Cartesian Dynamics of Simple Molecules III Non-Linear Triatomics (C2v Symmetry)

A simple spring model for the molecular vibrations of non-linear triatomic molecules with C_2v symmetry is described in terms of Cartesian co-ordinates. Analytical expressions for the stretching and bending mode frequencies are obtained and compared with previous derivations. Optimized values of force constants are calculated for models involving two or three adjustable parameters. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. The model provides a simple explanation of the near degeneracy of the symmetric and asymmetric stretching frequencies of H₂S and H₂Se.     

Cartesian Dynamics of Simple Molecules IV Centrosymmetric Linear Quadratomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centrosymmetric linear quadratomic molecules, such as cyanogen and acetylene and its halogenated derivatives. Analytical expressions for the three stretching and two bending mode frequencies are obtained in terms of five independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. The validity of the model is confirmed by the satisfactory agreement between calculated and observed frequencies of isotopic species.     

Cartesian Dynamics of Simple Molecules VIII planar quadratomics (D3h symmetry)

The vibrations of planar A₃B type molecules with D_3h symmetry are analysed, by treating these molecules as a special case of A₂BC types with C_2v symmetry. Analytical expressions for the four normal mode frequencies are derived in terms of four force constants, and optimized values of the latter for the boron trihalides and sulphur trioxide are obtained and briefly discussed. Frequencies of various isotopic species are also calculated.     

Cartesian Dynamics of Simple Molecules VI Centrosymmetric Linear Pentatomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centresymmetric linear pentatomic molecules such as carbon suboxide and carbon subsulphide. Analytical expressions for the four stretching and three bending mode frequencies are derived in terms of seven independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. Eigenvectors of the normal modes and eigenfrequencies of various isotopic species are also calculated.     

Cartesian Dynamics of Simple Molecules II Non-Centrosymmetric Linear Triatomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to non-centrosymmetric linear triatomic molecules. Analytical expressions for the stretching and bending mode frequencies are obtained, which are equivalent to those derived by conventional methods. For most molecules, the effects of the interaction between the outside atoms are shown to be negligible, but for N₂O, complex solutions are obtained unless this is included. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. For N₂O, frequency shifts resulting from isotopic substitution are explained by reference to the calculated eigenvectors.     

Cartesian Dynamics of Simple Molecules I Diatomics and Centrosymmetric Triatomics

A simple spring model for molecular vibrations is described in which Cartesian co-ordinates are used for both longitudinal and transverse displacements. The transverse restoring forces are shown to be electrostatic in origin and much weaker than the elastic longitudinal forces. The technique is applied to diatomic and centrosymmetric triatomic molecules. In the latter case, an analytical expression for the bending mode frequency is obtained which is equivalent to that derived by conventional methods using bending constants and internal co-ordinates. The model offers certain advantages when applied to the dynamics of crystals, for which Cartesian co-ordinates, aligned with the unit cell axes, are the natural choice. Reference is made to recent work on molecular and ionic crystals using extensions of this model.     

Cartesian Dynamics of Simple Molecules X Linear Quadratomics (C∞v Symmetry)

The vibrations of linear ABC₂ type molecules with C_∞V point group are analysed in terms of Cartesian co-ordinates. Algebraic expressions for the three stretching and two bending normal mode frequencies are derived in terms of longitudinal and transverse force constants, atomic masses and bond lengths. Values of non-valence interaction parameters are transferred from A₂B₂ (D_∞h) molecules, and values of the principal force constants are adjusted to reproduce the observed frequencies for a number of asymmetric halogen derivatives of acetylene. Normal mode frequencies of various isotopic species are also calculated. The nature of the computed eigenvectors for these molecules is briefly discussed. It is found that the carbon-carbon and carbon-hydrogen valence interactions remain approximately constant for these molecules, whereas the carbon-halogen bonds show a weakening trend with increasing halogen mass.     

Infrared vibrational spectra of -histidinium dihydrogen orthophosphate orthophosphoric acid (LHP)

The entire vibrational spectrum of a single crystal of -histidinium dihydrogen orthophosphate orthophosphoric acid (LHP) was studied by infrared (IR) spectroscopy from 10 up to 4000 cm⁻¹. The polarized infrared (IR) reflectivity spectra were measured between 7 and 250 K, in the frequency range 10–600 cm⁻¹. From the IR spectral analysis, the phonon modes were classified within their symmetry species, and their longitudinal (LO) and transversal (TO) optical frequencies were calculated. A tentative assignment of the various internal modes observed in the transmissivity spectrum of LHP, between 300 and 4000 cm⁻¹, is proposed. The present study did not reveal any low-temperature structural phase transition.     

Lattice dynamics of tetragonal R2BaCuO5 (R = La,Nd) oxides in the P4/mbm structure

A short‐range force constant model (SRFCM) has been applied to investigate the Raman and the infrared wavenumbers in R₂BaCuO₅ (R = La, Nd) in their tetragonal phase of space group P4/mbm. Calculations of zone‐center phonons are made with six stretching and five bending force constants. All the Raman and infrared values are then assigned to their corresponding modes. The force constants were evaluated by fitting ten Raman and eight infrared modes. The calculated Raman and infrared modes show good agreement with the observed values. Copyright © 2007 John Wiley & Sons, Ltd.     

Raman spectra and phase composition of MnGeO3 crystals

MnGeO₃ single‐crystal samples have been synthesized by optical zonal melting and spontaneous crystallization. X‐ray crystal analysis showed the first sample to be a two‐phase one with phase ratio as follows: 17% – monoclinic C2/c, and 83% – orthorhombic Pbca; the phase ratio of the second sample was unknown. Raman spectra have been produced for these samples. Lattice dynamics has been simulated and polarization dependencies of lines' intensities have been analyzed to interpret experimental Raman spectra and to attribute lines to the spectra of monoclinic and orthorhombic phases. Copyright © 2015 John Wiley & Sons, Ltd.     

Vibrational Dynamics and Heat Capacity of Poly(3-methylthiophene): A Conducting Polymer

Using the Urey–Bradley force field and Wilson's GF matrix method as modified by Higgs, normal modes of vibration and their dispersions in poly(3-methylthiophene) have been obtained. They provide a detailed interpretation of its I.R. and Raman spectra. Characteristic features of the dispersion curves, such as regions of high density-of-states, repulsion, and character mixing of dispersive modes, are discussed. Predictive values of the heat capacity as a function of temperature have been calculated.     

1H NMR study of N(CH3)4H(ClF2CCOO)2

The proton spin–lattice relaxation times and ¹H NMR second moments were measured over a wide range of temperature. The results were compared with those of the ¹⁹F NMR relaxation that we obtained earlier. For both nuclear species, the evolution of the longitudinal magnetizations with time is observed to be strongly bi-exponential and were in good quantitative agreement with the cross-relaxation theory.     

碳纳米管的结构、对称性及晶格动力学

本文介绍了单层碳纳米管的结构,对称性和晶格动力学,描述了单层碳纳米管结构的表征方式,碳纳米管的晶格振动模的对称性分类和声子色散曲线。     

Polarized Raman scattering and lattice eigenmodes of antiferromagnetic NdFeO3

The first‐ and second‐order Raman‐active phonons in the orthorhombic Pbnm NdFeO₃ single crystals were studied by means of polarized Raman scattering and lattice dynamics computations (LDC). The zone‐center phonons of A_g symmetry were distinguished from the B_1g eigenmodes by performing polarized Raman scattering experiments using two parallel polarization configurations, X′(ZZ)X′ and Z(X′X′)Z. With the help of LDC, we were able to assign most of the observed Raman‐active modes, including phonons of B_2g and B_3g symmetry. The LDC results indicated that among the 16 force constants employed, the one corresponding to the stretching vibration between the central Fe cation and the axial oxygen atom in a FeO₆ octahedron unit had the largest value. This suggests that the B‐site Fe cation is more tightly bound to the axial O1 ion than the other two equatorial O2 ions. It was further shown that at higher wavenumbers, the displacement of oxygen atoms contributed dominantly to the zone‐center vibrations. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Determination of the Absolute Intensities of Vibrational-Rotational Lines of XY3 Molecules with C 3v Symmetry

Analytical formulas are derived that describe the dependences of the transition probabilities in vibrational-rotational spectra of XY₃-type molecules with C _3v symmetry on the rotational quantum numbers.     

Surface lattice dynamics of thep(3×1)−Ag(110) system

Summary We present a detailed study of the lattice dynamics of thep(3×1)O-Ag(110) surface to determine the structural changes of the substrate upon oxygen chemisorption. The lattice dynamical calculations are carried out using central forces with nearest-neighbour interactions and assuming different surface structures. The limits of the models are discussed. A comparison with the dispersion curves measured along two azimuthal directions by means of energy-resolved He-atom scattering unambiguously shows the reconstruction of the silver substrate. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Raman and Infrared Spectra of Crystals with the Cadmium Iodide Structure

Abstract

Raman and far infrared spectra (in the frequency range 20–360 cm^?1) have been recorded for polycrystalline samples of six crystals having the cadmium iodide layered structure. The four fundamental zone-center vibrational frequencies are assigned for CoBr₂, FeBr₂, MgBr₂, MnBr₂, CdI₂ and MgI₂. Values of the principal interlayer force constants are deduced from a simple linear chain dynamical model, and comparisons are made with recent results from spectroscopic studies of crystals with the related cadmium chloride structure.     

Raman spectroscopic study of the multi‐anion mineral dixenite CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6

The mixed anion mineral dixenite has been studied by Raman spectroscopy, complemented with infrared spectroscopy. The Raman spectrum of dixenite shows bands at 839 and 813 cm⁻¹ assigned to the (AsO₃)³⁻ symmetric and antisymmetric stretching modes. The most intense Raman band of dixenite is the band at 526 cm⁻¹ and is assigned to the ν₂ AsO₃³⁻ bending mode. DFT calculations enabled the calculation of the position of AsO₂²⁻ symmetric stretching mode at 839 cm⁻¹, the antisymmetric stretching mode at 813 cm⁻¹, and the deformation mode at 449 cm⁻¹. The Raman bands at 1026 and 1057 cm⁻¹ are assigned to the SiO₄²⁻ symmetric stretching vibrations and those at 1349 and 1386 cm⁻¹ to the SiO₄²⁻ antisymmetric stretching vibrations. Both Raman and infrared spectra indicate the presence of water in the structure of dixenite. This brings into question the commonly accepted formula of dixenite as CuMn²⁺₁₄Fe³⁺(AsO₃)₅(SiO₄)₂(AsO₄)(OH)₆. The formula may be better written as CuMn²⁺₁₄Fe³⁺(AsO₃)₅(SiO₄)₂(AsO₄)(OH)₆·xH₂O. Copyright © 2009 John Wiley & Sons, Ltd.     

Lattice dynamics of tetragonal Nd2BaZnO5

A short‐range force constant model (SRFCM) has been applied to investigate the Raman and the infrared wavenumbers in Nd₂BaZnO₅ in its tetragonal phase of space group I4/mcm. Calculations of zone‐center phonons are made with five stretching and five bending force constants. All the Raman and infrared values are then assigned to their corresponding modes. Two Raman modes are reassigned on the basis of group theoretical calculations. The calculated Raman wavenumbers exhibit good agreement with the observed values. Copyright © 2007 John Wiley & Sons, Ltd.     

Structural and crystallization behavior of (Ba,Sr)TiO3 borosilicate glasses

Various glass samples were prepared by melt quench technique in the glass system [(Ba_{1? x} Sr _x ) TiO₃]–[2SiO₂–B₂O₃]–[K₂O] doped with 1?mole% of La₂O₃. Infrared spectra show the number of absorption peaks with different spliting in the wave number range from 450 to 4000?cm^?1. Absorption peaks occurs due to asymetric vibrational streching of borate by relaxation of the bond B–O of trigonal BO₃. Raman spectra show the Raman bands due to ring-type metaborate anions, symmetric breathing vibrations BO₃ triangles replaced by BO₄ tetrahedra, and symmetric breathing vibrations of six-member rings. The differential thermal analysis of a glass sample corresponding to composition x?=?0.0 shows crystallization temperature at 847°C and glass transition temperature at 688°C. X-ray diffraction (XRD) pattern of glass ceramic samples shows the major crystalline phase of BaTiO₃ whereas pyrochlore phases of barium titanium silicate. Scanning electron micrographs confirm the results of XRD as barium titanate is major crystalline phase along with pyrochlore phase of barium titanium silicate.