Antisite occupation induced single anionic redox chemistry and structural stabilization of layered sodium chromium sulfide

The intercalation compounds with various electrochemically active or inactive elements in the layered structure have been the subject of increasing interest due to their high capacities, good reversibility, simple structures, and ease of synthesis. However, their reversible intercalation/deintercalation redox chemistries in previous compounds involve a single cationic redox reaction or a cumulative cationic and anionic redox reaction. Here we report an anionic redox chemistry and structural stabilization of layered sodium chromium sulfide. It was discovered that the sulfur in sodium chromium sulfide is electrochemically active, undergoing oxidation/reduction rather than chromium. Significantly, sodium ions can successfully move out and into without changing its lattice parameter c, which is explained in terms of the occurrence of chromium/sodium vacancy antisite during desodiation and sodiation processes. Our present work not only enriches the electrochemistry of layered intercalation compounds, but also extends the scope of investigation on high-capacity electrodes.


Supplementary Tables
Supplementary Table 1 Table 4. Lattice parameters and the corresponding total energies for Na 1-x CrS 2 (0x<1) with and without Cr/V / Na antisites. The difference between two Na 0.5 CrS 2 configurations with Cr/V / Na antisites (See Supplementary Fig. 13d and Fig.   17a for 2×2×1 Na 0.5 CrS 2 conventional cells) lies in that three Na layers for the former have the same Na + numbers, whereas the Na + number of the middle Na layer for the latter is less than those of the two-sided ones so as to ensure the enough Na vacancies Supplementary Table 5. Cr-S, Na-S and S-S distances related to all S ions in Na 0.5 CrS 2 with 1/6 Cr/V′ Na antisite. Two pairs of dimers are (S4-S22) 2and (S8-S14) 2-, two dangling S ions are (S10)and (S20) -, and others are general S 2-. Note that the distances between Cr (Na)-S or S-S are within 3 Å. Labels of Cr and S are the same as those in Fig. 5(d-e) and Supplementary Fig. 17a.

Supplementary Notes
Supplementary Note 1. Fig. 1b  between Na and Cr column is ~14.59%. Supplementary Fig. 6, the structure evolution and lattice parameter change of NaCrS 2 electrode during the 3 rd cycle are almost consistent with those during the 1 st cycle. It can be seen that the (003) peak also keeps unchanged and (001) peak shows small shift during charge/discharge process.

Supplementary Note 3.
In order to compare the structure evolution of NaCrS 2 electrode in different cells, the in situ XRD of NaCrS 2 electrode during the first charging process in Li cell was investigated and shown in Supplementary Fig. 7. As shown in XRD pattern above, the (003) diffraction peak almost keeps unchanged, while the (110) peak gradually moves towards higher 2θ angle with the extraction of Na from NaCrS 2 . Obviously, these results are similar with the lattice change of NaCrS 2 electrode in Na cell.

Supplementary Note 4.
Cluster expansion is one of the approximate methods to calculate total energy of crystal system with a mass of atoms, which was proposed by Mayer at the beginning of 1940s and employed to express the partition function as a series of expansion in powers of density 3 . In the cluster expansion, the system energy is defined by specifying the energy associated with any atomic arrangement on a given lattice 4 . The general formalism of cluster expansion parameterizes the energy as follows 5-6 : where  denotes a cluster (a set of sites p), while ' is equivalent cluster of  by symmetry, The coefficients J  is called the effective cluster interaction (ECI). The

 
denote the energies of empty cluster, point cluster, pair cluster and triplet cluster, respectively. If the cluster scale is accordingly increased, the obtained energy is more close to first-principles-calculated value. Supplementary Fig. 9 shows the clusters in cluster expansion, which include point, pair and triplet clusters. The empty cluster is also included in cluster expansion but not shown in Supplementary Fig. 9. The yellow-filled circles correspond to sites in top layer. The blue-filled circles correspond to sites in middle layer. And the purple-filled circles correspond to sites in bottom layer. The circles with character c correspond to sites in conventional cell. The above processes would be repetitive execution till the ground state is correctly reproduced and no new ground state is predicted at the concentration.

Supplementary Note 5.
We explored the relative stability of Na 1-x CrS 2 with different Na concentrations ranging from x=0 to x=0.5. We considered a total of 42 configurations with many possible Na-vacancy arrangements, and calculated their corresponding formation energy per formula unit (E form (x), eV/f.u.) as: where  Table 3.

Supplementary Note 7.
As shown in Supplementary Fig. 14 Fig. 14b), which is in good agreement with the experimental result in Fig. 2c. Namely, it is the occurrence of Cr/V / Na antisite that results in the unchanged lattice c. In addition, we consider the cases of Na 1-x CrS 2 with 1/6 Cr/V / Na antisite (x=1/12, 1/2), and find that ΔE at x=1/12 reaches 3.24eV, although ΔE at x=1/2 is only 0.176 eV and the lattice parameter c of 19.342 Å is very close to that of pristine NaCrS 2 . Note that with the increase of deintercalated sodium concentration, there is a tendency that the lattice parameter a shortens gradually, which is in agreement with the experiment result in Fig. 2b.
Supplementary Note 8. The redox potential for the sodium removal in Na x CrS 2 , i.e., the average potential, can be approximately calculated via the following equation: where E(NaCrS 2 ) and E(Na 1-x CrS 2 ) are the total energies before and after the x sodium ions extraction from the NaCrS 2 compound per formula unit, and e is the elementary charge. The average potential of Na 1-x CrS 2 with Cr/V / Na (Na vacancy: V / Na in KrÖger-Vink notation) antisite is calculated by total energy of Na 1-x CrS 2 with Cr/V / Na antisite (1/12 and 1/6 Cr/V / Na antisites in Na 0.75 CrS 2 and Na 0.5 CrS 2 , respectively). The entropy, volume change, and temperature effects are ignored. We choose energetically the most favorable configuration.
The GITT profiles of Na 1-x CrS 2 (we define the Na 1-x CrS 2 electrode charged to 3.0 V with x=0.5 as fully charged sample in the first charge process according to the capacity) and the computed average voltage along the minimum energy path of formation energies are shown in Supplementary Fig. 15 Fig. 17a and Supplementary Fig. 13d for 2×2×1 Na 0.5 CrS 2 conventional cells). For the former, the Na + number of the middle Na layer is less than those of the two-sided ones so as to ensure the enough Na vacancies for Cr migration, whereas for the latter three Na layers have the same Na + numbers. Seeing from the energetics, the total energy of the former is higher than that of the latter by 0.0801eV/f.u., which signifies that it is entirely possible for both states to be existent during the electrochemical discharge/discharge process. The next migration occurs in the Na intra-layer, as shown during the substep 2, Cr (Cr3) travels from the Na