Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme

Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. These structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.

In comparison with the Li compounds, much less experimental work was carried out to investigate the orthosilicates as Na host matrix. The chemical similarities between Na and Li imply that exploration of the sodium equivalent offer more opportunities to advance energy storage technology through rechargeable batteries, owing to the even lower cost and ubiquitous availability of Na. Recently [20], Na2MnSiO4 was synthesized and investigated for use as a positive electrode material for Na secondary batteries. A reversible capacity of 125 mAh/g was found compared with the theoretical capacity of 278 mAh/g based on the two electron reaction. 2 The discrepancy between measured and calculated capacities has been attributed to the instability of the crystal structures upon delithiation/desodiation [3,12,13,20]. In order to circumvent the capacity fading and further improve the electrochemical properties, it is essential to understand their crystal structures and explore other possible polymorphs that may be stable in the delithiated/desodiated state. A2MSiO4 structures are generated from tetrahedral networks, where A = Li or Na; M = Mn, Fe or Co. For a given tetrahedral network, once one of its sites (e.g. the center of the tetrahedron) is assigned to oxygen, its four neighbors are randomly assigned to two A atoms, one M atom and one Si atom. Then, neighbors of A, M and Si are only assigned to oxygen atoms. In such an iterative manner, the occupations of all sites are determined. The oxygen-centered tetrahedron is shown by red, transparent planes. 3 Experimental data indicate that the crystal structures of the orthosilicate compounds A2MSiO4 (A = Li, Na; M = Mn, Fe, Co) belong to a family of tetrahedral structures that exhibit a rich polymorphism [21,22]. Polymorphs of these tetrahedral structures were classified into low-and high-temperature forms, which differ in the distribution of cations within tetrahedral sites of a hexagonal close-packed (hcp) based arrangement of oxygen. Five different structures were observed and studied for Li2FeSiO4 [1,4,5,[14][15][16], three as-synthesized (two are orthorhombic, Pmnb and Pmn21; one is monoclinic, P21/n) and two cycled phases (Pmn21-cycled and P21/n-cycled). Likewise, multiple phases have been reported for Li2MnSiO4 (Pmn21 [2], Pn [12], P21/n [17] and Pmnb [9]) and Li2CoSiO4 (Pnb21 [18], Pmn21 [11,18], and P21/n [18]). The recent work of Na2MnSiO4 [20] showed that Na2MnSiO4 has a monoclinic structure with space group Pn.
In the above reported structures of A2MSiO4, all the atoms form tetrahedral units, i.e. every atom is in the center of a tetrahedron and has a coordination number of 4. Taking advantage of this structural feature, we used a fast motif-network scheme based on genetic algorithm (GA) [23] to explore the complex crystal structures of these materials. Our results provide a more comprehensive tetrahedral structure database to assist future effort on the study of delithiation/desodiation process. 4 Although systematic enumerations of 4-connected crystalline networks have been applied to zeolites and other silicates [24][25][26], considering the great effort of selecting energetically preferable structures out of millions of possible configurations owing to the lack of decent classical potentials for A2MSiO4, here we took a different route to obtain tetrahedral networks from the low-energy crystal structures of silicon. Silicon is well known to have rich phases and forms sp3-hybridized framework structures [27]. We used GA and Tersoff potential [28] to search for silicon structures that form tetrahedral networks. Once such a silicon structure was located, all the sites were re-assigned to A (Li or Na), M (Mn, Fe or Co), Si and O atoms in the ratio of 2:1:1:4. During the substitution, only structures where every oxygen atom bonds with two A atoms, one M atom and one Si atom, as illustrated in Fig. 1, were accepted. This is because of the observation that structures with uniformly distributed A, M and Si atoms have noticeably lower energies. Newly generated structures that had not been visited were collected for further refinement by first-principles calculations. In this way, various A2MSiO4 structures were obtained. More details on the first-principles calculations can be found in the methods section.
Generation of the tetrahedral networks costs very little time due to the usage of classical potentials during the GA searches. In this work, up to 48 atoms in the unit cell were searched for Si to find tetrahedral networks, i.e. up to 6 formula units were considered for A2MSiO4. In order to obtain as many tetrahedral networks as possible, energies of the silicon structures that satisfy the 5 coordination constraints (every atom in the structure has a coordination number of 4) were lowered by a pre-set amount to increase their chance of survival.

Structures with 3D M-Si-O framework
In the first type (referred to as "Structure with 3D M-Si-O framework" from now   The structures plotted in Fig. 3g and 3h look distinct from the others, but the M and Si atoms share the same local tetrahedral environment. Although less favored in energy than the structures plotted in Fig. 3a-3f, the differences are very small. For instance, for Na2FeSiO4, the energies of the structures in Fig. 3g and 3h are about 0.11 and 0.12 eV/f.u. higher than the ground state structure, respectively.   Table 1. Lowest-energy structures of A2MSiO4 in three different types obtained in current study. r represents the atomic radius; E is the total energy in eV/f.u.; V is the volume of the structure in Å 3 /f.u.; a, b, and c are the lattice parameters in Å.
The corresponding figure of each structure is listed in the "plot" row.
Li2MnSiO4 Li2FeSiO4 Li2CoSiO4 Na2MnSiO4 Na2FeSiO4 Na2CoSiO4 r(A)/r(M)     for Na-systems). In Fig. 2b, we plotted the relative energies of the most stable structures with 3D, 2D and 1D M-Si-O framework for each system, from which the stabilities of each type can be compared. The preference of different structure types for different systems will be discussed next.

Structure preference and analysis
In   In Fig. 6d, we plotted the local environment of the alkali metal atoms and also the connections between the cation-centered tetrahedra for all the structures in Fig.   2a. To determine whether an oxygen atom is counted as a nearest neighbor of the cation atom, we first sorted all the cation's neighbors according to distance 15 and allowed 10% of increase in the bond length relative to the average of those which have been counted. The results show that for most Li2MSiO4 structures, the Li atoms bond with 4 oxygen atoms; while for Na2MSiO4, Na atoms in some structures have different coordination numbers. As shown in Fig. 6d, Na atoms can have coordination numbers of 3 or 5. What can be expected for the Na systems?
Since the Na-intercalation chemistry of the Na-based systems has been considerably less explored, there may be opportunity to find novel electrode materials for sodium-ion battery [30]. Experimental studies on the orthosilicates as Na host matrix have just begun.
In this work, we found that Na systems prefer structures with 3D M-Si-O framework and have relatively low symmetries. As shown in table 1, the lowestenergy structure for all the Na systems has space group Pn and similar lattice parameters. The Pn structure, which is plotted as Fig. 3a, has been reported for Na2MnSiO4 experimentally [20]. Among the structures with 2D M-Si-O framework obtained in current study, the lowest-energy one for all three Na systems has space group P-1. This P-1 structure is plotted in detail in Fig. 7.
Comparing with those plotted in Fig. 4, the lowest-energy structure with 2D M-Si-O framework for Na system is much more distorted under DFT relaxation and the coordination number of all Na atoms is 5. In Fig. 7d, the Na-O pyramids were plotted. We can see that the center Na atom sits very close to the base plane and four of the five Na neighbors are almost located on the same plane, i.e. such NaO5 pyramid can be considered as half of an octahedron.

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The much larger distortions observed in the Na systems indicates that structures with brand new motifs and more competitive energies could exist for the Na compounds, which cannot be fully covered using the method presented in this work. The search space starting from tetrahedral networks has been limited and further studies using more general search schemes should be carried out in order to get a more comprehensive picture of the Na2MSiO4 structures.

Conclusion
In conclusion, by taking advantage of known structural features, we developed a fast motif-network scheme to study the complex crystal structures of the silicate cathode systems for Li-ion/Na-ion batteries. Using the tetrahedral networks generated from silicon, we found that the structures of A2MSiO4 for both Li and Since the energy difference between ferromagnetic (FM) and antiferromagnetic (AFM) is very small and the resulting lattice parameters are almost the same [36,37], all calculations in present work were spin-polarized with FM configuration.
The effects due to the localization of the d electrons of the transition metal ions in the silicates were taken into account with the GGA + U approach of Dudarev et al. [38]. Within the GGA + U approach, the on-site coulomb term U and the exchange term J were grouped together into a single effective interaction parameter Ueff=U-J. In our calculations, U-J values were set to 4 eV for M = Fe, and 5 eV for M = Co, Mn, respectively.