urgent strategies worldwide. [1] Rechargeable lithium-ion batteries have achieved great success during the last 40 years, while they gradually display certain limitations in further large-scale applications, such as high cost, uneven geological distribution and short supplies of lithium resources (0.0017 wt%) around the world. As alternative energy storage sources, sodium ion batteries (SIBs) and potassium ion batteries (PIBs) have recently attracted tremendous interest owing to their natural abundance, low cost and environmental friendliness. Despite having a similar abundance with sodium (sodium and potassium represent 2.36 and 2.09 wt% in the Earth's crust, respectively), potassium presents some specific advantages. K + /K exhibit a lower standard redox potential of −2.93 V (vs E°) compared with that of Na + /Na (−2.71 V vs E°), implying a higher working voltage and energy density of PIBs. [2] Moreover, potassium ions have much better conductivity and relatively lower desolvation energy in organic solvents. [3] These merits of potassium make it a promising low-cost candidate for high-energy and power density energy storage applications.The progress of PIBs mainly follows the development of electrode materials, especially considering the large-size of Metallic bismuth (Bi) has been widely explored as remarkable anode material in alkali-ion batteries due to its high gravimetric/volumetric capacity. However, the huge volume expansion up to ≈406% from Bi to full potassiation phase K 3 Bi, inducing the slow kinetics and poor cycling stability, hinders its implementation in potassium-ion batteries (PIBs). Here, facile strategy is developed to synthesize hierarchical bismuth nanodots/graphene (BiND/G) composites with ultrahigh-rate and durable potassium ion storage derived from an in situ spontaneous reduction of sodium bismuthate/graphene composites. The in situ formed ultrafine BiND (≈3 nm) confined in graphene layers can not only effectively accommodate the volume change during the alloying/dealloying process but can also provide high-speed channels for ionic transport to the highly active BiND. The BiND/G electrode provides a superior rate capability of 200 mA h g −1 at 10 A g −1 and an impressive reversible capacity of 213 mA h g −1 at 5 A g −1 after 500 cycles with almost no capacity decay. An operando synchrotron radiation-based X-ray diffraction reveals distinctively sharp multiphase transitions, suggesting its underlying operation mechanisms and superiority in potassium ion storage application.

X-ray microscopes are powerful tools in the nano-inspection of materials owing to their ultra-high resolution at the molecular level. However, the focusing efficiency of binary zone plate lenses as key components in such probes is merely 5% in practice, hindering their application in advanced scientific research. Although kinoform zone plate lenses are in principle supposed to possess high efficiency beyond binary ones, little progress has been reported so far due to the shortage of both a theoretical calculation approach and greyscale lithography for generating fine three-dimensional (3D) kinoform zones of the lenses. This paper reports our theoretical work for a modified beam propagation method to compute the focusing performance and state-of-the-art 3D greyscale electron beam lithography for kinoform zone plate lenses. Three different zone shapes – binary, kinoform and top-flat kinoform (nicknamed the trapezoid-kinoform) – were compared both theoretically and experimentally. Theoretical calculations suggest, for the first time, that the trapezoid-kinoform zone plate gives rise to the highest focusing efficiency among the three lenses, which was proved by optical characterization of the fabricated lens with hard X-rays. As high as 40% of the focusing efficiency by Au trapezoid-kinoform lenses with resolution of 250 nm at 8 keV has been achieved, which is two times higher than that of binary zone plate lenses. The origin of the enhanced efficiency in the trapezoid-kinoform zone plate lens was explained by the joint contributions from both the refraction through the kinoform slope and the diffraction through the top flat part of the trapezoid-kinoform zone plate. Such a breakthrough in focusing efficiency sheds light on the further development of X-ray lenses with both high resolution and high efficiency.