Materials design principles of amorphous cathode coatings for lithium-ion battery applications

Abstract

Cathode surface coatings present one of the most popular and effective solutions to suppress cathode degradation and improve cycling performance of lithium-ion batteries (LIBs). In this work, we carry out an extensive high-throughput computational study to develop materials design principles governing amorphous cathode coating selections for LIBs. Our high-throughput screening includes descriptors to evaluate the thermodynamic stability, electrochemical stability, chemical reactivity with electrolytes and cathodes, and ionic diffusion of the cathode coatings. In the ionic diffusion analysis, we mainly focus on Li-containing compounds. From the 20 selected materials, we highlight the formidable challenge of mitigating oxygen diffusion when selecting an ideal cathode coating, and suggest 7 promising coating candidates: Li₃B₁₁O₁₈, LiZr₂(PO₄)₃, LiB₃O₅, LiPO₃, LiSb₃O₈, LiAlSiO₄ and LiTaSiO₅. Combining the screening results and detailed ionic diffusion analysis of the selected cathode coatings, we summarize the general selection guidelines of amorphous cathode coatings for LIBs.

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Introduction

Lithium-ion batteries (LIBs) are ubiquitous in portable electronic devices and have enabled the development of cleaner energy storage and electric vehicles (EVs). For the past decade, LIB-powered EVs have gradually penetrated the automotive market. With an increasing demand of reducing greenhouse gas emissions, the global fleet of EVs will continue to rise for the coming decade.¹ Future improvements in LIBs include high energy density cathode materials to enable longer driving range; however these materials frequently operate at high potential and experience surface degradation with associated performance degradation under extended cycling. The current commercialized cathode materials of LIBs are classified as layered (LiNi_aCo_bMn_cO₂, NMC), spinel (LiMn₂O₄) and olivine (LiFePO₄). Regardless of their crystal structure, these cathode materials all exhibit surface degradation and detrimental surface phase transformations, which compromise the cycle life and thermal stability of LIBs. For example, upon a higher voltage operation (>4.3 V), surface oxygen evolution triggers an irreversible transformation in NMC cathodes from layered phase into a mixture of spinel and rock salt phases that deteriorates capacity retention.² Similarly, in LiMn₂O₄, surface oxygen loss causes considerable compressive lattice strain, which densifies the cathode surface and blocks the Li-migration pathways.³ The LiFePO₄ cathode exhibits an excellent capacity retention, however, its eventual failure is associated with the surface amorphization and oxygen loss after the prolonged cycling.⁴ In addition, side reactions between the electrolyte and cathode lead to transition metals dissolution and surface impedance build-up, which further accelerate the capacity/voltage fade.⁵ Therefore, it is of high interest to engineer the cathode surface to achieve high energy density LIBs with a stable, safe, and long-term cycling performance.⁵⁶

A common strategy to stabilize the cathode surface is to apply a multifunctional protective layer to mitigate surface degradation and simultaneously maintain facile Li⁺ transport.⁶ Such cathode coatings typically exhibit an amorphous character, with a thickness between 1 to 10 nm.^7,8 A variety of coating materials have been explored and shown varying degrees of effectiveness in enhancing the cyclability of LIBs, such as metal oxides (e.g., Al₂O₃ (ref. 9)), nonmetal oxides (e.g., B₂O₃ (ref. 10)), polyanionic oxides (e.g., Li₃B₁₁O₁₈ (ref. 11)), and fluorides (e.g., AlF₃ (ref. 12)), etc. However, several reported cathode coatings have been found to exhibit chemical and/or electrochemical instability and large overpotential during cycling. For example, Al₂O₃ and ZnO effectively mitigate the side reactions of the cathode surface with the electrolyte,^9,13 however, the metal oxide coating layer forms a metal oxyfluoride or a metal fluoride layer by scavenging F⁻ from HF in the electrolyte.^13,14 Furthermore, because of its inherent low Li⁺ ion diffusivity, Al₂O₃ coatings can lead to large overpotentials and reduced capacity, even at a thickness as low as 2 nm.^15,16 On the other hand, Li-containing compounds have been found to exhibit better capacity retention than their non-lithiated counterparts, due to their improved ability to transport Li⁺.¹⁷ However, a recent study found that an NMC cathode surface still transforms from a layered structure into an oxygen loss-induced rock-salt structure after cycling, even when conformally coated with a Li₃B₁₁O₁₈ layer.¹¹ Similar surface reconstruction phenomenon has been observed in Al₂O₃- and AlF₃-coated cathodes,^12,18 regardless of liquid-electrolyte or solid-electrolyte battery implementations. As different coating materials may enhance one aspect of performance while hindering or falling short of another, ultimately, the question is what are the optimal coating design choices given the battery application, and can we provide a systematic guidance to identify them?

Given the complex reactions between the cathode, coating and electrolyte and the difficulty in deconvoluting experimentally measured solid state ionic diffusion, first-principles modeling provides robust guidelines for new cathode coatings. Aykol et al. reported a high-throughput screening of crystalline oxides materials that can stabilize the cathodes in a liquid-electrolyte battery system.¹⁹ However, ionic diffusivity in the coatings was not considered. Liu et al. screened Li-containing crystalline fluoride materials and identified 10 promising coating materials along with their calculated Li⁺ migration barriers.²⁰ Xiao et al. screened crystalline Li-containing cathode coatings for solid-state batteries and proposed three polyanionic compounds as the most appealing candidates.²¹ We note that the ionic diffusion analyses in all previous computational screening work have addressed exclusively the crystalline coating materials, whereas cathode coatings are often amorphous or polycrystalline. In addition, due to their isotropic non-periodic structures, amorphous films tend to be more conformal than polycrystalline films, with reduced grain boundaries, dislocations, or other defect regions.²² Therefore, amorphous coatings provide a better cathode surface protection against surface oxygen loss and side reactions with electrolytes than polycrystalline coatings. Their unique processability also enables high degrees of interfacial contact with electrodes.²² Moreover, many amorphous solids, such as Li₃PO₄ and Al₂O₃, have been found to exhibit higher Li⁺ conductivity than their crystalline phases.^23,24 However, to our best knowledge, no study has considered O²⁻ diffusion in amorphous films, which is directly related to the oxygen-loss-induced cathode surface densification. In addition, Li⁺ and O²⁻ diffusion corresponds to the kinetics of the coatings but has never been applied broadly or systematically enough to derive design rules. In this work, we carry out an extensive high-throughput computational study to develop materials design principles governing amorphous cathode coating selections for LIBs. We evaluate the thermodynamic stability, electrochemical stability, chemical reactivity with electrolytes and cathodes, as well as the Li⁺ and O²⁻ diffusion in amorphous cathode coatings. Based on the trends in the screening results and ionic transport, we summarize general guidelines for selecting amorphous cathode coatings.

Computational details

First-principles calculation

All density functional theory (DFT) calculations are performed using the Vienna Ab initio Simulation Package (VASP),^25,26 with Projector Augmented Wave (PAW) potentials.²⁷ The generalized gradient approximation (GGA) as parameterized by the Perdew–Burke–Ernzerhof (PBE)²⁸ is used for the exchange-correlation functional. For AIMD simulations, we employ Γ-point only Brillouin zone integration at a plane-wave cutoff energy of 400 eV and a time step of 2 fs.

We utilize a “liquid-quench” process to generate the amorphous structures, in which heating, equilibration, and quenching are performed through an AIMD workflow, which can be found as part of the open-source mpmorph package at https://github.com/materialsproject/mpmorph. We use the Packmol package²⁹ to generate all initial amorphous structures. To generate the “liquid” phase of the amorphous structures, we equilibrate the structures at 3000 K using a sequence of 4 ps AIMD simulations in the NVT ensemble until the external pressure and energy are converged. Next, the structures are simulated for an additional 10 ps, from which three independent configurations are selected and quenched to 0 K to obtain the ground-state amorphous structures. To perform ion diffusion analysis, we equilibrate the ground-state structure at T = 1800, 2000, 2200, 2400, 2600, and 2800 K, and then simulate an 80 ps diffusion trajectory at each corresponding temperature. The equilibration procedure follows the same steps used to equilibrate the “liquid” amorphous structure. In the end, there are three independent diffusion trajectories at each temperature. Further details about the entire AIMD and DFT workflows can be found in ref. 30.

Self-diffusion coefficients and overpotentials

From the obtained diffusion trajectories, we calculate the self-diffusion coefficients (D) of Li⁺ and O²⁻ ions in amorphous structures using the Einstein relation: , where t is the time, r is the ion position and 〈Δr²〉 is the mean square displacement (MSD). Within the temperature window 1800–2800 K, there are three D values calculated from three independent diffusion trajectories at each temperature. The D values at room temperature are extrapolated from those at high temperatures using the Arrhenius relation of D as a function of T: D = D₀ exp(−E_a/k_BT), where k_B is the Boltzmann constant, D₀ is the pre-exponential factor and E_a is the activation energy of ion diffusion. In addition, the trajectories at lower temperatures (e.g. 1800 K) frequently exhibit fewer ionic hops, which incurs higher statistical uncertainties of fitted D values than those at higher temperatures (e.g. 2800 K). Therefore, we consider the uncertainty of the D values at each temperature when linearly fitting log D vs. 1/T by assigning the standard deviation of log  D as the uncertainty for each averaged D.

From the calculated room temperature Li⁺ diffusivity D^Li_rt, we estimate the overpotential, ΔV, across a cathode coating layer using a theoretical model which assumes a constant potential gradient, a uniform Li⁺ concentration and the Einstein relation to relate Li⁺ mobility and diffusion coefficient in the coating.^31,32 The model calculates ΔV as a function of current density, coating thickness, Li⁺ concentration, Li⁺ diffusivity and temperature, providing a qualitative evaluation on coating's ability to transport Li⁺ ions. The relation between ΔV and D^Li_rt follows the methodology used in the earlier work,^24,33 namely:

where l_c is the coating thickness, k_B is the Boltzmann constant, T is the temperature, c^Li is the Li⁺ concentration in the coating, q is the electron charge, i.e., q = |e| = 1.602 × 10⁻¹⁹ C, and J is the current density through the cathode coating, which results from a flux of Li⁺ ions and can be approximated as:²⁴where ρ is cathode density, V_P is the particle volume, S_P is the particle surface area, r is the particle radius, C is the cathode capacity, and t is the charging/discharging time. Combining eqn (1) and (2), ΔV can be expressed as:

In the ESI† we provide the full derivation and assumptions for eqn (1). According to eqn (2), the current density J is normalized by the cathode surface area, while experimentally, J is more commonly normalized by geometric area of the cathode disk. In addition, we assume that the entire spherical cathode particle surface area is available for Li⁺ intercalation.

Oxygen flux and transport time

We use the Onsager transport equations to estimate the O²⁻ flux J^O under the driving force of the oxygen chemical potential gradient ∇μ^O across the coating layer, which can expressed as:

J^O = −L^OO∇μ^O (4)

where L^OO is the Onsager transport coefficient for oxygen transport. It should be noted that in this study we ignore the contributions from cross-correlations between oxygen and other species, such as L^OLi, and between distinct oxygen sites, i.e. L^OO_distinct, to J^O. We approximate the ∇μ^O to be a constant across the thickness of the coating under steady-state conditions. Therefore, eqn (4) can be expressed as:where μ^O_c and μ^O_e are the oxygen chemical potential at the cathode and electrolyte sides, respectively. Ignoring the L^OO_distinct term, L^OO can be directly related to the self-diffusion coefficient D^O:³⁴where c^O is the O²⁻ concentration in the coating. The room-temperature L^OO_rt is extrapolated from L^OO values at high temperatures by fitting eqn (6). It should be noted that previous experiments have reported several active oxygen intermediates during oxygen evolution reactions at cathode surface, such as covalent peroxide bonds, oxygen radicals and singlet oxygen (¹O₂).^35–37 Because of their high reactivity, we assume these oxygen intermediates will react with the coating materials and become O²⁻. Therefore, we use O²⁻ diffusion to represent oxygen diffusion in the coatings.

Materials database and descriptors

The entire database used in this study contains 146 323 crystalline compounds, which are queried from the Materials Project (v2021.11.10).³⁸ The materials properties include DFT calculated total energies, formation energies, energies above convex hull (E_hull), band gaps (E_g), etc. It should be noted that at zero temperature, the Gibbs free energy of a crystalline polymorph is always lower than that of its amorphous state.³⁹ However, there is no universal description for the energetics of the amorphous materials, therefore we use the energies of the crystalline phases to approximate the stability of the amorphous phases. Indeed, the distribution of synthesizable crystalline polymorph energies tends to follow the trend of the amorphous energies.³⁹

Phase stability. A compound's E_hull value is calculated by constructing the convex hull that includes the formation energies of all known crystalline phases in the same chemical space. The compounds that constitute the convex hull, i.e. have E_hull = 0, are deemed stable phases (at low temperature) or ground states for the system studied. The E_hull value for metastable phases therefore provides a measure of the driving force for decomposition and a descriptor for the phase stability of each compound.

Electrochemical stability. The calculations of the electrochemical stability window follow the methodology proposed by Aykol et al.,¹⁹ which combines DFT formation energies in the Materials Project, experimental thermochemical data for gaseous species and experimental electrochemical data for solvated ions. First, we calculate the standard Gibbs free energy of a reaction (ΔG⁰), which is obtained as:

ΔG⁰ = G_products − G_reactants (7)

At room temperature, we assume the entropy contributions of solid phases are negligible while the entropy contributions of gaseous species (O₂, F₂, Cl₂, H₂ and N₂) are much higher than that of solid phases. For the gaseous species, their entropy values S at room temperature are taken from the JANAF tables.⁴⁰ Thus, ΔG⁰ can be approximated as:

ΔG⁰ ≈ H_products − H_reactants − T(S_{gaseous products} − S_{gaseous reactants}) (8)

where H represents enthalpy. For solid phases, we assume PΔV contributions are negligible and H can be approximated with the DFT calculated internal energy E at 0 K. For gaseous species, we add the anion corrections, which also includes the PΔV contribution to their enthalpy.⁴¹ For a reaction involved with solvated ions, we assume a one-step single ion dissolution: A = Aⁿ⁺ + ne⁻ and we add the standard free energy of formation of a solvated ion, , to ΔG⁰ in eqn (8). can be calculated as:where n is the valence state of the ion, F is the Faraday's constant, and is the standard oxidation potential of the Aⁿ⁺ ion taken from the IUPAC publication.⁴² Next, the free energy of a given reaction can be obtained as:where a_i is the activity of species i. In Aykol's work, they assumed a small activity of a_ion≠Li = 10⁻⁶ for non-Li solvated ions to approximate their dilute concentration in the electrolyte.¹⁹ As this a_ion≠Li is arbitrary and its effect on the calculated reaction potential is trivial, i.e., −0.35/z, where z is the number of electrons transferred in the reaction, we assumed a_i values of unity for condensed phases and all solvated ions, thus ΔG ≈ ΔG⁰. Finally, the reaction potential (versus Li metal), V, can be obtained using the Nernst equation:

Chemical stability. The chemical stability of a cathode coating involves the reactivity of the coating with cathode and electrolyte as described by the reaction energy ΔE_rxt.^21,43 For two reactants a and b in contact, the reaction can consume arbitrary amounts of either phase: xc_a + (1 − x)c_b → c_equil, where c_a and c_b are the compositions of a and b normalized by the numbers of atoms, respectively, c_equil is the composition of ground-state or phase equilibrium structure determined from the convex hull and x is the mixing parameter between 0 and 1. ΔE_rxt is determined with an x that yields the largest reaction driving force: ΔE_rxt = min_x∈[0,1]{E[c_equil] − xE[c_a] − (1 − x)E[c_b]}.

Results and discussion

Screening process

Fig. 1 illustrates the sequential high-throughput screening procedure for cathode coating materials with descriptors including radioactivity, energy above convex hull (E_hull), band gap (E_g), reduction limit (V_red), oxidation limit (−V_ox), and reaction energy (ΔE_rxt) with cathodes and electrolytes.

Fig. 1 The flowchart of the high-throughput computational screening of cathode coating materials. Compounds with radioactivity or energy above convex hull (E_hull) greater than 0 are excluded. Compounds with band gap (E_g) smaller than 0.5 eV are excluded. Compounds with reduction limit (V_red) above 3 V or oxidation limit (−V_ox) below 4 V are excluded. Compounds with reaction energy (ΔE_rxt) with cathode or electrolyte smaller than −0.1 eV per atom are excluded.

We exclude compounds containing radioactive elements and categorize the remaining compounds in 8 groups based on their anion chemistry: fluorides, chlorides, oxyfluorides, oxychlorides, metal oxides, nonmetal oxides, polyanionic oxides and others. We use E_hull values given in the Materials Project database³⁸ to screen for the thermodynamically stable compounds and select only the compounds that are on the convex-hull, i.e., E_hull = 0. Furthermore, we are interested in electronically insulating coating materials that can block the electron transfer between the cathode and electrolyte and the subsequent electrolyte oxidation at high voltage.¹² Therefore, we exclude all metallic compounds and compounds that exhibit a bandgap, E_g, less than 0.5 eV. However, it should be noted that there is a positive effect of a conductive surface coating on the performance of the cathode, as it provides an electron-conducting media that facilitates the charge transfer at the electrode surface.⁴⁴ For example, carbon-coating on LiFePO₄ has proven to deliver a higher active material loading and energy density in a full-size battery.⁴⁵ The use of E_hull and E_g descriptors returns 13 498 compounds for further consideration.

In addition, a coating material that participates in the redox reaction during extensive cycling may cause degradation of the surface film, thus a loss of the surface protection.¹⁵ Therefore, we retain only electrochemically stable compounds that can sustain the desirable voltage window. The electrochemical stability window of a cathode coating represents the voltage range (versus Li metal) in which the material is thermodynamically stable upon Li (de)intercalation. It consists of two components: the reduction limit (V_red) during discharge and oxidation limit (−V_ox) during charge. The reduction (cathodic) limit of a cathode coating with composition A_aB_bC_c… is defined as the voltage limit at which the material lithiates to A_aB_bC_c…Li_δ. The discharge reaction can be expressed as:

A_aB_bC_c… + δLi⁺ + δe⁻ → [aA,bB,cC,…,δLi]_min (12)

where [aA,bB,cC,…,δLi] represents the compositions of the products, which are determined from the stable phases in the relevant phase diagram. δ represents a dilute amount of Li, such that [aA,bB,cC,…,δLi] remains within the first phase-region formed by A_aB_bC_c… and other stable phases towards the Li-node of the phase diagram. In this phase-reigon, [aA,bB,cC,…,δLi] has the lowest Li chemical potential, therefore the highest V_red, along the composition path from A_aB_bC_c… towards the Li-node of the phase diagram. For a cathodically stable cathode coating, V_red in eqn (12) should be lower than the discharge cutoff voltage of the cathode as shown in Fig. 1. We set the criterion for V_red to be 3 V.¹⁹ The oxidation (anodic) limit is defined as the voltage limit at which the material oxidizes and decomposes into one or more phases. The charge reaction can be expressed as:

A_aB_bC_c… → δAⁿ⁺ + nδe⁻ + [(a − δ)A,bB,cC,…]_min (13)

where Aⁿ⁺ represents the dissolved ion. For a Li-containing compound, we take Li⁺ as the dissolved ion due to its high standard oxidation potential (3.04 V). For a compound that does not contain Li, we determine the dissolved ion by calculating the reaction potentials for all elements in the compound and conservatively selecting the element that leads to the highest reaction potential, thus the highest dissolution tendency. It should be noted that in this study, we assume a one-step single ion dissolution while the actual dissolution process may involve multi-step/multi-ion dissolution. For a non-Li-containing compound with ion dissolution reactions involving other species, we use the oxidation limit of the lithiated, stable compound with the lowest Li chemical potential along the composition path from the compound towards the Li-node of the phase diagram. For example, the dissolution reaction of boron is B(s) + 3H₂O → B(OH)₃(aq) + 3H⁺ + 3e⁻ and the oxidation limit of B₂O₃ is estimated using the −V_ox value of Li₃B₁₁O₁₈. In the ESI,† we illustrate the procedures of calculating [V_red, −V_ox] for LiAl₅O₈, Al₂O₃ and B₂O₃ coatings. For a cathode coating to be electrochemically stable during charge, its |V_ox| magnitude should be larger than the charge cutoff voltage of the cathode, as shown in Fig. 1. As the oxidation reaction processes are likely to exhibit slow kinetics, an overpotential is expected during the charging cycle. Therefore, we set |V_ox| to be 4 V, even though a typical cathode material can be charged up to as high as 4.5 V. The use of electrochemical stability descriptor returns 2602 compounds for further consideration. Fig. 2a illustrates the reduction and oxidation limits of the compounds that are thermodynamically stable. The electrochemical stability of each category is denoted by two violin plots: the left and right represent oxidation and reduction limits, respectively. We find that in general, fluorides, such as AlF₃ and LiAlF₄, have the largest electrochemical stability window with high oxidation limits and low reduction limits. On the other hand, metal oxides, such as BaO and Bi₂O₃, exhibit low oxidation limit, and nonmetal oxides, such as P₂O₅ and SeO₂, have high reduction limit. The bar graph in Fig. 2a summarizes the numbers of compounds for each category of materials that pass the electrochemical stability screening. After this screening tier, polyanionic oxides have the largest number of candidates, followed by fluorides and chlorides. There are only 12 metal oxides and 1 nonmetal oxide, B₂O₃, left for further screening.

Fig. 2 (a) Distribution of the reduction and oxidation limits for each category that pass thermodynamic stability descriptor. (b) Distribution of the reaction energy ΔE_rxt with LiNiO₂, LiCoO₂, LiMn₂O₄ and LiFeOP₄ cathodes for each category that pass electrochemical stability descriptor. Both lithiated and half-lithiated cathodes are evaluated and the most negative ΔE_rxt is selected as ΔE_rxt with cathodes. The horizontal dash lines represent the limits of the descriptors. The histograms in (a) and (b) illustrate the numbers of compounds for each category that pass the descriptors.

The fourth attribute we consider is the chemical stability of the cathode coatings. It has been shown that a coating material can react with cathodes and electrolytes to form new phases at cathode/coating and coating/electrolyte interfaces, respectively.^7,16 Therefore, we screen for cathode coatings that are inert to chemical reactions with both cathodes and electrolytes. The reaction energy ΔE_rxt is calculated using DFT-computed energies of the reactants and products, and a more negative ΔE_rxt indicates a more reactive chemical reaction. We set the criterion for chemically stable cathode coatings as: ΔE_rxt ≥ −0.1 eV per atom.²¹ We calculate ΔE_rxt between cathodes and coating materials using the commonly used cathodes, layered LiNiO₂ and LiCoO₂, spinel LiMn₂O₄, and olivine LiFeOP₄. Both lithiated and half-lithiated cathodes are considered corresponding to the discharge and charge cycles, respectively. We select the most negative ΔE_rxt, i.e., the most favorable chemical reaction, as the ΔE^cathodes_rxt for each compound, and we plot ΔE^cathodes_rxt for each category that pass the electrochemical stability descriptor in Fig. 2b. In Fig. S2,† we also plot ΔE_rxt of each selected cathode material. We find that compared with other cathodes, LiNiO₂ tends to exhibit a more negative ΔE_rxt, therefore reacts more favorably with the coating materials. In addition, oxides coatings are less prone to react with cathodes than fluorides and chlorides. Specifically, all the electrochemically stable metal oxides exhibit low reactivity with common cathodes and pass the chemical stability descriptor. This round of screening returns 1790 compounds for further consideration with polyanionic oxides having the largest number of candidates (714).

Similarly, we calculate ΔE_rxt between coating materials and representative electrolyte components. In this study, we consider the commonly used Li₃PS₄ solid electrolyte and LiPF₆-based non-aqueous liquid electrolytes, respectively, and categorize the coating materials based on their reactivity. In the case of LiPF₆-based electrolytes, we calculate ΔE_rxt between coating materials and HF, which is known to react strongly with both cathodes and coating materials. Fig. 3 illustrates the distribution of ΔE_rxt with Li₃PS₄ and HF for the compounds that are chemically stable with the cathodes. We find that most fluorides and chlorides have lower chemical reactivity with both Li₃PS₄ and HF than oxides compounds, thus are chemically compatible with both the cathodes and electrolytes. On the other hand, most oxides compounds are not chemically inert in LiPF₆-based liquid electrolytes due to a high reactivity with HF. It should be noted that these chemical reactions may only happen at the coating/electrolyte interface and render a partially fluorinated oxides coating layer, which could be beneficial for the cycling performance.⁴⁶ Therefore, even though we categorize the coatings based their chemical compatibility with liquid and solid electrolyte, the materials may be effective in both conditions. It should be noted that in LiPF₆-based liquid electrolyte systems, besides fluorination of the coating layer from an HF attack, other organic species and Li₂CO₃ can also be found on the surface of the coated cathodes. We only consider the HF attack to broadly capture the chemical compatibility between coatings and LiPF₆-based liquid electrolytes in a high-throughput fashion. This round of screening returns 902 and 508 coating candidates that are chemically compatible with Li₃PS₄ and LiPF₆ based electrolytes, respectively.

Fig. 3 Distribution of the reaction energy ΔE_rxt with Li₃PS₄ (a) and HF (b) for each category that pass chemical stability with the cathodes descriptor. The horizontal dash lines represent the limits of the descriptors. The histograms in (a) and (b) illustrate the numbers of compounds for each category that pass the descriptors.

In this study, we are mainly interested in the Li-containing compounds, as lithiated compounds tend to exhibit a higher ionic conductivity.³⁰ Adding the Li-containing criterion, the entire screening procedure returns 89 and 51 Li-containing compounds that pass the proposed criteria for stability with respect to Li₃PS₄ solid state electrolyte and HF, respectively, with 36 compounds that are chemically compatible with both Li₃PS₄ and HF. In Fig. S2,† we summarize the numbers of Li-containing compounds for each category that pass the phase stability, electrochemical stability, and chemical stability descriptors. We find that oxides coatings, especially polyanionic oxides, account for the largest number of coatings for Li₃PS₄-based LIB, followed by fluorides and chlorides. On the other hand, the majority of coatings for LiPF₆-based LIB are fluorides and chlorides. The common coatings only consist of the fluorides and chlorides. In Table S3,† we list the calculated voltage windows, reduction and oxidation reactions, and reaction energies for the 104 Li-containing compounds that pass the screening criteria. In ESI,† we list the calculated material attributes of coating candidates.

Ion diffusion analysis

Our computational screening procedure has narrowed down the coatings of interest to 104 Li-containing compounds. Besides providing facile Li⁺ diffusion pathways, an optimal cathode coating should block O²⁻ diffusion such that the oxygen-loss-induced cathode surface reconstruction can be mitigated. Therefore, to evaluate Li⁺ and O²⁻ transport in the screened amorphous coatings, we calculate ionic diffusivity, flux, and transport time through the coating materials using ab initio molecular dynamics (AIMD) simulations and Onsager transport models, as described in Computational details. Due to the high computational cost of investigating the ionic diffusivity of all promising coating candidates, we select 9 representative compounds, consisting of polyanionc oxides Li₃B₁₁O₁₈, LiZr₂(PO₄)₃, Li₃PO₄, Li₂B₃PO₈ and LiB₃O₅, fluorides Li₃AlF₆, LiCaAlF₆, LiYF₄ and chloride Li₂ZnCl₄, and analyze their ion diffusion. Fig. 4 illustrates the distribution of D^Li_rt and D^O_rt in the selected compounds, along with 7 Li-containing compounds that are filtered out by electrochemical or chemical stability criterion: LiNbO₃, Li₂HfO₃, LiAlO₂, LiTaSiO₅, LiPO₃, LiAlSiO₄, and LiSb₃O₈, and 4 binary oxides: Li₂O, ZnO, Al₂O₃, Sb₂O₅. Our calculations show that in general, Li⁺ and O²⁻ diffusion is correlated, i.e., a compound with a higher D^Li_rt also has a higher D^O_rt. For example, the D^Li_rt and D^O_rt in Li₃PO₄ are 10⁻⁹ and 10⁻¹⁰ cm² s⁻¹, respectively, both of which are higher than those in LiAlSiO₄ (D^Li_rt = 10⁻¹⁴ cm² s⁻¹, D^O_rt = 10⁻²³ cm² s⁻¹). The correlation between Li⁺ and O²⁻ diffusion can be explained by ionic conduction mechanism in amorphous structures. Our previous study³⁰ showed that Li⁺ and O²⁻ diffusion consists of discrete vibrational and translational motions. During vibrational motions, Li⁺ is bonded to more O²⁻ ions than during translational motions, and its translation to another vibration site is activated by the Li–O bond breaking/formation process, which effectively explains the correlated transport between Li⁺ and O²⁻. In addition, we find that for compounds consisting of the same species, a compound with a higher Li⁺ concentration also has a higher Li⁺ and O²⁻ diffusion. For example, comparing Li₃B₁₁O₁₈ and LiB₃O₅, we find that LiB₃O₅, which has a higher Li⁺ concentration, exhibits a higher D^Li_rt and D^O_rt. Similar behavior is found in LiPO₃ and Li₃PO₄, relating to their D^Li_rt and D^O_rt. Our results are consistent with Xu et al.'s work in which they found that a higher Li⁺ solubility will enhance the Li⁺ transport across the coating.²⁴ In our work, we further demonstrate that, unfortunately, a higher Li⁺ concentration also correlates with increased, detrimental O²⁻ transport.

Fig. 4 Calculated room-temperature self-diffusion coefficients of Li⁺ (D^Li_rt) and O²⁻ (D^O_rt) in the selected compounds. The dash lines represent the approximated D^Li_rt and D^O_rt limits based on a coating thickness between 1 to 10 nm.

From the calculated D^Li_rt and D^O_rt, we evaluate the coating suitability of the selected compounds in terms of their ability to facilitate Li⁺ transport while blocking O²⁻ transport. Low Li⁺ diffusivity within the cathode coating layer can increase resistance and capacity loss at higher C-rates due to the resulting large overpotential at higher currents.⁴⁷ Thus, for the selected coating compounds, we estimate the overpotential, ΔV, at the cathode surface. We set the criterion for overpotential imposed by the coating as ΔV ≤ 0.1 V, above which the Li⁺ transport across the coating will be significantly compromised. In this study, we choose LiNiO₂ as the relevant cathode material, with density ρ = 4.78 g cm⁻³ and a theoretical capacity C = 274 mA h g⁻¹. Eqn (3) shows that a smaller ΔV can be realized by reducing the cathode particle size and coating thickness, and selecting a coating with high Li⁺ diffusivity D^Li_rt and concentration c^Li. By assuming a radius r = 1 μm LiNiO₂ primary particle and a 1C rate current density through the coating, the current density J is estimated to be 0.044 mA cm⁻². Finally, using D^Li_rt and the Li⁺ concentration of the compounds, we calculate the ΔV values across a 1 and 10 nm conformal coating, respectively. Fig. 5a shows that for 1 nm surface coatings, all the selected compounds, except Sb₂O₅ (23 V) and LiSb₃O₈ (0.18 V), result in overpotentials below 0.1 V, which indicates a sufficient Li⁺ transport in these compounds. The overpotential of the Al₂O₃ coating is found to be 0.07 V. When the coating thickness is increased to 10 nm, the overpotentials of Sb₂O₅, LiSb₃O₈ and Al₂O₃ coatings increase to 230 V, 1.8 V and 0.7 V, respectively, while the overpotentials of other compounds are still below 0.1 V. Using an r = 1 μm LiNiO₂ primary particle in a 1C rate current density, we estimate the minimum Li⁺ diffusivity D^Li_rt to meet the overpotential criterion of ΔV ≤ 0.1 V. By assuming a Li⁺ concentration c^Li = 10²² cm⁻³, we find that D^Li_rt = 7 × 10⁻¹⁶ cm² s⁻¹ and 7 × 10⁻¹⁵ cm² s⁻¹ for a 1 and 10 nm cathode coating, respectively, which are represented by the horizontal dashed lines in Fig. 4.

Fig. 5 (a) Calculated overpotentials (ΔV) for a current density of 0.044 mA cm⁻² across room temperature cathode coatings of l_c = 1 and 10 nm. The dashed line represents ΔV = 0.1 V. (b) Calculated O²⁻ diffusion time t in the selected compounds assuming an r = 1 μm primary particle and an l_s = 2 nm surface rocksalt phase. The dashed line represents t = 1 h.

To evaluate the effectiveness of these coatings in blocking O²⁻ transport, we estimate the O²⁻ flux J^O and the time t required for O²⁻ to diffuse through the coating. We assume the oxygen-loss-induced surface rocksalt layer mainly consists of NiO, which is densified from the layered NiO₂. As NiO₂ → NiO + 1/2O₂, we estimate t for surface NiO₂ layer to lose half of its oxygen and transform into an NiO layer. Let c^O_max denote the O²⁻ concentration in NiO₂ and V_s represent the shell volume of the surface NiO layer. , where l_s is the thickness of the surface NiO layer. Thus, the upper bound value of the number of O²⁻ ions removed from the cathode surface is N = 0.5V_sc^O_max and the O²⁻ diffusion time t can be expressed as:

where S_P = 4πr² is the cathode particle surface area. Combining eqn (14) and (15), t can be expressed as:

μ ^O_c can be estimated from the cathode densification reaction consistent with the phase diagram. At a high charge state, layered NiO₂ would densify to rocksalt NiO and spinel Ni₃O₄ with oxygen being released at μ^O_c = −4.95 eV, which is equal to the DFT-calculated total energy of an O₂ atom. μ^O_e can be estimated from two different conditions: (1) using the condition where the electrolyte reacts with O²⁻ and forms a new compound (Li₃PS₄ reacts with O²⁻ and forms Li₃PO₄ at μ^O_e = −8.39 eV) and (2) using the condition where O²⁻ loses electrons to the carbon network and forms O₂ (at room temperature and PO_² = 0.21 atm, μ^O_e = −5.24 eV). Thus, we estimate −8.39 ≤ μ^O_e ≤ −5.24 eV. Eqn (15) indicates that for a given cathode coating and a given size of LiNiO₂ primary particle, a longer O²⁻ diffusion time t can be realized by a smaller oxygen chemical potential gradient, i.e., higher l_c and μ^O_e. By assuming an r = 1 μm LiNiO₂ primary particle and an l_s = 2 nm surface NiO layer, we estimate the time t for O²⁻ ions to diffuse through the selected coatings (see Fig. 5b). We consider a range of conditions by varying l_c and μ^O_e, with l_c = 10 nm, μ^O_e = −5.24 eV corresponding to the slowest O²⁻ diffusion and l_c = 1 nm, μ^O_e = −8.39 eV corresponding to the fastest O²⁻ diffusion. Fig. 5b shows the calculated O²⁻ diffusion time t in the selected compounds. We select the compounds with an estimated O²⁻ diffusion time longer than 1 h such that not all O²⁻ ions that are evolved from surface NiO₂ layer have diffused through the coating under 1C rate. We find that LiSb₃O₈, LiAlSiO₄, Sb₂O₅, Al₂O₃, LiTaSiO₅, LiPO₃, Li₃B₁₁O₁₈, LiZr₂(PO₄)₃ and LiB₃O₅ exhibit an estimated O²⁻ diffusion time longer than 1 h. Next, we estimate the upper limit of O²⁻ diffusivity to have t ≥ 1 h. As mentioned earlier, we approximate L^OO_rt ≈ L^OO_rt,self. Using eqn (6), we can directly calculate L^OO_rt from self-diffusion coefficient D^O_rt:

Next, we use the same cathode particle configuration and assume an O²⁻ concentration c^O = 10²² cm⁻³ in a coating layer. We find that D^O_rt = 8 × 10⁻²⁰ cm² s⁻¹ for l_c = 1 nm, μ^O_e = −8.39 eV and D^O_rt = 1 × 10⁻¹⁷ cm² s⁻¹ for l_c = 10 nm, μ^O_e = −5.24 eV, which are represented by the vertical dashed lines in Fig. 4. Therefore, the green region in Fig. 4 represents the favorable Li⁺ and O²⁻ diffusivity window, and a compound falling on the top left area is more desirable in terms of facilitating Li⁺ transport while blocking O²⁻ transport. It should be noted that the effect of different cathode materials on ΔV and t is marginal (see Fig. S4†). Therefore, the calculated ΔV, t, and Li⁺ and O²⁻ diffusivity window are applicable for other cathodes, such as Ni-based NMC and LiCoO₂.

Five observations can be made from the high-throughput screening results and the estimated overpotential ΔV and O²⁻ diffusion time t:

(1) Among the nine Li-containing compounds that pass the computational screening, only Li₃B₁₁O₁₈, LiZr₂(PO₄)₃ and LiB₃O₅ have been found to exhibit both ΔV ≤ 0.1 V and t ≥ 1 h. However, the thickness of the considered coatings should be large enough (e.g. 10 nm) to improve their oxygen-retaining ability. Experimentally, Zhang et al. demonstrated that an amorphous Li₃B₁₁O₁₈ coating layer with a few nanometers thickness exhibits excellent chemical/electrochemical stability and can significantly improve the capacity retention of NMC cathodes.¹¹ However, the surface structure of NMC particles still evolved from a layered phase to a rocksalt phase after cycling. Our recent calculations showed facile O²⁻ transport in the amorphous Li₃B₁₁O₁₈ material, which leads to an oxygen-loss induced surface phase transition. In this work, we predict that a thicker Li₃B₁₁O₁₈ coating layer (e.g. 10 nm) is beneficial to mitigate the oxygen-loss induced surface densification and further improve the cycling performance of NMC cathodes. In addition, Wang et al. reported that amorphous LiZr₂(PO₄)₃ coated LiCoO₂ exhibits better capacity retention and rate performance than bare LiCoO₂.⁴⁸ The enhanced cycling performance was attributed to an enhanced Li-ion diffusion and a significantly mitigated chemical reactions between LiCoO₂ and sulfide-based solid electrolytes by the protective LiZr₂(PO₄)₃ coating layer, which agrees well with our ion diffusion and chemical stability analysis. However, based on our O²⁻ diffusion in amorphous LiZr₂(PO₄)₃ analysis, we expect that the 2 nm LiZr₂(PO₄)₃ coating used in their study is not thick enough to mitigate oxygen loss from LiCoO₂ surface and it's likely that the LiCoO₂ cathodes still suffer from oxygen-loss induced surface reconstruction at prolonged cycling and high charge.⁴⁹ Therefore, we predict that a thicker LiZr₂(PO₄)₃ coating (e.g. 10 nm) could further improve the cycling performance of LiCoO₂.

(2) Among the nine Li-containing compounds that do not pass the computational screening, LiPO₃, LiSb₃O₈, LiAlSiO₄ and LiTaSiO₅ can also be considered as promising cathode coatings mainly because of their exceptional oxygen retaining ability. LiPO₃ exhibits a high oxidation limit (4.9 V) and a reaction energy ΔE_rxt = −0.11 eV per atom with LiNiO₂ to form LiNiPO₄ and Li₃PO₄, therefore is screened out by our chemical stability criterion: ΔE_rxt ≥ −0.1 eV per atom. However, both LiNiPO₄ and Li₃PO₄ coatings have been reported to enhance the rate capability and cycle performance of cathode materials^50,51 and the chemical reaction may only happen at the interface of LiPO₃ and LiNiO₂ considering the sluggishness of solid state reactions. Experimentally, Chong et al.⁸ coated LiNi_0.5Mn_1.5O₄ (LNM) particles with a 1 nm thickness of amorphous LiPO₃ and found that the LiPO₃ coating can significantly reduce the cell impedance and facilitate Li⁺ ion transport, which is in good agreement with our calculations. LiSb₃O₈ also exhibits a high oxidation limit (5.0 V), but its predicted reduction limit (3.2 V) is higher than our reduction limit criterion: V_red ≤ 3 V. However, its lithiated compound LiSbO₃ is expected to exhibit a higher Li⁺ diffusion, which may offset its relatively high overpotential. In addition, LiSb₃O₈ reacts favorably with both HF and LiS₃PS₄, i.e. ΔE_rxt ≤ 0.1 eV per atom. We note that these chemical reactions may only happen at the coating/electrolyte interface and the reaction products could form a passivation layer to prevent further reactions. LiAlSiO₄ exhibits excellent oxygen retention, but its oxidation limit (|V_ox| = 3.9 V) is lower than our oxidation limit criterion: |V_ox| ≥ 4 V. However, LiAlSiO₄ decomposition involves the O₂ evolution reaction, which is likely to have sluggish kinetics.^52,53 Therefore, the overpotential of the LiAlSiO₄ decomposition reaction may increase its oxidation limit, i.e., |V_ox| ≥ 4 V. Experimentally, Deng et al.⁵⁴ cycled an amorphous LiAlSiO₄-coated LNM cathode with an electrochemical window from 3.5 to 4.9 V for 150 cycles and found improved capacity retention, lower Mn-dissolution and faster Li⁺ transport in LiAlSiO₄-coated LNM, compared to uncoated LNM. Our calculated Li⁺ diffusivity in LiAlSiO₄, 1.16 × 10⁻¹⁴ cm² s⁻¹, is also in good agreement with their reported value, 7.96 × 10⁻¹⁵ cm² s⁻¹. Therefore, despite its limitations, we include LiAlSiO₄ in the list of promising cathode coatings. Similarly, LiTaSiO₅ is another potentially effective cathode coating, despite its low oxidation limit (|V_ox| = 3.9 V).

(3) Fluoride and chloride materials exhibit exceptional electrochemical and chemical stability as well as low overpotentials due to their fast Li⁺ transport. However, our calculations also show that the fluoride and chloride coatings are O²⁻ transparent, which means that halide-coated cathode surfaces will be prone to oxygen loss and are likely to transform over time into a densified rocksalt phase.

(4) Although non-Li containing, Al₂O₃ can be considered as a promising cathode coating. We estimate that the diffusion time of oxygen in an Al₂O₃ coating varies between 2 to 227 h, depending on l_c and ∇μ^O (see Fig. 4). Thus, we predict that an NMC cathode coated with a thin Al₂O₃ coating layer, such as 1 nm, is still prone to surface oxygen loss, especially when cycled at low C-rate. This result could explain why a 3 nm Al₂O₃ surface coating is not sufficient to stabilize NMC cathode surface when cycled at C/7.¹⁸ On the other hand, a thicker Al₂O₃ coating layer can effectively mitigate O²⁻ transport, which results in a better cathode surface protection; David et al. showed that an Al₂O₃ ALD coating can effectively prevent surface reconstruction of NMC cathodes even after 760 cycles,⁵⁵ which indicates that a thick and conformal Al₂O₃ coating was applied on the NMC cathodes in their study.

(5) An optimal amorphous cathode coating should not only exhibit sufficient thermodynamic stability, electrochemical stability and chemical stability, but also a low O²⁻ diffusivity and a high Li⁺ diffusivity to achieve oxygen-retaining and surface-protective functions while avoiding significant losses in rate capability. However, the correlation between Li⁺ and O²⁻ diffusion in amorphous coatings highlights the inherent contradiction in identifying cathode coating materials with optimal Li⁺ transport as well as O²⁻ blocking ability. In general, Li⁺ diffusion in Li-containing compounds is fast enough to avoid a large overpotential. As a higher Li⁺ diffusion may compromise a coating's ability to block O²⁻ diffusion, for compounds with same chemistry, a compound with a lower Li⁺ concentration is thus preferred. For example, the Li⁺ concentrations in LiPO₃ and Li₃PO₄ are 20% and 37.5%, respectively. Fig. 4 shows that both LiPO₃ and Li₃PO₄ exhibit a facile Li⁺ diffusion, but LiPO₃ exhibits an improved oxygen retention as compared to Li₃PO₄. In addition, the oxidation limit of LiPO₃ (4.9 V) is higher than that of Li₃PO₄ (4.0 V).

Conclusions

In summary, we have carried out an extensive high-throughput computational study to develop materials design principles governing amorphous cathode coating selections for Li-ion battery applications. Our high-throughput screening includes descriptors to evaluate the thermodynamic stability, electrochemical stability, chemical reactivity with electrolytes and cathodes, and ionic diffusion in the cathode coatings. We consider reactivity with the commonly used Li₃PS₄ solid state electrolyte and with HF as a particularly detrimental representative of liquid electrolyte degradation. We find that polyanionic oxides account for the largest number of cathode coatings for Li₃PS₄-based LIB, followed by fluorides and chlorides. On the other hand, the majority of cathode coatings that are inert to chemical reactions with HF are fluorides and chlorides. Combing the screening results and ionic diffusion analysis of 20 selected compounds, we summarize the promising cathode coatings and general materials design principles:

(1) Li⁺ and O²⁻ diffusion are highly correlated, therefore, a higher Li⁺ transport promotes higher O²⁻ transport. In Li-containing compounds, the Li⁺ diffusion rate is generally fast enough to avoid a large overpotential. When selecting a cathode coating with same chemistry, a compound with a lower Li concentration is preferred, as it exhibits an improved oxygen retention as well as a higher oxidation limit.

(2) Mitigating O²⁻ diffusion is a formidable challenge when selecting an ideal cathode coating as most thin conformal coatings will transport oxygen under prolonged cycling and high voltage. Our results show that in addition to the four experimentally confirmed cathode coatings: Li₃B₁₁O₁₈, LiZr₂(PO₄)₃, LiPO₃ and LiAlSiO₄, we also identify three new promising cathode coatings: LiB₃O₅, LiSb₃O₈ and LiTaSiO₅.

(3) Based on our ionic diffusion analysis, we find that BO_x^y−, SiO_x^y−, PO_x^y− and SbO_x^y− anion groups tend to exhibit an improved oxygen retention. Therefore, we expect that compounds such as LiBa(B₃O₅)₃, LiAl(Si₂O₅)₂, LiTi₂(PO₄)₃, LiScP₂O₇, LiK(PO₃)₂, and LiCs(PO₃)₂ could also be potentially effective cathode coatings. On the other hand, F⁻ and Cl⁻ anion groups tend to exhibit faster Li⁺ and O²⁻ diffusion as compared to the oxides. Thus, they are not ideal for high-voltage cathode coatings where the driving force for oxygen loss is high. However, their inherent fast Li⁺ diffusivity may render them promising candidates as the solid-state electrolytes or lithium metal coatings.

(4) A non-Li-containing compound generally exhibits slower Li⁺ diffusion but better oxygen retention ability as compared to its lithiated counterpart. We mainly consider Li-containing compounds in this study, however, we expect that effective cathode coatings can also be found in non-lithiated compounds, such as Al₂O₃. Based on our identified anion groups above, we expect that compounds, such as ScBO₃, HfSiO₄, ZrP₂O₇ and AlPO₄, could be potentially effective cathode coatings. A follow-up study on non-Li-containing coatings will be presented in a later report.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors thank Dr. Gerbrand Ceder and Dr. Muratahan Aykol for useful discussions. This work was intellectually led by the Battery Materials Research (BMR) program under the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy, Contract DEAC02-05CH11231. This research used resources of the National Energy Research Scientific Computing Center (NERSC).

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Footnote

† Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2ta06051e

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