The Hasse norm principle for some non-Galois extensions of square-free degree

In this paper, we study the Hasse norm principle for some non-Galois extensions of number fields. Our main theorem is that for any square-free composite number $d$ which is divisible by at least one of $3$, $55$, $91$ or $95$, there exists a finite extension of degree $d$ for which the Hasse norm principle fails. To accomplish it, we determine the structure of the Tate--Shafarevich groups of norm one tori for finite extensions of degree $d$ under the normality of $p$-Sylow subgroups of the Galois groups of their Galois closures for a square-free prime factor $p$ of $d$. Moreover, we reduce the assertion to an investigation of $2$-dimensional $\mathbb{F}_p$-representations of some groups of order coprime to $p$.Comment: 39pages, comments are welcom

Cohomological properties of multinorm-one tori

In this paper we investigate the Tate--Shafarevich group Sha^1(k, T) of a multinorm-one torus $T$ over a global field $k$. We establish a few functorial maps among cohomology groups and explore their relations. Using these properties and relations we obtain a few basic structural results for Sha^1(k, T) and extend a few results of Bayer-Fluckiger--Lee--Parimala [Adv. in Math., 2019] to some more general multinorm-one tori. We also give a uniform proof of a result of Demarche--Wei for a criterion of the vanishing of Sha^1(k, T), and of the main result of Pollio [Pure App. Math. Q., 2014] for the case where the \'etale $k$-algebra in question is a product of two abelian extensions. Moreover, we improve the explicit description of Sha^1(k, T) in Lee [J. Pure Appl. Alg., 2022] by removing an intersection condition.Comment: 26 pages, comments welcom

Simultaneous Improvements in Performance and Durability of an Octahedral PtNix/C Electrocatalyst for Next-Generation Fuel Cells by Continuous, Compressive, and Concave Pt Skin Layers

Simultaneous improvements in oxygen reduction reaction (ORR) activity and long-term durability of Pt-based cathode catalysts are indispensable for the development of next-generation polymer electrolyte fuel cells but are still a major dilemma. We present a robust octahedral core–shell PtNix/C electrocatalyst with high ORR performance (mass activity and surface specific activity 6.8–16.9 and 20.3–24.0 times larger than those of Pt/C, respectively) and durability (negligible loss after 10000 accelerated durability test (ADT) cycles). The key factors of the robust octahedral nanostructure (core–shell Pt73Ni27/C) responsible for the remarkable activity and durability were found to be three continuous Pt skin layers with 2.0–3.6% compressive strain, concave facet arrangements (concave defects and high coordination), a symmetric Pt/Ni distribution, and a Pt67Ni33 intermetallic core, as found by STEM-EDS, in situ XAFS, XPS, etc. The robust core–shell Pt73Ni27/C was produced by the partial release of the stress, Pt/Ni rearrangement, and dimension reduction of an as-synthesized octahedral Pt50Ni50/C with 3.6–6.7% compressive Pt skin layers by Ni leaching during the activation process. The present results on the tailored synthesis of the PtNix structure and composition and the better control of the robust catalytic architecture renew the current knowledge and viewpoint for instability of octahedral PtNix/C samples to provide a new insight into the development of next-generation PEFC cathode catalysts

In situ study of oxidation states of platinum nanoparticles on a polymer electrolyte fuel cell electrode by near ambient pressure hard X-ray photoelectron spectroscopy

We performed in situ hard X-ray photoelectron spectroscopy (HAXPES) measurements of the electronic states of platinum nanoparticles on the cathode electrocatalyst of a polymer electrolyte fuel cell (PEFC) using a near ambient pressure (NAP) HAXPES instrument having an 8 keV excitation source. We successfully observed in situ NAP-HAXPES spectra of the Pt/C cathode catalysts of PEFCs under working conditions involving water, not only for the Pt 3d states with large photoionization cross-sections in the hard X-ray regime but also for the Pt 4f states and the valence band with small photoionization cross-sections. Thus, this setup allowed in situ observation of a variety of hard PEFC systems under operating conditions. The Pt 4f spectra of the Pt/C electrocatalysts in PEFCs clearly showed peaks originating from oxidized Pt(II) at 1.4 V, which unambiguously shows that Pt(IV) species do not exist on the Pt nanoparticles even at such large positive voltages. The water oxidation reaction might take place at that potential (the standard potential of 1.23 V versus a standard hydrogen electrode) but such a reaction should not lead to a buildup of detectable Pt(IV) species. The voltage-dependent NAP-HAXPES Pt 3d spectra revealed different behaviors with increasing voltage (0.6 → 1.0 V) compared with decreasing voltage (1.0 → 0.6 V), showing a clear hysteresis. Moreover, quantitative peak-fitting analysis showed that the fraction of non-metallic Pt species matched the ratio of the surface to total Pt atoms in the nanoparticles, which suggests that Pt oxidation only takes place at the surface of the Pt nanoparticles on the PEFC cathode, and the inner Pt atoms do not participate in the reaction. In the valence band spectra, the density of electronic states near the Fermi edge reduces with decreasing particle size, indicating an increase in the electrocatalytic activity. Additionally, a change in the valence band structure due to the oxidation of platinum atoms was also observed at large positive voltages. The developed apparatus is a valuable in situ tool for the investigation of the electronic states of PEFC electrocatalysts under working conditions

Key Structural Transformations and Kinetics of Pt Nanoparticles in PEFC Pt/C Electrocatalysts by a Simultaneous Operando Time-Resolved QXAFS–XRD Technique

This account article treats with the key structural transformations and kinetics of Pt nanoparticles in Pt/C cathode catalysts under transient voltage operations (0.4 VRHE→1.4 VRHE→0.4 VRHE) by simultaneous operando time-resolved QXAFS–XRD measurements, summarizing and analyzing our previous kinetic data in more detail and discussing on the key reaction steps and rate constants for the performance and durability of polymer electrolyte fuel cells (PEFC). The time-resolved QXAFS–XRD measurements were conducted at each acquisition time of 20 ms, while measuring the current/charge of the PEFC. The rate constants for the transient responses of Pt valence, CN(Pt–O) (CN: coordination number), CN(Pt–Pt), and Pt metallic-phase core size under the transient voltage operations were determined by the combined time-resolved QXAFS‒XRD technique. The relationship of the structural kinetics with the performance and durability of the PEFC Pt/C was also documented as key issues for the development of next-generation PEFCs. The present account emphasizes the time-resolved QXAFS and XRD techniques to be a powerful technique to analyze directly the structural and electronic change of metal nanoparticles inside PEFC under the operating conditions

Observation of Degradation of Pt and Carbon Support in Polymer Electrolyte Fuel Cell Using Combined Nano-X-ray Absorption Fine Structure and Transmission Electron Microscopy Techniques

It is hard to directly visualize spectroscopic and atomic–nanoscopic information on the degraded Pt/C cathode layer inside polymer electrolyte fuel cell (PEFC). However, it is mandatory to understand the preferential area, sequence, and relationship of the degradations of Pt nanoparticles and carbon support in the Pt/C cathode layer by directly observing the Pt/C cathode catalyst for the development of next-generation PEFC cathode catalysts. Here, the spectroscopic, chemical, and morphological visualization of the degradation of Pt/C cathode electrocatalysts in PEFC was performed successfully by a same-view combination technique of nano-X-ray absorption fine structure (XAFS) and transmission electron microscopy (TEM)/scanning TEM–energy-dispersive spectrometry (EDS) under a humid N2 atmosphere. The same-view nano-XAFS and TEM/STEM–EDS imaging of the Pt/C cathode of PEFC after triangular-wave 1.0–1.5 VRHE (startup/shutdown) accelerated durability test (tri-ADT) cycles elucidated the site-selective area, sequence, and relationship of the degradations of Pt nanoparticles and carbon support in the Pt/C cathode layer. The 10 tri-ADT cycles caused a carbon corrosion to reduce the carbon size preferentially in the boundary regions of the cathode layer with both electrolyte and holes/cracks, accompanied with detachment of Pt nanoparticles from the degraded carbon. After the decrease in the carbon size to less than 8 nm by the 20 tri-ADT cycles, Pt nanoparticles around the extremely corroded carbon areas were found to transform and dissolve into oxidized Pt2+–O4 species

Visualization Analysis of Pt and Co Species in Degraded Pt3Co/C Electrocatalyst Layers of a Polymer Electrolyte Fuel Cell Using a Same-View Nano-XAFS/STEM-EDS Combination Technique

In order to obtain a suitable design policy for the development of a next-generation polymer electrolyte fuel cell, we performed a visualization analysis of Pt and Co species following aging and degradation processes in membrane-electrode assembly (MEA), using a same-view. Nano-X-ray absorption fine structure (XAFS)/Scanning transmission electron microscope (STEM)-energy dispersive X-ray spectroscopy (EDS) technique that we developed to elucidate durability factors and degradation mechanisms of a MEA Pt3Co/C cathode electrocatalyst with higher activity and durability than a MEA Pt/C. In the MEA Pt3Co/C, after 5000 ADT-rec (rectangle accelerated durability test) cycles, unlike the MEA Pt/C, there was no oxidation of Pt. In contrast, Co oxidized and dissolved over a wide range of the cathode layer (∼70% of the initial Co amount). The larger the size of the cracks and pores in the MEA Pt/C and the smaller the ratio of Pt/ionomer of cracks and pores, the faster the rate of catalyst degradation. In contrast, there was no correlation between the size or Co/ionomer ratio of the cracks and pores and the Co dissolution of the MEA Pt3Co/C. It was shown that Co dissolved in the electrolyte region had an octahedral Co2+–O6 structure, based on a 150 nm × 150 nm nano-XAFS analysis. It was also shown that its existence suppressed the oxidation and dissolution of Pt. The MEA Pt3Co/C after 10,000 ADT-rec cycles had many cracks and pores in the cathode electrocatalyst layer, and about 90% of Co had been dissolved and removed from the cathode layer. We discovered a metallic Pt–Co alloy band in the electrolyte region of 300–400 nm from the cathode edge and square planar Pt2+–O4 species and octahedral Co2+–O6 species in the area between the cathode edge and the Pt–Co band. The transition of Pt and Co chemical species in the Pt3Co/C cathode electrocatalyst in the MEA during the degradation process, as well as a fuel cell deterioration suppression process by Co were visualized for the first time at the nano scale using the same-view nano-XAFS/STEM-EDS combination technique that can measure the MEA under a humid N2 atmosphere while maintaining the working environment for a fuel cell

Thermodynamics of the Schwinger model in a two-dimensional de Sitter space-time

The finite temperature Schwinger model in a background 1-1 de Sitter space is studied. We take account of the curvature effect on the two point Green\u27s function in a short distance. It is shown that the massless and massive boson excitations can not be decoupled and have the interactions through the de Sitter curvature