction energy is knowing what phases compete against the phase under evaluation during the thermodynamic cycle. Researchers above have reported the use of the binary phases such as Li2O and TiO2 to assess the phase stability of LTO. However, using another competing phase, Li2TiO3, based on experimental evidence [77] will result in different reaction energy as shown in Eq. (4):
$$E_{r} \left( {Li_{4} Ti_{5} O_{12} } \right) = E_{form} \left[ {Li_{4} Ti_{5} O_{12} } \right] - 2E_{form} \left[ {Li_{2} TiO_{3} } \right] - 3E_{form} \left[ {TiO_{2} } \right],$$
(5)
where \(E_{form} \left[ {Li_{4} Ti_{5} O_{12} } \right]\), \(E_{form} \left[ {Li_{2} O} \right]\), \(E_{form} \left[ {TiO_{2} } \right]\), \(E_{form} \left[ {Li_{2} TiO_{3} } \right]\) are the formation energies with respect to pure elements at their most stable structures at 0 K. The reaction energies are indicative if the phase is thermodynamically stable. So in a case given by Eqs. (4) and (5), where the competing compounds are chosen are different, then the Er might be overestimated for the former (− 158.73 meV/atom and − 44.45 meV/atom, respectively). Yet, both reaction energies indicate the LTO is thermodynamically stable.

Phase stability evaluation is very crucial for materials design. We can design a multitude of doping in varying concentrations and different doping sites which can all report enhanced properties. However, we might have a false sense of validation by just checking the total energy and the formation energy, and even when calculating the reaction energy with an incorrect set of competing phases. A robust method to identify the appropriate competing phases for higher-order systems (ternary systems and above) is needed so we can correctly evaluate the phase stability of the material. Phase stability evaluation also provides information about the chemical potential where researchers can use as a guide to design the specific experimental variables needed such as oxygen partial pressure and temperature. With the knowledge of the phase stability, we can predict a material’s phase stability and site energetics (preferred site and relative doping ability).

Activation Energy and Li-Ion Mobility in the LTO Structure

Lithium-ion diffusivity is an intrinsic material property and can be the key to enhancing the rate-capability especially for materials like LTO which have sluggish Li-ion transport (2.5 × 10−5 S cm−1) [78]. It can be estimated by calculating the activation barrier, which is the energy difference at the initial and activated state during the ionic hop [51]. Ab initio calculations using the nudged elastic band (NEB) [79] method can be used to determine the energy along a path of two neighboring Li sites. The minimum energy paths (MEP) for Li ion jumping between sites were calculated using the NEB method. The nudged elastic band utilizes an efficient way of finding the MEP between an initial and final state of transition. Climbing image NEB (c-NEB) [80] applies a small modification to the NEB method; the shape of the MEP is retained, but there is a rigorous convergence to a saddle point. Ionic diffusivity in a solid is governed by thermally activated hopping of atoms between interstitial sites or vacancies. For some cases, there is only a two-dimensional diffusion network through the lattice such as for graphite. However, LTO has a three-dimensional diffusion network because of the system of possible Li sites.

Published atomistic studies using DFT on the LTO activation energies are varying. It is because that some authors are reporting based on the approximations of incorrect stoichiometry such as the ideal spinel LiTi2O4, where the 16d sites are fully occupied by Ti as compared to the defect spinel where it is randomly occupied by Li and Ti atoms. This ideal spinel arrangement leads to only a single diffusion path from the 8a sites. Bhattacharya et al. [81] calculated the activation energies for Li1+xTi2O4. Since they utilized the ideal spinel structure, all 8a and 16c sites are equivalent. Also since only Ti atoms are present in the 16d site, the 16d site does not participate in any diffusion event. All reported diffusion path lengths were also symmetrical, meaning there is no energy difference in the forward and backward ionic hops. The reported activation barriers were from 0.375 to 0.50 eV. Chen et al. [41] considered the correct stoichiometry but only examined a limited number of possible diffusion paths. They reported that slower lithium diffusion in the fully delithiated state which takes advantages of the empty 48f sites (16c-48f-16c diffusion pathway) with energy barriers of 0.7–1.0 eV. Diffusion of Li atoms in the fully lithiated state occurs thru a cooperative hopping mechanism where a Li atom from the 8a site moves to the 16c site and simultaneously a Li from the 16c’ site moves to a nearby empty 8a site resulting in a much lower energy barrier of 0.13–0.35 eV.

Ziebarth et al. [38] reported that diffusion paths in the LTO are nonequivalent due to the mixed occupation of Li and Ti atoms at the 16d sites. For the LTO, they investigated four paths connecting five different lithium atoms as shown in Fig. 6. Paths 1-3 and 3-5 are asymmetric and are about 0.10 eV higher than the energy barrier for the opposite direction (3-1). Path 2-5 is perfectly symmetric and shows an activation barrier of 0.48 eV. Path 8*-5, which corresponds to Li+ exchange from the 16d site towards an empty 8a site, is very asymmetric, and the activation barrier is 0.92 eV. They proposed that lithium vacancy is preferentially trapped at the 16d site (numbered 8*), and can explain the low lithium diffusivity for the LTO host structure. For the Li7Ti5O12 phase, there are eight paths. The paths connecting the 16c positions passing an 8a site shows activation barriers between 0.20 and 0.51 eV.
Fig. 6

a Investigated diffusion paths of lithium vacancies in the spinel and rocksalt phases. b MEPs of all calculated paths in the spinel phase cMEPs of all paths in the rocksalt phase.

Taken from Ref. [38]

In contrast to LTO, there is no vacancy trapping in the 16d site because the moving Li occupies a 48f position at the intermediate state, but is surrounded by both Li and Ti ions. Heenan et al. [82] explored the LTO configuration space using canonical Metropolis Monte Carlo (MC) sampling based on DFT. They reported stabilization of Ti antisite-like defects on 16c sites in the LTO configuration space. The mobility-enhancing Ti16c antisite defects which generated regions in the LTO host structure with localized and correlated diffusion. NEB calculations indicate the MEP barriers in the range of 0.1–0.2 eV. However, embedding the same mechanism within regions not close to a Ti 16c antisite defect resulted in energy barriers above 0.8 eV. Their proposed mechanism also explains percolating channels observed during lithiation of LTO [83] and even addresses the sharp rise in conductivity reported for LTO during initial stages of lithiation [24].

Table 6 shows a compilation of the reported absolute values for the activation energies/barriers only for the LTO structure. Experimentally reported activation barriers are slightly higher than theoretical calculations. There is also some disagreement about the existence and energetic level of metastable transitions states, but there has been an agreeable trend: Activation barrier for the spinel phase (delithiated) is higher than that of the rocksalt phase (lithiated).
Table 6

Reported activation energies for the Li4Ti5O12 and Li7Ti5O12 phases

Pathway

Activation barrier (eV)

Pathway

Activation barrier (eV)

References

Li4Ti5O12

Li7Ti5O12

Ab initio calculations

 8a–8a

0.375

[81]

 8a–16c–8a

0.70

16c–8a–16c

0.35

[41]

 8a–16c–8a

0.30–0.48a

16c–8a–16c

0.2–0.37a

[38]

 16d–8a

0.92a

16d–16c

0.56–0.63a

[38]

 8a–16c

0.29–0.31b

[47]

Experimental (300–410 K)

0.76

All measurements for activation energy are done with lithiated phases (using various intermediate compositions)

0.43

[84]

Experimental (148–473 K)

0.31

0.31

[85]

Experimental (298–673 K)

0.55

0.39–0.45

[86]

Experimental (1173 K)

0.80

[87]

Experimental (450 K)

0.62

0.36–0.51

[88]

aOnly considered one way since the shapes of the paths are asymmetric and not equal for both directions

bThe obtained activation energies from various MD simulations

Elucidating Enhancements in Electrochemical Performance

Doping has been a simple but effective strategy in addressing the main issues regarding the poor rate-capability of LTO such as poor electronic conductivity and sluggish Li ion conductivity. Experimental efforts has been done for almost all ions such Akali earth group (Na+ [89], Mg2+ [90], Ca2+ [91], Sr2+ [92]), Transition metal group (V2+ [93], Cr2+ [94], Mn4+ [95], Co3+ [94], Zr4+ [96], Nb5+ [97], Mo4+ [98]), rare metals (La3+ [99], Ru4+ [100]) and even extremely large anions (F [101], Br [102]). There are also special cases where oxygen vacancies and hydrogen doping have been studied to improve electrochemical performance of LTO. In which all have reported enhanced rate-capability as compared to the undoped LTO. However, there has been no systematic study for verifying the possible doping sites and assessing individual doping ability. Researchers have tried multiple compositions and various doping sites, but it is still very unclear despite all the experimental effort. We cannot still systematically answer why doping improves rate performance for LTO. Which are the best dopant and their actual contribution to the electrochemical performance? As an example, the Na dopant (116 pm) being a larger ion than Li (90 pm) might effectively enlarge the lattice and improve Li transport, but since it just substituted Li+ with the same charge, there is no change in the valence electron in the system. There is no expected enhancement in the electronic conductivity since the conduction mechanism in LTO is based on electron hopping. However, researchers reported conflicting effects on Na doping on the electronic conductivity of LTO [103, 104, 105].

Given the very time-consuming, and very costly nature of performing a trial-and-error way of comparing enhancements brought about by different dopants at different sites with varying doping concentrations, ab initio can give us information on the enhanced material property before synthesis. Insights about the enhancements on electrochemical performance are usually obtained thru the electronic structure of LTO. For the initial host compound, the band gap is mainly contributed by the O-2p and Ti-3d bands and reveals that LTO is an insulator. There also exists a strong bonding between Ti and O. It is because that the O atom takes sp3 hybridization and the hybrid orbits overlap effectively with the 3d band of the three nearest Ti neighboring atoms. This covalent bonding also relates to the thermodynamic stability of LTO and its lithiated phases [23]. Therefore, one of the more recognized approaches in addressing the insulating character for LTO is doping the system with aliovalent elements (extra valence electrons). If free electrons are brought into the system either by lithiation or induced by doping, then these electrons occupy the empty Ti-3d, and the Fermi level is shifted up to the tail of the conduction band, now indicating a metallic character.

Also, the annealing process under an oxidizing and reducing atmosphere for oxides like LTO can accompany the significant formation of defects that affect the electrochemical properties. Thermodynamic information such as free energy changes and defect formation energies are difficult to measure experimentally. Therefore, it is essential to consider the formation and the effects of the point defects to allow researchers precise control during synthesis. Cho et al. [106] used ab initio to study the effects of charge-compensated point defects for Mg-doped LTO and its electronic properties. LTO has two metallic elements, Li and Ti; the Mg dopant can prefer only one site or occupy both sites. Their results emphasized the importance of site energetics as it is possible to substitute Mg, a known Li site dopant, into a Ti site with the necessary experimental conditions. The results of the proper site energetics are shown in Fig. 7, where doping at the Li site would enhance the conductivity for LTO and doping at the Ti site would not increase the charge carrier concentration.
Fig. 7

Schematic diagram of Mg site energetics and their corresponding density of states.

Taken form Ref. [106]

Liu et al. [27] were the first to incorporate ab initio calculations in predicting electronic structural changes induced by cation doping (Mg, Cr, Ni or Fe) in LTO. As shown in Fig. 8, the DOSs of the undoped and composite models Li26MTi26O64 were calculated and analyzed. New bands appeared for transitional metal dopants (Cr, Ni, and Fe). However, the Fe and Ni 3d bands are localized, consequently making it difficult to excite electrons towards the Ti 3d conduction bands. Only the Cr 3d bands are close to the Ti 3d bands, which makes the 3d electron hopping more feasible. More Cr atoms will lead to more charge carriers and result in a sufficient increase in electronic conductivity. The Mg dopant also gave insight about improved electronic conductivity because the position of the Fermi level shifted towards the tail of the conduction band, which is from the increased valence electron compared to the Li+ (vs. Mg2+) atom.
Fig. 8

Total density of states X-doped LTO (X=Cr, Fe, Ni, and Mg).

Taken from Ref. [27]

Yang et al. [107] performed a systematic ab initio study based on DFT of the Li8Ti10O23X about using extra large anions (X = F, Cl, Br, N, P, S). They also reported favorable doping by comparing the total energies. Figure 9 shows the calculated charge density where they can elucidate the delocalization of electrons for F, Cl and Br. Finally, by comparing the accompanied lattice expansion by doping F, Cl, and Br, it was reported that Br dopant caused a significant distortion in the neighboring atoms due to its ionic radii difference with O ions.
Fig. 9

a Schematic atomistic models of LTO doped b Br, c Cl, d F. e Schematic atomistic models of LTO doped—f N, g, P, h S.

Taken from Ref. [107]

Zhang et al. [50] used DFT to elucidate electronic and structural changes induced by Gd doping in LTO. They also considered the furthest Li–Li pair distance in the 16d sites when constructing the initial host structure. They compared the energy of Gd substitution in any of the Li and Ti sites and reported that Gd substituted into the Li 16d site lead to the most stable structure. The effect of Gd doping is highlighted by investigating the DFT band structure. All projected DOSs is shifted left concerning the normalized energy, and the tail of the conduction band is now overlapping with the Fermi level: suggesting that Gd-doped LTO is an electronic conductor, where Gd acts as a donor. This also suggests that only little energy is necessary for an electron to move to an energy level higher than the Fermi level.

Zhang et al. [108] used DFT calculations to determine the energetically optimized models for LTO, individually W and Br doped and codoped LTO. They built the LTO structure using a 1 × 1 × 2 supercell using two formula units. They reported to the effect of W and Br doping utilizing the DFT band structure calculation as shown in Fig. 10, in which it showed that the typical 2.3 eV band gap for pristine LTO was improved and a shifting of the Fermi level to the tail of the conduction band resulting in partial occupancy of electrons. NEEDS MORE
Fig. 10

a Lattice models for LTO and W and Br co-doped LTO and their corresponding density of states.

Taken from Ref. [108]

Song et al. [109] reported Na substitution in the rock-salt LTO leading to a 0.22% volume expansion. The activation energies for the ionic hop between the nearest neighbor of the substituted Na ion (Li1 and Li2) and second nearest neighbor (Li3 and Li4) are shown in Fig. 11. However, the activation barrier for Li1–Li2 diffusion path was 201 meV higher than the rock-salt LTO because the Na ion can act as the point defect blocking the Li diffusion pathway. The activation barriers for between Li3 and Li4 are also higher, which may be attributed to the of the electrostatic repulsion with the Larger Na ion.
Fig. 11

a Chemical potential diagram of LTO. b Chemical potential diagram of Zn-doped LTO.

Taken from Ref. [110]

The approach of defining a “stability window,” based on a set of proper thermodynamic constraints are imperative into reliably knowing the atomic chemical potential because they help us design our controlled synthesis conditions which can enhance the LTO’s electrochemical performance. Duan et al. [110] reported the ab initio DFT study on Zinc impurities, which also included a systematic analysis of native defects. The role of Zn impurities can be observed with its direct effect on the accessible chemical potentials as shown in Fig. 12. The energies reported and used for calculation are with significant discrepancy and may render an incorrect stability window. Also, the complete chemical potential diagram for LTO should have been in the three-dimension considering the individual chemical potentials of Li, Ti, and O. Other Li and Ti-based phases were chosen as thermodynamic conditions, but no justification was given for their selection. Experimental verification of the existence of these phases during the solid-state formation LTO is also not reported [77]. A known competing phase such Li2TiO3 might result in a more conservative stability window rending the analysis of other invariant points meaningless. As for the doping analysis, ZnO was used as a thermodynamic equilibrium condition, A more robust analysis of the stable phases based on the binary, ternary and quarternary phase diagram since doped-LTO will have four components (Li–Ti–O-X). Phase stability evaluation is susceptible to the energetics of the phase under evaluation, and what phases are competing in the thermodynamic cycle. They pointed out that substitutional Zn located at the Li 8a site is preferable to form under O-poor conditions, which has a potential effect on the Li ion diffusion. Substitutional Zn located at the Ti 16d site was pointed out to behave like a double acceptor but during O-rich conditions.
Fig. 12

a Charge density difference plots for LTO with oxygen vacancy. b The corresponding total density of states.

Taken from Ref. [25]

Recently, Nasara et al. [25] reported highly oxygen-deficient lithium titanate oxide with conformal amorphous carbon coating obtained by a one-step thermal reduction process. A model for reduced LTO with one oxygen vacancy was constructed following the supercell made by Tsai et al. [45]. Ab initio density of states (DOSs) shows that the Fermi level shifted to the bottom of the conduction bands and the number of electrons is two following the charge compensation from one oxygen vacancy. Figure 13 shows the different charge distribution, and the negative charges are locally shared by neighboring Ti ions around the oxygen vacancy.
Fig. 13

a The supercell of the H-doped LTO. b The ab initio density of states for the pristine LTO. c The ab initio density of states for the H-doped LTO.

Taken from Ref. [111]

Qiu et al. [111] clarified the origin of the mid-gap states of their blue hydrogenated lithium titanate by DFT calculations based on a 3 × 1 × 1 supercell. They reported that during hydrogenation H dopants at the interstitial sites can introduce mid-gap states below the Fermi level without shifting the conduction band as shown in Fig. 14. Moreover, they also pointed out that oxygen vacancies can lead to the same mid-gap states. Hydrogen in the LTO lattice could significantly reduce the negative charge density, removing the strong electrostatic hindrance between positive Li ions and negative oxygen and consequently improving Li transport.
Fig. 14

a Schematic of the Li diffusion pathway for Na-doped LTO in a projected abc plane. b Energy barriers concerning the lithium position.

Taken from Ref. [109]

Challenges and Outlook

This review gave a snapshot of the recently complementary use of ab initio based on DFT to adequately explain fundamental mechanisms that help design high-rate LTO anode materials. The challenges attributed with poor electronic conductivity and moderate ionic conductivity should be addressed to highlight the potential application of the highly stable and abundantly cheap LTO. One of the main concerns about LTO is its high operating voltage, which leads to a much lower cell voltage when assembled to a full working cell: lower energy density. We can incorporate ab initio and find ways to reduce the working potential of LTO. Any reduction in the 1.55 V plateau will lead to a direct increase in the energy density of the system. It is also anticipated that coating, doping and nanocrystallization will be the solution for LTO. Despite performing vast experiments on doping, we still do not have a full understanding of its role in enhancing the performing of LTO, the same goes to the inclusion of oxygen vacancies and larger atomic species that either improve the conductivity or enlarge the lattice. A thorough analysis and reconstruction of the LTO surface is another challenging area to explore due to different possible terminations and stoichiometry in both the Li4Ti5O12 and Li7Ti5O12 surfaces [112]. However, a better understanding of the LTO surface will lead to critical insights about interfacial kinetics and SEI formation which can address an inherent problem such the gassing problem in LTO [113, 114] during the charge and discharge process.

There have been multiple macroscopic and microscopic models which attempted to describe the Li ion electrochemistry in LTO accurately. Models are usually based on the Newman pseudo-2D (P2D) model which uses the porous electrode theory to treat the homogenous electrode [115, 116]. The concentrated solution theory is used in conjunction to describe transport in the solution phase. Kashkooli et al. [117] matched their P2D with experiments using LTO nanoparticles of varying particle sizes (50–250 nm). They focused on the nanosizing effect to enhance the electrochemical performance for LTO. However, synthesis difficulty and processing becomes a major concern, and a more tailored application of LTO should first be identified which gives the proper materials design. Christensen et al. [117] focused on an optimizing the achievable specific energy for a full-cell of LTO and LiMn2O4. Optimization strategies involve varying the positive electrode thickness and porosity, while maintaining constant values for the negative electrode porosity, and all other parameters, in order to generate the maximum specific energy. They added an adjustable parameter which was the negative electrode porosity and attributed LTO’s excellent cyclability to the absence of a passivating film. However, at this point, researchers have thought that Li ion diffusion was the limiting factor and have focused on its description. Knowledge of thermodynamics of the phase separation was also not as mature as compared to systems like LiFePO4 [118, 119]. Therefore, recent work by Vasileiadis et al. [120] revisited all the modeling work and have applied a phase-field model for LTO based on nonequilibrium electrochemical thermodynamics. There was a great debate to which factors are limiting the rate-capability of LTO: intrinsic low conductivity, moderate Li diffusivity and poor interfacial kinetics. By direct comparison of active particle fraction and multiple factors (current rates, electrode thickness, and electronic conductivity), they have reported that particle agglomeration, electrode tortuosity, and porosity are local bottlenecks for high-performance LTO. It was suggested that spherical particles (with high tortuosity) and well-dispersed particles (no agglomeration) could improve discharge rates by a factor of 4 (also reported for graphite particles [121]). It can be argued that most of the LTO researches which have been implementing carbon coating on LTO (in situ and ex situ) have a more significant effect on the particle dispersion rather than the claimed enhancement in electronic conductivity.

The most suited application for LTO is not yet realized but with the advent of solid-state electrolytes, higher voltage cathodes and new designs such as bipolar batteries (12 V-class bipolar batteries) [122] which undermine the LTO flaws such as low operating voltage and capacity and shifts the spotlight to its very stable cycling and high safety due to the internal short-circuit suppression [123].

Notes

Funding

This work was financially supported by the Ministry of Science and Technology (MOST) under the projects 105-2221-E-006-189-MY3 and 107-2923-E-006-005-MY2, and also the Hierarchical Green-Energy Materials (Hi-GEM) Research Center, from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) and MOST (107-3017-F-006-003) in Taiwan.

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Copyright information

© Korean Multi-Scale Mechanics (KMSM) 2019

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringNational Cheng Kung UniversityTainanTaiwan
  2. 2.Hierarchical Green-Energy Materials (Hi-GEM) Research CenterNational Cheng Kung UniversityTainanTaiwan
  3. 3.Center for Micro/Nano Science and TechnologyNational Cheng Kung UniversityTainanTaiwan

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