Calculation Of Vibrational Modes Research Articles

Dislocation‐induced local symmetry reduction in single‐crystal KNbO3 observed by Raman spectroscopy

AbstractIn recent years, dislocation‐tuned functionalized ceramics have become one of the focal points of modern materials research due to their outstanding properties. These range from improved electrical conductivity and ferroelectric properties to dislocation‐enhanced toughening and superconductivity, caused by local strain fields. The aim of this work is to investigate the dislocation‐induced structural changes in single‐crystal KNbO3 by micro‐Raman spectroscopy. Dislocation‐rich regions with tailored densities have been generated using the Brinell indenter scratching method. The influence of the dislocations on the single‐crystal structure can be observed in the Raman spectra. The activation of additional Raman modes is observed, which does not occur in regions of low dislocation density. This observation is confirmed by DFT calculations of vibrational modes and is attributed to a reduction in the crystal symmetry due to increased defect densities in plastically deformed KNbO3. In addition, an increase in compressive stress at higher dislocation densities can be demonstrated by a blueshift in Raman mode positions.

Application and practice optimization of vibratory modes in the teaching of fundamental sight-singing and ear training

Abstract This paper first introduces the vibration modal analysis system and its general design, then improves the smoothing function and wavelet function transform algorithms in the system, and then determines and verifies the characteristic parameter algorithms in the structure of the improved wavelet transform vibration modal algorithms based on longitudinal waves, transverse shear waves, and bending waves in beams. The application of vibrational modes in sight-singing and ear training is examined and analyzed. The results show that the wavelet transform algorithm has the highest accuracy in calculation results. The calculation of vibration modes can be more effective using this basis. The investigation of students’ attitudes towards sight-singing and ear-training learning found that 52.3% of the students like sight-singing and ear-training learning, 40.13% and 7.37% of the students have no feeling for sight-singing and ear-training learning as well as disliking sight-singing and ear-training classes.48.68% and 37.45% of the students agree that sight-singing and ear-training training can help to improve their music literacy, and 25.79% and 56.14% of them think that Less gain in sight-singing ear training class is caused by boring teaching mode and single content. The investigation of vibrational modes in the teaching process of sight-singing and ear training found that 63.27% of the students had a better understanding of the learning process of vibrational modes; 68.59% of the students liked the teaching process of vibrational modes and the teaching method; and 70.79% of the students thought that the vibrational modes were helpful to the learning of sight-singing and ear training.

Architecture of a dinuclear Co(II) complex based on 3-amino-1,2,4-triazole-5-carboxylic acid: molecular structure, thermal behavior, optical properties, and DFT calculations

The dinuclear compound [Co2(Hatzc)2(H2O)6](NO3)2·4H2O containing the polytopic ligand Hatzc‒ = 3-amino-4H-1,2,4-triazole-5-carboxylate was synthesized and characterized. Single-crystal X-ray diffraction showed that two monoanionic N,O-chelating Hatzc‒ ligands bridge two Co(II) ions in a µ-N1,N2 fashion. Both Co(II) centers are further coordinated by three H2O ligands making up an octahedral coordination. A complex network of intra- and intermolecular O‒H···O and N‒H···O hydrogen bonding interactions characterize the structure. Hirshfeld surface analysis, ATR–FTIR, and FT-Raman spectroscopy in combination with density functional theory (DFT) calculation of vibrational modes confirm this multitude of H bonds. Thermogravimetric and differential thermal analysis experiments under an argon atmosphere in the temperature range of 25–900 °C showed thermal stability till about 100 °C and multi-step decomposition yielding Co2O3 at about 280 °C. The octahedral environment of Co(II) was confirmed by UV–vis absorption spectroscopy, which shows weak absorption bands at around 520 nm assignable to electronic d‒d transitions alongside with π‒π* transitions dominating the 250–350 nm range. Time-dependent DFT calculated excited states agree very well in terms of energy match with the observed transitions. The direct and indirect optical band gap values were determined using the Tauc plot method to 3.33 eV and 2.75 eV, respectively, indicating semiconducting properties.

Effect of M site cation ordering on the lattice dynamical properties of the tetragonal Sr2MO4 (M=Cr, Fe, Co, Mo, and Sn) crystals

ABSTRACT Using normal coordinate analysis, the Raman and Infrared phonons are investigated for the tetragonal Ruddlesden-Popper series in phase I4/mmm and symmetry D4h 17. Three stretching and six bending force constants have been included for the calculations of the zone centre vibrational modes. Theoretical assignments for the Raman and infrared wavenumbers for Sr2CrO4, Sr2MoO4, and Sr2SnO4 compounds have been reported for the first time. As per our knowledge, no theoretical assignment has been done for the infrared frequencies for Sr2FeO4 and Sr2CoO4 compounds in I4/mmm phase so far. A strong correlation of the M site has been observed for the various frequencies giving insight into the structure of the studied compounds. The force constants involving the M-site atom show an expected set trend and also indicate the changes in values whenever the atomic orbit changes. Also, the frequencies which are completely dominated by the M atoms show a specific nature as the atomic number changes indicating the strong effect of the size of the M atom in the vibrational properties. In the tetragonal structure of the Ruddlesden-Popper phase of Sr2MO4 (M=Cr, Fe, Co, Mo, and Sn) crystals for each normal mode, the potential energy distributions have been analysed and the contributions of bending and stretching force constants towards different frequencies have been determined.

Vibrational (FT-Raman and FTIR) spectroscopic study, molecular structure, thermodynamic properties and non-linear optical properties of benzyl-3-oxopyperazine-1-carboxylate by density functional theory

In this work, the new organic-inorganic hybrid molecule benzyl-3-oxopyperazine-1-carboxylate (B3O1C) has been investigated with experimental and theoretical studies. The titled molecule B3O1C has been examined by FT-IR and FT-Raman vibrational spectra in the region 4000–600 cm−1 and 4000–100 cm−1, respectively. Quantum chemical calculations of energies, geometrical structure and vibrational modes of stretching, bending and torsion are carried out by density functional theory (DFT) with B3LYP/6-311++G(d,p) and B3LYP/CCPVDZ basis sets. The experimental vibrational data is compared with the theoretical data. The thermodynamic parameters such as heat capacity, entropy and enthalpy at different temperatures are calculated by DFT calculations. Nonlinear optical (NLO) properties are also calculated by DFT Calculations. Gaussian09W and Gaussview 6.0 softwares are used for theoretical calculations.

Structures and localized vibrational states of defects in graphite by tight-binding calculations.

The structural and vibrational properties of pristine graphite and point defects in graphite are studied by tight-binding (TB) calculations using a three-center TB potential model. We showed that the three-center TB potential without "ad hoc" van der Waals interaction corrections can accurately describe the inter-layer distance of graphite and the lowest-energy structures and stabilities of typical point defects in graphite. The results from our TB calculations are in good agreement with those from density-functional theory calculations with van der Waals interaction corrections. We also investigated the vibrational properties to gain better understanding on the localization of vibrational states induced by the point defects. Our calculation results show that although localized or quasi-localized vibrational modes can be found in all defected graphite, the localization induced by Frenkel pair, dual-vacancy, and dual-interstitial defects is much stronger. Atomic displacements associated with the localized vibrational modes induced by these three point defects are also analyzed.

Vibronic interaction in trans-dichloroethene studied by vibration- and angle-resolved photoelectron spectroscopy using 19-90 eV photon energy.

Valence photoelectron spectra and photoelectron angular distributions of trans-dichloroethene have been measured with vibrational resolution at photon energies between 19 eV and 90 eV. Calculations of photoelectron anisotropy parameters, β, and harmonic vibrational modes help provide initial insight into the molecular structure. The photon energy range encompasses the expected position of the atomic Cl 3p Cooper minimum. A corresponding dip observed here in the anisotropy of certain photoelectron bands permits the identification and characterization of those molecular orbitals that retain a localized atomic Cl character. The adiabatic approximation holds for the X2Au state photoelectron band, but vibronic coupling was inferred within the A-B-C and the D-E states by noting various failures of the Franck-Condon model, including vibrationally dependent β-parameters. This is further explored using the linear vibronic coupling model with interaction parameters obtained from ab initio calculations. The A/B photoelectron band is appreciably affected by vibronic coupling, owing to the low-lying conical intersection of the A2Ag and B2Bu states. The C2Bg band is also affected, but to a lesser extent. The adiabatic minima of the D2Au and E2Ag states are almost degenerate, and the vibronic interaction between these states is considerable. The potential energy surface of the D2Au state is predicted to have a double-minimum shape with respect to the au deformations of the molecular structure. The irregular vibrational structure of the resulting single photoelectron band reflects the non-adiabatic nuclear dynamics occurring on the two coupled potential energy surfaces above the energy of their conical intersection.

Density functional LCAO calculations of vibrational modes and phonon density of states in the strained single-layer phosphorene

The paper presents an investigation of phosphorene under axial strain on the phonon density of states and vibrational modes. The studies were performed by means of density functional theory (DFT) within the linear combination of atomic orbitals (LCAO). The strained models were constructed using optimised supercell techniques. The vibrational mode spectra were estimated for strains applied for both the zigzag and armchair directions of phosphorene. This approach is an attractive candidate for the calculation the dynamical matrix of the system because its numerical complexity gradually increases together with the size of the analysed cell. The shift of peaks in the PDOS of black phosphorene is monotonic, and inversely proportional to the applied strain over the zigzag direction. This relation is valid for small strains (below 10%) of peaks corresponding to modes B2g and Ag2. For a strain applied over the armchair PDOS, the shifts are proportional to the strain. The peak shifts tend to become higher as the strain increases. This dependence is not monotonic, and is clearly more rapid for compressing strains. Moreover, the peaks shift slower for an armchair strain than for a zigzag strain, revealing its strong anisotropy.

Properties of RhP predicted by first-principles

Using density functional theory combined with a global crystal structure search with the particle swarm optimization method, we propose three stable three-dimensional (3D) metallic RhP structures, namely, the Cmcm (RhP-I), P6/mmm (RhP-II), and P63mc (RhP-III) phases. All these structures are found to be dynamically stable through vibrational normal mode calculations, indicating that they could be successfully synthesized in experiments. We show that the RhP-I phase has a relatively high thermodynamic stability and high mechanical strength in comparison with the others. The RhP-II and RhP-III phases have porous structures which could accommodate small atoms or molecules. However their thermodynamics are poor, especially the RhP-III phase. The RhP-II structure is stable at 500 K, but the RhP-III fails to survive even at the freezing point of water. Importantly, all these materials have one dimensional conducting channels corresponding to ultrahigh Fermi velocities. Moreover, the porous hexagonal RhP-II and III structures exhibit excellent ability to trap lithium, hydrogen, oxygen, and boron atoms. The RhP-II structure could be especially useful for directly dissociating the hydrogen molecule into two atoms without an energy barrier. In the present study, we identify three new metallic structures to the family of RhP structures, and anticipate their potential for technological applications.

Density Functional Theory Study of the Gas Phase and Surface Reaction Kinetics for the MOVPE Growth of GaAs1-yBiy.

The kinetics of chemical reactions occurring during the metal-organic vapor phase epitaxy (MOVPE) of GaAs1-yBiy have been studied using density functional theory (DFT). GaAs1-yBiy is a metastable semiconductor alloy that has potential applications in high-performance long-wavelength emitters. Its growth is complicated by the low solubility of Bi within the GaAs lattice, which leads to phase segregation under conventional III-V semiconductor growth conditions. In this study, the thermochemical and kinetic parameters of the gas-phase pyrolysis and surface reactions occurring in the MOVPE growth of GaAs1-yBiy from trimethyl bismuth, tertiary butyl arsine, and triethyl gallium are calculated from first-principles electronic structure and vibrational mode calculations. These calculations indicate that the pyrolysis products AsH2 and Bi(CH3)2 are the principle sources for the deposition of their respective metallic elements. The surface-adsorbed methyl species and their interaction with the gas-phase pyrolysis products lead to the self-limiting growth described within this model. The calculated thermochemical and kinetic values provide initial parameters for the development of a microkinetic model of GaAs1-yBiy deposition.

Temperature-Dependent Structural Changes in Liquid Benzene.

Benzene is the simplest aromatic molecule with intermolecular π-π interactions. Because ordered liquids are key structures used to study chemical and biological phenomena in the liquid state, ordered structures of benzene confined in nanopores have been extensively studied, whereas those in the liquid state are still unknown. In this study, we address fundamental questions regarding whether ordered structures of benzene are formed in the liquid state by using carbon K-edge X-ray absorption spectroscopy (XAS) as a sensitive local probe. By comparing unexpected temperature behaviors of the π* peak in XAS spectra with model calculations, we have investigated temperature-dependent changes of ordered structures in liquid benzene caused by the increase in abundance of the parallel sandwich orientation relative to parallel displaced structures for the higher temperature. These results are confirmed by infrared spectroscopy with additional support of vibrational mode calculations.

Calculation of Dipole-Forbidden 5f Absorption Spectra of Uranium(V) Hexa-Halide Complexes.

Restricted-active-space wave function calculations including spin-orbit coupling, in combination with Kohn-Sham density functional calculations of vibrational modes, were used to determine the vibronic and electronic absorption intensities of the near-infrared electric dipole-forbidden 5f-5f transitions of representative uranium(V) hexa-halide complex ions. The agreement with experimentally assigned vibronic and electronic transitions measured for powder or solution samples of salts of the complex ions is reasonable overall and excellent for the experimentally best-resolved E5/2u → E5/2u' bands. The intensity of the vibronic transitions may be borrowed from ligand-to-metal charge-transfer excitations as well as 5f-to-6d metal-centered transitions. Magnetically allowed electronic transitions contribute to the two lower-frequency bands of the ligand-field spectrum.

Influences of physical and structural parameters on vibration modes for large-scale rotating wind turbine blades

For large-scale offshore wind turbine blades, ANSYS and UG were respectively used to complete the solid modeling and the calculation of vibration modes, and the influences of the rotating speed on each order vibration mode and their main reasons were analyzed. Furthermore, the effects of material categories, the deviations of physical parameters in the process of material manufacture and structural parameters on the natural frequencies of rotating blades were respectively compared. Numerical results show that the dynamic stiffening effect of rotating blades is obvious, and the stress stiffness and the geometric stiffness play a dominant role on the natural frequencies from the first to the sixth order and from the seventh to the tenth order respectively. The influences of material categories on natural frequencies of the blades are significantly higher than those of physical parameter deviations and chord length changes. The effects of the equal amplitude increase of elasticity modulus or the chord length and the equal amplitude decrease of density on the tenth order frequency for the torsional vibration are less than those of them on the first nine orders' frequencies for the shimmy and flapping vibration, making that the increase amplitude of the blade natural frequencies first increases and then decreases with the increase of the order number. In addition, the results in this work can provide technical references for the optimization design and the further analysis of vibration characteristics of wind turbine blades.

Numerical and Experimental Research of Natural Frequencies and Mode Shapes for Runner of Francis Turbine

The construction of the physico-mathematical model for the runner of a Francis turbine for calculation of natural frequencies and vibration modes taking into account the influence of liquid is given. Calculation studies on the analysis of natural frequencies and modes of oscillations of the runner were performed on the basis of the application of a coupled finite and boundary elements method.The developed methods also used for comparison of numerical and experimental parameters of natural vibrations for different types of hydraulic machines. The results of calculations for runner Francis turbine and the blade of the runner Kaplan turbine showed good agreement with the experimental data

Monitoring Photochemical Reaction Pathways of Tungsten Hexacarbonyl in Solution from Femtoseconds to Minutes

Metal-organic complexes are widely used across disciplines for energy and biological applications, however, their photophysical and photochemical reaction coordinates remain unclear in solution due to pertaining molecular motions on ultrafast time scales. In this study, we apply transient absorption and tunable femtosecond stimulated Raman spectroscopy (FSRS) to investigate the UV photolysis of tungsten hexacarbonyl and subsequent solvent binding events. On the macroscopic time scale with UV lamp irradiation, no equilibrated intermediate is observed from W(CO)6 to W(CO)5(solvent), corroborated by vibrational normal mode calculations. Upon 267 nm femtosecond laser irradiation, the excited-state absorption band within ∼400-500 nm exhibits distinct dynamics in methanol, tetrahydrofuran, and acetonitrile on molecular time scales. In methanol, solvation of the nascent pentacarbonyl-solvent complex occurs in ∼8 ps and in tetrahydrofuran, 13 ps which potentially involves the associative oxygen-donating ligand rearrangement reaction. In contrast, a stimulated emission feature above 480 nm emerges after ∼1 ps in acetonitrile with a nitrogen-donating ligand. These structural dynamics insights demonstrate the combined resolving power of ultrafast electronic and stimulated Raman spectroscopy to elucidate photochemistry of functional organometallic complexes in solution. The delineated reaction pathways in relation to ligand nucleophilicity and solvent reorientation time provide the rational design principles for solution precursors in nanowrite applications.

Modal Analyses of Deployable Truss Structures Based on Shape Memory Polymer Composites

With large spatial deployable antennas used more widely, the stability of deployable antennas is attracting more attention. The form of the support structure is an important factor of the antenna’s natural frequency, which is essential to study to prevent the resonance. The deployable truss structures based on shape memory polymer composites (SMPCs) have made themselves feasible for their unique properties such as highly reliable, low-cost, light weight, and self-deployment without complex mechanical devices compared with conventional deployable masts. This study offers deliverables as follows: an establishment of three-longeron beam and three-longeron truss finite element models by using ABAQUS; calculation of natural frequencies and vibration modes; parameter studies for influence on their dynamic properties; manufacture of a three-longeron truss based on SMPC, and modal test of the three-longeron truss. The results show that modal test and finite element simulation fit well.

Two‐Dimensional Boron Hydride Sheets: High Stability, Massless Dirac Fermions, and Excellent Mechanical Properties

AbstractTwo‐dimensional (2D) boron sheets have been successfully synthesized in recent experiments, however, some important issues remain, including the dynamical instability, high energy, and the active surface of the sheets. In an attempt to stabilize 2D boron layers, we have used density functional theory and global minimum search with the particle‐swarm optimization method to predict four stable 2D boron hydride layers, namely the C2/m, Pbcm, Cmmm, and Pmmn sheets. The vibrational normal mode calculations reveal all these structures are dynamically stable, indicating potential for successful experimental synthesis. The calculated Young's modulus indicates a high mechanical strength for the C2/m and Pbcm phases. Most importantly, the C2/m, Pbcm, and Pmmn structures exhibit Dirac cones with massless Dirac fermions and the Fermi velocities for the Pbcm and Cmmm structures are even higher than that of graphene. The Cmmm phase is reported as the first discovery of Dirac ring material among boron‐based 2D structures. The unique electronic structure of the 2D boron hydride sheets makes them ideal for nanoelectronics applications.

Two-Dimensional Boron Hydride Sheets: High Stability, Massless Dirac Fermions, and Excellent Mechanical Properties.

Two-dimensional (2D) boron sheets have been successfully synthesized in recent experiments, however, some important issues remain, including the dynamical instability, high energy, and the active surface of the sheets. In an attempt to stabilize 2D boron layers, we have used density functional theory and global minimum search with the particle-swarm optimization method to predict four stable 2D boron hydride layers, namely the C2/m, Pbcm, Cmmm, and Pmmn sheets. The vibrational normal mode calculations reveal all these structures are dynamically stable, indicating potential for successful experimental synthesis. The calculated Young's modulus indicates a high mechanical strength for the C2/m and Pbcm phases. Most importantly, the C2/m, Pbcm, and Pmmn structures exhibit Dirac cones with massless Dirac fermions and the Fermi velocities for the Pbcm and Cmmm structures are even higher than that of graphene. The Cmmm phase is reported as the first discovery of Dirac ring material among boron-based 2D structures. The unique electronic structure of the 2D boron hydride sheets makes them ideal for nanoelectronics applications.

Assessment of different basis sets and DFT functionals for the calculation of structural parameters, vibrational modes and ligand binding energies of Zr4O2(carboxylate)12 clusters

Different basis sets and functionals in the framework of Density Functional Theory (DFT) were assessed for an accurate prediction of structural parameters and vibrational modes of the cluster Zr4O2(methacrylate)12. A basis set of at least triple-ξ quality is necessary to accurately model the geometry and the IR spectra. Bond distances are best reproduced with hybrid functionals, while IR frequencies are best described by the generalized gradient approximation family of functionals. LDA functionals give the highest GGA functionals the lowest ligand binding energies. Increasing the amount of Hartree Fock exchange in the hybrid functionals results in higher binding energies. Binding energies of ligands in different positions of Zr4O2(methacrylate)12 were calculated. The ligand binding energy decreases when the H atoms in an acetate ligand are successively replaced by F atoms with concomitant lengthening of the Zr–O bond. A chelating acetylacetonate ligand shows a higher ligand binding energy than chelating carboxylate ligands.

Calculation of Vibration Modes of Mechanical Waves on Microtubules Presented like Strings and Bars

The study describes a physical model of vibrating microtubules in living cells, presented as strings and bars. Calculated are proper-frequencies of first four vibration modes of transverse and longitudinal waves on microtubules. For microtubules with length 1-30µm and shear modulus 5.0×106 N/m2 the proper-frequencies of standing transverse waves fall in diapason of 1×103 - 5×107 Hz. For microtubules with same length and Young’s modulus 108–109 N/m2 the proper-frequencies of standing longitudinal waves fall in diapason of 5×106 - 3×109 Hz. These calculated diapasons of frequencies overlap with experimentally registered diapasons of frequencies of mechanical and electric vibrations in bacteria, yeast cells, erythrocytes, infuzorii and soma cells. Some theoretical problems related to the present model are discussed.