Nickel-based ferrocyanides have attracted wide interest as cathode for aqueous sodium-ion batteries in fields of sustainable energies such as wind and solar, owing to excellent cycling stability and high-rate capability. However, they suffer from low specific capacities (∼60 mAh g–1). Herein, Na2Ni0.4Co0.6[Fe­(CN)6] nanocrystallites are reported for the first time as high-capacity cathode for aqueous sodium-ion batteries. Its electrochemical properties and redox mechanism have been understood by combining the X-ray diffraction technique, Fourier-transform infrared spectroscopy, cyclic voltammetry, electrochemical impedance microscopy, and charge/discharge measurements. It is revealed that the material undergoes a reversible three-step single-phase reaction mechanism during Na extraction through sequential electrochemical oxidation of nitrogen-coordinated Co2+ ions and carbon-coordinated Fe2+ ions and achieves superior electrochemical performance with a high reversible capacity of 85 mAh g–1 at 0.5 C, an average operating potential of 0.62 V (vs Ag/AgCl), and a high capacity retention of 90% after 100 cycles. The combination of high specific energy and good cycling performance enables the Na2Ni0.4Co0.6[Fe­(CN)6] material exhibiting promising application for high-performance aqueous sodium-ion batteries.

Nickel‐based ferricyanides have attracted much attention as cathode materials for aqueous sodium‐ion batteries, owing to their room‐temperature synthesis and open structural framework. However, factors affecting their electrochemical performance are still not clear. Herein, the effect of electrolyte concentrations on electrochemical properties of the ferricyanide cathode has been investigated by combining cyclic voltammetry, charge/discharge tests, and electrochemical impedance microscopy. It is found that high‐concentration electrolyte can not only raise the working potential, owing to increased activity of Na+ ions, but also increase the initial coulombic efficiency due to suppression of side reactions. The optimized electrolyte enables it cycling with an initial coulombic efficiency of 99.3 %, excellent high‐rate capability (68.1 mAh g−1 at 0.5 C and 63.1 mAh g−1 at 10 C), and outstanding cycling stability (96.3 % capacity retention after 1000 cycles at 10 C). The finding indicates that designing high‐concentration electrolytes is an effective strategy to improve electrochemical performance of ferricyanide cathodes for aqueous sodium‐ion batteries.

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Copper‐based hexacyanoferrates have received important interest as cathode candidates for aqueous sodium‐ion batteries (SIBs), owing to the room‐temperature synthesis route, fast reaction kinetics, and high working potential. However, they suffer from insufficient cycling performance in medium aqueous electrolytes. Herein, a nickel‐substituted copper hexacyanoferrate (Na2Cu0.6Ni0.4[Fe(CN)6]) is reported as a superior cathode for aqueous SIBs, which is developed by studying the effect of Ni substitution on the electrochemical properties of Na2Cu1‐xNix[Fe(CN)6] (0≤x≤1) series. It exhibits a reversible capacity of 62 mAh g−1 and an average working potential of 0.62 V (vs. Ag/AgCl) at a current rate of 0.5 C. Even though being cycled at a high current rate of 10 C, it can achieve a discharge capacity of 56 mAh g−1 and render a capacity retention of 96 % after 1000 cycles. Relative to most previously reported cathode materials, the material shows superior overall performance including improved specific energy, outstanding high‐rate capability, and excellent cycling performance. This indicates that Na2Cu0.6Ni0.4[Fe(CN)6] is a promising cathode candidate for aqueous SIBs.

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Design problems in structural engineering are often modeled as differential equations. These problems are posed as initial or boundary value problems with several possible variations in structural designs. In this paper, we have derived a mathematical model that represents different structures of beam-columns by varying axial load with or without internal forces including bending rigidity. We have also developed a novel solver, the LeNN-NM algorithm, which consists of weighted Legendre polynomials, and a single path following optimizer, the Nelder–Mead (NM) algorithm. To evaluate the performance of our solver, we have considered three design problems representing beam-columns. The values of performance indicators, MAD, TIC, NSE, and ENSE, are calculated for a hundred simulations. The outcome of our statistical analysis points to the superiority of the LeNN-NM algorithm. Graphical illustrations are presented to further elaborate on our claims.