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A Progress Report on Metal–Sulfur Batteries

Nonaqueous conversion-reaction sulfur chemistry has been attracting increasing attention over the past decade for the development of next-generation lithium-based batteries. Li–S batteries are currently approaching a nexus stage from lab-scale experiments to possible pragmatic applications. Inspired by the success of Li–S chemistry, other metal–sulfur batteries with a variety of metallic anodes, such as sodium, potassium, magnesium, calcium, and aluminum, have also started to attract attention. In comparison to lithium, Na, Mg, Al, K, and Ca are naturally more abundant and affordable. The Na-S, Mg-S, Al-S, K-S, and Ca-S battery systems provide a great potential for improving the volumetric energy density of sulfur-based batteries. The multivalent metal-sulfur systems, Mg-S, Al-S, and Ca-S, offer better safety features as well. However, the research and development on Na-S, Mg-S, Al-S, K-S, and Ca-S batteries is far behind the Li–S system due to many critical challenges. In this progress report, the fundamental principles of various metal–sulfur chemistries are first presented and compared. Then, the historical progress, recent advances, and key challenges of the Li–S, Na-S, Mg-S, Al-S, K-S, and Ca-S systems are summarized and discussed. Finally, future efforts and directions for both the fundamental and practical research are prospected.

25 ENERGY STORAGE↗

Electrolyte Design and Optimization for Alkali Metal‐Sulfur Batteries

Alkali metal-sulfur batteries, including lithium-sulfur (Li-S), sodium-sulfur (Na-S), and potassium-sulfur (K-S) systems, have garnered significant attention as promising electrochemical energy storage (EES) technologies. Among them, Li-S batteries stand out as strong contenders for next-generation energy storage, owing to their high energy density and the cost-effectiveness of sulfur-based cathodes. However, with the rapid technological advances and the escalating energy demand, lithium resources are becoming increasingly scarce, making it imperative to explore alternative metal anodes to replace lithium. Therefore, Na-S and K-S batteries, serving as counterparts to Li-S systems, are emerging as formidable contenders for next-generation energy storage technologies due to the abundant and cost-effective nature of sodium and potassium. Although Na-S and K-S batteries possess considerable potential in the energy sector, their development is still in its infancy, with performance constrained by the nascent state of electrolyte design and optimization. This review article provides a comprehensive overview of recent advancements and developments in liquid electrolytes for alkali metal-sulfur batteries. Additionally, it identifies key challenges and proposes future research directions aimed at enhancing electrolyte stability, optimizing interfacial compatibility, and improving the overall performance of alkali metal-sulfur batteries.

25 ENERGY STORAGE↗

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

97 MATHEMATICS AND COMPUTING↗

Higher Compact Multiple Occurrence around Metal-poor M-dwarfs and Late-K-dwarfs

The planet–metallicity correlation serves as a potential link between exoplanet systems as we observe them today and the effects of bulk composition on the planet formation process. Many observers have noted a tendency for Jovian planets to form around stars with higher metallicities; however, there is no consensus on a trend for smaller planets. Here, we investigate the planet–metallicity correlation for rocky planets in single- and multi-planet systems around Kepler M-dwarf and late-K-dwarf stars. Due to molecular blanketing and the dim nature of these low-mass stars, it is difficult to make direct elemental abundance measurements via spectroscopy. We instead use a combination of accurate and uniformly measured parallaxes and photometry to obtain relative metallicities and validate this method with a subsample of spectroscopically determined metallicities. We use the Kolmogorov–Smirnov (K-S) test, Mann–Whitney U-test, and Anderson–Darling (AD) test to compare the compact multiple planetary systems with single-transiting planet systems and systems with no detected transiting planets. We find that the compact multiple planetary systems are derived from a statistically more metal-poor population, with a p-value of 0.015 in the K-S test, a p-value of 0.005 in the Mann–Whitney U-test, and a value of 2.574 in the AD test statistic, which exceeds the derived threshold for significance by a factor of 25. We conclude that metallicity plays a significant role in determining the architecture of rocky planet systems. Compact multiples either form more readily, or are more likely to survive on gigayear timescales, around metal-poor stars.

47 OTHER INSTRUMENTATION↗

X-ray fluorescence and XANES spectroscopy revealed diverse potassium chemistries and colocalization with phosphorus in the ectomycorrhizal fungus Paxillus ammoniavirescens

Ectomycorrhizal (ECM) fungi play a major role in forest ecosystems and managed tree plantations. Particularly, they facilitate mineral weathering and nutrient transfer towards colonized roots. Among nutrients provided by these fungi, potassium (K) has been understudied compared to phosphorus (P) or nitrogen (N). The ECM fungus Paxillus ammoniavirescens is a generalist species that interacts with the root of many trees and can directly transfer K to them, including loblolly pine. However, the forms of K that ECM fungi can store is still unknown. Here, we used synchrotron potassium X-ray fluorescence (XRF) and K-edge X-ray Absorption Near Edge Structure (XANES) spectroscopy on P. ammoniavirescens growing in axenic conditions to investigate the K chemistries accumulating in the center and the edge of the mycelium. We observed that various K forms accumulated in different part of the mycelium, including K-nitrate (KNO 3 ), K-C-O compounds (such as K-tartrate K 2 (C 4 H 4 O 6 ) and K-oxalate (K 2 C 2 O 4 )), K-S and K-P compounds. Saprotrophic fungi have been shown to excrete carboxylic acids, which in turn play a role in soil mineral weathering. Our finding of several K counter-ions to carboxylic acids may suggest that, besides their direct transfer to colonized roots, K ions can also be involved in the production of compounds necessary for sourcing nutrients from their surrounding environment by ECM fungi. Additionally, this work reveals that XANES spectroscopy can be used to identify the various forms of K accumulating in biological systems.

Ectomycorrhizal symbiosis↗

Investigation of the thermal decomposition of Pu(IV) oxalate: a transmission electron microscopy study

The degradation of the internal structure of plutonium (IV) oxalate during calcination was investigated with Transmission Electron Microscopy (TEM), electron diffraction, Electron Energy-Loss Spectroscopy (EELS), and 4D Scanning TEM (STEM). TEM lift-outs were prepared from samples that had been calcined at 300°C, 450°C, 650°C and 950°C. The resulting phase at all calcination temperatures was identified as PuO 2 with electron diffraction. The grain size range was obtained with high-resolution TEM. In addition, 4D STEM images were analyzed to provide grain size distributions. In the 300°C calcined sample, the grains were <10 nm in diameter, at 650°C, the grains ranged from 10 to 20 nm, and by 950°C, the grains were 95–175 nm across. Using the Kolmogorov-Smirnov (K-S) two sample test, it was shown that morphological measurements obtained from 4D-STEM provided statistically significant distributions to distinguish samples at the different calcination conditions. Using STEM-EELS, carbon was shown to be present in the low temperature calcined samples associated with oxalate but had formed carbon (possibly graphite) deposits in the 950°C calcined sample. This work highlights the new methods of STEM-EELS and 4D-STEM for studying the internal structure of special nuclear materials (SNM).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Materials Data on K2S by Materials Project

K2S is Fluorite structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. K1+ is bonded to four equivalent S2- atoms to form a mixture of edge and corner-sharing KS4 tetrahedra. All K–S bond lengths are 3.23 Å. S2- is bonded in a body-centered cubic geometry to eight equivalent K1+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on KS by Materials Project

SK1 is alpha boron-derived structured and crystallizes in the hexagonal P-62m space group. The structure is three-dimensional. there are two inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a 6-coordinate geometry to six S1- atoms. There are two shorter (3.25 Å) and four longer (3.35 Å) K–S bond lengths. In the second K1+ site, K1+ is bonded in a 6-coordinate geometry to six S1- atoms. There are four shorter (3.17 Å) and two longer (3.25 Å) K–S bond lengths. There are two inequivalent S1- sites. In the first S1- site, S1- is bonded in a 7-coordinate geometry to six K1+ and one S1- atom. The S–S bond length is 2.13 Å. In the second S1- site, S1- is bonded in a 7-coordinate geometry to six K1+ and one S1- atom. The S–S bond length is 2.14 Å.

36 MATERIALS SCIENCE↗

Materials Data on K2S5 by Materials Project

K2S5 crystallizes in the orthorhombic P2_12_12_1 space group. The structure is three-dimensional. there are two inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a 7-coordinate geometry to eight S+0.40- atoms. There are a spread of K–S bond distances ranging from 3.32–3.67 Å. In the second K1+ site, K1+ is bonded in a 8-coordinate geometry to eight S+0.40- atoms. There are a spread of K–S bond distances ranging from 3.29–3.62 Å. There are five inequivalent S+0.40- sites. In the first S+0.40- site, S+0.40- is bonded in a 5-coordinate geometry to five K1+ and one S+0.40- atom. The S–S bond length is 2.06 Å. In the second S+0.40- site, S+0.40- is bonded in a 5-coordinate geometry to three K1+ and two S+0.40- atoms. The S–S bond length is 2.08 Å. In the third S+0.40- site, S+0.40- is bonded in a 5-coordinate geometry to four K1+ and one S+0.40- atom. The S–S bond length is 2.06 Å. In the fourth S+0.40- site, S+0.40- is bonded in a 5-coordinate geometry to three K1+ and two S+0.40- atoms. The S–S bond length is 2.09 Å. In the fifth S+0.40- site, S+0.40- is bonded in a 3-coordinate geometry to one K1+ and two S+0.40- atoms.

36 MATERIALS SCIENCE↗

Materials Data on K2S by Materials Project

K2S crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. there are two inequivalent K1+ sites. In the first K1+ site, K1+ is bonded to five equivalent S2- atoms to form distorted KS5 trigonal bipyramids that share corners with twelve equivalent KS6 octahedra, corners with eight equivalent KS5 trigonal bipyramids, edges with six equivalent KS5 trigonal bipyramids, and faces with six equivalent KS6 octahedra. The corner-sharing octahedra tilt angles range from 31–60°. There are a spread of K–S bond distances ranging from 3.06–3.65 Å. In the second K1+ site, K1+ is bonded to six equivalent S2- atoms to form distorted KS6 octahedra that share corners with twelve equivalent KS6 octahedra, corners with twelve equivalent KS5 trigonal bipyramids, edges with six equivalent KS6 octahedra, faces with two equivalent KS6 octahedra, and faces with six equivalent KS5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 51°. There are four shorter (3.56 Å) and two longer (3.58 Å) K–S bond lengths. S2- is bonded in a 3-coordinate geometry to eleven K1+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on KS by Materials Project

SK1 is Tetraauricupride structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K1+ is bonded in a body-centered cubic geometry to eight equivalent S1- atoms. All K–S bond lengths are 3.32 Å. S1- is bonded in a body-centered cubic geometry to eight equivalent K1+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on KS by Materials Project

SK1 is Halite, Rock Salt structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. K1+ is bonded to six equivalent S1- atoms to form a mixture of corner and edge-sharing KS6 octahedra. The corner-sharing octahedral tilt angles are 0°. All K–S bond lengths are 3.26 Å. S1- is bonded to six equivalent K1+ atoms to form a mixture of corner and edge-sharing SK6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗

Materials Data on KS by Materials Project

SK1 is Tetraauricupride structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. K1+ is bonded in a distorted body-centered cubic geometry to eight equivalent S1- atoms. All K–S bond lengths are 3.26 Å. S1- is bonded in a distorted body-centered cubic geometry to eight equivalent K1+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on KS3 by Materials Project

S2KS crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. there are two inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a 9-coordinate geometry to nine S+0.33- atoms. There are a spread of K–S bond distances ranging from 3.22–3.81 Å. In the second K1+ site, K1+ is bonded in a 8-coordinate geometry to eight S+0.33- atoms. There are a spread of K–S bond distances ranging from 3.24–3.80 Å. There are six inequivalent S+0.33- sites. In the first S+0.33- site, S+0.33- is bonded to four K1+ and one S+0.33- atom to form distorted SK4S square pyramids that share corners with two equivalent SK4S square pyramids, corners with four equivalent SK2S2 tetrahedra, corners with two equivalent SK4S trigonal bipyramids, edges with two equivalent SK4S square pyramids, and edges with two equivalent SK4S trigonal bipyramids. The S–S bond length is 2.06 Å. In the second S+0.33- site, S+0.33- is bonded in a 5-coordinate geometry to three K1+ and two S+0.33- atoms. The S–S bond length is 2.05 Å. In the third S+0.33- site, S+0.33- is bonded in a 4-coordinate geometry to two K1+ and two S+0.33- atoms. The S–S bond length is 2.19 Å. In the fourth S+0.33- site, S+0.33- is bonded in a 4-coordinate geometry to two K1+ and two S+0.33- atoms. The S–S bond length is 2.04 Å. In the fifth S+0.33- site, S+0.33- is bonded to two K1+ and two S+0.33- atoms to form distorted corner-sharing SK2S2 tetrahedra. The S–S bond length is 2.06 Å. In the sixth S+0.33- site, S+0.33- is bonded to four K1+ and one S+0.33- atom to form distorted SK4S trigonal bipyramids that share corners with two equivalent SK4S square pyramids, corners with four equivalent SK2S2 tetrahedra, corners with two equivalent SK4S trigonal bipyramids, edges with two equivalent SK4S square pyramids, and edges with two equivalent SK4S trigonal bipyramids.

36 MATERIALS SCIENCE↗

Materials Data on KS by Materials Project

SK1 crystallizes in the monoclinic C2/m space group. The structure is one-dimensional and consists of two SK1 ribbons oriented in the (0, 0, 1) direction. K1+ is bonded in a linear geometry to two equivalent S1- atoms. Both K–S bond lengths are 3.02 Å. S1- is bonded in a linear geometry to two equivalent K1+ atoms.

36 MATERIALS SCIENCE↗