The role of atomic-level understanding in optimizing lithium titanate oxide based anodes for lithium-ion batteries

Abstract

Lithium titanate oxide (LTO) has gained significant attention recently as a promising candidate for anode materials in lithium-ion batteries because of its stable operating potential and unique zero-strain behavior. Despite these advantages, its use is limited because of poor electronic conductivity and sluggish lithium-ion diffusion. This review highlights how the atomic-level understanding of various strategies, such as structural architecture engineering, doping, and defect engineering, is gained through advanced computational approaches. Computational studies on lithium vacancies and defects reveal how dopants like Nb⁵⁺ and Al³⁺ influence the charge transport and introduce charge compensation. Furthermore, density functional theory (DFT) based studies illustrate that the diffusion barrier of lithium ions at engineered sites is significantly lower than that of the bulk structure. The impact of these three modification strategies on the LTO structure is examined along with experimental validation of the computational results. Finally, this review highlights future directions of the role of computational tools in accelerating the performance and rational design of high-performance LTO anodes.

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1. Introduction

The global imperative of transitioning to a suitable energy economy and reducing carbon emissions has solidified the position of lithium-ion batteries, making them essential for everything from electric cars to phones and large-scale power grids.^1,2 As the lithium-ion battery market continues its rapid expansion, the demand for batteries that last longer, can store more energy, and are safer is increasing.^3,4 The anode is a key component in battery performance as it directly impacts the key metrics such as rate capability, capacity, and operational safety.^5,6 For several decades, graphite has been the governing anode material due to its low cost, reasonable specific capacity (∼372 mAh g⁻¹), and stable intercalation chemistry.^7–9 However, several limitations of graphite anodes limit their use in next-generation high-energy lithium-ion batteries.¹⁰ Graphite has a low operating voltage (<0.2 vs. Li/Li⁺), which is below the typical electrochemical stability window for carbonate-based electrolytes, resulting in the formation of a dynamic and fragile solid electrolyte interphase (SEI) that contributes to capacity decay due to its consumption of active lithium.^11–13 More critically, the dendrite formation at low temperatures and high charge rates is caused by the non-uniform deposition of metallic lithium on the anode surface. These dendrites can penetrate the separator and can lead to thermal runaway due to an internal short circuit. The major motivation behind an alternative anode material is the safety concern faced by the circuit. High energy density is also one of the main and rising demands that is fueling further research. Lithium metal and silicon are the widely used anode materials, but lithium metal suffers from safety issues and silicon faces a volume expansion of about 300%; all such kinds of issues emphasize the need for an anode material that overcomes these issues and has extraordinary performance.^14–16

Lithium titanate oxide (LTO) has gained considerable attention due to its zero-strain behavior, in this regard. It undergoes a structural two-phase transition from the cubic spinel phase to a rock-salt phase during the lithiation process.¹⁷ During this transition, the stoichiometry changes from Li₄Ti₅O₁₂ to Li₇Ti₅O₁₂, accompanied by a minor volume change (less than 1%) that enables an exceptionally long life cycle (often surpassing 10 000 cycles) and remarkable structural stability.^18–20 These features make LTO-based batteries more durable and inherently safer than their graphite counterparts. Fig. 1 illustrates the conversion of spinel Li₄Ti₅O₁₂ to its rock salt form, Li₇Ti₅O₁₂, through the lithiation process.

Fig. 1 (a) Spinel-type Li₄Ti₅O₁₂. (b) Structural changes. (c) Li₇Ti₅O₁₂. Reprinted with permission from open access.²¹

However, the broad implementation of LTO is hindered by two main intrinsic limitations. Firstly, pristine LTO exhibits relatively low theoretical capacity (∼175 mAh g⁻¹), restricting the overall energy density of the battery cell.^22,23 Secondly, it exhibits insulating behavior with a wide bandgap and low Li-ion diffusivity, resulting in poor ionic and electrical conductivity.²⁴ This low conductivity hinders the charging speed and rate capability, reducing its suitability for high-power applications such as electric vehicles. Understanding of a material at the atomic level is very important for studying its limitations and possible solutions, which is not possible through experimental studies alone. Density functional theory (DFT) based calculations offer effective ways to understand such materials and behaviors.²⁵

The main aim of this review is to provide a better understanding of the limitations of LTO as an anode and possible solutions to these limitations through various strategies, such as structural architecture engineering, doping and defect engineering, through first-principles and DFT simulations and studies.^26,27 This will provide a deeper understanding of the behavior and electronic properties of the material under different strategic conditions. The second strategy is strategic doping. It explains how the deliberate introduction of foreign atoms, both anions and cations, can be considered as an advanced form of defect engineering.²⁸ Through the substitution of titanium or lithium into the spinel framework, dopants are shown to effectively modulate the electronic bandgap, modify its working potential, and alter the lithium-ion diffusion pathway to reduce the migration barrier significantly.²⁹ Fig. 2 presents some of the drawbacks of the LTO anode and their possible solutions through some key strategies such as doping, defect engineering, and structural architecture engineering.

Fig. 2 Visual representation of issues faced by the LTO anode and the expected solutions.

This fine-tuning at the atomic level presents a promising strategy for optimizing the electrochemical performance of LTO by directly addressing its intrinsic conductivity limitations.³⁰ The third strategy analyzed in this review is structural architecture engineering. Unlike the previous two methods, it focuses on the physical modification of LTO. It investigates the profound impact of nano-structuring (nanosheets and nanoparticles) along with surface chemistry and interfacial engineering on charge transport behavior and transfer kinetics.³¹ It highlights how increasing the electrochemically active surface area and reducing diffusion lengths can markedly improve rate capability, providing a crucial complement to atomic-level enhancements introduced through such structural modifications.^32,33 By consolidating the mechanistic insights from these comprehensive methods and investigations, a high-level perspective emerges that bridges experimental and theoretical findings. This integrated understanding offers an atomic-scale design roadmap to engineer advanced high-performance next-generation LTO anode materials, providing strategic guidance to accelerate future development and research in this field.

2. Computational framework

The majority of first-principles investigations on lithium-ion battery materials, such as LTO, are based on DFT.³⁰ DFT represents a powerful quantum mechanical approach that enables the study of the electronic structure of a system without the need to solve complex many-body Schrödinger equations.³⁴ Its foundation lies in the Hohenberg–Kohn theorems, which predict that the ground-state electron density of a system uniquely determines its properties.³⁵ This allows the many-body problem to be simplified into a more manageable set of single-body equations.^36,37 The solution of these equations provides the electron density of the system, which helps yield the total energy and other critical properties of the system. In practical applications, the accuracy of DFT depends on approximations for the exchange–correlation functional, which approximates the quantum mechanical interaction among the electrons. The most commonly employed approximation are the generalized gradient approximation (GGA) and local density approximation (LDA), along with the Perdew–Burke–Ernzerhof (PBE) functional being widely adopted within the GGA family.³⁸ These functionals are very popular in describing many material systems, but often face challenges in modeling the systems with strongly localized electrons, such as in transition metal oxides like LTO.^39,40

Modeling of LTO faces distinct challenges due to the presence of titanium atoms with partially filled d-orbitals, which leads to electron correlation, a phenomenon of strong electron–electron repulsion. The standard GGA functional often fails to accurately capture this localization, leading to a significant underestimation of the bandgap and a misrepresentation of the electronic structure.⁴¹ To correct this deficiency, a DFT+U approach is widely employed as a corrective method.⁴² This semi-empirical method adds an on-site Hubbard U parameter into the Hamiltonian, which effectively penalizes the double occupancy of localized d-orbitals and corrects the self-interaction error inherent in conventional DFT.⁴³

The bandgap of LTO was predicted to be 1.5 eV using the standard GGA parameter. This severe underestimation was corrected by using the Hubbard U parameter of about 4.5 eV for the 3d orbitals of Ti, through which the values of E_g got aligned with the experimental value of 3.6 eV. For a specific kind of limitation, various kinds of doping are a promising strategy to overcome this by promoting the Ti³⁺ or Ti⁴⁺ mixed values. On the other hand, studies have also proved that the best stability and mitigating gassing are best achieved through surface coating or atomic layer deposition of Al₂O₃ or ZrO₂. For LTO, the appropriate selection of the U parameter for titanium d-states is paramount for obtaining accurate electronic and structural properties.⁴⁴ The computational modeling for LTO simulations requires meticulous attention to ensure reliable and meaningful results. To study defects and dopants, a supercell is constructed as an expanded version of the unit cell, and its size must be large enough to reduce artificial interactions among the defect periodic images, usually containing 56 atoms or more.⁴⁵ The critical factor in evaluating the rate capability of LTO is the identification of the energy barrier, which involves identifying the energy barriers of lithium ions, precisely done using the NEB method. The NEB method is the most accurate tool for this purpose, as it determines the minimum energy path and saddle point from which the migration energy barrier can be governed, providing valuable insight into ionic conductivity.^46,47 Beyond migration studies, DFT enables a range of calculations for essential properties, including the electronic density of states (DOS), dopant and defect formation energies, and the average working potential of the anode is obtained by comparing the total energies of lithiated and delithiated phases.⁴⁸ Table 1 summarizes the DFT functionals used to study different-sized supercells of LTO, along with the key properties investigated in these studies.

Table 1 Common DFT settings and functionals used in LTO studies

No.	DFT functional	Hubbard U for Ti (eV)	K-point sampling	Supercell size (atoms)	Key property investigated	Ref.
1	PBE	—	5 × 5 × 5	14	Lithium diffusion pathway	52
2	PBE+U	2.7	2 × 2 × 2	56	Intrinsic defects and conductivity	53
3	PBE sol+U	2.8	2 × 2 × 2	168	Anion doping	54
4	PBE sol+U	2.5	3 × 3 × 3	112	Cation doping	55
5	PBE+U	2.6	4 × 4 × 4	56	Surface effects on Li	56
6	PBE+U	2.9	3 × 3 × 3	224	Nano-structure properties	55
7	GGA+U	3.0	2 × 2 × 2	112	Co-doping strategies	56

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In the case of LTO, atomic-level insights primarily from MD and DFT simulations, guided the material optimization methods, replacing the trial-and-error methods. Initial DFT calculations accurately identify the rate-limiting step for the diffusion of lithium ions as the one with a high energy barrier of approximately 0.6 eV for the ionic movement.^49,50 The computational screening has prescribed the use of low concentration dopants such as Al³⁺ and Mg²⁺, which were calculated to reduce the local strain, further verified by the experimental studies that optimized synthesis routes, achieving 10⁻³ cm² s⁻¹ to 10⁻² cm² s⁻¹, confirming the structural and model design.⁵¹ The DFT+U is very efficient in diagnosing the limitations regarding the conductivity of LTO by confirming the presence of Ti³⁺ polarons and a process to track the charge transport. This atomic-level diagnosis regarding the LTO/electrolyte interface mandated a shift in experimental focus towards its betterment through techniques such as defect creation and doping, which are able to stabilize and enhance the material.¹⁶

3. Methodological advantages and limitations

DFT excels at providing exceptional atomic-level insights and predictive capability enabling rapid material screening and supporting exceptional synthesis of LTO. It has played a dominant role in quantifying the reduction in the Li-ion migration barrier due to doping and elucidating surface reactivity mechanisms.⁵⁷ However, the accuracy of DFT depends crucially on the chosen Hubbard U parameter and exchange correlation functional, resulting in significant variability in reported values.⁵⁸ As a ground-state and static method, it struggles with capturing complex, time-dependent phenomena like extensive diffusion or SEI formation, which demand more computationally intensive techniques such as ab initio molecular dynamics (AIMD), underscoring the importance and need for rigorous methodological validations and choices through experimental data.⁵⁹

4. Intrinsic defects in Li₄Ti₅O₁₂ anodes

The presence of native point defects profoundly influences the fundamental properties of any crystalline material, including diffusivity and ionic conductivity.⁶⁰ These defects, emerging from thermodynamic equilibrium during synthesis or battery operation, play a crucial role in critically determining the electrochemical performance of the LIB electrode material.⁶¹ In the case of pristine LTO, understanding the nature and concentration of these intrinsic defects is essential for elucidating its inherent limitations and developing strategies to improve performance.⁶²

4.1. Defect formation

In the spinel structure of LTO, a variety of intrinsic point defects can exist, each influencing the material properties differently. Among the most commonly investigated are lithium vacancies (V_li), oxygen vacancies (V_O), and antisite defects, especially lithium-titanate antisite (Li_Ti) and titanium-lithium antisite (Ti_Li).^63,64 Although interstitial defects like oxygen (O_i) and lithium (Li_i) are theoretically feasible, their higher formation energies under standard conditions generally render them relatively rare.⁶⁵

DFT calculations are indispensable for evaluating the formation energies of these defects in varying chemical potential environments and across varying Fermi levels.⁶⁶ Lower formation energy corresponds to a higher equilibrium concentration of a defect. Table 2 presents a summary of different kinds of defects in the LTO anode and their formation energies, along with their effect on band gaps. The defects in which the lithium sublattice is involved, such as lithium vacancies (V_Li) and lithium-titanium antisites, have the lowest values of formation energies, 0.1 to 0.5 and 0.2 to 0.7, respectively. These lower values of formation energies represent the stability and equilibrium of the defective structures of LTO anodes. This indicates that Li⁺ disorder is thermodynamically favorable as the intrinsic disorder for the spinel LTO anode structure, as it makes the movement of Li⁺ ions within the structure much easier.⁶⁷ On the other hand, the formation energy value of V_O is in the range of 1.5 to 3.0 eV, which is a higher value that is considered considerable only in high-temperature synthesis or in a reducing atmosphere for creating highly conductive LTO anode materials.⁶⁸ Moreover, the intermediate value of formation energy for titanium-lithium antisites (T_Li) which is 0.8–1.5 eV, confirms the local structural stability and potentially hinders a long lithium diffusion pathway.⁶⁹ Defect concentrations are highly sensitive to synthesis conditions such as oxygen partial pressure and temperature, which DFT accurately simulates through chemical potentials.⁷⁰ Fig. 3(a′) presents various types of defects created in the structure of Li₄Ti₅O₁₂ and the effects on structural atoms due to these defects and local structural distortions that influence the Li ion pathway.

Table 2 Summary of key defects in LTO

No.	Defect type	Formation energy (eV)	Effect on the bandgap	Electronic impact	Ionic impact	Ref.
1	Oxygen vacancy (VO)	1.5–3.0	Creates mid-gap due to Ti^3+ states	Enhances electronic conductivity	Influences the local Li environment	76
2	Lithium vacancy (VLi)	0.1–0.5	Introduces acceptor states near the valence band	Negligible electronic activity	Facilitates diffusion	77
3	Titanium-lithium antisite (TiLi)	0.8–1.5	Creates mid-gap due to Ti^3+ states	Negligible electronic activity	Can block the Li diffusion pathway	78
4	Lithium-titanate antisite (LiTi)	0.2–0.7	Introduces deeper acceptor states	Enhances electronic conductivity	Hinders Li diffusion	79

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Fig. 3 (a′), (a) V_Li, (b) T_Li, (c) V_Ti, (d) Li_Ti, (e) V_O, (f) Li_i, and (g) Ti_i. Relaxation directions of atoms are represented by blue arrows, and vacant spaces from where the atoms are removed are shown by dashed circles. (b′) The formation energies for the defect created LTO structure under equilibrium conditions. Reprinted with permission from American Chemical Society.⁶⁶

To understand the defect characteristics and intrinsic stability of LTO, the formation energies of various defects created in the material are presented in Fig. 3(b′). In this plot, the formation energies of all six defects from A to F are plotted against the equilibrium conditions, which represent the limits of chemical potential illustrated by the existence of specific competing phases. The phase boundaries of (A) Li₂TiO₃, (B) TiO₂, (C) Li₂O, (D) Li₂Ti₃O₇, (E) Ti₂O₃, and (F) LiTiO₂ represents the stability limit of LTO for various chemical potential conditions. The analysis indicates that under lithium-rich conditions, such as under condition C for Li₂O, the formation energies for lithium interstitials (Li_i) and lithium vacancies (V_Li) are relatively low, indicating the preference for lithium-related defects. On the other hand, the titanium-related defects (V_Ti) are less likely to form across the equilibrium condition because they are highly energetic. So, the antisite defects are considered as the most favorable among A to C, according to the existing understanding of the LTO structure, and suggesting that the minor mixing of Li or Ti is the dominant defect mechanism. These equilibrium conditions are also considered crucial because they define the chemical potentials μ_Li, μ_Ti, and μ_O of the constituent elements, and they are related to the phase boundaries to play their role in preventing the precipitation of secondary phases. μ_Li is reduced in the case of V_Li, which results in their increased energies and helps in determining the most favorable defects for the LTO structure.

4.2. Electronic properties

Intrinsic defects significantly modify the electronic structure of LTO, a critical factor in influencing the electronic conductivity. In its pristine stoichiometric form, LTO is considered an insulator with a wide band gap (∼3.5 eV), primarily due to fully occupied t_2g and empty e_g orbitals of Ti⁴⁺. However, the introduction of defects can create localized states in this bandgap, effectively reducing the activation energy for electronic transport.^71,72 For instance, V_O often triggers the formation of Ti³⁺ ions in its vicinity as a charge compensation mechanism. These Ti³⁺ states introduce electron polarons which are capable of hopping between adjacent titanium sites, thereby enhancing the material's electronic conductivity.⁷³ Similarly, Li_Ti can also generate Ti³⁺ species, contributing to electronic conduction and other electronic properties.⁶⁵ The effect of defect creation in LTO is discussed in Table 2; the V_O and Li_Ti enhance conductivity as Ti³⁺ localized states are created with these defects within the structure. Such states are referred to as mid-gap states because they are positioned just below the conduction band. On the other hand, the highly prevalent Li_Ti and V_Li only introduce deep and shallow acceptor states near the valence band, so the primary function remains electronic instead of being structural and ionic. DFT calculations, specifically through analysis of the electronic DOS and band structure, have clearly shown that these defect-induced mid-gap states play a vital role in altering LTO from an insulator with a wide bandgap to a semiconductor.⁷⁴ The defect engineering is also performed experimentally, where the creation of oxygen vacancies is proved to be purposeful through EPR spectra, which enable the quantification of paramagnetic Ti³⁺ defects that reduce the lithium migration activation energy, a result obtained using GITT, which indicates a Li-ion diffusion coefficient increase compared to the stoichiometric benchmark.^28,75

4.3. Electrochemical correlation

The DFT analysis of the impact of various types of defects in the structure of LTO anodes is discussed in Table 2. But these DFT predicted values also have their electrochemical correlation. Most critical types of defects are those which introduce n-type electronegativity such as V_O and Ti_L; both of these defects are charge compensated by the localized reduction of titanium, which causes bandgap narrowing and acts as quantitative underpinning for enhanced conductivity which directly correlates with experimentally observed values of conductivity enhancement of about ∼10⁻¹³ to ∼10⁻⁹ S cm⁻¹ reported for LTO having defects in its structure, overcoming the limitation of rate performance.⁸⁰ The conductivity is enhanced up to 10⁻⁷ S cm⁻¹ and it is further verified by impedance spectroscopy, which verifies the role of predicted polaron states. On the other hand, most of the formation energies lie in the region of 2 to 4 eV, which causes discrepancies among the experimentally predicted values using techniques like TGA and XPS analyses.^81,82 Hence, theoretical and experimental results complement each other.⁶⁶

5. Strategic doping for better performance

By substituting host atoms with foreign elements, the lattice structure can be modified, the lithium-ion diffusion pathways optimized, and the electronic band structure adjusted.⁸³ First-principles calculations have played a vital role in predicting the most promising dopants and revealing the underlying mechanisms, providing the rational basis for experimental work. The primary objectives of doping are to enhance the intrinsic ionic and electronic conductivity, improve specific capacity, and potentially increase the rate capability of LTO.^28,84

5.1. Cation doping

The substitution of host cations, Li⁺ and Ti⁴⁺, with foreign metal ions is the most extensively investigated doping approach. The effectiveness of a dopant depends on factors such as its ionic radius and its preferred substitution site within the lattice.⁸⁴ Aliovalent dopants have a different ionic state from the host structure they replace, so they are considered particularly effective as they can successfully alter the electronic properties by introducing charge carriers (electrons or holes).³¹ For instance, pentavalent dopants like tantalum (Ta⁵⁺) and niobium (Nb⁵⁺) are widely used for enhancing electronic conductivity. Fig. 4(a) and (b) present the atomic structure of c-LTO and the doping of niobium into the LTO structure, respectively. Fig. 4(c) shows that the charge rate and reversible capability of c-LTO-Nb are higher than those of c-LTO. It is 135 mAh g⁻¹ at 1C and 127 mAh g⁻¹ at 20C.⁵²

Fig. 4 (a) Atomic structure of c-LTO. (b) Atomic structure of c-LTO-Nb. (c) Cyclic characteristics of c-LTO and c-LTO-Nb. Reprinted with permission from open access.⁹¹

The conductivity of doped LTO also increases, as c-LTO exhibits a conductivity of 6.615 × 10⁻¹⁰ S cm⁻¹, and it improves to 1.127 × 10⁻⁹ after doping of niobium into⁸⁵ the structure. According to DFT studies, these kinds of dopants reside at Ti⁴⁺ sites. The substitution is a charge compensation process for another Ti⁴⁺ to Ti³⁺, which releases free electrons.⁸⁶ These released free electrons are delocalized and reside near the conduction band minimum, significantly narrowing the bandgap and enhancing the electronic conductivity.⁸⁷ The trivalent dopants, such as aluminium (Al³⁺), also reside as substituents at Ti⁴⁺ sites. The substitution makes a main contribution to reinforcing the structural stability of the LTO lattice. This enhanced stability improves long-term durability by reducing volume changes during cycling.⁸⁸ Isovalent dopants such as tin (Sn⁴⁺) and zirconium (Zr⁴⁺), having the same charge as the Ti⁴⁺ ion that they replace, do not directly affect the charge balance, so they do not increase the electronic conductivity. Instead, larger ionic radii than Ti⁴⁺ expand the lattice, which has been predicted computationally to reduce the activation energy for Li-ion hopping. Ionic conductivity is enhanced through this strain-induced modification without compromising LTO's insulating properties.^89,90

5.2. Anion doping

Anion doping, specifically the replacement of oxygen ions with other elements, is not common but an emerging strategy.⁹² The potential of fluorine (F) to enhance the electrochemical properties of LTO has been explored through DFT studies. Replacement of F⁻ with O⁻² causes a positive charge imbalance that is compensated by the formation of lithium interstitials or oxygen vacancies.^90,92,93 This can modify both the local diffusion environment and the electronic structure of LTO. Strong binding interactions that may also affect Li-ion transport result from the high electronegativity of fluorine. The computational literature on anion doping still suggests that it needs further research.⁹⁴

5.3. Co-doping

To explore further enhancements in properties of LTO, recent computational studies have begun to explore co-doping strategies, in which two different dopants are introduced simultaneously.⁹⁵ It aims to combine the positive effects of one dopant, such as electronic conductivity, with the benefits of others. DFT is used to understand the complex effect of the dopants on various properties of the material, such as lithium-ion diffusion and other electronic properties. Table 3 shows different kinds of doping in LTO and their respective impacts on material performance.

Table 3 Summary of doping strategies of Li₄Ti₅O₁₂

No.	Dopant	Suitable site	ΔEa,Li (%)	ΔEg (%)	Key predicted effects	Stability	Ref.
1	Ta^5+ (aliovalent)	16d (Ti^4+)	−15 to −25	−0.5 to −1	Reduces bandgap, enhances electronic conductivity	Highly stabilizing, strong suppression of Ti/Li disorder	86,98
2	Nb^5+ (aliovalent)	16d (Ti^4+)	−10 to −20	−0.3 to −8	Reduces bandgap, enhances electronic conductivity, and small lattice expansion	Strongly stabilizing, enhances the thermal stability of the structure	33,99
3	Al^3+	16d (Ti^4+)	+5 to −10	∼0.0	Does not affect electronic conductivity	Moderate stability, ensures zero-strain mechanism	100,101
4	Zr^4+ (isovalent)	16d (Ti^4+)	0.0 to −5	∼0.0	Induces lattice strain and minimal change to electronic properties	Moderate stability	102,103
5	F^− (aliovalent)	32e (Ti^4+)	−5 to −15	−0.1 to −0.3	May alter the diffusion path	Enhanced integrity, maintains the spinel structure	104,105
6	Al/Nb	16d (Ti^4+)	−20 to −30	−0.8 to −1.2	Balances structural stability and electronic conductivity	Synergistic stabilization, long term structural integrity	28,106

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5.4. Quantitative assessment of doping strategies

Table 3 summarizes various types of doping performed on LTO to improve its transport kinetics and other properties, such as electronic bandgap (E_g) and lithium ion migration barrier (E_aLi). The quantitative data compiled in this table reveal that cation dopants like Nb⁵⁺ and Ta⁵⁺ act like dual-function enhancers. Replacing Nb⁵⁺ or Ta⁵⁺ with Ti⁴⁺ introduces a localized positive charge, which is then compensated by either the reduction of Ti³⁺ to Ti⁴⁺ or by a higher concentration of mobile lithium vacancies. In the case of introduction of aliovalent and isovalent dopants into LTO, the electrostatic perturbation weakens the bond between O⁻² and Li⁺, leading to almost 10–25% decrease in migration barrier of such materials. In the same way, the introduction of Ti³⁺ species causes new mid-gap donor states to result in band-gap shrinkage of up to 1.0 eV for Ta⁵⁺, leading to the resultant band-gap of about 3.5 eV. This causes the conduction mechanism to shift towards more efficient small polaron hopping. When observed experimentally, the UV-V bandgap measured is almost 2.94 eV, proving that both kinds of studies have related results. The same is the case of the diffusion barrier, when measured for Nb-doped LTO, it is 0.4 eV, which is supported by GITT measurements by showing an increase in the Li-ion diffusion coefficient from 10⁻¹² to 10⁻¹⁰ cm² s⁻¹.^83,86 On the other hand, lower valent dopants show a very negligible change in band gap and act as structural stabilizers, and also offer a migration barrier relief by minor lattice expansion. This quantitative analysis shows that a decrease in migration barrier and lower E_g are effective for better rate capability of doped LTO. The doping with aliovalent ions is often confirmed by EPR and XPS studies, providing evidence of the formation of Ti³⁺ species, which are crucial for enhancing the electronic conductivity and proving the effectiveness of the doping strategy.⁹⁶ Electrochemical impedance spectroscopy (EIS) further shows increased lithium ion diffusion coefficients as compared to the pristine structure.⁹⁷

6. Structural architecture and nano-engineering

Surface architecture and nano-engineering are some of the widely used techniques for performance enhancement of the LTO anode material. In other techniques, various external materials are added, or some of the material atoms are removed, but in this technique, only by modifying the surface of the material structure or converting the bulk structure into any other form, such as nano-sheets or thin-films, the material's performance can be enhanced to a greater extent. Various computational studies have already been performed on LTO with a structural architecture applied to it. DFT investigations have meticulously compared various LTO surface facets, such as the more reactive (110) and low-energy (111) planes, to elucidate their roles in lithium-ion diffusion and insertion.^107,108

Fig. 5 shows a significant effect of surface architecture on the performance of LTO. It illustrates calculated voltage profiles of LTO nanoparticles having (1 0 0), (1 1 0), and (1 1 1) crystal facets, respectively. The different curves for each surface demonstrate that voltage and capacity during lithium insertion are directly influenced by the atomic-level surface geometry of the material. Red and black curves show the presence and absence of neighbouring atoms at the interface, respectively.¹¹⁰ This shows that the surrounding environment of the material is important in determining the diffusion barrier and activation energy.¹¹¹ One of the key findings is that, diffusion barrier of the bulk material is less than the surface, whereas the activation energy at the surface is noted to be lower than that of the bulk. The increased surface-to-volume ratio within the nano-materials causes faster diffusion and hence results in better rate performance. Advanced computational simulations play a vital role in a better understanding of these strategic processes.

Fig. 5 Voltage profiles of Li₄Ti₅O₁₂–Li₇Ti₅O₁₂ systems, corresponding to systems whose facets all have (a) (1 0 0), (b) (1 1 0), and (c) (1 1 1) surfaces, respectively. Reprinted with permission from American Chemical Society.¹⁰⁹

Doping, which has also been discussed in the previous sections, is also considered to be a kind of structural modification, but if compared with nano-engineering, both have their own benefits and limitations.¹¹² Nano-engineering is good at improving rate performance, whereas doping is suited for enhancing the electronic conductivity of LTO, but these effects are interconnected. Doping enhances the charge transfer. When aliovalent dopants are introduced into the LTO structure, they create charge-compensating Ti³⁺ species for this.¹¹³ As doping enhances the charge transfer, nano-engineering is crucial for improving the rate capability. For the betterment of rate capability, nano-engineering the path length of Li-ion solid-state diffusion also improves the electrolyte–electrolyte contact area.¹¹⁴ Reducing the Li-ion diffusion path is the best way for fast charge–discharge cycles at high C-rates. So we can say that if we combine doping with nano-engineering in the case of LTO, the best results in terms of performance and properties can be attained.

6.1. Interfaces in composites and all-solid-state materials

The combination of LTO with other conductive components can further enhance its performance as an anode.¹¹⁵ DFT modeling allows for the investigation of interfacial charge transfer, which can significantly alter the electronic properties of LTO near the contact region.^116,117 These models demonstrate that a strong electronic coupling, resulting from a work function mismatch between LTO and graphene, can reduce the overall interfacial resistance, thereby enabling faster electron transport.¹¹⁸ The structural stability of the interface is another critical factor, as maintaining robust interfacial bonding is crucial for maintaining structural integrity during repeated lithiation and delithiation cycles. In addition to carbon composites, computational work has begun to explore LTO's interfaces with solid-state electrolytes, a critical area for advancing all-solid-state battery technology.^119–121 DFT can resolve the electronic interactions and atomic configurations at solid-state interfaces, allowing predictions of interfacial resistance, the formation of a stable solid electrolyte interface, and chemical stability. Such insights are crucial for guiding the design of solid-state anodes and composites with long-term stability and superior performance.¹²² Structural engineering and modification aim to reduce Li⁺ diffusion path lengths. It is quantitatively confirmed through GITT and EIS studies that compare the lithium diffusion coefficient along various architectures.¹²³ Moreover, XPS analysis of near-surface electronic states verifies the surface engineering by confirming the higher concentration of Ti³⁺ near the surface coating.¹²⁴

6.2. Electrochemical correlation

The structural modifications basically affect the surface area, such as in the case of internal structural defects, the band gap narrows about 0.8 to 1.5 eV specifying the improvement in the electronic structure of the material.¹²⁵ Other strategies, like composite formation of LTO and carbon, for example, are used for reducing the diffusion distance and improving the conductivity pathway.¹²⁶ The surface coatings, most importantly, of Al₂O₃ or amorphous carbon, stabilize the SEI. On an experimental scale, these modifications are confirmed by about 50 to 70% reduction at the interface, referring to high-rate capability and cycling stability.¹²⁷ When the maximum number of lithium ions is adsorbed at the LTO structure, the insertion voltage shows a peak at 0.19 eV, which is confirmed by the experimental predictions, where the peak is observed at 0.2 eV.¹²⁸ In this way, both kinds of analysis complement each other. The structural modification causes a strain of about 5% in the LTO structure; it can cause a decrease in the insertion voltage plateau in DFT studies, but it does not validate the experimental results because in those results strain percentage can be higher due to factors like grain boundaries and surface effects.¹²⁹

7. Analysis, interplay, and validation

The insight derived from atomistic calculations, while powerful, must be interpreted carefully in the context of experimental reality. A truly impactful review goes beyond summarizing theoretical results; it provides a critical assessment of its accuracy and limitations, thereby shaping future directions. This section synthesizes the findings from previous discussions on doping, defects, and nano-structuring, emphasizing their interconnections and examining how the crucial validation of computational predictions aligns with experimental observations.^130,131

A primary strength of computational modeling is its ability to uncover the explanations of experimentally observed phenomena. For example, the DFT predictions of the formation of Ti³⁺ polarons in LTO, whether originating from aliovalent doping or intrinsic defects within elements such as Ta⁵⁺ or Nb⁵⁺, have been strongly validated by a suite of characterization techniques.^132–134 EPR and XPS are fluently used to directly quantify and detect the presence of Ti³⁺ species and provide compelling confirmation of theoretical models for improved electronic conductivity. This correlation provides a strong connection between the macroscopic electronic properties and the charge transfer mechanism.^135,136 The lithium-ion hopping activation energies, which are calculated via Nudged Elastic Band (NEB) calculations, are related to the experimental diffusion coefficient, which is measured by several techniques such as Electrochemical Impedance Spectroscopy (EIS).^137,138 In the DFT studies of LTO, performed at high rates, the zero-strain mechanism is predicted, which is further validated by operando XRD lattice parameter measurements (e.g. a = 8.356 ± 0.001 Å), which confirms the structural stability.¹³⁹ The pure DFT is not able to predict the accurate activation energy of the bulk Li ion diffusion at the low temperature regime, resulting in approximately 0.7 eV, when PFG-NMR and EIS results measure about 0.3 to 0.4 eV.¹⁴⁰ This inconsistency is attributed to the inability of DFT to simulate the necessary long-range defect-mediated pathways at the particle interface. This analysis, based on quantitative data, provides a clear boundary for various recent first-principles methods.¹⁴¹

However, discrepancies between theory and experiment are not rare and can create valuable new research questions. For example, standard DFT, being a zero-temperature and static approach, cannot capture the temperature-dependent dynamics and kinetic barriers of a complex synthetic process.^142,143 A dopant predicted to be thermodynamically favorable at a specific site might fail to incorporate effectively in an experiment due to non-equilibrium synthesis routes or kinetic barriers.³³ Moreover, the choice of exchange–correlation functional and, critically, the Hubbard U parameter for localized d-electrons of Ti can lead to variations in the predicted defect formation energies and band gaps.^144,145

More advanced methods, such as hybrid functionals, can improve accuracy but are computationally expensive and not always suitable for supercell modeling on a large scale. Furthermore, simulations are typically far from idealized, defect-free supercells.^146,147 In contrast, real materials contain grain boundaries, impurities and complex interfaces, which can introduce effects that are difficult for simplified computational models.¹⁴⁸ A notable example is the mismatch between predicted and experimental voltage profiles of LTO. While DFT reliably captures the flat voltage plateau, the exact voltage value is highly sensitive to the choice of U.^149,150 Moreover, the subtle variation observed at the start and end of the plateau is very difficult to reproduce without explicitly considering dynamic structural distortions and defect concentration, factors beyond the scope of DFT calculations.¹⁵¹ These mismatches are not failures but rather opportunities for an iterative and rigorous feedback loop between experimental synthesis and computational modeling, ultimately accelerating material discoveries.¹⁵²

8. Mutual interplay of design strategies

Achieving a deeper understanding of LTO requires moving beyond the study of isolated phenomena and considering how doping, defects and structural architecture interact.⁸⁶ Table 4 compares all the modification techniques discussed for improving LTO as an anode for lithium-ion batteries. This synergistic interplay is a critical frontier in computational research, since the properties of the final material are a result of the combined influence of these factors.^153,154 Fig. 5 shows a visual summary of the modification techniques for LTO, such as doping, defect creation, and structural engineering, and their atomic-level impacts on the structure to enhance its performance activities.

Table 4 Comparison of modification techniques for the LTO anode

No.	Strategy	Mechanism addressed	Key advantage	Limitation	Future aim	Ref.
1	Specific doping (Mg, Al)	Li-ion diffusion barrier	Lower intrinsic energy	Limited conductivity	Use in co-doping	75
2	Co-doping	Kinetic Li and electronic barrier	Improvement in bulk properties	Complicated phase control synthesis	Use in best comprehensive tuning	181
3	Defect engineering	Electronic conductivity (Ti^3+ defects)	Improved bulk properties	Risk of irreversible capacity loss	Use in electronic tuning	182,183
4	Structural modification (nano-structuring)	Li path length	High carbon-rate improvement at massive loads	Severe SEI growth	Requires surface stabilization	82
5	Surface engineering (N/C coating)	Electronic conductivity	Reduces interfacial impedance	Inactive mass addition to the electrode	Enhancing the conductivity	184

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Intrinsic defects, for example, can profoundly affect the stability of doping.¹⁵⁵ The presence of an oxygen vacancy is typically associated with a high formation energy of approximately 1.5 to 3 eV, which can significantly alter the local charge environment, making the nearby site favorable for specific dopant substitution.^156–158 A pentavalent dopant like Nb⁵⁺ usually generates a Ti³⁺ polaron for charge compensation, might interact with already existing defect clusters in a manner that either suppresses or enhances its electronic effect.^159,160 Computational studies have shown that the dopant incorporation energy landscape is not uniform but is modulated by the local defect environment, highlighting that doping and defects are independent variables.^161–163

A similar principle governs the interplay between nano-structuring and doping. Both DFT and classical MD calculations show that dopant segregation often occurs when dopants preferentially move to the surface to lower the surface energy and relieve the lattice strain.^164,165 This suggests that a dopant primarily affects the surface diffusion and reactivity.¹⁶⁶ This highlights a crucial link between the efficacy of a doping strategy and the scale of the material (nanoparticles vs. bulk) and the efficacy of the doping process.¹⁶⁷ For instance, a dopant with a large ionic radius, such as Zr⁴⁺, may be unsuitable for bulk LTO because of lattice strain but can generate unique surface structures that enhance lithium-ion transfer when segregated to the surface (Fig. 6).^168,169

Fig. 6 Summary of engineering strategies for LTO and their atomic-level impacts on the structural properties.

Finally, in nano-materials, surface defects play an essential role due to the significant surface-area-to-volume ratio. The faster Li-ion diffusion pathways on a surface, along with a migration barrier of less than 0.2 eV, are notably lower than the typical range of 0.2–0.5 eV.^170,171 These low-barrier pathways are further enhanced or blocked by surface defects.¹⁷² For example, surface lithium vacancies could act as the best hopping sites, whereas antisite defects may act as bottlenecks or traps. Furthermore, the formation energy and thermodynamic stability of defects in a nanoparticle can vary from those in the bulk due to surface energy effects.¹⁷³ The intricate relationship between the defect landscape and nano-structuring creates complex and highly non-linear effects on overall performance, necessitating a holistic and integrated computational approach.^174,175 Upon the analytical comparison of all the discussed techniques, different computational methods are applied in each case. MD and KMC (Kinetic Monte Carlo) simulations are used for analyzing the Li-ion diffusion within the structure at the atomic level.¹⁷⁶

The choice of the Hubbard U parameter is very important as it governs the localized electrons within the d-orbital, which mainly impacts the quantitative results. The electronic properties of transition metal oxide-based electrodes in LIBs are very sensitive to the U parameter. For example, in the case of LTO with U at 0 eV, the value of the bandgap is ∼2 eV, but when the value is set at 7 eV, it changes the bandgap value to 3.5 eV, in excellent agreement with the experimental values.¹⁷⁷ In the same way, changing the U_Co from 3.3 eV to 5.5 eV in the case of LiCoO₂ shifts the bandgap up to 1 eV.¹⁷⁸ In the case of LiFePO₄, the standard value of U of 0 eV underestimates the delithiation voltage of the material; the U value of 4.3 eV predicts the voltage of 3.45 eV, which is very near to the experimentally observed value of 3.46 eV.¹⁷⁹ Hence, the U parameter is not just an adjustable parameter, but it has its major role in chemical accuracy against experimental results.¹⁸⁰

9. Future perspectives and emerging research directions

The preceding sections have highlighted the profound impact of computational modeling on advancing and understanding LTO at the atomic scale. Yet, significant challenges persist, demanding a shift towards more integrated, dynamic, and advanced computational approaches. The future of LTO research lies in moving beyond static, high-throughput approaches that can bridge the gap between real-world and idealized models, single-variable investigations towards multi-scale and real-world electrochemical performance, enabling the rational design of future LTO anodes.^185–187

A key limitation of conventional DFT is its emphasis on static pathways and ground-state properties.¹⁸⁸ While excellent for migration barriers and formation energies, it falls short in describing the dynamic processes that are critical for governing battery performance.¹⁸⁹ The next frontier for computational research in LTO is to portray complex phenomena such as full charge–discharge kinetics and the formation of a solid–electrolyte interphase (SEI) under realistic operation conditions.¹⁹⁰ The SEI is a notoriously complex, reactive layer whose growth and nucleation are governed by dynamic reaction on the surface of LTO, processes beyond the scope of conventional DFT.^191,192 Similarly, understanding capacity fading and stability under repeated cycling requires a computational framework capable of simulating atomic motions over finite temperatures and an extended time scale.¹⁹³

These techniques are useful in overcoming the challenges faced by modified LTO; still, some key areas require further improvements. The major bottleneck lies in having control over the evolution of SEIs; although LTO operates at a typical reduction potential of electrolyte, low temperature, and accelerated cycling can induce heterogeneous SEI formation. This causes impedance growth and capacity fading as well.¹⁹⁴ The future DFT studies are supposed to move beyond static surface models to incorporate the role of localized defects and electrolyte decomposition kinetics, providing a strong and direct link to experimental cell aging. Secondly, the effectiveness of the bulk is compromised by the dopant segregation. Atomic-resolution STEM-EEL experimental analysis consistently reveals that p-block dopants and transition metals preferentially migrate to the particle surface or towards grain boundaries, forming secondary insulating and resistive phases, effectively counteracting the improvements in electronic conductivity.¹⁹⁵ A very focused experimental work is required to match the results of the DFT studies performed on all the techniques of enhancing the performance of LTO. Moreover, significant discrepancies remain between experimental and DFT-based profiles for the LTO/Li₇Ti₅O₁₂ phase transition. The standard GGA+U functional normally overmeasures the characteristic ∼1.55 V plateau by 0.1–0.2 V, due to insufficient treatment of weak interaction within the spinel lattice and redox processes.¹⁹⁶ The development of more advanced functionals such as Dynamic Mean Field Theory (DMFT) and Hybrid Density Functionals (HSE06) is important to achieve the sub-0.05 accuracy needed to make new materials with modified designs and fill the gap between theoretical and experimental works.¹⁹⁷

To overcome these simulations, two emerging computational directions are set to reshape the field. The first is Machine Learning (ML) potentials, poised to enable high-throughput screening of vast chemical design spaces.¹⁹⁸ This strategy eliminates the need for the time-consuming process of individual DFT calculations for each defect configuration or dopant. For instance, ML-based calculations are approximately 10⁶ times faster than traditional DFT, enabling the rapid screening of potential dopants to identify suitable candidates for further experimental investigation.^185,199,200 Likewise, AIMD offers a powerful framework to study the dynamic evolution of LTO systems. In contrast to static NEB calculations, which provide a single minimum-energy migration pathway, AIMD can capture complex, Li-ion hopping mechanisms and describe ion transport under thermal agitation. It is also an ideal tool for investigating the initial stages of SEI development at the electrode–electrolyte interface, offering critical insights into structural changes and chemical reactions that lead to the formation of the protective layer.^152,201,202

DFT, as the base of AIMD, exhibits the highest accuracy as a quantum mechanical method. It is, though limited by the computational cost (O(N³) or worse, here N is the number of atoms), which tries to reduce the scalability to short simulations and small systems.²⁰³ The machine learning potentials offer near DFT accuracy and bridge this gap at a reduced computational cost (O(N)). This results in better scalability and a larger timescale.²⁰⁴ The AIMD simulations therefore, provide finite-temperature information with accuracy and suffer from the same computational scaling, so they are considered as the least scalable and most expensive among the three of the larger systems.²⁰⁵ Recent studies have shown that the cubic scaling cost of DFT restricts the simulations to a smaller cell size and time scale, which is considered insufficient for ion transport at a long range. On the other hand, the ML trained on the principles of DFT data can attain the ab initio accuracy within the cost of MD at approximately 10⁻³ of the speed of DFT.²⁰⁶ This is a high-scale efficiency as it allows the AIMD-level accuracy over the extended timescale of nano-seconds and large-scale simulations of approximately 10³ atoms.²⁰⁷ It enables the investigation of various crucial phenomena like the temperature-dependent lithium diffusion pathway, which governs the cyclability and stability of the electrode material.²⁰⁸

The true value of machine learning approaches such as the Gaussian Approximation Potential (GAP) resides in their exceptional capability to bridge the computational gap. Specifically, in the case of LTO anode materials for lithium-ion batteries, this has been demonstrated by ML interatomic potentials to reproduce the DFT-level energy barriers for the migration of Li-ions in LiFePO₄.²⁰⁹ Mainly, these potentials allow the larger simulations to happen in the nanoscale time range for the supercells containing thousands of atoms, such as bulk LTO containing nano-voids.²¹⁰ The diffusion studies and the traditional AIMD simulations, which are difficult to attain a specific magnitude, can easily be reached. Such computational gain is very important in accurately capturing the long-range defect-mediated diffusion and grain boundary effects in any kind of materials, including lithium-ion battery materials.²¹¹

The ultimate goal of these advanced methodologies is to establish a stronger feedback loop between computational modelers and experimentalists, which is crucial for evolving the development of new LTO anode strategies. Traditionally, these two fields have progressed in silos. In the future, this relationship will become a reciprocal exchange.^212,213 Experimentalists will provide the real-world data about various failure modes of the material related to strategies such as defect concentration, structural design, or doping. The computational community can use these data to address issues such as why a specific dopant showed a different rate performance than expected.^214,215 In turn, dynamic simulations and high-throughput screening can be used to propose valid predictions for complex co-doping strategies and new defect-engineered structures. This iterative cycle is crucial for accelerating the rational design of next-generation anode materials and moving beyond the serendipitous discovery that has long dominated battery research.^216–218

10. Summary

This comprehensive review has demonstrated that computational modeling has been instrumental in advancing the basic understanding of Li₄Ti₅O₁₂ and designing strategies for its enhanced performance. First-principles calculations have demonstrated the atomic-scale origin of LTO's electrochemical behavior, revealing how targeted doping and defect engineering address its electronic conductivity-related issues, while the principles have provided pathways to overcome its slow ionic kinetics. The key finding from this body of work is the non-linear interplay between these strategies. A comprehensive understanding of the influence of these strategies upon each other is essential for the design of a high-performance LTO anode.

Despite significant progress, major challenges such as long-term capacity fading, unlocking higher theoretical capacities, and understanding SEI evolution still require a more integrated and dynamic approach. Overcoming these obstacles requires moving beyond the static limitations of conventional methods. This review highlights that the ultimate objective of these strategies is to enhance the performance of LTO anodes. By introducing intrinsic defects, we can enhance charge transport within the bulk material, enabling faster charging and higher power density. Theoretical insights into antisite defects and lithium vacancies have paved the way for controlled synthesis methods to enhance lithium-ion mobility. Charge carriers are created due to doping in the structure; these charge carriers play a vital role in enhancing the electronic conductivity. Designing a material with better diffusion rates and structural stability results in higher C-rates and enhanced material performance. One of the major points in understanding strategic techniques, such as co-doping, for enhanced electrochemical performance is to understand the screening methods that overcome the kinetic limitations and play a vital role in stabilizing the reactive surfaces. Designing complex composites of conductive materials with LTO also enhances material performance to a greater extent. Along with all these techniques for performance enhancement, understanding of factors, such as interactions between the solid electrolyte and LTO, is important for predicting interfacial resistance and enhancing material stability. Most importantly, the ultimate goal is to pick the most accurate strategy for incorporation in the material, according to the needs of the time, and study its effects accurately through appropriate DFT simulations.

Conflicts of interest

There are no conflicts to declare.

Data availability

No primary research results, software or code have been included and no new data were generated or analysed as part of this review.

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