Intercalation Hosts for Multivalent‐Ion Batteries

Among intercalation, alloying, and conversion battery chemistries, the intercalation chemistry is most widely used in commercial applications due to its superior reversibility, round trip efficiency, and stability, albeit at the expense of reduced specific capacity. While intercalation hosts for monovalent ions (e.g., lithium and sodium) are well developed, the jury is still out on the best available intercalation host materials for multivalent ions such as magnesium, zinc, calcium, and aluminum. In multivalent systems, it is challenging to find electrode materials that can act as a durable host, and accommodate large number of ions, while also permitting fast diffusion kinetics. In this perspective, the electrochemical performance of five distinct class of materials (prussian blue analogues, sodium super ionic conductors, organic, layered, and open‐tunnel oxides) for multivalent ion storage is evaluated. The analysis reveals that open‐tunnel oxides show noticeably superior performance in multivalent ion batteries. Herein, the underlying reasons for this are discussed and the case is made for an in‐depth machine‐learning‐driven “materials exploration effort” directed toward discovery of new open‐tunneled oxides that could lead to vastly superior multivalent ion batteries.

we have compared five broad classes of intercalation compounds (prussian blue analogues [PBA], sodium super ionic conductors [NASICON], organic, layered, and open-tunnel oxides) for multivalent ion insertion. Our study reveals that among these five classes of materials, layered oxides and particularly open-tunneled oxides show the greatest potential in multivalent-ion batteries. Our analysis has been limited to "known" open-tunneled oxide materials, which are limited. We therefore recommend that the battery community conduct an exhaustive materials exploration effort to find hitherto unknown open-tunnel oxides that might outperform existing (known) compounds. Given the vast possibilities that exist in terms of material compositions and stoichiometries, it is clear that this is a "needle-in-a-haystack" type problem, with experimental trial and error approaches unlikely to yield the optimal solution. We therefore make the case for machine-learning (ML)-and inverse-machine-learning (IML)-driven approaches to efficiently screen the parameter space and accelerate the materials discovery process. Forward ML predicts the properties of a given material but cannot generate new crystal structures satisfying the material property criteria. By contrast, IML can create new crystal structures which meets our desired properties criteria. Therefore, one must first train an IML algorithm to create various possible structures. Subsequently, all the newly developed systems must undergo a material property screening check with forward ML. In this way, coupling inverse and forward ML is necessary to enable materials discovery. We hope that this perspective will assist the battery community in accelerating the discovery and deployment of superior intercalation hosts for future multivalent-ion batteries.

Intercalation Materials for Multivalent-Ion Insertion
Alloying and conversion chemistries are not being considered here, and in this perspective, we focus the discussion on the intercalation chemistry. Based on the literature, we have analyzed and compared five different classes of compounds as candidate materials for multivalent ion storage. The electrochemical performance of these compounds has been observed to be relatively stable (Table 1) for Zn-, Mg-, Ca-, and Al-ion batteries. These compounds are PBA, NASICON, organic materials, layered oxides, and open-tunnel oxides. Rather than studying the entire family of layered materials, we have chosen to focus on layered oxides since they are stable intercalation hosts and show good performance for a variety of multivalent ion species. Each of the aforementioned compounds exhibits unique characteristics and these are briefly discussed later.
PBAs are porous materials with cage-like structure ( Figure 2a). The general formula for such compounds is A x [B(CN) 6 ] y .H 2 O. Here, A and B are transition metal ions and H 2 O molecules are observed because of interstitial water introduced during the synthesis process. Metal ions A and B are coordinated to six nitrogen and six carbon atoms respectively, forming big cubical voids in the structure. [12] Such large voids can accommodate big and/or densely charged multivalent ions. PBAs tend to have high cyclic stability and high insertion potential. The major drawback of this class of compound is low specific capacity.
NASICON is a class of compounds known for its unique structure and faster ion insertion (Figure 2b). The general formula is AMM'(PO 4 ) 3 , where A is for alkali ion sites, M is for trivalent transition metal ion and M' is for tetravalent transition metal ion. One of the most common NASICON materials is Na 3 V 2 (PO 4 ) 3 , and in almost all synthesis processes, a thin carbon coating is introduced for enhancing cyclic stability. The structure consists of corner-shared VO 6 octahedra and PO 4 tetrahedra and it consists of 6b and 18e alkali metal sites. [13] During electrochemical cycling, ions located at 6b sites remain immobilized and maintain the skeleton of the compound, whereas ions at 18e sites get extracted providing open spaces for subsequent insertion of multivalent ions. [13] These compounds exhibit outstanding cyclic stability and high insertion potential. To further escalate the insertion potential, these compounds are fluorinated in which one of the PO 4 unit is substituted by three fluorine atoms. One of the demerits of these compounds is low specific capacity, as well as the need for high temperature and inert environment during material synthesis. Challenges associated with multivalent-ion batteries. a) Effect of charge density. Ions are solvated in the electrolyte and higher charge density ions tend to form a bigger solvation sheath, which is detrimental for ionic conductivity and desolvation. Such ions are difficult to intercalate due to their relatively large solvation sheath size. b) Lack of facile pathways for ion diffusion. Electrostatic interaction between multivalent ions and the ions that are present in the intercalation host leads to slow diffusion kinetics and poor rate capability. The ReO 3 structure [68] Reproduced with permission. Data retrieved from the Materials Project for ReO 3 (mp-190) from database version v2021.11.10. c) Structural degradation during ion insertion. Incoming ions impart volume expansion, and the electrode material tends to degrade (stress-induced fracture) during this process. .03 V at 10 mA g À1 75 mAh g À1 at 50 mA g À1 0.02% 500 cycles 43.6 mAh g À1 at 500 mA g À1 [98] www.advancedsciencenews.com www.small-structures.com Small Struct. 2023, 4, 2200290 Another material system that shows significant promise in multivalent ion batteries are organic compounds (Figure 2c). Frequently employed organic materials in electrochemical systems are conductive polymers. These compounds have a conjugated system to stabilize the charges. [14] Polyaniline, polypyrrole, and polythiophene are the most exploited compounds in this category. These compounds have functional groups that can undergo oxidation (p doped) and reduction (n doped) reactions. Low cost and high-rate capability are advantages of these materials. On the flip side, these compounds tend to have low cyclic stability because of slow dissolution in the liquid electrolyte. Relatively low volumetric capacity is another disadvantage associated with this class of compounds. Recent work has shown that certain organic crystals exhibit synergistic effect of conjugation and intercalation and demonstrate higher specific capacity and better cyclic stability. However, capacitive charge storage still tends to provide a larger overall contribution than ion intercalation, which limits their gravimetric and volumetric capacity. [15] A promising class of compounds for multivalent ion insertion are layered oxides (Figure 2 d). These materials consist of transition metal octahedra covalently bonded in 2D planes and neighboring planes are bridged using van der Waals interactions. By carefully tuning the interplanar spacing, bigger ions including multivalent ions can be accommodated. These compounds are generally vanadium based. Vanadium being a light transitional metal and offering variable oxidation states, is well suited for multivalent ion insertion. [16] Vanadium reduction occurs at high potential; hence, these compounds also show high insertion voltage. Birnessite MnO 2 is another layered oxide that has been frequently utilized for multivalent ion storage. [17,18] Bigger   ions/molecules such as K þ , NH 4 þ , and H 2 O are typically introduced into layered oxides to increase their interplanar spacing and hence facilitate facile multivalent ion insertion. These compounds show high-rate performance and relatively high specific capacity. However, the synthesis process for such compounds can be non-economical and may not easily lend itself to largescale production.
Open-tunneled compounds are typically oxides that contain large 1D tunnels for charge storage (Figure 2e). These compounds are generally manganese based (viz. α-MnO 2 and λ-MnO 2 ). [19][20][21] Recent work has shown that open-tunnels are also ubiquitous in certain complex oxide materials [22] such as molybdenum vanadium oxides (Mo 3 VO x ) that exhibit pentagonal-, hexagonal-, and heptagonal-shaped tunnels. [22][23][24] Such open tunnels with large pores enable facile diffusion of multivalent ions. Especially, in an aqueous battery, ions along with its solvation sheath can get inserted. The solvated ions shield the ionic charge which minimizes coulombic interaction and hence allows faster diffusion in the host. [23] It should be emphasized that "pore size" is paramount when it comes to multivalent ion systems. Crystal structures with trigonal, tetragonal, or pentagonal tunnels are usually not large enough. This is the reason why niobium tungsten oxides (Nb 16 W 5 O 55 and Nb 18 W 16 O 93 ) [4] allow Li þ intercalation but cannot intercalate multivalent ions such as Mg 2þ or Ca 2þ . Similarly, our group has shown [23] that in Ca-ion batteries, Mo 3 VO x containing hexa-and heptagonal tunnels delivered %213% more specific capacity (after 100 charge/discharge steps) than its allotrope containing trigonal-, tetragonal-, and pentagonal-shaped tunnels. To achieve significant capacity, hexagonal or bigger pores are suggested for multivalent ions. In addition to large pores, structural subunits within the unit cell need to be edge-or corner-shared (Figure 2e) to prevent undesirable phase changes and maintain mechanical stability. So far, only a small set of open-tunnel oxides with large pore tunnels and edge/corner sharing have been discovered, [22][23][24][25][26][27][28] and synthesis processes to produce such materials are not well developed.

Performance Comparison
We used the Ragone plot format (power density vs energy density) to compare the electrochemical performance of the aforementioned materials. Data is plotted for Zn-ion (Figure 3a), Mg-ion (Figure 3b), Ca-ion (Figure 3c), as well as Al-ion (Figure 3d) batteries. This data has been derived from the information listed in Table 1 (taken from Refs When considering power density, organic materials displayed the best overall performance. The power densities of layered oxides and open-tunneled materials are comparable to organic compounds in case of Zn-ion and Mg-ion batteries but fell short of organics for Ca-ion and Al-ion batteries. PBAs showed intermediate levels of power density. NASICON structures, in general, were poor performing from a power density perspective for all types of multivalent ions. It should be noted that capacitive storage tends to dominate over intercalation for organics, which explains why their power densities are outstanding, but energy densities are lower than layered and open-tunnel oxides. When considering overall battery performance (i.e., both energy and power density), layered and especially "open-tunneled oxides" showed the best overall performance in multivalent-ion batteries with electrode-level energy densities in the range of 300-500 Wh Kg À1 , while maintaining an electrode-level power density of %100 W Kg À1 . Open-tunneled oxides with large pores can accommodate multivalent ions despite their relatively large sizes and high charge densities. Further, the prevalence of large (open) tunnels in these particles provides highways for relatively fast multivalent-ion diffusion. The prevalence of tunnels with robust edge-shared or corner-shared subunits also provides internal buffer space for volume expansion, which mitigates stress-induced fracture or phase changes during ion intercalation, leading to relatively stable cycling performance. For a combination of the aforementioned reasons, open-tunneled oxides exhibit superior electrochemical performance for multivalent-ion storage.

Materials Exploration Effort: The Discovery of New Open-Tunnel Oxides
Given the promise of open-tunneled structures for multivalention batteries, there is a need to systematically search the available design space for new open-tunneled oxide material compositions and stoichiometries. Open-tunnel oxides are typically synthesized using the polyoxometalate (POM) chemistry. POMs are large building blocks which are present in ionic form. By tweaking reaction conditions (viz. pH, temperature, pressure), a variety of open channel crystal structures can be engineered. [25][26][27] POM chemistry is a vast field with diverse possibilities of elements and compositions. Further, not all open-tunnel structures are meaningful for multivalent-ion insertion. For example, niobium tungsten oxides (such as Nb 16 W 5 O 55 and Nb 18 W 16 O 93 ) contain pentagonal, tetragonal, and triangular tunnels (Figure 4a,b). These tunnels allow Li-ion intercalation but are unable to act as efficient conduits for larger multivalent ions. In general, Figure 3. Ragone plot of multivalent-ion batteries comparing candidate materials. a) Zn-ion, b) Mg-ion, c) Ca-ion and d) Al-ion batteries. Only best performing materials from the class of compounds in Figure 2 were chosen. Data plotted for energy and power density is at the electrode level. Table 1 provides detailed information based on which the energy and power density was calculated. open-tunnels with hexagonal, heptagonal, or even larger voids and edge-/corner-shared subunits (as observed in Mo 3 VO x - Figure 4c,d) are needed for effective intercalation of multivalent ions. [23]

Needle in a Haystack Problem
Known open-tunnel oxides with the correct pore sizes to accommodate multivalent ions are very limited. Therefore, an exhaustive materials exploration effort to discover new compounds is essential. In this context, there are numerous possibilities including ternary, quaternary, quinary, and even senary-based transition metal oxides (TMOs). Experimental exploration of the entire TMO family is a challenging task. For example, let us consider the ternary TMO crystal structure, having the formula A n B m O l (n, m, l are integer numbers denoting stoichiometry). Here, A could be any element in the periodic where X and Y could be any metal in the periodic table excluding rare gases and the subscripts are integers denoting stoichiometry. The experimental investigation of all these possibilities is impractical considering time and cost. A priori, we also do not know whether a potential TMO structure is stable or not. Therefore, one must first determine structural stability that ensures their synthesizability. Then, among the stable (synthesizable) structures, one must select those with sufficient conductivity and suitable pore/tunnel structures for multivalent-ion intercalation. Therefore, finding the best candidate among millions of possibilities is indeed a "Needle in a Haystack" problem.

Limitations of Density-Functional Theory, Molecular Dynamics, and Continuum Approaches
The density-functional theory (DFT)-computed energy hull diagram can predict structural stability of materials. [29,30] This involves establishing the formation energy of the desired composition for all the possible stoichiometry ratios by DFT (structures with the lowest formation energy are the most stable). However, DFT-based study of TMOs is computationally expensive due to their complex crystal structures with large unit cells. [31][32][33] Furthermore, solving the aforementioned "Needle in a Haystack" problem by DFT is painstaking because of the many possible intercalation sites for multivalent ions and the possibility of cation disorder. [34,35] Another approach is molecular modeling by solving Newtonian Equations (i.e., the molecular dynamics [MD] method). However, this requires the interatomic potential to calculate the potential energy of a system, given atomic positions in space. Interatomic potentials are widely used as the physical basis of MD simulations to predict and explain material properties. However, this is problematic, since suitable potentials for most oxide materials are unavailable or very limited. [36] Moreover, developing the interatomic potentials depends on DFT-computed data. However, the DFT method itself has limitations, as described before. Furthermore, in general, formation energy prediction by MD is less accurate, as compared to DFT. Therefore, exploring all possible combinations of the TMO crystal structure is unachievable by the MD approach.
There are many continuum approaches for modeling battery electrodes, including phase field, and finite element. [37,38] However, oxide-based materials have an internal porous structure that the continuum approximation cannot capture adequately. Moreover, continuum modeling cannot accurately determine crucial properties such as the formation energy. In summary, conventional approaches (viz. DFT, MD, and continuum modeling) are either infeasible or impractical to solve the "Needle in a Haystack" type problem described in this perspective.

ML and IML Approaches
Various deep learning-based ML algorithms [39][40][41][42] can predict the formation energy and bandgap, as well as establish structureproperty relationships with reduced computational cost. The ML approach can predict stability of an unknown structure by estimating Energy Above Hull (eV atom À1 ) denoted by ΔE hull . In general, when ΔE hull ≤ 40 meV atom À1 , the structure can be synthesized experimentally as it lies in the stable phase range. [43] The stable TMOs must also be electronically and ionically conductive. ML models can be trained with DFT-computed and experimentally available data on conductivity. The trained ML model can be used to screen out those TMOs that lack sufficient conductivity. Another key property is the Packing Fraction (PF), which provides insight into the "porosity" inside the structure. PF is a unitless parameter and it is the ratio of the total crystal atomic volume to the unit cell volume. ML-based models have been successfully used to predict PF, [44,45] and this can help to identify TMOs with the correct pore structure for multivalention storage.
ML approaches are well suited to efficiently screen the available parameter space. First, using input features (derived from known databases such as the Materials Project [MP], [46] Open Quantum Materials Database, [47] AFLOW-lib, [48] and Inorganic Crystal Structure and Database (ICSD) [49] ), different models can be trained simultaneously-with respect to ΔE hull , conductivity, and PF. After training, the model can predict the aforementioned Energy Above Hull for any unknown material. If the structure passes the stability condition, then the ML model can predict the material's conductivity, PF, and pore structure. ML predictions for the most promising TMO structures can then be verified by DFT calculations prior to embarking on experimental synthesis.
The performance of any ML model depends on atomic representations of material structure, called "descriptors". Descriptors help to describe both the local and global atomic environments of any material compound. [50,51] Various descriptors such as Sine Coulomb Matrix (SCM), [52] Orbital Field Matrix (OFM), [53] Coulomb Matrix, [54] Atom-centered Symmetry Functions, [41] and Smooth Overlap of Atomic Positions [55] have been established to replicate structure-property relationships. Recently, compound (or hybrid) descriptors have been applied to improve the accuracy of ML models. [56,57] As a starting point, we suggest that a state-of-the-art deep-learning algorithm, such as convolutional neural network (CNN) [58][59][60][61] with hybrid descriptors, should be explored for predicting the properties of TMO materials.
The aforementioned ML approach predicts properties for a given material structure. By the same token, IML, in Figure 4. Typical open-tunneled oxide structures and proposed machine-learning-based approach for materials discovery. a) Crystal structure of Nb 16 W 5 O 55 , composed of blocks (red rectangles) of 4 Â 5 (Nb,W)O 6 octahedra connected at corners (the parallelogram with black lines indicates the unit cell). Channels with tetragonal pores are evident in the crystal structure. Reproduced with permission. [2] Copyright 2022, Springer Nature Limited. b) Crystal structure of Nb 18 W 16 O 93 consisting of tetragonal tungsten bronze (blue) with pentagonal tunnels (grey) partially filled by -W-O chains (the rectangle with black lines indicates the unit cell). Reproduced with permission. [2] Copyright 2022, Springer Nature Limited. Presence of channels with trigonal, tetragonal, and pentagonal pores is evident in the material. Crystal structure of c) orthorhombic and d) trigonal polymorphs of Mo 3 VO x containing channels with large hexagonal-and heptagonal-shaped pores. Reproduced under the terms of CC-BY license. [23] Copyright 2022, the Author(s). Published by PNAS. Rectangle with black lines in c) and parallelogram with black lines in d) indicates the unit cell. e) Overview of a possible machine-learning approach for discovery of new open-tunnel oxide materials. The inverse machine-learning model generates feasible test structures using a Generative Adversarial Network (GAN) architecture. Test structures generated by the GAN are screened for desired characteristics by a traditional forward machine-learning model. www.advancedsciencenews.com www.small-structures.com combination with ML, can be used to predict materials for given properties. For example, imagine that we are searching for materials with a certain porosity, tunnel structure, formation energy, and conductivity. Given these desired target properties, can a model predict new potential materials with these properties? IML is still at the nascent stage but has already shown immense potential for discovering new materials. [62][63][64] One of the most promising inverse design algorithms that can generate new promising crystal structures is Generative Adversarial Network (GAN). [65] Figure 4e shows conceptually how GAN could be combined with forward ML for discovering new TMO battery materials. GAN is divided into two partsgenerator and discriminator. The generator creates test material structures from the random gaussian noise in latent space and feeds these test structures to the discriminator. The discriminator, a multilayer neural-network-based classification algorithm, gets trained with both real structures from the material database and test structures from the generator. The discriminator identifies whether the generated test structure is close to a realistic (i.e., feasible) structure by calculating structural dissimilarity, also called loss function (L f ). If the loss function is close to zero, the generated structure is considered for further calculations. The generator also tries to improve the newly generated structure, based on the loss function from the discriminator report (feedback loop in Figure 4e). To apply this proposed GAN approach, first, the model can be trained for a specific material composition by collecting data from known databases (e.g., MP). [46] Data augmentation techniques [66] can also be applied to generate more training data from MP, if needed. Following this approach, Kim et al. [65] have generated 23 new promising crystal structures based on the Mg-Mn-O composition, wherein 14 of them were "not" previously available in the MP database. The IML-generated structures can be fed to the forward ML [67] model ( Figure 4e) for predicting desired properties. First, stability can be checked by predicting ΔE hull ≤ 40 meV atom À1 . The "stable" TMOs can be further checked for electronic and ionic conductivity. The next screening is PF calculations. One might consider 0.25 < PF < 0.75 as a desirable range. TMOs having excessive void space (i.e., PF > 0.75) may be mechanically weak and prone to failure. Moreover, two TMO structures can have the same PF but different pore sizes and shapes. The final stage would be to select TMOs that are stable, electronically and ionically conductive, and have the desired pore dimensions as well as a robust tunnel structure with edge/corner sharing. We believe that there are enormous opportunities in the emerging fields of ML and IML to address the "Needle in a Haystack" type problem described in this perspective.

Concluding Remarks
If multivalent-ion batteries are to become a reality, it is essential to develop high-performing intercalation hosts for multivalent ions such as Zn 2þ , Ca 2þ , Mg 2þ , and Al 3þ . This is challenging for four reasons: 1) multivalent ions are often larger in size than Li þ , which makes it difficult to insert and extract these ions from an intercalation host; 2) multivalent ions due to their larger charge density tend to form a bigger solvation sheath in a liquid electrolyte as compared to their monovalent counterparts. As a consequence, a larger de-solvation penalty must be incurred to enable multivalent-ion intercalation; 3) multivalent ions exhibit higher charge density than monovalent ions (such as Li þ ). Hence, they experience a greater degree of coulombic interaction with ions present in the intercalation host, which makes it difficult to intercalate and diffuse multivalent species; 4) The larger size and charge density of multivalent relative to monovalent ions result in significantly greater stress buildup in the intercalation host, which can result in electrode cracking and rapid capacity fade during battery cycling.
In this perspective, we have explored various candidate materials as intercalation hosts for multivalent-ion storage. Our survey indicates five possible material systems that can accommodate a variety of multivalent ions in a stable manner, namely, PBA, NASICON, organic, layered, and open-tunnel oxides. Among these, we find that open-tunnel oxides are highly promising for multivalent-ion batteries. These materials are endowed with large size pores to accommodate multivalent ions and minimize electrostatic interaction with the host. More importantly, the pores are in the form of open tunnels that provide a conduit for rapid multivalent-ion diffusion, which facilitates fast charging. In addition, the open tunnels also offer internal buffer space for expansion and contraction, which mitigates stress-induced fracture during battery operation. For these reasons, open-tunnel TMO structures exhibit superior electrochemical performance for multivalent-ion storage.
So far, we know of only a few open-tunnel TMOs [19][20][21][22][23][24] such as α-MnO 2 and Mo 3 VO x that are capable of multivalent-ion storage. That being said, we have likely only scratched the surface in terms of what is possible. The possibilities in terms of open tunnel TMOs are vast and include binary-, ternary-, quaternary-, quinary-, as well as senary-based TMOs. In fact, millions of different potential structures are possible, considering various permutations and combinations of elemental composition and stoichiometry. This represents the archetypical "Needle in a Haystack problem, which is not amenable to experiments or computationally demanding methods such as DFT or MD. We therefore encourage the battery materials community to explore emergent ML-and IML-based techniques to efficiently screen the available parameter space. The goal would be to discover new TMO structures that are stable, electronically and ionically conductive, and have the desired pore/tunnel structure for multivalent-ion storage. Note that we have not considered electrolyte design in this perspective. After discovery of the electrode material is completed, design of an electrolyte that is compatible with the electrode material by ML and IML techniques should also be pursued. The aforementioned efforts could lead to high-performing multivalent-ion batteries based on abundant and low-cost elements (e.g., calcium, magnesium, and aluminum) that are more affordable and sustainable than today's lithium-ion technology.