Most P2-type layered oxides suffer from multiple voltage plateaus, due to Na+/vacancy-order superstructures caused by strong interplay between Na–Na electrostatic interactions and charge ordering in the transition metal layers. Here, Mg ions are successfully introduced into Na sites in addition to the conventional transition metal sites in P2-type Na0.7[Mn0.6Ni0.4]­O2 as new cathode materials for sodium-ion batteries. Mg ions in the Na layer serve as “pillars” to stabilize the layered structure, especially for high-voltage charging, meanwhile Mg ions in the transition metal layer can destroy charge ordering. More importantly, Mg ion occupation in both sodium and transition metal layers will be able to create “Na–O–Mg” and “Mg–O–Mg” configurations in layered structures, resulting in ionic O 2p character, which allocates these O 2p states on top of those interacting with transition metals in the O-valence band, thus promoting reversible oxygen redox. This innovative design contributes smooth voltage profiles and high structural stability. Na0.7Mg0.05[Mn0.6Ni0.2Mg0.15]­O2 exhibits superior electrochemical performance, especially good capacity retention at high current rate under a high cutoff voltage (4.2 V). A new P2 phase is formed after charge, rather than an O2 phase for the unsubstituted material. Besides, multiple intermediate phases are observed during high-rate charging. Na-ion transport kinetics are mainly affected by elemental-related redox couples and structural reorganization. These findings will open new opportunities for designing and optimizing layer-structured cathodes for sodium-ion batteries.

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Abstract-We introduce a tuning space-mapping technology for microwave design optimization. The general tuning space-mapping algorithm is formulated, which is based on a so-called tuning model, as well as on a calibration process that translates the adjustment of the tuning model parameters into relevant updates of the design variables. The tuning model is developed in a fast circuit-theory based simulator and typically includes the fine model data at the current design in the form of the properly formatted scattering parameter values. It also contains a set of tuning parameters, which are used to optimize the model so that it satisfies the design specification. The calibration process may involve analytical formulas that establish the dependence of the design variables on the tuning parameters. If the formulas are not known, the calibration process can be performed using an auxiliary space-mapping surrogate model. Although the tuning space mapping can be considered to be a specialized case of the standard space-mapping approach, it can offer even better performance because it enables engineers to exploit their experience within the context of efficient space mapping. Our approach is demonstrated using several microwave design optimization problems.Index Terms-Computer-aided design (CAD), engineering optimization, space mapping, surrogate models, tuning.

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