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At least 379 records · Page 21

Shape Dependence of Pressure-Induced Phase Transition in CdS Semiconductor Nanocrystals

Understanding structural stability and phase transformation of nanoparticles under high pressure is of great scientific interest, as it is one of the crucial factors for design, synthesis, and application of materials. Even though high-pressure research on nanomaterials has been widely conducted, their shape-dependent phase transition behavior still remains unclear. Examples of phase transitions of CdS nanoparticles are very limited, despite the fact that it is one of the most studied wide band gap semiconductors. Here we have employed in-situ synchrotron wide-angle X-ray scattering (WAXS) and transmission electron microscopy (TEM) to investigate the high-pressure behaviors of CdS nanoparticles as a function of particle shapes. We observed that CdS nanoparticles transform from wurtzite to rocksalt phase at elevated pressure in comparison to their bulk counterpart. Phase transitions also vary with particle shape—rod-shaped particles show a partially reversible phase transition and the onset of the structural phase transition pressure decreases with decreasing surface-to-volume ratios, while spherical particles undergo irreversible phase transition with relatively low phase transition pressure. Additionally, TEM images of spherical particles exhibited sintering-induced morphology change after high-pressure compression. Calculations of the bulk modulus reveals that spheres are more compressible than rods in the wurtzite phase. These results indicate that the shape of the particle plays an important role in determining their high-pressure properties. Our study provides important insights into understanding of the phase-structure-property relationship, guiding future design and synthesis of nanoparticles for promising applications.

36 MATERIALS SCIENCE↗

Hydride-Containing Eight-Electron Pt/Ag Superatoms: Structure, Bonding, and Multi-NMR Studies

Recent reports on hydride-doped noble metal nanoclusters strongly suggest that the encapsulated hydride is a part of the superatom core, but no accurate location of the hydride could be experimentally proved, so far. Here, we report herein a hydride-doped eight-electron platinum/silver alloy nanocluster in which the position of four-coordinated hydride was determined by neutron diffraction for the first time. X-ray structures of [PtHAg 19 (dtp/desp) 12 ] (dtp = S 2 P(O n Pr) 2 , 1; dsep = Se 2 P(O i Pr) 2 , 2) describe a central platinum hydride (PtH) unit encapsulated within a distorted Ag 12 icosahedron, the resulting (PtH)@Ag 12 core being stabilized by an outer sphere made up of 7 capping silver atoms and 12 dichalcogenolates. Solid-state structures of 1 and 2 differ somewhat in the spatial configuration of their outer spheres, resulting in overall different symmetries, C 1 and C 3 , respectively. Whereas the multi-NMR spectra of 2 in solution at 173 K reveal that the structure of C 3 symmetry is the predominant one, 1 H and 195 Pt NMR spectra of 1 at the same temperature disclose the presence of isomers of both C 1 and C 3 symmetry. DFT calculations found both isomers to be very close in energy, supporting the fact that they co-exist in solution. They also show that the [PtH@Ag 12 ] 5+ kernel can be viewed as a closed-shell superatomic core, the μ4-hydride electron contributing to its eight-electron count. On the other hand, the 1s(H) orbital contributes only moderately to the superatomic orbitals, being mainly involved in the building of a Pt–H bonding electron pair with the 5d z 2 (Pt) orbital.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Metal–Organic Frameworks as a Tunable Platform to Deconvolute Stereoelectronic Effects on the Catalytic Activity of Thioanisole Oxidation

The local environment of a metal active site plays an important role in affecting catalytic activity and selectivity. In re-cent studies, tailoring the behavior of a molybdenum-based active site via modulation of the first coordination sphere has led to improved thioanisole oxidation performance, but disentangling electronic effects from steric influences that arise from these modifications is nontrivial, especially in heterogeneous systems. To this end, the tunability of metal–organic frameworks (MOFs) makes them promising scaffolds for controlling the coordination sphere of a heterogene-ous, catalytically-active metal site while offering additional, attractive features such as crystallinity and high porosity. Herein, we report a variety of MOF-supported Mo species, which were investigated for catalytic thioanisole oxidation to methyl phenyl sulfoxide and/or methyl phenyl sulfone using tert-butyl hydroperoxide (tBHP) as the oxidant. In particular, MOFs of contrasting node architectures were targeted, presenting a unique opportunity to investigate ste-reoelectronic control of Mo active sites in a systematic manner. A Zr 6 -based MOF, NU-1000, was employed along with its sulfated analog Zr 6 -based NU-1000-SO 4 to anchor a dioxymolybdenum species, which enabled examination of sup-port-mediated active site polarizability on catalytic performance. In addition, a MOF containing a mixed metal node, Mo-MFU-4l, was used to probe the stereoelectronic impact of an N-donor ligand environment on the catalytic activity of the transmetalated Mo center. Furthermore, characterization techniques including single crystal X-ray diffraction, were concomi-tantly used with reaction kinetic profiles to better comprehend the dynamics of different Mo active sites, thus correlat-ing structural change with activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mechanistic Insights into the Origins of Selectivity in a Cu-Catalyzed C–H Amidation Reaction

The catalytic transformation of C-H to C-N bonds offers rapid access to fine chemicals and high-performance materials, but achieving high selectivity from undirected aminations of unactivated C(sp 3 )-H bonds remains an outstanding challenge. Here, we report the origins of the reactivity and selectivity of a Cu-catalyzed C-H amidation of simple alkanes. Using a combination of experimental and computational mechanistic studies and energy decomposition techniques, we uncover a switch in mechanism from inner-sphere to outer-sphere coupling between alkyl radicals and the active Cu(II) catalyst with increasing substitution of the alkyl radical. The combination of computational predictions and detailed experimental validation shows that simultaneous minimization of both Cu-C covalency and alkyl radical size increases the rate of reductive elimination and that both strongly electron-donating and electron-withdrawing substituents on the catalyst accelerate the selectivity-determining C-N bond formation process as a result of a change in mechanism. These findings offer design principles for the development of improved catalyst scaffolds for radical C-H functionalization reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development, Application, and Mechanistic Interrogation of a Dual Ni Catalysis Approach to Photoredox-Based C(sp 3 )–C(sp 3 ) Cross-Coupling

The installation of alkyl substituents such as methyl groups is a crucial tactic for the synthesis and diversification of medicinal compounds with improved pharmacological profiles. However, strategies that leverage methyl radical for C(sp 3 ) methylation remain underdeveloped due to the challenge of obtaining cross-selectivity between fleeting aliphatic radicals and alkyl electrophiles. Here, we report the development, application, and interrogation of a conceptually novel mechanistic framework for C(sp 3 )–Me bond formation using two distinct Ni catalysts capable of cross-coupling sterically and electronically diverse alkyl halides (chlorides and bromides) with methyl radical generated photocatalytically from benzaldehyde dimethyl acetal. Furthermore, by modifying the alkyl substituents on the acetal coupling partner, we demonstrate cross-couplings beyond methylation to access an array of 1°–1° and 1°–2° alkyl–alkyl bonds. Experimental and computational mechanistic studies provide support for cooperativity between an in situ-generated (bpy)Ni I (X) catalyst that facilitates XAT and inner-sphere C–C bond formation and a (Tp*)Ni II (acac) cocatalyst that captures methyl radical and engages in concurrent outer-sphere S H 2 coupling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Correlating Protein Dynamics and Catalytic Activity of a Model Hydrogenase Using Paramagnetic and Biological Nuclear Magnetic Resonance Spectroscopy

Rational catalyst design remains a significant challenge, with electronic structure, steric, and electrostatic effects known to contribute to activity. Recently, dynamics has been recognized as another factor that impacts catalysis, though identifying and predicting these effects has remained out of reach. Nickel-substituted rubredoxin (NiRd), a protein-based mimic of a hydrogenase enzyme, serves as a model catalytic system in which dynamics can be systematically investigated with respect to activity. While over 30 secondary-sphere mutants of NiRd have been shown to be catalytically active, no significant correlation was observed between the rates and catalytic overpotential or electronic structure, prompting questions about the protein-derived factors that modulate activity. Here, in this work, NMR spectroscopy was used to investigate the roles of substrate accessibility, protein dynamics, and protein stability in controlling catalysis. Significant paramagnetic effects from the nickel center (S = 1) isolate the methylene proton resonances of the metal-coordinating cysteine residues. The sensitivity of resonance positions and linewidths to local environment offers an opportunity to study dynamical molecular changes around the metal center with high resolution. Machine learning algorithms were employed to identify correlations between the catalytic activity and the paramagnetic NMR spectra. These analyses revealed spectroscopic features of specific cysteine protons that report on catalytic overpotential and increased turnover rates, which are further supported by the results obtained using high-field NMR techniques. Collectively, these studies indicate the potential for multifrequency NMR techniques to resolve key contributors to catalytic activity and highlight the importance of local and outer-sphere dynamics.

Protein Engineering↗

Selective Reduction of Carbon Dioxide in Water Using [M(bpy2+)(CO)3(I)]2+ (M = Mn, Re) Electrocatalysts with Pendent Cations

Manganese(I) carbonyl complexes are promising electrocatalysts for CO2 reduction, yet their application in homogeneous aqueous media remains limited by poor solubility and selectivity. Here, we report water-soluble Mn(I) and Re(I) complexes fac-[M(bpy2+)(CO)3X]2+ (X = I or Cl), featuring bipyridine ligands functionalized with -Ph-CH2-(NMe3)+ cationic ammonium groups that integrate water solubility with secondary-sphere stabilization. In bicarbonate buffer at pH 6.8, the Mn catalyst is completely selective for CO production at a low overpotential (η = 0.3 V), operating by a protonation-first mechanism with observed rates of ~10 s−1. Pulse radiolysis reveals that the one-electron reduced Mn species undergoes dimerization in the absence of CO2 but uniquely reacts competitively with CO2 through an initial pre-equilibrium followed by fast formation of a dinuclear CO2-bridged species (ΔGo = −12.4 kcal mol−1). At a higher 0.6 V over-potential, a faster reduction-first pathway (~100 s−1) is available upon reduction of the metallo-carboxylic acid intermediate, Mn-CO2H2+; however, this regime is functionally limited by the formation of a resistive, noncatalytic film on the electrode surface. Comparison to the analo-gous water-soluble Re catalyst (kobs = 440 s−1, η = 0.6 V) highlights the distinct mechanistic ad-vantages of earth-abundant Mn in low-potential catalysis. These results demonstrate how cati-onic second-sphere design enables selective, homogeneous CO2 reduction in water while reveal-ing competing radical and electrode-mediated processes that govern catalytic performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tailoring the Selective Oxidation of Hydroxyl-Containing Compounds via Precisely Tuning the Hydrogen-Bond Strength of Catalyst H-Bond Acceptors

The unique performance of the enzyme is mainly achieved via weak interactions between the “outer coordination sphere” and the substrate. Inspired by this process, we developed 3D encapsulated-structure catalysts with hydrogen-bond engineering on the shell, which mimics the “outer coordination sphere” of an enzyme. Various hydrogen bond acceptors (C=O, S=O, and N–O groups) are imparted in the shell. Concentration-dependent 1H NMR, inverse-phase gas Chromatography (IGC) measurements, and DFT calculations underscore that the hydrogen bond strength between the acceptor groups and alcohol follows the order of C=O < S=O < N–O. The hydroxyl compound oxidation rate vs the hydrogen bond strength follows a volcano behavior, reminiscent of Sabatier’s principle. The performance variation among catalysts is attributed to the adsorption strength of the substrate. The proposed bioinspired design principle expands the scope of encapsulated catalysts, enabling fine regulation of catalytic activity through precise microenvironment control via weak interactions with substrates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topology-enhanced mechanical stability of swelling nanoporous electrodes

Abstract Materials like silicon and germanium offer a 10-fold improvement in charge capacity over conventional graphite anodes in lithium-ion batteries but experience a roughly threefold volume increase during lithiation, which challenges ensuring battery integrity. Nanoporous silicon, created by liquid-metal-dealloying, is a potentially attractive anode design to mitigate this challenge, exhibiting both higher capacity and extended cycle lifetimes. However, how nanoporous structures accommodate the large volume change is unknown. Here, we address this question by using phase-field modeling to produce nanoporous particles and to investigate their elastoplastic swelling behavior and fracture. Our simulations show that enhanced mechanical stability results from the network topology consisting of ligaments connected by bulbous, sphere-like nodes. The ligaments forcefully resist elongation while the nodes, behaving like isolated spherical particles, experience large stresses driving fracture. However, being smaller compared to a sphere of the same volume as the entire nanoporous particle, the nodes are more protected against fracture.

36 MATERIALS SCIENCE↗

Poincaré beams from a free electron laser

Poincaré beams are light beams that have spatially inhomogeneous polarization structure that spans a finite portion of the Poincaré sphere. This feature bestows the beams with intriguing topological properties and has led to a surge in research on their fundamental characteristics, their controlled generation and on emerging applications. Here we present an experimental demonstration of a Poincaré beam generated in the extreme ultraviolet (16.7 nm) at the FERMI free electron laser (FEL). The ‘star’ type Poincaré beam is generated by exploiting the phase and intensity structure intrinsic to FEL radiation without relying on optical elements. Here, we controlled the spatial polarization distribution through a precise overlap and power balance between two FEL pulses, each with different transverse phase distributions and orthogonal circular polarizations. The spatial polarization structure was mapped in detail and shows extensive coverage of the Poincaré sphere, in agreement with analytic predictions. This method of in situ Poincaré beam production in FELs enables straightforward flexibility in the orientation and balance of polarization states, and can readily be extended to other vector beams and to shorter wavelengths enabling novel science applications in modern light sources.

Morgan, Jenny [SLAC National Accelerator Laborator↗

Programmable topotaxis of magnetic rollers in time-varying fields

We discuss how spatially uniform, time-periodic magnetic fields can be designed to power and direct the migration of ferromagnetic spheres up (or down) local gradients in the topography of a solid substrate. Our results are based on a dynamical model that considers the time-varying magnetic torques on the particle and its motion through the fluid at low Reynolds number. We use both analytical theory and numerical simulation to design magnetic fields that maximize the migration velocity up (or down) an inclined plane. We show how “topotaxis” of spherical particles relies on differences in the hydrodynamic resistance to rotation about axes parallel and perpendicular to the plane. Importantly, the designed fields can drive multiple independent particles to move simultaneously in different directions as determined by gradients in their respective environments. Experiments on ferromagnetic spheres provide evidence for topotactic motions up inclined substrates. The ability to program the autonomous navigation of driven particles within anisotropic environments is relevant to the design of colloidal robots.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predicting 1 H NMR relaxation in Gd 3+ -aqua using molecular dynamics simulations

Atomistic molecular dynamics simulations are used to predict 1 H NMR T 1 relaxation of water from paramagnetic Gd 3+ ions in solution at 25 °C. Simulations of the T 1 relaxivity dispersion function r 1 computed from the Gd 3+ – 1 H dipole–dipole autocorrelation function agree within ≃8% of measurements in the range f 0 ≃ 5 ↔ 500 MHz, without any adjustable parameters in the interpretation of the simulations, and without any relaxation models. Here the simulation results are discussed in the context of the Solomon-Bloembergen-Morgan inner-sphere relaxation model, and the Hwang-Freed outer-sphere relaxation model. Below f 0 ≲ 5 MHz, the simulation overestimates r 1 compared to measurements, which is used to estimate the zero-field electron-spin relaxation time. The simulations show potential for predicting r 1 at high frequencies in chelated Gd 3+ contrast-agents used for clinical MRI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Carbon nanospike coated nanoelectrodes for measurements of neurotransmitters

Here, carbon nanoelectrodes enable the detection of neurotransmitters at the level of single cells, vesicles, synapses and small brain structures. Previously, the etching of carbon fibers and 3D printing based on direct laser writing have been used to fabricate carbon nanoelectrodes, but these methods lack the ability of mass manufacturing. In this paper, we mass fabricate carbon nanoelectrodes by growing carbon nanospikes (CNSs) on metal wires. CNSs have a short, dense and defect-rich surface that produces remarkable electrochemical properties, and they can be mass fabricated on almost any substrate without using catalysts. Tungsten wires and niobium wires were electrochemically etched in batch to form sub micrometer sized tips, and a layer of CNSs was grown on the metal wires using plasma-enhanced chemical vapor deposition (PE-CVD). The thickness of the CNS layer was controlled by the deposition time, and a thin layer of CNSs can effectively cover the entire metal surface while maintaining the tip size within the sub micrometer scale. The etched tungsten wires produced tapered conical nanotips, while the etched niobium wires were long and thin. Both showed excellent sensitivity for the detection of outer sphere ruthenium hexamine and the inner sphere test compound ferricyanide. The CNS nanosensors were used for the measurement of dopamine, serotonin, ascorbic acid and DOPAC with fast-scan cyclic voltammetry. The CNS nanoelectrodes had a large surface area and numerous defect sites, which improved the sensitivity, electron transfer kinetics and adsorption. Finally, the CNS nanoelectrodes were compared with other nanoelectrode fabrication methods, including flame etching, 3D printing, and nanopipettes, which are slower to make and more difficult for mass fabrication. Thus, CNS nanoelectrodes are a promising strategy for the mass fabrication of nanoelectrode sensors for neurotransmitters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Concentration Dependent Interfacial Chemistry of the NaOH(aq):Gibbsite Interface

Caustic conditions are often employed for dissolution of a wide variety of minerals, where ion sorption, surface diffusion, and interfacial organization impact surface reactivity. In the case of gibbsite, gamma-Al(OH)3, the chemistry at the NaOH(aq) interface is deeply intertwined with industrial processing of aluminum, including metal production and the disposition of Al-containing wastes. To date, little is known about the structure, speciation, and dynamic behavior of gibbsite interfaces (and that of many other minerals) with NaOH(aq)—particularly as a function of ionic strength. Yet concentration-dependent interfacial organization and dynamics are a critical starting point to develop a fundamental understanding of the factors that influence dissolution. This work reports equilibrium molecular dynamics simulations of the gamma-Al(OH)3:NaOH(aq) interface, revealing the sorption behavior and speciation of ions from 0.5–10 M [NaOH]. As inner-sphere complexes, Na+ primarily coordinates to the side of the gibbsite hexagonal cavities, while OH accepts hydrogen-bonding from the surface-OH groups. The mobility of inner-sphere Na+ and OH ions is significantly reduced due to a strong surface affinity in comparison to previous reports of NaCl, CaCl2, or BaCl2 electrolytes. At high [NaOH], contact ion pairing that is observed in the bulk solution is partially disrupted upon sorption to the gibbsite surface by the individual ion–surface interactions. The molecular-scale changes to surface speciation and competition between ion–surface vs. ion–ion interactions influence surface characterization of gibbsite and potential dissolution processes, providing a valuable baseline for starting conditions needed within future reactive molecular simulations.

alkaline solutions, IDREAM, gibbsite, molecular dy↗

Short- vs . long-range elastic distortion: structural dynamics of a [2 × 2] tetrairon( II ) spin crossover grid complex observed by time-resolved X-Ray crystallography

Spin crossover complexes (SCO) are among the most studied molecular switches due to their potential use in displays, sensors, actuators and memory components. A prerequisite to using these materials is the understanding of the structural changes following the spin transition at out-of-equilibrium conditions. So far, out-of-equilibrium studies in SCO solids have been focused on mononuclear complexes, though a growing number of oligonuclear SCO complexes showing cooperative effects are being reported. Here, we use time-resolved pink Laue crystallography to study the out-of-equilibrium dynamics of a [2 × 2] tetranuclear metallogrid of the form [Fe II 4 L Me 4 ](BF 4 ) 4 ·2MeCN ([L Me ] - = 4-methyl-3,5-bis{6-(2,2'-bipyridyl)}pyrazolate). The out-of-equilibrium spin state switching induced by a ps laser pulse demonstrates that the metallogrid exhibits a multi-step response similar to that reported for mononuclear complexes. Contrary to the mononuclear complexes, the metallogrid shows two types of elastic distortions at different time scales. The first is a short-range distortion that propagates over the entire Fe 4 grid complex during the ps time scale, and it is caused by the rearrangement of the coordination sphere of the photo-switching ion and the constant feedback between strongly linked metal ions. The second is a long-range distortion caused by the anisotropic expansion of the lattice during the ns time scale, observed in mononuclear materials. The structural analysis demonstrates that the long-range prevails over the short-range distortion, inducing the largest deformation of both the entire grid and the coordination sphere of each metal ion. The present study sheds light on the out-of -equilibrium dynamics of a non-cooperative oligonuclear complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pre-equilibrium reactions involving pendent relays improve CO 2 reduction mediated by molecular Cr-based electrocatalysts

Homogeneous earth abundant transition-metal electrocatalysts capable of carbon dioxide (CO 2 ) reduction to generate value-added chemical products are a possible strategy to minimize rising anthropogenic CO 2 emissions. Previously, it was determined that Cr-centered bipyridine-based N 2 O 2 complexes for CO 2 reduction are kinetically limited by a proton-transfer step during C–OH bond cleavage. Therefore, it was hypothesized that the inclusion of pendent relay groups in the secondary coordination sphere of these molecular catalysts could increase their catalytic activity. Here, it is shown that the introduction of a pendent methoxy group favorably impacts a pre-equilibrium protonation prior to the catalytic resting state, resulting in a significant increase in catalytic activity without a loss of product selectivity for generating carbon monoxide (CO) from CO 2 . Interestingly, combining the pendent methoxy group with a cationic acid causes a positive shift of the catalytic reduction potential of the system, while maintaining increased activity and quantitative selectivity. This work suggests that tuning the secondary coordination sphere with respect to cationic proton sources can result in activity improvements by modifying the kinetic and thermodynamic aspects of proton transfer in the catalytic cycle.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quasars with large proper motions: A selection from the LQAC-5 catalogue combined with Gaia EDR3: Focusing on astrometric and photometric properties

Thanks to the cross-identification between the Gaia EDR3 (E-Data Release 3) catalogue and the quasars’ compiled catalogue LQAC-5 (Large Quasar Astrometric Catalogue-5), accurate astrometric parameters as well as photometric measurements were available for a set of 416 113 quasars. After analysing the astrometric and photometric properties of these quasars, we concentrate our study on objects characterized by significant proper motion, which contradicts the postulate that they are fixed in the celestial sphere. We derived statistical properties of the positions, parallaxes, and proper motions of the quasars cross-matched with Gaia EDR3. We carried out a specific investigation of quasars with a proper motion larger than 10 mas yr -1 , and used colour-colour diagrams in mid-infrared to discriminate these quasars from stellar contamination. We discuss, in detail, a few cases where the abnormal proper motion could be caused by misidentifications. We note that 43% of LQAC-5 quasars were not detected by Gaia EDR3, mainly because of the cut-off magnitude at G = 21. The comparison between r(G) (Gaia) and r (SDSS) shows a normal distribution. The normalized distributions of parallaxes and proper motions are identical to that of the Gaia CRF2, as well as the distribution of the G BP -G RP colour index. We have identified 937 LQAC-5 objects (0.27% of the sample) with Gaia EDR3 proper motion which is significant at the 5σ level. We have clearly shown that below z = 0.35, the integrated magnitude G(r) obtained from SDSS spectra is smaller than G (Gaia), leading to the statement that the quasars are generally resolved under this threshold, which should lead to a bad determination of proper motion. Moreover, to discriminate quasars from stellar contamination, we have plotted them in a mid-infrared colour–colour diagram. Finally, we have made a final selection of 41 objects with μ > 10 mas yr -1 , satisfying drastic constraints, which makes them potential candidates for considering their proper motion as real. In this paper we carried out a complete analysis of the quasars of the LQAC-5 which were cross-identified with Gaia EDR3 ; this serves as an alternative and complementary study with respect to Gaia CRF2, involving a different population of quasars. We selected a set of 41 quasars with a proper motion exceeding 10 mas yr -1 , which can be considered as very high for objects which are a priori fixed in the celestial sphere.

79 ASTRONOMY AND ASTROPHYSICS↗