Molecular grafting towards high-fraction active nanodots implanted in N-doped carbon for sodium dual-ion batteries

Sodium-based dual-ion batteries (Na-DIBs) show a promising potential for large-scale energy storage applications due to the merits of environmental friendliness and low cost. However, Na-DIBs are generally subject to poor rate capability and cycling stability for the lack of suitable anodes to accommodate large Na+ ions. Herein, we propose a molecular grafting strategy to in situ synthesize tin pyrophosphate nanodots implanted in N-doped carbon matrix (SnP2O7@N-C), which exhibits a high fraction of active SnP2O7 up to 95.6 wt% and a low content of N-doped carbon (4.4 wt%) as the conductive framework. As a result, this anode delivers a high specific capacity ∼400 mAh g−1 at 0.1 A g−1, excellent rate capability up to 5.0 A g−1 and excellent cycling stability with a capacity retention of 92% after 1200 cycles under a current density of 1.5 A g−1. Further, pairing this anode with an environmentally friendly KS6 graphite cathode yields a SnP2O7@N-C||KS6 Na-DIB, exhibiting an excellent rate capability up to 30 C, good fast-charge/slow-discharge performance and long-term cycling life with a capacity retention of ∼96% after 1000 cycles at 20 C. This study provides a feasible strategy to develop high-performance anodes with high-fraction active materials for Na-based energy storage applications.

On the Estimation of Confidence Intervals for Binomial Population Proportions in Astronomy: The Simplicity and Superiority of the Bayesian Approach

I present a critical review of techniques for estimating confidence intervals on binomial population proportions inferred from success counts in small to intermediate samples. Population proportions arise frequently as quantities of interest in astronomical research; for instance, in studies aiming to constrain the bar fraction, active galactic nucleus fraction, supermassive black hole fraction, merger fraction, or red sequence fraction from counts of galaxies exhibiting distinct morphological features or stellar populations. However, two of the most widely-used techniques for estimating binomial confidence intervals — the ‘normal approximation’ and the Clopper & Pearson approach — are liable to misrepresent the degree of statistical uncertainty present under sampling conditions routinely encountered in astronomical surveys, leading to an ineffective use of the experimental data (and, worse, an inefficient use of the resources expended in obtaining that data). Hence, I provide here an overview of the fundamentals of binomial statistics with two principal aims: (I) to reveal the ease with which (Bayesian) binomial confidence intervals with more satisfactory behaviour may be estimated from the quantiles of the beta distribution using modern mathematical software packages (e.g.r, matlab, mathematica, idl, python); and (ii) to demonstrate convincingly the major flaws of both the ‘normal approximation’ and the Clopper & Pearson approach for error estimation.