Developing cost-effective and high performance sodium-ion batteries (SIBs) relies mostly on advanced cathode materials with high electrode voltage, high capacity and fast sodium-ion diffusion. Here, we propose mixed sodium manganese oxides Na${}_x$(M${}_{0.44}$Mn${}_{0.56}$)O${}_2$ (M = Mn, Fe, Co, Ni) as improved potential cathode materials for SIBs based on first-principles calculations. Our calculations reveal that these materials have relatively low volume expansion rates below 5%, and are thermodynamically stable. We find that the binding strength between the host and inserted Na atom gradually decreases as increasing the Na content $x$ from 0.11 to 0.67 for each mixed compound, whereas it increases as going Mn$\to$Fe$\to$Co$\to$Ni at each value of Na content. Identifying the intermediate phases during Na insertion/extraction, we find a slight increase of electrode voltage with remarkably higher specific capacities by mixing due to extending the lower limit of Na content. We also investigate the sodium-ion diffusion by identifying plausible pathways and determining the activation barriers and diffusion coefficients, and find fast migration within the S-shaped tunnel and moderate one within the small-sized tunnel. Through analysis of density of states, we find that these compounds exhibit half-metallic behaviour, demonstrating an enhancement of metallicity by mixing with higher valent transition metal atoms. Our calculation results show that these mixed compounds can be advanced cathode materials for high performance SIBs.

开发具有成本效益和高性能的钠离子电池（SIBs）主要依赖于具有高电极电压、高容量和快速钠离子扩散的先进正极材料。在这里，我们提出混合钠锰氧化物 Na${}_X$(男${}_{0.44}$锰${}_{0.56}$)O${}_2$（M = Mn、Fe、Co、Ni）作为基于第一性原理计算的改进的 SIBs 潜在正极材料。我们的计算表明，这些材料具有低于 5% 的相对较低的体积膨胀率，并且在热力学上是稳定的。我们发现主体和插入的 Na 原子之间的结合强度随着 Na 含量的增加而逐渐降低$X$ 每个混合化合物从 0.11 到 0.67，而随着 Mn 的增加而增加$\to$铁$\to$公司$\to$各值的 Na 含量下的 Ni。确定 Na 插入/提取过程中的中间相，我们发现由于延长了 Na 含量的下限，通过混合，电极电压略有增加，比容量显着提高。我们还通过确定可能的途径和确定激活势垒和扩散系数来研究钠离子扩散，并发现 S 形隧道内的快速迁移和小型隧道内的中等迁移。通过对态密度的分析，我们发现这些化合物表现出半金属行为，表明通过与更高价的过渡金属原子混合来增强金属丰度。我们的计算结果表明，这些混合化合物可以成为高性能 SIB 的先进正极材料。