The Li₂Ti₆O₁₃ and Li₂Zr₆O₁₃ composite as a high-performance anode for alkali-ion batteries: a molecular dynamics study

Abstract

The current development of technology has highlighted the necessity of compounds that enhance the durability and performance of alkali-ion batteries. The anodes of these batteries need to overcome the challenges of low dc-conductivity at ambient temperatures and interfacial resistance between the solid-state electrolyte. By conducting large-scale molecular dynamics simulations, we investigated the transport properties of Li₂Ti₆O₁₃ and Li₂Zr₆O₁₃ mono- and bi-crystals, as well as Li₂Ti₆O₁₃@Li₂Zr₆O₁₃ composites. While the monocrystalline and bi-crystalline Li₂Zr₆O₁₃ show similar transport properties, the composite materials, combining both compounds, exhibit the highest diffusion coefficients and dc-conductivity. The transport properties of the composite materials are found to be significantly higher than those mono- and bi-crystalline samples due to the Li interstitial mechanism and the presence of grain boundaries. Our study offers valuable insights for the development of high-performance energy storage materials.

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1. Introduction

Lithium hexatitanate (Li₂Ti₆O₁₃) is one of the materials that can be used as a negative electrode in lithium ion batteries (LIBs). Li₂Ti₆O₁₃ has a tunnel structure with a large surface area, a theoretical capacity of 170 mA h g⁻¹, open cell voltage of 1.5–1.7 V and dc conductivity at 25 °C of 5.6 × 10⁻⁶ S cm⁻¹. These structural and electrochemical properties make this compound an intriguing anode material.^1–5 Despite such intrinsic properties, many experimental strategies were considered to improve the anode performance, and it appears that Li₂Ti₆O₁₃ is less promising than lithium pentatitanate (Li₄Ti₅O₁₂) for use as a anode.^1–6

In a previous work, a new compound, lithium hexazirconate (Li₂Zr₆O₁₃), and its anode performance were studied by using density functional theory computations.⁵ The Li₂Zr₆O₁₃ possesses the lattice structure of Li₂Ti₆O₁₃, including the lattice, electronic and mechanical properties. The open cell voltage of Li₂Zr₆O₁₃ is close to the reported value for Li₂Ti₆O₁₃ and other anode materials.^1–5,7 Various experimental strategies have been devoted to improve the performance of similarly active materials for anodes.^1–12 For instance, Li₂TiO₃ was used as a co-material to stabilize the structure and enhance the electrode material with better electrochemical performance of the combined Li₄Ti₅O₁₂–Li₂TiO₃ whose ionic conductivity is higher than that of Li₄Ti₅O₁₂.^8,9 Carbon-coating free, β-Li₂TiO₃ delivers a specific capacity of 200 mA h g⁻¹ within 100 cycles and 170 mA h g⁻¹ after 500 cycles preserving a coulombic efficiency above 97%.¹⁰ Graphene supported Li₂SiO₃/Li₂SnO₃ prepared through a hydrothermal method has an initial specific capacity of 1016.5 mA h g⁻¹ and its specific capacity amounts to 440.8 mA h g⁻¹ after 200 cycles. The enhancement of lithium storage of this composite was explained by the synergy among the composite components.¹¹ In addition, the temperature dependence of electrical properties of composites formed by biphasic sodium titanate and poly(o-methoxyaniline) (Na₂Ti₃O₇/Na₂Ti₆O₁₃/POMA) with different concentrations of POMA was determined from complex impedance measurements.¹² Differences on the electrical properties between the composite and individual components were reported.¹²

In this context we set out to search for a co-material which can be combined with Li₂Ti₆O₁₃ using molecular dynamics simulations. In fact, atomistic simulation is a powerful tool to investigate structure–property relations and for theoretical design of new materials.^13–16 In particular, classical molecular dynamics computations provide us with relevant information concerning the transport properties in large systems.^13–16

The nudged elastic band (NEB) method and molecular dynamics (MD) simulations are popular computational methods used to investigate the behaviour of molecules and materials at the atomic level. The main difference between the two methods consists in the fact that NEB computations are used to evaluate the energy barriers and reaction pathways between different stable states, whereas MD is used to probe the behaviour of materials over time and their dynamic behaviour. In addition, MD computations allow the investigation of very large molecular systems including the polycrystalline materials.

Various theoretical studies on Li₂Ti₆O₁₃ have been reported, disclosing its thermodynamic stability, lattice properties, doping effect, and partially diffusion process.^5,7,17–19 To our knowledge, full molecular dynamics simulations disclosing the transport properties of Li₂Ti₆O₁₃ have not been reported yet. To further understand the factors influencing the electrochemical behaviour, the transport properties are essential keys for determine the Li insertion/de-insertion rates.

Transport properties depend not only on the atomic mass and net charge of the mobile, but also on the migration path and the proper structure of the system. It is well-known that the effect of grain boundary is important on transport properties in polycrystalline materials.^20–22 In the present study, we conduct large-scale MD computations with the aim to disclose transport properties of both mono- and bi-crystalline Li₂B₆O₁₃ with the metal B = Ti, Zr, and as mentioned above, of a new ceramic composite materials combining for the first time both Li₂Ti₆O₁₃ and Li₂Zr₆O₁₃ compounds. In particular, the influence of the grain boundary on transport properties are disseminated, providing us with some relevant strategies stimulating future experimental investigations.

2. Computational protocols

Fig. 1 displays the unit cell of the hexa-metaloxide Li₂B₆O₁₃ with B = Ti and Zr in the conventional representation. The monoclinic Li₂B₆O₁₃ crystal structure consists of a corner-sharing [BO₆] octahedron and a [LiO₄] tetrahedron. The [BO₆] octahedron forms chains along the b-axis of the crystal, which are connected by the [LiO₄] tetrahedron to form a three-dimensional (3D) structure. The tunnels running along the b-axis serve as ion channels for lithium ion diffusion.^1–5,7

Fig. 1 Conventional representation of the hexa-metal-oxide Li₂B₆O₁₃ (B = Ti, Zr) unit cell in the C2/m. Blue balls represent the Li ions and the grey polyhedron the [BO₆] octahedron.

High diffusion coefficient and high dc-conductivity, complemented by low activation energies at operative temperatures, are crucial parameters for evaluating potential battery materials as they ensure fast Li transport properties. In fact, the exceptional ion transport properties enable the desirable anode to exhibit better cycling performance, preventing a certain chemical reactivity between the anode and the solid-state electrolyte.^23–27 In this study, the Large-Scale Atomic-Molecular Massively Parallel Simulator (LAMMPS)²⁸ code is used to perform large-scale MD simulations with periodic boundary conditions to disclose Li⁺ transport properties. The potential parameters employed, also known as force fields, are taken from previous reports.^18,29 The Buckingham approximation is used for the short-range interactions, while long-range are purely coulombic describing the long-range potential energy.

Fig. 2 displays the workflow followed in this study. The mono- and bi-crystalline structures of the hexa metal-oxide Li₂B₆O₁₃ for both metals B = Ti, Zr, as well as the Li₂Ti₆O₁₃@Li₂Zr₆O₁₃ and Li₂Zr₆O₁₃@Li₂Ti₆O₁₃ composite samples, are constructed by using the Voronoi tessellation method as compiled in the Atomsk code.³⁰ For monocrystalline Li₂Ti₆O₁₃ (Li₂Zr₆O₁₃) samples, we use a supercell containing 360 unit cells (4 × 15 × 6 unit cells). In this sense, monocrystalline samples consist of a single grain. In contrast, bi-crystalline Li₂Ti₆O₁₃ (Li₂Zr₆O₁₃) have two randomly oriented grains shown as Grain I and Grain II in Fig. 2.

Fig. 2 Workflow describing the construction models used in the present study.

Regarding composite materials, Li₂Ti₆O₁₃@Li₂Zr₆O₁₃ and Li₂Zr₆O₁₃@Li₂Ti₆O₁₃, they are constructed from the template of their bi-crystalline simulation boxes. The label (Grain I)@(Grain II) indicates that in Li₂Ti₆O₁₃@Li₂Zr₆O₁₃, Grain I consists of Li₂Ti₆O₁₃, while Grain II comprises Li₂Zr₆O₁₃. Similarly, for Li₂Zr₆O₁₃@Li₂Ti₆O₁₃, Grain I is Li₂Zr₆O₁₃, and Grain II is Li₂Ti₆O₁₃. In this paper, the term composition refers hereafter to the Li₂B₆O₁₃ (B = Ti, Zr) structure present in each grain.

Simulation boxes of 60 × 60 × 60 ų are used for modelling the bi-crystalline and composite samples. To probe the Li⁺ migration, we introduce low concentration (0.09) of Li⁺ vacancies compensated by O²⁻ vacancies (in accordance with the Li₂O Schottky defect) inside the simulation boxes. The size of simulation boxes for monocrystalline samples, resulting in a 61.71 × 56.63 × 55.94 ų, close to the bi-crystalline and composite samples.

During the tessellation process, certain ions are placed too close to each other or even superimposed. As a result, these ions are either removed or separated prior to introducing defects into the bi-crystalline sample. Any extra charge which may arise due to the introduction of defect concentration is compensated by Li⁺ vacancies.

To ensure the accuracy of the simulation results, the simulation boxes undergo equilibration using an isothermal–isobaric ensemble (NPT). Once equilibrated, constant volume–temperature NVT ensemble is used for production, with the mean square displacement (MSD) for the Li⁺ ions being saved to calculate their diffusion coefficient (D).

The slope of the MSD plots is used to obtain the diffusion coefficient as follows:

MSD = 6Dt (1)

where t is the simulation time. For MD simulations, 2 ns with a time step of 2 fs is used for the production run and the temperature ranges between 900–1400 K.

In the ESI,† a sample of LAMMPS input files of mono-, bi-crystalline Li₂Zr₆O₁₃ samples, and Li₂Zr₆O₁₃@Li₂Ti₆O₁₃ composite are included for reproducibility providing further simulation details for use by the readers.

The diffusion data computed are then converted to the dc-conductivity by using the Nernst–Einstein equation:

σ(T) = H_VNq²D(T)/k_BT (2)

where σ(T) and D(T) represent the dc-conductivity and diffusion coefficient at the temperature T, respectively, N the charge density of the mobile ion; q is the charge of the mobile ion, k_B the Boltzmann constant and H_V represents the Haven's ratio which considers the effect of the external electric field on the mobility of the charge carrier (ion) in real samples.^13,15,22,29

We assume H_V = 1 due to the lack of experimental measurements of diffusion and conduction processes in these materials, in particular for Li₂Zr₆O₁₃. Both the diffusion and conduction processes are thermally activated; it implies that the relevant kinetics follow the conventional Arrhenius equation Δ(T) = Δ₀ exp(−E^Δ_a/k_BT), where k_B represents the Boltzman constant, T the temperature, Δ₀ the pre-exponential factor (Δ(T) → Δ₀, T → ∞) and E^Δ_a the activation energy, with Δ = D the Arrhenius dependence for diffusion can be obtained, while for Δ = σ, the conduction process is determined.

Together with the activation energy, the diffusion and dc-conductivity at 25 °C are the magnitudes characterizing the transport properties in ionic materials.^13,15,22,29

3. Results and discussion

3.1 Tracking Li⁺-ion in mono-, bi-crystalline Li₂B₆O₁₃ (B = Ti, Zr) and Li₂Ti₆O₁₃@Li₂Zr₆O₁₃ composite samples

The temporal evolution of MSDs with respect to the temperature of Li₂Ti₆O₁₃ and Li₂Zr₆O₁₃ are depicted in Fig. 3. As it is shown, the slope of all MSD plots increases with the increment of the temperature, indicating the presence of a thermally activated process. Another interesting finding is that the MSD plots for Li₂Ti₆O₁₃ are placed higher than that for Li₂Zr₆O₁₃.

Fig. 3 Mean square displacement (MSD) versus simulation time of monocrystalline (a) Li₂Ti₆O₁₃ and (b) Li₂Zr₆O₁₃.

The diffusion coefficient, obtained from eqn (1), are thus larger in Li₂Ti₆O₁₃ as compared to the monocrystalline Li₂Zr₆O₁₃. It can be attributed to the ionic radius difference of 0.115 Å between the Zr⁴⁺ and Ti⁴⁺ ions with direct implications on the structural characteristics such as lattice parameters the [LiO₄] space channels, the Li–Li distance, the [BO₆] octahedral volume, bond angle variance and average O–O distance.^5,31

The Li–Li distance is related to the diffusion jump distance where the diffusion mechanism strongly depends on the diffusion jump distance. Li₂Zr₆O₁₃ has longer Li–Li distance as compared to their isostructural Li₂Ti₆O₁₃,⁵ in such a way that lower Li⁺ diffusion coefficients are expected in monocrystalline Li₂Zr₆O₁₃.

Fig. 4 shows the temporal evolution of MSD of the bi-crystalline Li₂Ti₆O₁₃ and Li₂Zr₆O₁₃ samples. In this case, the linear dependence of MSD with respect to time is more appreciable in the entire range of the simulation time; it is ascribed to the presence of grain boundaries.

Fig. 4 Mean square displacement (MSD) versus simulation time of bi-crystalline (a) Li₂Ti₆O₁₃ and (b) Li₂Zr₆O₁₃.

The grain boundary affects the transport properties introducing additional Li⁺ vacancies in the sample, thereby favouring the Li⁺ migration. Analogously, the diffusion characteristic in Li₂Ti₆O₁₃ is better than the one in its Zr counterpart. The effect of [BO₆] octahedral distortion, together with the grain boundaries, are the sources of better transport properties in bi- against monocrystalline samples. ^5,20–22

The next step deals with the Li⁺ transport properties of the target Li₂Ti₆O₁₃@Li₂Zr₆O₁₃ and Li₂Zr₆O₁₃@Li₂Ti₆O₁₃ composite samples. As was described in Section 2 (and depicted in Fig. 2), the Li₂Ti₆O₁₃@Li₂Zr₆O₁₃ composite consists in a bi-crystal where Grain I contains Li₂Ti₆O₁₃ and Grain II, Li₂Zr₆O₁₃ (denoted as LTZO), while the Li₂Zr₆O₁₃@Li₂Ti₆O₁₃ composite is the inverse: the Grain II contain Li₂Ti₆O₁₃ and Grain I is constituted by Li₂Zr₆O₁₃ (denoted as LZTO).

Fig. 5 displays the MSD plots of both composite materials. Comparison of both MSD versus time points out appreciable similarities between the slopes of each temperature and better linear dependence as compared to the individual monocrystalline samples. These results suggest that a change in the grain composition does not affect the Li⁺ transport properties in these composite materials.

Fig. 5 Mean displacement (MSD) versus simulation time of composite Li₂Ti₆O₁₃@Li₂Zr₆O₁₃ materials: (a) LTZO and (b) LZTO.

3.2 Transport properties of Li⁺-ion in mono-, bi-crystalline Li₂B₆O₁₃ and composite Li₂Ti₆O₁₃@Li₂Zr₆O₁₃ samples

In order to quantitatively measure the Li⁺ transport properties of the compounds of interest, the Arrhenius dependence of both diffusion and conduction processes is performed. With the collected diffusion data in each sample, the dc-conductivity at each temperature is obtained by using eqn (2). Fig. 6 displays the Arrhenius dependence of the diffusion and conduction data for each sample. There are various findings concerning the diffusion/conduction behaviour:

Fig. 6 Arrhenius-type dependence of (a) diffusion coefficient and (b) dc-conductivity with temperature for Li₂Ti₆O₁₃/Li₂Zr₆O₁₃ samples: monocrystalline (LTO_m/LZO_m), bi-crystalline (LTO/LZO), and composite (LTZO/LZTO). In each case, the lines represent the Arrhenius fit.

• The monocrystalline Li₂Zr₆O₁₃ sample exhibits transport properties similar to those of the bi-crystalline Li₂Zr₆O₁₃ sample.

• Both the largest diffusion coefficients and dc-conductivity are observed in the composite materials, followed by monocrystalline and bi-crystalline Li₂Ti₆O₁₃ samples.

• The diffusion coefficients and dc-conductivity for the composite materials are found to be about two orders of magnitude higher as compared to the rest of the samples.

From such a first conclusion, one can assume an insignificant contribution of the grain boundary on the Li⁺ transport properties of Li₂Zr₆O₁₃. As a matter of fact, the additional Li⁺ migration sites created by the grain boundaries do not considerably affect the overall Li⁺ diffusion within the structure. On the other hands, introduction of grain boundary, together with the composition of the composite, tends to improve the Li⁺ transport properties as compared to those of mono and bi-crystalline samples. In this case, the additional migration sites generated by the grain boundaries result in an alternative Li⁺ migration paths with shorter diffusion jump distances, thus favouring the diffusion through the composite materials.

Another interesting observation is that the composite has similar values of diffusion coefficient and dc-conductivity upon temperature change, indicating that the composition, i.e., the grain characteristics, does not affect significantly the Li⁺ mobility. From the results of the Arrhenius fitting, the diffusion activation energy (E^D_a) and the diffusion coefficient at 25 °C (D̃), together with the conduction activation energy (E^σ_a) and conductivity at ambient temperature (σ[small sigma, Greek, tilde]) are determined. Table 1 collects these data calculated for each sample. The obtained activation energy lies between 0.58–0.70 and 0.48–0.56 eV for both diffusion and conduction, respectively. These low values are beneficial for their use as anode materials.^1–12

Table 1 Activation energy for diffusion (E^D_a) and conduction (E^σ_a) processes and diffusivity (D̃) and conductivity (σ[small sigma, Greek, tilde]) at 25 °C of each compounds

Compound	E^Da (eV)	D̃ (cm^2 s^−1)	E^σa (eV)	σ[small sigma, Greek, tilde] (S cm^−1)
LTOm	0.58	2.96 × 10^−14	0.48	4.84 × 10^−9
LZTm	0.65	1.23 × 10^−15	0.49	1.22 × 10^−9
LTO	0.70	6.10 × 10^−16	0.60	1.05 × 10^−10
LZO	0.64	1.25 × 10^−15	0.55	2.16 × 10^−10
LZTO	0.65	1.20 × 10^−13	0.55	2.43 × 10^−8
LTZO	0.66	1.02 × 10^−13	0.56	1.77 × 10^−8

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The lowest and highest diffusion/conduction activation energy are found for monocrystalline and bi-crystalline Li₂Ti₆O₁₃ samples. The difference of E^D_a and D̃ (E^σ_a and σ[small sigma, Greek, tilde]) between mono- and bi-crystalline Li₂Zr₆O₁₃ is low. In addition, composite materials have similar activation energy and D̃ (σ[small sigma, Greek, tilde]) at ambient temperature. These results consolidate the previous analysis pointing out no influence of grain boundary on the transport properties of Li₂Zr₆O₁₃ as well as the grain composition in the targeted composite materials.

The results of transport properties obtained in this study are in line with those reported in the literature. For instance, values of D̃ ranging between 10⁻⁹ to 10⁻¹² cm² s⁻¹ have been reported for the knowing anodes Li₄Ti₅O₁₂, Na₂Ti₃O₇ and Na₂Ti₆O₁₃ compounds.³² Values ranging between 10⁻¹⁷ to 10⁻¹⁵ cm² s⁻¹, in Na₂Li₂Ti₆O₁₄ result in a poor performance at high charge–discharge rates were reported.^33–35 Value of conduction activation energy of 0.65 eV was found in a comparative study.³⁶ Even a lower value of Li⁺ diffusion activation energy (0.47 eV) had been reported with a different theoretical approach.¹⁷

Fig. 7 illustrates the trajectory density plots of each sample at 900 K for monoclinic and bi-crystalline samples, and for the composite material, the trajectory density plots are recorded at 500 K to better observe the role of the composition at lower temperatures. From Fig. 7a and d, it is observed that the Li⁺ migration occurs along the [LiO₄] channels in monoclinic Li₂Ti₆O₁₃ and Li₂Zr₆O₁₃ samples, including migration between layers. Higher density plot is observed in monocrystalline Li₂Zr₆O₁₃ as compared to Li₂Ti₆O₁₃. In addition, Li⁺ ions migrate via an interstitial mechanism, as evidenced by density plots between [LiO₄] layers in agreement with the lower diffusion activation energy in monocrystalline Li₂Zr₆O₁₃.

Fig. 7 Li-trajectory density maps (blue lines) of monocrystalline: (a) Li₂Ti₆O₁₃, (d) monocrystalline Li₂Zr₆O₁₃, bi-crystalline: (b) Li₂Ti₆O₁₃, (e) Li₂Zr₆O₁₃ and composite: (c) Li₂Ti₆O₁₃@Li₂Zr₆O₁₃, (f) Li₂Zr₆O₁₃@Li₂Ti₆O₁₃ samples.

For bi-crystalline samples (Fig. 7b and e), larger density plots are observed, including migration between grain boundaries.

The trajectory density plots of composite materials are very similar to each other, which is also confirmed by their activation energies. In this case, the most relevant findings consist of the evidence of large-scale Li⁺ migration across the entire composite, irrespective of the grain composition. After all, the presence of grain boundaries and interstitial mechanism improve the transport properties of these materials.

4. Concluding remarks

Large-scale molecular dynamics simulations are performed to explore the transport properties of mono- and bi-crystalline Li₂B₆O₁₃ (B = Ti, Zr) and the composite Li₂Ti₆O₁₃@Li₂Zr₆O₁₃. Calculated results demonstrate that the monocrystalline Li₂Zr₆O₁₃ exhibits similar transport properties as the bi-crystalline Li₂Zr₆O₁₃ sample. The highest diffusion coefficients and dc-conductivity are obtained in the composite material, followed by monocrystalline and bi-crystalline Li₂Ti₆O₁₃ samples. The obtained activation energies amount to the range of 0.58–0.70 and 0.48–0.56 eV for both diffusion and conduction, respectively.

The diffusion coefficients and dc-conductivity for the composite material are found to be about two orders of magnitude higher as compared to the rest of the samples. The trajectory density maps indicate that the Li interstitial mechanism, together with the presence of grain boundaries, are the sources for improvement of transport properties of the composite material.

Considering the much improved transport properties revealed in this study, further experimental verification is highly recommended to assess the potential of these compounds, especially the new composites, as active materials for anodes in the current and future energy storage devices. This also suggests a more general strategy for improvement making use of composite materials.

Data availability

The data supporting this article have been included as part of the ESI.†

Author contributions

YAZ: conception, data acquisition and interpretation, original draft preparation, editing, review. MTN: conception, project supervision, manuscript editing, review. MPPH: data analysis, editing, review. All authors reviewed the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

MTN thanks Van Lang University for support.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: LAMMPS input files of mono, bi-crystalline Li₂Zr₆O₁₃ samples, and Li₂Zr₆O₁₃@Li₂Ti₆O₁₃ composite for reproducibility providing further simulation details for the readers. See DOI: https://doi.org/10.1039/d4ra02998d

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