Number Of Atoms Research Articles

Annihilator intersection graph of a lattice

For a lattice [Formula: see text], we associate a graph called the annihilator intersection graph of [Formula: see text], denoted by [Formula: see text] The vertex set of [Formula: see text] is the set of all nonzero zero-divisors of [Formula: see text] and any two distinct vertices [Formula: see text] and [Formula: see text] are adjacent in [Formula: see text] if and only if [Formula: see text]. It has shown that the [Formula: see text] is disconnected if and only if the number of atoms in [Formula: see text] is two. If [Formula: see text] is connected, then we determine the diameter and the girth of [Formula: see text] We characterize all lattices whose annihilator intersection graph is planar. Further, we obtain the clique number and chromatic number of [Formula: see text] when [Formula: see text] is a finite Boolean lattice. We show that the domination number of [Formula: see text] is not exceeding two. Finally, we obtain a condition under which the annihilator intersection graph is identical with the zero-divisor graph and the annihilator ideal graph of lattices.

ION-PAIR CONVERSION THERMODYNAMICS IN ALCOHOL SOLUTIONS OF HYDROGEN HALIDES

The calculation of thermodynamic characteristics of dissociation of contact and solvent-separated ion pairs into ions, conversion of contact ion pairs into solvent-separated ion pairs of ionogens HCl, HBr and HI in n-alcohols from methyl alcohol to n-octyl alcohol by the method described earlier for the systems HCl – n-alcohol in the same solvents at the same temperatures was carried out. The following regularities were established in this work: a) positive values of the change in the Gibbs energy of dissociation (ΔdisG°) of contact and solvent-separated ion pairs increase in the case of increasing temperature and the number of carbon atoms in the n-alcohol molecule and decreasing radius of the halide ion, and their sign and magnitude are determined by the entropic component (–TΔdisS°). In this case, the values of ΔdisG° of contact ion pairs exceed the same values for ion pairs separated by solvent; b) the values of the Gibbs energy change (ΔconvG°) for the studied ionogens HCl, HBr, and HI are also positive, except for the values of ΔconvG° of ionogens in methanol and HBr solutions in ethanol. In these cases, the ΔdisG° values for solvent-separated ion pairs exceed the same values for contact ion pairs, and the ΔconvG° values are negative. With increasing temperature and radius of the halide ion, ΔconvG° become more negative, and vice versa with increasing hydrocarbon radical; c) the concentration of contact ion pairs increases in the methanol – n-octanol series for all ionogens, decreases slightly with increasing temperature and radius of the anion, and varies from ~30% (methanol) to ~95% (n-octanol). In methanol, solvent-separated ion pairs predominate; in alcohols from n-propyl to n-octyl, contact ion pairs predominate, i.e., deconversion of ion pairs occurs.

Molecular dynamics simulations into rolling scraping of nickel-copper bilayer film

In order to investigate the nanoscale friction mechanism and deformation behavior of nickel-copper bilayer film under rolling scraping, the effects of different factors during friction process such as the translation velocity, rotation velocity, radius of abrasive grain, contact depth, texture direction and crystallographic orientation are analyzed through molecular dynamics methods in terms of contact force, atomic lattice structure, internal substrate dislocation, kinetic energy and temperature. Results show that the contact force increases with the increase of the translation velocity or the decrease of the rotation velocity. Abrasive grains in a purely rolling state cause the most serious damage to the substrate. The contact force increases with the increase of contact depth or the decrease of abrasive grain radius. The crystallographic orientation has a significant effect on rolling scraping process and there is a crystallographic orientation with the minimum contact force. The degrees of substrate dislocation and the numbers of lattice reconstruction atoms under different factors and levels vary widely.

Unraveling Hydrogen Adsorption on Transition Metal-Doped [Mo3S13]2- Clusters: Insights from Density Functional Theory Calculations.

Molecular and dissociative hydrogen adsorption of transition metal (TM)-doped [Mo3S13]2- atomic clusters were investigated using density functional theory calculations. The introduced TM dopants form stable bonds with S atoms, preserving the geometric structure. The S-TM-S bridging bond emerges as the most stable configuration. The preferred adsorption sites were found to be influenced by various factors, such as the relative electronegativity, coordination number, and charge of the TM atom. Notably, the presence of these TM atoms remarkably improved the hydrogen adsorption activity. The dissociation of a single hydrogen molecule on TM[Mo3S13]2- clusters (TM = Sc, Cr, Mn, Fe, Co, and Ni) is thermodynamically and kinetically favorable compared to their bare counterparts. The extent of favorability monotonically depends on the TM impurity, with a maximum activation barrier energy ranging from 0.62 to 1.58 eV, lower than that of the bare cluster (1.69 eV). Findings provide insights for experimental research on hydrogen adsorption using TM-doped molybdenum sulfide nanoclusters, with potential applications in the field of hydrogen energy.

Compression and fretting wear studies of γ/α 2 duplex TiAl alloys at the nanoscale

The study investigated the nanofabrication behavior of TiAl alloys with a duplex structure of γ/α 2. The process included downward pressure followed by reciprocating friction with diamond grinding balls and was simulated using molecular dynamics (MD). It was found that a certain number of dislocations in the workpiece was low, and the resilience was high during the initial pressing stage. The dislocations increased, the resilience decreased, and the plastic deformation capacity was enhanced under continuous pressing. The α 2 phase did not deform significantly during the compression process. The presence of the α 2 phase increases the overall hardness of the material, and elastic-plastic deformation occurs mainly where the γ phase is present; the endowment layer dislocations generated during the intrinsic stacking fault rebound via the phase boundary to form V-shaped dislocations. During the reciprocating friction of the workpiece, forward friction produces V-shaped dislocations, and reverse friction makes the dislocations disappear. This process results in the forward average friction force being more significant than the reverse average. γ/α 2 phase boundary has an impeding effect on the downward proliferation of defects, and the phase boundary makes the temperature transfer appear discontinuous. During friction, the specific number of vacancy atoms in the γ-phase increases, and the transition between FCC and HCP occurs.

Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement.

We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose-Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled optical microcavity under genuine grand canonical conditions, we apply our formalism to a system of non-interacting Bose particles confined in a two-dimensional harmonic trap. We discuss in detail the mathematical origin of the inequivalence of ensembles observed in the condensed phase, giving place to the so-called grand canonical catastrophe of density fluctuations. We also provide explicit analytical expressions for the internal energy and specific heat and compare them with available experimental data. For these quantities, we show the equivalence of ensembles in the thermodynamic limit.

Enhanced sensing properties of CoFe2O4 nanosheet and sensing reaction molecule mechanism of polar CoFe2O4 {111} surfaces

The sensitivity of nanostructures to gases can be improved by exposing their polar surfaces. In this project, a CoFe2O4 nanosheet with {111} polar surface was obtained by selective adsorption of -OH, -OHC2H5OH, and SO42-. By hydrogenating the polar surface of Fe-CoFe2O4 (111), the -OH, -OC2H5OH and SO42- groups were effectively removed, which greatly improved the gas sensing sensitivity of CoFe2O4 nanosheets. This innovative technique provides a feasible way to improve the gas sensing performance of nanosheets. The results show a significant increase in the number of coordination-unsaturated metal-iron atoms (Fe3c) on polar surfaces, which improves sensitivity. As a gas sensing centre, Fe3c can adsorb oxygen, generate free electrons and catalyse sensing reactions. A microscopic mechanism for gas sensing is thus proposed. These results suggest that coordinated unsaturated metal atoms on the surface of metal oxides are active sites for gas sensing and that this gas sensing mechanism is universal.

Theoretical investigation on the optical absorption spectra in cyclo[[formula omitted]]carbons ([formula omitted] 10, 14, 18)

The optical absorption spectra of cyclo[n]carbons (n= 10, 14, 18) are investigated in the framework of time-dependent density functional theory. The collective plasmon excitations well develop as the increases of the ring size and the symmetry group of cyclo[n]carbons. An increase in intensity for the main peaks with the growing number of atoms in cyclo[n]carbons is observed. With the increase of the radius of the monocyclic ring, as more electrons participate in the dipole oscillation the main excitation peaks are red-shifted to the lower energy. The highly symmetrical structures of cyclo[n]carbons (Dnh) possess degenerate levels, leading to simpler spectra with fewer peaks. The Fourier transform of the induced electron density of the cyclo[n]carbons (n= 10, 14, 18) is investigated at the excitation frequencies.

Discriminative dictionary learning for nonnegative representation based classification

Representation based classification (RC) algorithms have been successfully applied to pattern classification. However, most existing RC algorithms are not robust to bad training samples, since they ignore learning more discriminative dictionary atoms and instead directly use training samples as dictionary atoms. In addition, in order to improve expression ability and recognition accuracy, RC algorithms often need to expand the number of dictionary atoms, resulting in a surge in storage and computing costs. To obtain a more discriminative and compact dictionary, this study proposes discriminative dictionary learning for nonnegative representation based classification (DDLNRC). Specifically, in the DDLNRC, this paper utilizes nonnegative constraint to obtain a nonnegative representation for each training sample on the dictionary. In the dictionary learning stage, for a training sample, the DDLNRC minimizes the intra-class reconstruction error of the training sample and simultaneously enlarges the distance between the training sample and the atom that has the most influence on inter-class reconstruction error. Experiments demonstrate the effectiveness of the DDLNRC. Combined with the deep neural network features, it also can achieve higher accuracy than using the Softmax.

Spectroscopy of the 5s5p3P0→5s5d3D1 transition of strontium using laser cooled atoms

This article presents spectroscopy results of the 5s5p3P0→5s5d3D1 transition in all isotopes of laser cooled Sr atoms and the utility of this transition for repumping application. By employing the 5s5p3P0→5s5d3D1 (483 nm) transition in combination with the excitation of 5s5p3P2→5s6s3S1 (707 nm) transition, we observe a significant increase (∼13 fold) in the steady state number of atoms in the magneto-optic trap. This enhancement is attributed to the efficient repumping of Sr atoms that have decayed into the dark 5s5p3P2 state by returning them to the ground state 5s21S0 without any loss into the other states. The absolute transition frequencies were measured with an absolute accuracy of 30 MHz. To support our measurements, we performed Fock-space relativistic coupled-cluster calculations of the relevant parameters in Sr To further increase the accuracy of the calculated properties, corrections from the Breit, quantum electrodynamical and perturbative triples were also included. The calculated branching ratio for the repumping state confirms the significantly increased population in the 3P1 state. Thereby, leading to an increase of population of atoms trapped due to the enhanced repumping. Our calculated hyperfine-splitting energies are in excellent agreement with the measured values. Moreover, our calculated isotope shifts in the transition frequencies are in good agreement with our measured values.

Time-resolved solvation of alkali ions in superfluid helium nanodroplets.

The sinking of alkali cations in superfluid 4He nanodroplets is investigated theoretically using liquid 4He time-dependent density functional theory at zero temperature. The simulations illustrate the dynamics of the buildup of the first solvation shell around the ions. The number of helium atoms in this shell is found to linearly increase with time during the first stages of the dynamics. This points to a Poissonian capture process, as concluded in the work of Albrechtsen et al. on the primary steps of Na+ solvation in helium droplets [Albrechtsen et al., Nature 623, 319 (2023)]. The energy dissipation rate by helium atom ejection is found to be quite similar between all alkalis, the main difference being a larger energy dissipated per atom for the lighter alkalis at the beginning of the dynamics. In addition, the number of helium atoms in the first solvation shell is found to be lower at the end of the dynamics than at equilibrium for both Li+ and Na+, pointing to a kinetic rather than thermodynamical control of the snowball size for small and strongly attractive ions.

Mechanism and deformation behavior of elliptical vibration-assisted cutting of FeNiCrCoAl high entropy alloy

The mechanical response of FeNiCrCoAl high entropy alloy (HEA) under conventional cutting and ultrasonic elliptical vibration-assisted cutting (UEVAC) was investigated using molecular dynamics (MD) methods. The effects of vibration period, axial amplitude, and normal amplitude on the material removal mechanism were studied. The results show that the average cutting temperature of the workpiece under UEVAC is significantly higher than that under conventional cutting. The high-temperature distribution area under UEVAC presents an intermittent distribution pattern, which not only facilitates the cutting process but also plays a positive role in the protection of the tool. Furthermore, as the vibration period shortens, both the average principal stress experienced by the workpiece and the triaxial cutting force decrease, while the height and quantity of chip atoms significantly increase. When the vibration period is shortened to 5 ns, the number of chip atoms is about twice that of conventional cutting, which is equivalent to doubling the removal efficiency of the material. Although an increase in axial amplitude causes an increase in the average temperature of the workpiece, it also results in larger negative principal stress. When the axial amplitude A increases to 20 Å, the peak value of the negative principal stress generated inside the base material exceeds 8000 GPa, and the triaxial cutting force tends to increase, without a significant increase in the number of chip atoms. With the increase in normal amplitude B, the average cutting temperature of the matrix also increases. But there is no significant change in the direction and magnitude of the principal stress, and the triaxial cutting force continuously increases. This study provides a theoretical basis for achieving high surface quality of HEAs.

Heliconical nematic and smectic phases: the synthesis and characterisation of the CB4O.m and CB8O.m series

ABSTRACT The synthesis and characterisation of two series of nonsymmetric dimers belonging to the family of compounds, the 1-(4-cyanobiphenyl-4′-yl)-ω-(4-alkylanilinebenzylidene-4′-oxy)alkanes (CBnO.m) is reported; in the acronym, n refers to the number of carbon atoms in the spacer, and m in the terminal alkyl chain. The two series reported, CB4O.m and CB8O.m, both show twist-bend nematic (NTB) and smectic phases (SmCTB-SH and SmCTB-DH). Their phase behaviour is compared to that of the CB6O.m and CB10O.m series. For each series, locally intercalated molecular packing is observed for short terminal chains and interdigitated packing for long terminal chains. The intercalated anticlinic smectic CA phase is observed for the CB8O.m and CB10O.m series. All four series exhibit the SmCTB-SH and SmCTB-DH phases for the longer terminal chains and all have an interdigitated molecular arrangement. The absence of an intercalated heliconical phase is attributed to the high viscosity associated with the network intercalated structure.

Magnetism and electronic properties of ConMoP (n = 1 ~ 5) cluster: a DFT study.

Hydrogen has emerged as a promising clean energy carrier, underscoring the imperative need to comprehend its adsorption mechanisms. This study delves into the magnetic and electronic properties of Co-Mo-P clusters, aiming to unveil their catalytic potential in hydrogen production. Employing density functional theory (DFT), we optimized cluster configurations and scrutinized their magnetic behaviors. Our investigation unveiled 16 stable configurations of the ConMoP (n = 1 ~ 5) cluster, predominantly in steric forms. The magnetic attributes were primarily ascribed to the d orbitals of Co metal atoms, with Co3MoP exhibiting exceptional magnetic characteristics. Analysis of density of state diagrams revealed the prevalence of spin-up α-electrons in d orbitals, while spin-down β-electrons attenuated overall magnetic properties. Localized orbital (LOL) analysis highlighted stable covalent bonds within the clusters, affirming their catalytic potential. Orbital delocalization index (ODI) analysis revealed diverse spatial distribution ranges for orbitals across different configurations, suggesting a progressive attenuation of off-domain properties with increasing cluster size. Furthermore, infrared spectroscopy unveiled distinct vibrational peaks in various configurations, indicative of unique infrared activities. These findings contribute to a nuanced theoretical understanding of Co-Mo-P clusters and pave the path for future research aimed at augmenting their catalytic efficiency in hydrogen production. This study underscores the viability of Co-Mo-P clusters as alternatives to conventional Pt catalysts, offering insights into the design of novel materials for sustainable energy applications. Further research is warranted to explore the behavior of the Co-Mo-P system under diverse reaction conditions, fostering advancements in materials and energy science. In this study, we harnessed the ConMoP (n = 1 ~ 5) cluster as a simulation platform for probing the local structure of the material. Our aim was to scrutinize the magnetism, electronic characteristics influenced by the varying metal atoms within these clusters. A systematic exploration involved incrementing the number of metal atoms and expanding the cluster size to elucidate the corresponding property variations. Density functional theory (DFT) calculations were pivotal to our methodology, employing the B3LYP hybrid functional implemented in the Gaussian16 software package. The ConMoP (n = 1 ~ 5) cluster underwent optimization calculations and vibrational analysis at the def2-tzvp quantization level, yielding optimized configurations with diverse spin multiplet degrees. To comprehensively characterize and visually represent the stability, electronic features, and catalytic attributes of these configurations, we employed a suite of computational tools. Specifically, quantum chemistry software GaussView and wave function analysis software Multiwfn played integral roles. Through the integrated use of these computational tools, we acquired valuable insights into the magnetism, electronic characteristics of the ConMoP (n = 1 ~ 5) cluster, shedding light on their dependency on distinct metal atoms.

Synergistic influence of dislocations and helium cluster on hydrogen atom in tungsten

Dislocations are common line defects in the preparation and irradiation processes of tungsten (W), and they can serve as trapping sites for hydrogen (H) and helium (He) atoms. Existing studies have indicated that dislocations preferentially capture He atoms to form dislocation-He cluster structures. The focus of this study was on the effects of this new structure on the trapped and diffusion behavior of H atoms using molecular dynamics (MD) method. The study considered the number of He atoms from 1 to 150, and they were classified as small He cluster and large He cluster. By calculating the binding energy, the study revealed that the capture strength is positively correlated with the He clusters’ size. However, it is negatively correlated with the distance from the dislocation core and the captured H atoms’ number. This study output the stable configurations to analyze the growth patterns of He cluster in dislocations, and it was observed that the interstitial atoms caused by trap mutation preferentially aggregate into dislocation loops due to the dislocation core structure. Moreover, the study investigated the diffusion behavior of H atoms around the dislocation-He cluster structure at 600 K within 1 ns. The hydrogen atoms tend to migrate towards the He cluster and distribute around it uniformly. The distribution range narrows with the helium cluster's size, and the distribution pattern depends on the dislocations’ type. This demonstrated the formation of dislocation-He cluster structure, promoting the increased H retention.

Insights on selective Pb adsorption via O 2p orbit in UiO-66 containing rich-zirconium vacancies

Herein, we constructed defective UiO-66 with rich Zr vacancy structure model, in which the defective structure was verified by various characterizations. Also, the Pb adsorption experiments affirmed that defective UiO-66 could display better adsorption and selective adsorption ability than that of perfect UiO-66. The results of partial density of states (PDOS) and Mulliken charge population indicated that the blue shift of O 2p and Zr 4d orbit induced the electron rearrangement of atoms closed to the bonding sites, while the positive charge number of Zr atoms decreased than before. Combining with the expansion of pore size, Pb atom was more inclined to transfer and bond with unsaturated coordination oxygens. More significantly, quantitative structure-activity relationships (QSARs) demonstrated that selective capture of Pb instead of Zn, Cu, Cd and Hg displayed by defective UiO-66 was determined jointly by bond strength, adsorption energy and electron transfer. This work provided some theoretical direction for the purpose of the fabrication of adsorbent and the investigation of mechanism.

Introducing hafnium to atomically small- and medium-sized tin clusters (HfSnn0/-/2- (n = 4–17)): A computational investigation of geometrical and growth behavior, spectral properties, electronic configuration and thermochemistry

The global and local minimum configurations of single Hf atom doped Sn clusters are conducted via density function theory (DFT) combined with artificial bee colony algorithm (ABCluster). Furthermore, DFT method is also used to systematically investigate on their structural growth evolution, spectral and electronic information, thermochemical properties following the size of tin clusters doped Hf atom. Structurally, the ground-state geometries of neutral, anion and di-anion are discovered that, from n = 4, the number of Sn atoms in cluster, HfSnn0/-/2- adsorb additional Sn atom on the prior architecture one by one until forming n = 17 for HfSnn-10/-, as well as forming n = 16 for HfSnn-12-. And for the HfSn110/- and HfSn102- as beginning the species veritably develop sealed architectures. The strongest vibrational modes of sealed nanoclusters are stretching modes of Hf atom with infrared actives and breathing modes of the Sn cage framework with Raman actives, respectively. The natural population analysis (NPA) elucidates the stronger relationship between the Hf atoms and the tin frameworks in sealed clusters than that in unsealed clusters. The results of thermochemical properties, molecular orbital shell (MOs), adaptive natural density partitioning (AdNDP) and ultraviolet visible absorption spectrum (UV–Vis) indicate that, the HfSn16 with high symmetry of Td exhibits thermochemical stability and optoelectronic properties, which is utilized potentially as zero-dimensional unit of self-assembling fluorescent nanomaterials.

Dicke State Generation and Extreme Spin Squeezing via Rapid Adiabatic Passage.

Considering the unique energy level structure of the one-axis twisting Hamiltonian in combination with standard rotations, we propose the implementation of a rapid adiabatic passage scheme on the Dicke state basis. The method permits to drive Dicke states of the many-atom system into entangled states with maximum quantum Fisher information. The designed states allow us to overcome the classical limit of phase sensitivity in quantum metrology and sensing. We show how to generate superpositions of Dicke states, which maximize metrological gain for a Ramsey interferometric measurement. The proposed scheme is remarkably robust to variations of the driving field and has favorable time scaling, especially for a small to moderate (∼1000) number of atoms, where the total time does not depend on the number of atoms.

The rule of four: anomalous distributions in the stoichiometries of inorganic compounds

Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence—named here the rule of four—has to our knowledge not previously been reported or studied. Here, we first highlight the rule’s existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the rule of four are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method.

Biomarker Hydrocarbons and Carbon Isotopes of Individual n-Alkanes in Paraffin Oils and Bitumens of the Middle Devonian–Lower Frasnian Terrigenous Complex of the Timan–Pechora Basin

Abstract ––The objects of study were bitumens of sedimentary rocks and paraffin oils of the Middle Devonian–lower Frasnian terrigenous complex of the Timan–Pechora basin. We studied the composition of biomarker hydrocarbons and the carbon isotope composition of individual n-alkanes of bitumens from the cores of the wells of the Omra–Lyzha saddle. The results were compared with similar data on the composition of paraffin oils from the south of the Pechora–Kozhva megaswell. The generation potential and thermal maturity of organic matter were studied by the Rock-Eval pyrolysis method. The maturity of organic matter in the rocks of the studied complex in the Omra–Lyzha saddle and the Pechora–Kozhva megaswell corresponds to the oil window. Data on the carbon isotopy of n-alkanes and on the composition of biomarker hydrocarbons do not contradict the possible genetic relationship between paraffin oils and the organic matter of the host sedimentary complex. Both the studied paraffin oils and the rock bitumens contain early eluting rearranged hopanes atypical of oils of other petroliferous complexes and show high contents of n-alkanes relative to iso-alkanes and polycyclic biomarkers. The content of 13C tends to decrease with an increase in the number of carbon atoms in the n-alkane molecule in both oils and bitumen rocks.