Atomistic simulation study of Li₅GaO₄ for lithium-ion batteries Open Access

The search for new electrode materials for next-generation lithium-ion batteries is a highly active area of research, especially focusing on applications such as hybrid electric vehicles.^1–3 Several factors are crucial when considering electrode materials for lithium-ion batteries, including cost-effectiveness, non-toxicity, and lithium-ion conductivity. Innovations in electrode materials continue to drive progress toward safer, more cost-effective, and higher-performing lithium-ion batteries, addressing the growing demand for energy storage solutions in various industries, including automotive, electronics, and renewable energy.^4–6 

Li₅GaO₄ has garnered attention as a potential electrolyte candidate in Li-ion batteries.^7,8 The ionic conductivity of Li₅GaO₄ has been noted to exhibit a notable dependency on moisture content. Moreover, Li₅GaO₄ has been explored for its ionic conductivity in moist air environments, presenting the prospect of their use as humidity sensors in high-temperature applications.⁹ This material exhibited an exponential increase in ionic conductivity at 500 °C with rising moisture content, reaching conductivity levels 2–3 orders of magnitude higher. Li₅GaO₄ demonstrated good reproducibility in conductivity changes during wet–dry cycles, indicating stability and suitability as humidity sensors. While they operate at temperatures above 450 °C and cover a wide relative humidity range, requiring oxygen partial pressure for stability, their higher conductivities compared to other sensor materials make them promising candidates.^10,11 A pioneering study by Esaka and Greenblatt⁷ laid the foundation for understanding Li-ion conductivity in Li₅GaO₄. This work identified that substitution with divalent cations in the Li₅GaO₄ structure leads to heightened Li⁺ conduction. This observation highlights the role of dopants in influencing the electronic and ionic conductivity of Li₅GaO₄, serving as a crucial aspect for further investigation.

Recent developments in Ga-doped LLZO (La₃Li₇O₁₂Zr₂) systems suggest that Li₅GaO₄ could potentially exist as a significant product at grain boundaries.¹⁰ This introduces a novel perspective, emphasizing the importance of understanding the role of Li₅GaO₄ within a broader material context. The potential presence of Li₅GaO₄ at grain boundaries in Ga-doped LLZO raises questions about its impact on Li-ion migration and the overall electrochemical performance of the material.

Due to the limited availability of experimental data in the existing literature, there is a crucial need for a more comprehensive understanding of Li₅GaO₄ to enhance its efficacy in Li-ion batteries. Exploring the intrinsic defect energetics, ion migration, and dopant substitution at the atomistic level through computational studies^12–18 becomes imperative. Remarkably, there is a notable absence of research addressing the defect and diffusion characteristics of Li₅GaO₄. This study aims to investigate the defect structures, Li-ion diffusion pathways, and the impact of isovalent and aliovalent dopants on Li₅GaO₄ through classical potential simulations.¹⁹ The chosen simulation method, widely employed in examining various oxide materials, including those used in batteries, provides a well-established foundation for this investigation.

All calculations were performed using the GULP (General Utility Lattice Program) code.²⁰ Interactions were modeled by combining long-range (Coulombic) and short-range (Pauli repulsion and van der Waals attraction) forces, employing Buckingham potentials for short-range repulsion (see Table I). Structural relaxations utilize the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm,²¹ ensuring forces on all atoms remain below 0.001 eV/Å in relaxed configurations.

The Mott–Littleton method²⁵ was applied for modeling point defects and migrating ions. Lithium-ion migration was assessed at seven interstitial points with equal intervals between neighboring lithium sites. Defect energies along the diffusion path are determined, utilizing the midpoint between adjacent Li vacancy sites as the defect calculation center to minimize systematic errors. Ions were treated as spherical objects with a full charge at the diluted limit. The crystal is partitioned into region I and region II around the floor. Substantial forces from faults in region I necessitate specific ion encapsulation. In region II, where stresses are milder, quasi-continuum techniques are employed to stabilize ions. The core–shell technique is used to model ion polarization, building upon earlier research that presented the formula for determining migratory paths and detailing activation energies of migration.

Performing Bader charge analysis²⁶ and calculating the density of states (DOS) using density functional theory (DFT) simulations provides a comprehensive understanding of the electronic structure and properties of the material. Using the Vienna Ab initio Simulation Package (VASP) for DFT simulations is an excellent choice for calculating Bader charges and DOS as it is well-regarded for its accuracy and efficiency in handling a variety of material systems.²⁷ In all calculations, PAW (projected augmented wave) pseudopotentials,²⁸ a 500 eV plane wave cutoff, and a 4 × 4 × 4 Monkhorst–Pack k-point mesh²⁹ were used. The exchange–correlation term using the generalized gradient approximation (GGA) as formulated by Perdew, Burke, and Ernzerhof (PBE) was executed.³⁰ A high accuracy in the relaxed structures was achieved using the conjugate gradient algorithm³¹ with a force tolerance of less than 0.001 eV/Å.

Li₅GaO₄ exhibits a polar orthorhombic structure within the pbca space group.³² The crystal structure consists of 24 atoms (8 Li, 4 Ga, and 12 O), with lattice parameters in the x, y, and z directions specified as a = 9.03 Å, b = 9.09 Å, and c = 9.11 Å. The angles α, β, and γ are all set at 90°. Each Ga and Li-ion are intricately coordinated with four O ions, forming GaO₄ and LiO₄ tetrahedral units. The crystal structure presents itself as a layered arrangement comprising edge-sharing LiO₄ and GaO₄ tetrahedra [see Fig. 1(a)]. While the tetrahedral coordination gives a clear picture of the structural symmetry, it does not fully capture the complexities of the electronic states. The electronic states are influenced by the distribution of electrons around each atom and the overall electronic interactions within the crystal. The Bader charge analysis of Li₅GaO₄, showing charges of Li +1.00, Ga +3.00, and O −2.00, indicates that the ions possess charges close to their nominal oxidation states with ionic characteristics. This significant ionic character is indicative of strong electrostatic interactions between the constituent ions, influencing the overall properties and behavior of materials. Understanding these charge distributions is crucial for predicting and tailoring the performance of material in various applications. Li₅GaO₄ exhibits a wide bandgap (∼4 eV), indicating that it is likely to have low electrical conductivity at room temperature [see Fig. 1(b)]. The density of electronic states is distributed symmetrically about the x-axis, leading to a non-magnetic nature. The wide bandgap coupled with a non-magnetic nature agrees with a previous DFT simulation.³³ Our calculations reproduced the experimental lattice parameters by validating the potentials used in this study (see Table II).

The Schottky defect exhibits an energy of 2.94 eV, while the Li₂O Schottky defect shows an energy of 2.19 eV. These values suggest that creating Li vacancies in Li₅GaO₄ through the Schottky process may require higher energy compared to the reference Li₂O. The ionic conductivity of Li₅GaO₄ in the presence of water vapor, along with its structural stability indicated by the higher energy for Li₂O release, makes it suitable for high-temperature humidity sensors.⁹ The energy required for the release of Li₂O from Li₅GaO₄ is 2.19 eV, which is significantly higher than the Frenkel defect energy for Li⁺ ions (1.00 eV). This higher energy indicates that the detachment of Li₂O units from the lattice is less favorable compared to the creation of Li⁺ Frenkel defects. The higher energy requirement for Li₂O release ensures the structural integrity of Li₅GaO₄, preventing the loss of lithium oxide units and maintaining its stability under operational conditions. The Ga₂O₃ Schottky defect, with an energy of 6.01 eV, indicates a higher energy barrier for gallium vacancies. Considering anti-site defects, the cluster defect involving Li and Ga has a lower energy of 0.87 eV compared to the isolated defect (3.05 eV). This suggests that the formation of anti-site cluster defects is more favorable and likely to occur than anti-site isolations in Li₅GaO₄. These calculated defect energies, along with the low Frenkel energies for Li, indicate that Li₅GaO₄ could be a promising material for lithium-ion batteries.

Li-ion diffusion studies, as outlined by extensive research,³⁵ play a pivotal role in propelling battery technology forward. This involvement stems from a comprehensive understanding of the intricate mechanisms governing the movement of lithium ions within electrodes. Such knowledge is indispensable for enhancing various aspects of battery performance, including lifespan and energy density. In parallel, the comprehension of Li-ion diffusion serves as a key element in the optimization of electrode materials.³⁶ This understanding ensures that these materials can adeptly accommodate and facilitate the rapid and efficient transport of lithium ions. The optimization process significantly contributes to the development of battery materials characterized by high performance and durability. Notably, it proves highly applicable in the in-depth exploration of Li-ion diffusion within battery materials. Furthermore, the capability of the current modeling technique extends to the simulation of Li-ion movement within crystal structures.³⁷ This facet provides valuable insights into diffusion pathways, activation energies, and other critical parameters. The versatility of software renders it invaluable for studying a diverse array of materials employed in battery electrodes. Researchers leveraging GULP can anticipate not only a simulation of Li-ion movement but also the prediction of material properties pertinent to Li-ion diffusion³⁸ Through these computations across multiple planes, a comprehensive analysis emerges. The combined outcomes reveal the minimum activation energy barrier necessary for the molecule as it traverses various planes along fixed combinations of the a, b, and c axes at a given distance.

Six different local Li hops were identified for vacancy-mediated Li-ion migration (see Table III). A reported activation energy of 0.055 eV for the migration pathway of a local Li–Li hop (A) signifies that this specific transition requires an energy input of 0.055 eV per Li-ion to occur. The lower activation energy of 0.065 eV suggests that hop B is also favorable in terms of energy requirements for the migration pathway of lithium ions within the material (see Fig. 3). Activation energy increases with increasing hop distance. The activation energy increases with increasing hop distance, implying that longer migration pathways require more energy for the ion to transition between sites within this material. Energy profile diagrams exhibiting the activation energies for the local Li hops are shown in Fig. 4.

We found long-range diffusion pathways connecting lithium local hops within the material, especially the zigzag pattern observed in the pathway D → C → A → D with Li-ion movement occurring along the c axis, as depicted in Fig. 3. This long-range Li-ion diffusion has an overall activation energy of 0.42 eV. Connecting to other hops resulted in higher overall activation energies for long-range Li-ion diffusion. Thus, we exclude the discussion on the other long-range migration pathways.

The stability of oxygen atoms within the spinel structure of materials, such as Li₅GaO₄, plays a crucial role in maintaining the structural integrity and electrochemical performance of cathode materials in lithium-ion batteries.³⁹ The higher Frenkel energy for oxygen atoms implies that creating an oxygen vacancy is energetically unfavorable. This stability prevents the breakdown of the structure during lithium-ion movement, ensuring that the material retains its integrity over repeated cycles. The energy required for the release of Li₂O is higher than for the removal of individual lithium ions. This further suggests that Li⁺ ions can migrate without causing significant structural degradation, as the oxygen framework remains intact.

The introduction of dopants, or impurities, into a material can significantly alter its properties, leading to tailored functionalities for specific applications. Dopants can affect the electrical conductivity of a material by introducing additional charge carriers (electrons or holes) or altering the band structure, modify the optical properties of a material, such as its absorption and emission spectra, influence the mechanical behavior of a material by affecting its strength, elasticity, and hardness, alter the thermal conductivity and thermal expansion coefficient of a material, can impact the chemical stability of a material, influencing its reactivity with other substances or environments, induce magnetic ordering in materials that are otherwise non-magnetic, and alter the catalytic activity of a material, making it more effective in promoting chemical reactions.

In this study, we considered a variety of dopants at the Li and Ga sites. Necessary charge compensating defects were created for the doping of aliovalent dopants.

The reported solution energies shed light on the energetic characteristics of the process. Interestingly, in all cases, solution energies were endoergic, indicating an energy-absorbing nature except for the case of sodium, where the solution energy is negative (−0.92 eV) (see Fig. 5). This observation shows the high feasibility of employing Na as a doping element in place of Li, and notably, the process does not necessitate stringent thermal conditions. The determination of the lowest solution enthalpy further enhances the understanding of the energetics involved. Considering that Li⁺ possesses an ionic radius of 0.76 Å, the favorability of Na can be attributed, in part, to its comparable ionic radius of 1.02 Å, aligning more closely with that of Li⁺. In contrast, solution energies were found to be positive for both K and Rb, rendering them less favorable due to their higher values. This evaluation provides valuable insights into the intricacies of monovalent doping and its implications for the substitution of Li with alternative elements.

The most favorable dopant is Al³⁺ due in part to its ionic radius matching that of Ga³⁺. Trivalent dopants like Sc³⁺ and La³⁺ have larger ionic radii compared to Al³⁺, which leads to a significant increase in the solution energy required for their incorporation into the crystal lattice of Li₅GaO₄. The solution energies for these dopants fall in the range between 6.50 and 10.50 eV, indicating a substantial energy demand (see Fig. 6).

The endoergic solution energy of Si is 0.28 eV, surpassing the higher solution energies of Ge and Sn at the Ga site (see Fig. 7). This supports the feasibility of aliovalent doping at the Ga site with Si, enhancing lithium vacancies and thereby increasing Li ion conductivity. This indicates the potential of exploring Si doping in Li₅GaO₄ as a promising battery material.

In conclusion, a comprehensive investigation into the Li₅GaO₄ structure, guided by meticulous computational calculations, has shed light on the intricate dynamics of intrinsic defects, Li-ion migration, and solution of dopants. Noteworthy among these revelations is the energy-efficient nature of the Li Frenkel defect process and the superior feasibility of the Li–Ga anti-site cluster, boasting an impressive binding energy of −2.18 eV. The calculations conducted have unveiled Li-ion migration pathways with a remarkably low activation energy of 0.42 eV, indicating a heightened Li-ion conductivity compared to prevalent materials, thereby warranting further in-depth examination. The introduction of isovalent dopants has pointed toward a preference for Na at the Li site, presenting a promising avenue for pioneering sodium-based research. In addition, the aliovalent doping of Si at the Ga site, with an unexpectedly low energy value of 0.28 eV, beckons further exploration. Beyond the confines of this study, these findings hold transformative implications for experimental endeavors.

Computational facilities and support were provided by the Department of Chemistry, University of Jaffna, Sri Lanka.

The authors have no conflicts to disclose.

Sathiyamoorthy Mathushan: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal); Writing – original draft (equal). Poobalasingam Abiman: Project administration (equal); Supervision (equal); Writing – review & editing (equal). Poobalasuntharam Iyngaran: Project administration (equal); Supervision (equal); Writing – review & editing (equal). Navaratnarajah Kuganathan: Formal analysis (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.