Theoretical exploration of the structural evolution of sodium sulfide clusters in Na-S batteries

The nanosized sodium sulfide species greatly enhance the performance of Na-S batteries. However, as a typical ionic compound, the diminished stability with decreasing cluster size has been rarely considered. Numerous theoretical works only simulated the Na-S binary system based on quite small sodium sulfide clusters, with no account of the stability of the sub-nanoscale cluster. Here, by using an advanced structure search algorithm, we built a binary phase diagram of the sodium sulfide clusters (NSCs). The commonly studied monomer model with low sulfur concentrations is indeed energetically unfavorable, especially for the final discharge product, the Na2S monomer. Therefore, the aggregation of monomers should take place to form multimers. According to the energy, charge, and geometry, relatively stable clusters with low sulfur concentrations are located, including (Na2S5)2, (Na2S4)2, (Na2S3)3, (Na2S2)4, and (Na2S)6 clusters. Furthermore, these multimers bind more intensely to four typical models of carbon-based substrates. The B-doped carbon material exhibits outstanding affinity to NSCs, which may facilitate overcoming the shuttle effect in applications. This work represents a significant step toward understanding the evolution mechanism of NSCs that may guide the future development of high-performance Na-S batteries.