Rational D(q)-quintuples Dražić, Goran
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas,
2022/1, Volume:
116, Issue:
1
Journal Article
Peer reviewed
For a nonzero rational number
q
, a
rational
D
(
q
)-
n
-tuple
is a set of
n
distinct nonzero rationals
{
a
1
,
a
2
,
⋯
,
a
n
}
such that
a
i
a
j
+
q
is a square for all
1
⩽
i
<
j
⩽
n
. We ...investigate for which
q
there exist infinitely many rational
D
(
q
)-quintuples. We show that assuming the Parity Conjecture for the twists of several explicitly given elliptic curves, the density of such
q
is at least
295026
/
296010
≈
99.5
%
.
Oxygen vacancies are known to play a crucial role in tuning the physical properties and technological applications of titanium dioxide TiO2. Over the last decades, defects in substoichiometric TiO2 ...have been commonly associated with the formation of Ti n O2n–x Magnéli phases, which are extended planar defects originating from crystallographic shear planes. By combining advanced transmission electron microscopy techniques, electron energy-loss spectroscopy and atomistic simulations, we reach new understanding of the oxygen vacancy induced structural modulations in anatase, ruling out the earlier shear-plane model. Structural modulations are instead shown to be due to the formation of oxygen vacancy superstructures that extend periodically inside the films, preserving the crystalline order of anatase. Elucidating the structure of oxygen defects in anatase is a crucial step for improving the functionalities of such material system and to engineer devices with targeted properties.
Current trends in data processing have given impetus for an intense search of new concepts of memory devices with emphasis on efficiency, speed, and scalability. A promising new approach to memory ...storage is based on resistance switching between charge-ordered domain states in the layered dichalcogenide 1T-TaS2. Here we investigate the energy efficiency scaling of such charge configuration memory (CCM) devices as a function of device size and data write time τW as well as other parameters that have bearing on efficient device operation. We find that switching energy efficiency scales approximately linearly with both quantities over multiple decades, departing from linearity only when τW approaches the ∼0.5 ps intrinsic switching limit. Compared to current state of the art memory devices, CCM devices are found to be much faster and significantly more energy efficient, demonstrated here with two-terminal switching using 2.2 fJ, 16 ps electrical pulses.
PGM-free catalysts have high initial activity for O2 reduction reaction, but they suffer from low stability in acid medium in proton exchange membrane fuel cells (PEMFC) and direct methanol fuel ...cells (DMFC). Here, we shed light on the atomic-scale structure of hybrid Pt/FeNC catalysts (1–2 wt % of Pt), revealing, via scanning tunnelling electron microscopy and energy-dispersive X-ray spectroscopy, the presence of Pt@FeO x particles. The absence of exposed Pt on the surface is confirmed by the suppression of methanol oxidation reaction and CO stripping experiments. The promising application of such Pt/FeNC catalysts, comprising FeN x sites and Pt@FeO x particles, is demonstrated at the cathode of DMFC. To gain fundamental understanding on the stability in acid medium and on the intrinsic ORR activity of Pt@FeO x , we constructed model surfaces by depositing FeO x films with controlled thickness (from 1.0 nm to 6.4 nm), fully covering the Pt(111) surface, which resulted stable in acid medium in the potential range of 0.45–1.05 V vs RHE. The specific ORR activity of Fe2O3/Pt(111) increases exponentially with decreasing overlayer thickness, which is explained by the tunneling of Pt electrons through Fe2O3. This special phenomenon sheds light onto recently reported excellent durability of Pt/FeNC composites in PEMFC and identify a promising core@shell strategy leading to stable PGM-free surfaces in acid medium, and tolerant to methanol.
This study targets one of the grand challenges of electrochemical hydrogen production: a durable and cost-effective oxygen-evolution catalyst. We present a thin-film composite electrode with a unique ...morphology and an ultralow loading of iridium that has extraordinary electrocatalytic properties. This is accomplished by the electrochemical growth of a defined, high-surface-area titanium oxide nanotubular film, followed by the nitridation and effective immobilization of iridium nanoparticles. The applicative relevance of this production process is justified by a high oxygen-evolution reaction (OER) activity and high stability. Enhanced OER performance is due to the strong metal–support interaction (SMSI). The high durability is achieved by self-passivation of the titanium oxynitride (TiON) surface layer with TiO2, which in addition also effectively embeds the Ir nanoparticles while still keeping them electrically wired. An additional contribution to the enhanced durability comes from the nitrogen atoms, which according to our density functional theory (DFT) calculations reduce the tendency of the Ir nanoparticles to grow. Materials are analyzed by advanced electrochemical characterization techniques. Namely, the entire process of the TiON–Ir electrode’s preparation and the electrochemical evaluation can be tracked with scanning electron microscopy, X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS) at identical locations. In general, the experimental approach allows for the unique morphological, structural, and compositional insights into the preparation and electrocatalytic performance of thin films, making it useful also outside electrocatalysis applications.
Catalytic properties of advanced functional materials are determined by their surface and near-surface atomic structure, composition, morphology, defects, compressive and tensile stresses, etc; also ...known as a structure–activity relationship. The catalysts structural properties are dynamically changing as they perform via complex phenomenon dependent on the reaction conditions. In turn, not just the structural features but even more importantly, catalytic characteristics of nanoparticles get altered. Definitive conclusions about these phenomena are not possible with imaging of random nanoparticles with unknown atomic structure history. Using a contemporary PtCu-alloy electrocatalyst as a model system, a unique approach allowing unprecedented insight into the morphological dynamics on the atomic-scale caused by the process of dealloying is presented. Observing the detailed structure and morphology of the same nanoparticle at different stages of electrochemical treatment reveals new insights into atomic-scale processes such as size, faceting, strain and porosity development. Furthermore, based on precise atomically resolved microscopy data, Kinetic Monte Carlo (KMC) simulations provide further feedback into the physical parameters governing electrochemically induced structural dynamics. This work introduces a unique approach toward observation and understanding of nanoparticles dynamic changes on the atomic level and paves the way for an understanding of the structure–stability relationship.
The positive effect of intermetallic ordering of platinum alloy nanoparticles on oxygen reduction reaction (ORR) activity has been well established. What is still missing is an understanding of ...selective leaching of the less noble metal from the ordered structure and its correlation to long-term ORR performance. Using a combination of kinetic Monte Carlo simulations and advanced characterization techniques, we provide unprecedented insight into dealloying of intermetallic PtCu3 nanoparticlesa well-known binary alloy. Comparison of ordered and disordered samples with identical initial compositions and particle size distributions reveals an unexpected correlation: whereas the copper dealloying rates in the ordered and disordered counterparts are almost the same, in the ordered structure Pt atoms are surrounded by 15–30% more Cu atoms throughout all the stages of acid leaching. This more convenient Pt–Cu coordination explains the statistically significant increase of 23–37% in ORR activity of the ordered structure at all stages of alloy degradation.
Engineered solid–liquid interfaces will play an important role in the development of future energy storage and conversion (ESC) devices. In the present study, defective graphene oxide (GO) and ...reduced graphene oxide (rGO) structures were used as engineered interfaces to tune the selectivity and activity of Pt disk electrodes. GO was deposited on Pt electrodes via the Langmuir–Blodgett technique, which provided compact and uniform GO films, and these films were subsequently converted to rGO by thermal reduction. Electrochemical measurements revealed that both GO and rGO interfaces on Pt electrodes exhibit selectivity toward the oxygen reduction reaction (ORR), but they do not have an impact on the activity of the hydrogen oxidation reaction in acidic environments. Scanning transmission electron microscopy at atomic resolution, along with Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), and scanning electron microscopy (SEM), revealed possible diffusion sites for H2 and O2 gas molecules and functional groups relevant to the selectivity and activity of these surfaces. Based on these insights, rGO interfaces are further demonstrated to exhibit enhanced activity for the ORR in nonaqueous environments and demonstrate the power of our ex situ engineering approach for the development of next-generation ESC devices.
The atomic-level response of zigzag ferroelectric domain walls (DWs) was investigated with in situ bias scanning transmission electron microscopy (STEM) in a subcoercive-field regime. Atomic-level ...movement of a single DW was observed. Unexpectedly, the change in the position of the DW, determined from the atomic displacement, did not follow the position of the strain field when the electric field was applied. This can be explained as low mobility defect segregation at the initial DW position, such as ordered clusters of oxygen vacancies. Further, the triangular apex of the zigzag wall is pinned, but it changes its shape and becomes asymmetric under electrical stimuli. This phenomenon is accompanied by strain and bound charge redistribution. We report on unique atomic-scale phenomena at the DW level and show that in situ STEM studies with atomic resolution are very relevant as they complement, and sometimes challenge, the knowledge gained from lower resolution studies.
True doping levels in hydrothermally derived copper-doped ceria Mužina, Katarina; Kurajica, Stanislav; Dražić, Goran ...
Journal of nanoparticle research : an interdisciplinary forum for nanoscale science and technology,
07/2021, Volume:
23, Issue:
7
Journal Article
This work brings a thorough investigation of hydrothermally derived ceria nanoparticles doped with copper in a wide range of concentrations: Cu
x
Ce
1-x
O
2
, where
x
= 0, 0.1, 0.2, 0.3, 0.4, and ...0.5, respectively. X-ray diffraction (XRD) analysis showed no additional phases for all samples up to
x
= 0.4, which exceeds the maximum amount of copper incorporated into ceria without the appearance of copper oxide phase reported in the literature. However, the inductively coupled plasma mass spectrometry (ICP-MS) and energy-dispersive X-ray spectroscopy (EDS) analyses showed that copper is incorporated into the ceria crystal lattice in amounts far lower than the nominal. Nevertheless, the addition of copper has a significant influence on the ceria properties. The size of the obtained nanoparticles was determined by transmission electron microscopy (TEM) and it decreases with the increase of the copper amount from 6 nm for the pure sample to 3.8 nm for the 40 mol. % Cu-doped CeO
2
sample. In accordance with the small particle size, the specific surface area, determined from nitrogen adsorption–desorption isotherms at 77 K, is in the range of 196 to 222 m
2
g
−1
. The increase in the copper amount also causes the reduction of the band gap, as determined by UV–Vis reflectance analysis (UV–Vis DRS), and an increase of reducibility, as proven by temperature-programmed reduction by hydrogen (H
2
-TPR).
PDF
