Impact of Intermediate Sites on Bulk Diffusion Barriers: Mg Intercalation in Mg$_2$Mo$_3$O$_8$

The ongoing search for high voltage positive electrode materials for Mg batteries has been primarily hampered by poor Mg mobility in bulk oxide frameworks. Motivated by the presence of Mo$_3$ clusters that can facilitate charge redistribution and the presence of Mg in a non-preferred (tetrahedral) coordination environment, we have investigated the Mg (de)intercalation behavior in layered-Mg$_2$Mo$_3$O$_8$, a potential positive electrode. While no electrochemical activity is observed, chemical demagnesiation of Mg$_2$Mo$_3$O$_8$ is successful but leads to amorphization. Subsequent first-principles calculations predict a strong thermodynamic driving force for structure decomposition at low Mg concentrations and high activation barriers for bulk Mg diffusion, in agreement with experimental observations. Further analysis of the Mg diffusion pathway reveals an O--Mg--O dumbbell intermediate site that creates a high Mg$^{2+}$ migration barrier, indicating the influence of transition states on setting the magnitude of migration barriers.

Rechargeable Mg batteries have received interest as an energy storage system that potentially offers high energy density. The major advantage relies on the benets of Mg metal as the negative electrode, which, in addition to being inexpensive, abundant and safe in handling and storage, also provides high volumetric capacity (3833 mA h cm À3 ) and can be free of dendrite growth when operating in an electrochemical cell. [1][2][3] However, the development of corresponding positive electrode materials has been slow. 2 Since the discovery of the rst seminal functional Mg insertion positive electrodethe Chevrel phase (CP, Mo 6 S 8 ), 4 only recently have two other structures been shown to be suitable for Mg (de)intercalation in a full cell arrangement with a Mg anode, namely the spinel and layered titanium sulde. 5,6 The above materials take advantage of a "so" anionic framework that interacts weakly with the Mg 2+ and assists its mobility. In contrast, sluggish multivalent ion mobility is generally observed in oxide lattices. Nevertheless, oxides are still of great interest due to their potentially higher operating voltage. [7][8][9][10][11][12][13][14][15] Levi et al. have speculated that the presence of Mo 6 clusters in the CP structure is one of the key factors for facile Mg 2+ mobility by the promotion of charge redistribution. 8 The possibility that a similar principle may apply to oxides guided us to Mg 2 Mo 3 O 8 (Fig. 1a), which has Mo 3 clusters in the Mo 3 O 8 layers (Fig. 1b). 16,17 In this structure, Mg occupies both octahedral and tetrahedral sites between the layers. While octahedral Mg shares both edges and corners with MoO 6 octahedra (Fig. 1a), tetrahedral Mg shares corners with MoO 6 and MgO 6 octahedra. Since Mg is also present in a "non-preferred" tetrahedral coordination (Fig. 1a), 18 a Mg diffusion pathway with lower migration barriers is expected than when Mg is exclusively found in its preferred octahedral coordination, 9 such as in conventional layered oxides. In the case of layered oxides, the Mg diffusion pathways contain an intermediate tetrahedral site presumably with high energy relative to the stable octahedral site, leading to poor Mg mobility. 9 We note that the Li analogue (Li 4 Mo 3 O 8 ) has previously been examined in a Li cell, offering an initial specic capacity of 218 mA h g À1 . 19 Other materials with similar structures containing Mo 3 clusters, such as LiMoO 2 and Li 2 MoO 3 , also function well as Li-ion positive electrodes. [19][20][21] On the other hand, only limited work has been done on Mg intercalation in Mo-oxides, 12,22,23 motivating us to examine the Mg 2+ diffusion properties in Mg 2 Mo 3 O 8 and its potential to be a positive electrode material for Mg batteries. Mg 2 Mo 3 O 8 was obtained by solid-state synthesis (see the ESI †), which provided particles of a few micrometers in size (Fig. 2a). Its X-ray diffraction (XRD) pattern was indexed to the P6 3 mc space group characteristic of this material (Fig. 2b). In order to study the possibility of Mg removal from such a structure, chemical demagnesiation was carried out using NO 2 BF 4 , a commonly used oxidizing agent for chemical delithiation. 24 Mg 2 Mo 3 O 8 and NO 2 BF 4 were reacted in a 1 : 4 ratio, which would allow complete Mg de-intercalation if each NO 2 BF 4 sustained a one electron reduction as anticipated. Energy dispersive X-ray spectroscopy (EDX) reveals that the majority of the Mg was removed from the structure ( Table 1). The particles become smaller aer demagnesiation (Fig. 2c), suggesting some changes in the material. Despite these differences, the XRD results indicate no shi of the peaks (Fig. 2d). The atomic positions obtained by Rietveld renement 25 are almost the same as those of the pristine (Table S1 in the ESI †), suggesting that a two-phase reaction takes place, with the demagnesiated phase being amorphous. During this process, Mg is presumably rst removed from the outer shell, leading to the destabilization of the parent lattice and eventual amorphization. The amount of the amorphous phase in the demagnesiated product is estimated to be around 87 wt% using Si as an external standard (Fig. 2d, see ESI † for details), giving an overall composition of Mg 0.24 Mo 3 O 8 , which is similar to the cationic ratio determined by EDX (Table 1) S1b †), the XRD data suggest that part of Mg 2 Mo 3 O 8 undergoes complete demagnesiation and becomes amorphous with some fraction of material not participating in the reaction.
Since the degree of chemical oxidation was hard to control, we attempted to evaluate stepwise the demagnesiation behavior by an electrochemical method. As it has been suggested that the Mg desolvation process depends on the solvent, 26,27 and this is critical for the electrochemical mechanism at the positive electrode, 28 19 or at $2.6 V as predicted by rst principles calculations (Fig. S4, see the ESI † for details) could be expected. Both electrolytes offer a stable voltage window for this range; however, no electrochemical activity was observed in either system (Fig. S2 †). Such results potentially indicate the existence of a high Mg 2+ diffusion barrier in the structure, hence kinetics being the main limitation. Chemical oxidation, on the other hand, might involve a mechanism other than simple cation diffusion, such as a partial dissolution/re-precipitation process. This helps in lowering the kinetic barrier and establishes successful Mg removal.
In order to understand the amorphization upon chemical demagnesiation and rationalize the lack of electrochemical activity in Mg 2 Mo 3 O 8 , we carried out rst principles calculations to determine the energy above hull (E hull ) indicating the stability of the structure, and the activation barriers for Mg diffusion within the structure (methodological details of the calculations are provided in the ESI †).
The energy above the convex ground state hull (E hull ) of the Mg X Mo 3 O 8 structure, calculated with respect to the stable compounds in the Mg-Mo-O ternary phase diagram, can be used to evaluate the thermodynamic stability of the structure on demagnesiation. 13,15 Typically, a thermodynamically stable structure will have an E hull of 0 meV per atom, while more positive E hull values indicate a greater driving force to form other phases, which may be reected as a difficulty in synthesizing a compound, or as decomposition during (de) intercalation. Also, E hull values are evaluated at 0 K and entropic contributions can stabilize a structure at higher temperatures. The values listed in Table 2 have been determined from the available compounds in the Materials Project database. 31 The trends in Table 2 indicate an increasing E hull with increasing Mg removal from the Mg 2 Mo 3 O 8 structure, corresponding to an increase in the thermodynamic driving force for decomposition. The E hull values at lower Mg concentrations are very highconsistent with the experimentally observed amorphization during chemical Mg extraction from Mg 2 Mo 3 O 8 (Fig. 2) and the naturally amorphous occurrence of Mo 3 O 8 . 32,33 To evaluate Mg mobility in the Mg 2 Mo 3 O 8 structure, the possible Mg diffusion hops within the structure were determined. Being a layered structure, Mg 2 Mo 3 O 8 can be visualized on a 2D-plane, as shown in Fig. 3, with octahedral Mo, tetrahedral Mg and octahedral Mg indicated by purple, green and orange triangles, respectively. The four possible Mg/Mg hops that can occur in the structure are illustrated by the black circle and arrows in Fig. 3. Three hops (black arrows) occur in the same Mg-plane and the fourth hop (black circle) moves Mg across a Mo-plane. The shortest hops (type 1 and 2) span $3.38 A and $4.33Å, respectively, and involve Mg migration from a tetrahedral site to an octahedral site (or vice versa), while hops 3 and 4 are $5.76Å in distance and involve Mg jumps between similarly coordinated sites (oct / oct or tet / tet). Although hops 3 and 4 are direct between octahedral or tetrahedral Mg sites, they are likely to be constituted by two consecutive hops of type 1 (i.e. an oct / tet hop followed by a tet / oct hop and vice versa). Alternate routes for hops 3 and 4 are not possible due to intermediate Mg tetrahedral sites, which will face-share with MoO 6 octahedra and experience strong electrostatic repulsions as a result. Hence, hops 1 and 2 are the relevant Mg migration pathways that need to be considered in calculations. Fig. 4a displays the calculated Mg migration barriers (at x Mg $ 2 with a dilute vacancy limit) along the hop 1 (black) and 2 (red) pathways, with the respective hop distances normalized on the xaxis. Both hops begin at a tetrahedral Mg and terminate at an octahedral Mg, explaining the difference in energy between the end points ($250 meV). Notably, Mg mobility along both hops 1 and 2 is expected to be poor, given the large migration barriers ($1200 meV and $2000 meV for hops 1 and 2, respectively), compared to the 525-650 meV required for bulk Mg mobility at reasonable rates. 9 The high migration barriers also explain the lack of electrochemical activity observed. Nevertheless, if any Mg migration is observed in the structure, the Mg 2+ ions are likely to diffuse along the in-plane hop 1 pathway.
While the high barrier for hop 2 is due to the strong electrostatic repulsion Mg experiences from Mo atoms as it passes   Fig. S5 †). Notably, scenarios involving a Mg 2+ ion diffusing through an intermediate (tetrahedral) site that face-shares with a transition metal polyhedron lead to high migration barriers in oxides (e.g., high Mg barriers in layered NiO 2 (ref. 9)), while analogous trends have been observed for Li-diffusion in disordered rock-salt structures. 34 Thus, the high Mg migration barrier in Mg 2 Mo 3 O 8 can be attributed to the intermediate O-Mg-O dumbbell conguration, which occurs in the absence of alternate low energy pathways. This indicates the importance of intermediate sites along a diffusion path, determined by the specic topology of cation sites in an anion lattice, in addition to the occurrence of the mobile cation with a non-preferred coordination and a preferentially coordinated metastable site. 9 One of the challenges towards the development of high energy density secondary Mg batteries is the design of an ideal positive electrode, which can reversibly intercalate Mg at a high voltage with high capacities at reasonable rates. The Mg 2 Mo 3 O 8 structure used in this study was primarily motivated by the presence of Mo 3 clusters (similar to the Mo 6 clusters in the Chevrel-positive electrodes) and the occurrence of Mg in a nonpreferred tetrahedral coordination (satisfying one of the design rules known in the literature 9 ). While Mg could be chemically extracted from the structure, albeit with signicant amorphization, no electrochemical activity was observed. Further analysis using rst-principles calculations revealed high E hull values (structural instability) at a low Mg content and high Mg migration barriers (poor bulk Mg mobility in the structure), explaining the aforementioned experimental observations. The high activation barrier for Mg diffusion in Mg 2 Mo 3 O 8 arises from the O-Mg-O dumbbell hop, reecting the impact of intermediate sites along a diffusion pathway besides cation coordination preferences. Thus, in the search for high Mgmobility oxide positive electrodes, a careful analysis of the diffusion pathway and the topology of cation sites is advantageoussuch as identifying low-energy intermediate sitesin addition to the requirement of Mg being found in a nonpreferred coordination environment. 9 Such understanding of Mg diffusion pathways will help to nd suitable positive electrodes for multivalent batteries.