Frequencies Of Internal Modes Research Articles

Practical tutorial on cylindrical structure vibro-acoustics Part 2 - Acoustics

In part 1 of this tutorial (proceedings of Inter-noise 2022) I explained vibrations in cylindrical shell structures. In that paper I limited the mathematics and focused on the key behavior of shells based on critical parameters like the ring frequency, helical wavenumbers, and mean mobilities over different frequency ranges. I compared measured data to the simple theories. In part 2, I focus on the acoustics of cylindrical shells, including sound within shells and the sound radiated outside them. Exterior sound radiation depends strongly on the circumferential order of the shell modes. Breathing modes near the ring frequency radiate sound extremely well, but have very high impedances, so can be difficult to excite. Beam-like modes, where the entire shell cross-section vibrates transversely, radiate less efficiently, but can be easily driven. Higher order, or 'lobar' modes radiate even less efficiently, but nevertheless are commonly observed in radiated sound spectra due to their low impedances. I also review statistical estimates of radiation efficiency of groups of shell modes, which show clear peaks at both the ring frequency as well as at the critical frequency of bending waves. The mathematics of sound inside cylindrical shells is some of the most challenging in vibro-acoustics. At low frequencies, however, the interior sound is dominated by simple one-dimensional planar acoustic waves. At higher frequencies, the sound depends on how well a shell vibration field matches the interior acoustic field based on proximity of resonance frequencies and the similarity of mode shape orders, as well as the 'cut on' frequencies of higher order internal acoustic modes. Finally, I review the well-known phenomenon of how a low shell wall impedance can reduce the effective acoustic sound speed of one-dimensional waves inside cylindrical shells.

Temperature dependent structural, vibrational and magnetic properties of K3Gd5(PO4)6.

Herein we report the evolution of the crystal structure of K3Gd5(PO4)6 in the temperature range from 20 K to 1073 K, as observed from variable temperature X-ray diffraction and Raman spectroscopic studies. K3Gd5(PO4)6 has an open tunnel containing a three dimensional structure built by [Gd5(PO4)6]3- ions which in turn are formed of PO4 tetrahedra and GdOn (n = 8 and 9) polyhedra. The empty tunnels in the structure are occupied by K+ ions and maintain charge neutrality in the lattice. Evolution of unit cell parameters with temperature shows a systematic increase with temperature. The average axial thermal expansion coefficients between 20 K and 1073 K are: αa = 10.6 × 10-6 K-1, αb = 5.5 × 10-6 K-1 and αc = 16.4 × 10-6 K-1. The evolution of distortion indices of the various coordination polyhedra with temperature indicates a gradual decrease with increasing temperature, while those of Gd2O9 and K2O8 polyhedra show opposite trends. The overall anisotropy of the lattice thermal expansion is found to be controlled largely by the effect of temperature on GdOn polyhedra and their linkages. Temperature dependent Raman spectroscopic studies indicated that the intensities and wavenumbers of most of the Raman modes decrease continuously with increasing temperature. Anharmonic analyses of Raman modes indicated that the lattice, rigid translation and librational modes have larger contributions towards thermal expansion of K3Gd5(PO4)6 compared to high frequency internal modes. The temperature and field dependent magnetic measurements indicated no long range ordering down to 2 K and the observed effective magnetic moment per Gd3+ ion and the Weiss constant are 7.91 μB and 0.38 K, respectively.

Temperature-Dependent Crystal Structure Study of a Small Heterobicycle, C9H12O4

1,7,7-Trimethyl-2,6-dioxabicyclo[2.2.2]octan-3,5-dione is a dipseudoacyl ketal formed by a double intramolecular dehydration/cyclization of 2-carboxy-3,3-dimethyl-5-oxohexanoic acid. The compound is a volatile, colorless crystalline solid (mp 137 °C) which forms prisms and plates from ethanol by slow solvent evaporation. Crystals are orthorhombic, space group P212121 (#19), a = 8.0557(2) A, b = 10.3545(3) A, c = 10.7583(3) A, V = 897.37(11)A3 (101 K). The crystal and molecular structure has been determined on a single prismatic specimen at 280, 250, 200, 150 and 101 K (±1 K). The ostensibly rigid molecule possesses mirror symmetry, which is not retained in the solid state. Each six-membered ring has a boat conformation, with torsions-0.2°, 1.3°, −2.7° (101 K). Carbonyl groups are eclipsed with a common methine C–H bond, and the OCC(H) bond angles are enlarged to 126.9°, 127.0°, while the intraring CCO angles are contracted to 112.0, 112.1° (uncorrected for libration). The coefficients of thermal expansion are 3.34 × 10−4, 6.97 × 10−4 and 6.54 × 10−4A/K for the three orthorhombic axes, respectively, over the range studied. A rigid-body librational model fit to the anisotropic librational parameters grows worse at lower temperatures, suggesting at least two lower frequency internal modes make contributions to the librational terms. A bicyclic rigid dipseudoacyl ketal shows libration which on analysis of the thermal motion from 280 to 101 K suggest two active low frequency vibrational modes.

Study of the P-T phase diagram of pyridinium perchlorate by X-ray diffraction and Raman spectroscopy

The crystal structure and vibrational spectra of deuterated pyridinium perchlorate (d5PyH)ClO4 (C5D5NHClO4) are studied by means of neutron diffraction in ambient conditions, X-ray diffraction at high pressures up to 3.5 GPa in the temperature range 297–420 K, and Raman spectroscopy at high pressures up to 5.7 GPa. Deuterated pyridinium perchlorate at ambient conditions has rhombohedral structure with the R3m symmetry (paraelectric phase I). Over the pressure range of 0.5–1.2 GPa, the phase II with monoclinic symmetry Cm exists. At pressure P ∼ 1.2 GPa, the phase transition to monoclinic phase III with the Pm symmetry is observed at ambient temperature. The lattice parameters, unit cell volume, and frequencies of internal vibrational modes as functions of pressure are obtained for different phases of deuterated pyridinium perchlorate. The P-T phase diagram of (d5PyH)ClO4 over the extended pressure and temperature range is discussed.

Crystal structure and phase transition of 4-aminopyridinium tetrachlorobismuthate(III),[4-NH2C5H4NH ][BiCl4 ], as studied by x-ray diffraction, dielectric, proton NMR and infrared spectroscopy

The crystal structure of 4-aminopyridinium tetrachlorobismuthate(III),[4-NH2PyH ][BiCl4 ], has been determined at 100 and 260 K by the x-ray diffraction method as monoclinic space group,P 21/c and C 2/c, respectively. Differential scanning calorimetry and dilatometryreveal one perfectly reversible discontinuous phase transition at254/255 K (cooling/heating)with ΔS = 10.1 J mol−1 K−1. The1H NMR spin–latticerelaxation time (T1)and second moment (M2) measurements disclose a significant change in the motional state of the cationsnear the phase transition temperature. Infrared spectra of polycrystalline[4-NH2PyH ][BiCl4 ] have been studied in the temperature range 10–306 K. Substantial changes in thetemperature evolution of frequencies of internal modes of the 4-aminopyridiniumcations near 255 K are due to the change in the dynamics of cationic moieties.The experimental results indicate that the motion of the organic cationscontributes mainly to the mechanism of an ‘order–disorder’ transition in[4-NH2PyH ][BiCl4 ].

Structure, phase transitions, dielectric and spectroscopic studies of the 2-aminopyrimidinium salts: [(2-NH 2C 4N 2H 3) 2H][ClO 4] and [2-NH 2C 4N 2H 4][BF 4

Crystal structure of the 2-aminopyrimidinium derivatives: [(2-NH 2C 4N 2H 3) 2H][ClO 4] (I) and [2-NH 2C 4N 2H 4][BF 4] (II) has been determined at 100 K (I) and 293 K (II) by means of single crystal X-ray diffraction as monoclinic space group, P 2 / c and P 2 1 / n , respectively. The asymmetric part of the unit cell of (I) contains two symmetry independent 2-aminopyrimidine forming one dimeric cation and one disordered perchlorate anion. The structure of (II) consists of 2-aminopyrimidinium cation, [2-NH 2C 4N 2H 4] +, protonated at a pyrimidine ring-N atom and [BF 4] − anion. Differential scanning calorimetry (DSC) on perchlorate derivative ( 1 : 1 ), [2-NH 2C 4N 2H 3][ClO 4] (III)—being isomorphic to tetrafluoroborate one (I) at room temperature, reveals two phase transitions of first order: at 250/275 K and 390/410 K (cooling–heating, respectively), whereas the analog (II) only one transition at high temperatures—343/385 K. The dielectric studies in the frequency range 75 kHz – 10 MHz disclose relaxation process at high temperatures in salt (I). Infrared spectra of polycrystalline [2-NH 2C 4N 2H 4][BF 4] have been studied in the temperature range 300–420 K. Substantial changes in the temperature evolution of frequencies of internal modes of the 2-aminopyrimidinium cations and [BF 4] − anions near 390 K are due to the variations in the motion of both moieties and hydrogen bond configuration. The experimental studies indicate that all phase transitions taking place in studied 2-aminopyrimidinium derivatives are classified as an order–disorder.

Terahertz spectroscopy of solid serine and cysteine

Terahertz (THz) absorption spectra of the similarly structured amino acids l-serine and l-cysteine in the solid phase at 77 and 298 K are reported and compared to isolated molecule and solid-state infrared vibrational spectral calculations using empirical force field and density functional theory. These comparisons suggest that many higher frequency internal modes can readily be assigned but lowest frequency intermolecular and phonon modes can adequately be understood with more advanced solid-state theory using currently available potential functions.

High-Pressure Study of Adamantane: Variable Shape Simulations up to 26 GPa

We report simulations of adamantane by carefully combining ab initio and empirical approaches to enable simulations with internal degrees of freedom on crystalline adamantane up to a pressure of 26 GPa. Two sets of simulations, assuming the adamantane molecule as a rigid (RB) and flexible body (FB), have been carried out as a function of pressure up to 26 GPa to understand changes in the crystal structure as well as molecular structure. The flexible body simulations have been performed by including 6 lowest frequency internal modes (obtained from DFT calculations performed with Gaussian98) out of the total of 72. The calculated variation in c/a and V/V(0) from the RB and FB calculations as a function of pressure have been compared with the experimental curve. Other relevant thermodynamic and structural properties reported are the radial distribution functions, deviation in the position of a given type of atom with respect to its position at standard pressure, delta(s), cell parameters, volume, and energy. With an increase in pressure, three additional peaks are seen to develop gradually at three different pressures in the center of mass (com)-com radial distribution function (rdf). We attribute these changes to structural transformations (probably second-order phase transitions) which is consistent with the three phase transitions reported by Vijayakumar et al. for adamantane in the pressure range of 1 atm-15 GPa. Our simulations also show that these additional peaks in the rdf's are associated with the differences between opposite and parallel spin neighbors of Greig and Pawley as well as the crystallographic directional dependence of intermolecular distances in the first three shells of the neighbors. Also, the structural quantities from the RB calculation show considerable deviation from the FB calculation for pressures greater than 5 GPa, which suggests that the rigid body assumption for molecules may not be valid above this pressure.

Low frequency internal modes of 1,2,4,5-tetramethylbenzene, tetramethylpyrazine and tetramethyl-1,4-benzoquinone: INS, Raman, infrared and theoretical DFT studies

The results of inelastic neutron scattering (INS), Raman and infrared (IR) studies on 1,2,4,5-tetramethylbenzene (durene), tetramethylpyrazine (TMP) and tetramethyl-1,4-benzoquinone (TMBQ) in the solid state are reported. The observed frequencies are analyzed on the basis of DFT calculations. The low frequency region, below 400 cm −1, related to the torsional and bending out-of-plane vibrations of the CH 3 groups, is of particular interest. The detailed analysis is possible due to the simulation of the INS spectra by using the auntie-CLIMAX program. It is shown that the observed low frequency INS bands are dramatically shifted, compared to the calculated ones, towards higher frequencies. Although one cannot exclude deficiencies of theoretical methods as applied to low frequency modes, it seems more probable the interpretation based on an existence of non-conventional C H …π, C H …N, C H …O hydrogen bonds formed by the methyl groups in crystalline phases.

A note on the small oscillation regimes of rotating liquid bridges: Transition from surface to internal wave modes

An analysis of the small oscillation modes of rotating liquid bridges is carried out. The study is performed in the particular conditions when both surface and internal wave mode frequencies almost coincide for a certain meridional and azimuthal wave number. The critical values of the rotation speed and the natural frequencies for which this transitional condition takes place are obtained numerically as a function of the parameters characterizing the fluid configuration. The influence of both the outer bath and the liquid bridge equilibrium shape on the transition is analyzed. Analytical expressions providing the critical values of the rotation speed and the natural frequencies are obtained for cylindrical liquid bridges.

Crystal structure, thermal, dielectric and vibrational studies of the [4-C 2H 5PyH] 4[Sb 2Cl 10] crystal

Crystal structure of tetra(4-ethylpyridinium) decachlorodiantimonate(III), [4-C 2H 5PyH] 4[Sb 2Cl 10], has been determined at 245 K by X-ray diffraction (tetragonal, space group P 4 1 2 1 2 ). DSC and dilatometric studies indicate a presence of two reversible phase transitions of the first order type, at 370/373 and 233/238 K (cooling/heating) with Δ S = 4.0 and 10.1 J mol −1 K −1, respectively. Infrared spectra of polycrystalline [4-C 2H 5PyH] 4[Sb 2Cl 10] have been studied in the temperature range 20–306 K. Substantial changes in the temperature evolution of frequencies of internal modes of the 4-ethylpyridinium cations near 233 K are due to the ordering of the cationic sublattice. The experimental results indicate that both phase transitions may be classified as the order–disorder ones.

A powerful, repetitively pulsed 1444-nm Nd:YAG laser

A powerful, repetitively pulsed 1444-nm Nd:YAG laser is studied. It is shown that the efficiency of this laser is mainly limited by the absorption at 1444 nm in the active element, the UV radiation of the pump lamps, the lasing at the internal mode frequencies of the active elements, and the amplified luminescence at 1444 nm. An optimisation procedure resulted in the creation of a powerful laser producing 1.4-J pulses at a repetition rate of between 1 and 10 Hz at 1444 nm.

High pressure Raman scattering studies on adamantane

High pressure behavior of adamantane is investigated up to pressures of 26 GPa at ambient temperature using Raman spectroscopy. A detailed study of changes in the Raman spectrum of the C–H stretching modes across the disorder–order transition around 0.5 GPa is reported. Pressure dependence of the internal mode frequencies suggest two more subtle transitions around 2.8 GPa and 8.5 GPa, respectively, which are reversible. Evolution of spectra at higher pressures show evidence for another structural transition above 24 GPa.

High-pressure phase transitions in Li 2SO 4·H 2O

High-pressure Raman spectroscopic investigations are carried out on Li 2SO 4·H 2O up to a pressure of 18.1 GPa. Changes in the Raman spectra suggest two structural transitions occurring around 2.6 and 7.0 GPa, respectively. Discontinuous changes in the internal mode frequencies of sulfate ions around 2.6 GPa indicate that the transition involves reorientation of SO 4 ions. A comparison of the behavior of the high-pressure phase in this compound with those in other Li-based binary sulfates indicates that the orientational disorder in these compounds at high pressures arises due to dissimilar cations.

Dynamics of domain walls and solitons in easy-plane magnets with weak exchange interaction

Internal spin dynamics of collinear domain walls and collinear soliton-like localized states in easy plane magnets is investigated. The dependence of internal mode frequencies of these excitations on the exchange interaction is determined using the essentially discrete Takeno–Homma model for low values of this interaction.

Anharmonic behaviour of BaFCl using Raman scattering

Raman scattering from oriented single crystals of BaFCl was recorded at various temperatures from 20 to 1073 K for the first time. The Raman spectra, corrected for phonon population, were fitted to the sum of four Lorentzian peaks. The peak frequencies and full width at half maximum (FWHM) of the peaks were obtained from the fit. The FWHM is accounted for by cubic and quartic anharmonic processes. The quartic anharmonicity of the mode increases with the mode frequency. The quartic anharmonicity of the fluorine mode is exceptionally high. The peak frequencies decrease linearly with the increasing temperature. Fluorine mode frequencies decrease more than the internal mode frequencies do. The LO-TO splitting of the fluorine modes and that of the internal modes increases with temperature indicating the increase of the ionic bonding character. The results are discussed.

A new way of analyzing vibrational spectra. IV. Application and testing of adiabatic modes within the concept of the characterization of normal modes

The CNM characterization of normal modes method for extracting chemical information out of vibrational spectra is tested for vibrational spectra of molecules with relatively strong or relatively weak coupling between internal vibrational modes. Symmetry, parameter set stability, and frequency uncertainty tests are applied to check whether internal vibrational modes, internal mode frequencies, and amplitudes A comply with symmetry, are independent of the set of internal parameters O used to nU n describe molecular geometry or fulfill a Lorentzian correlation between amplitudes AnU and frequency differences a a â a a a . In all cases considered, amplitudes A nU n U n U based on adiabatic internal modes and mass or force constant matrices as metric O are superior to any other definition of amplitude. They represent the basic elements of the new CNM method that leads to chemically reasonable results and presents a new way of extracting chemical information out of vibrational spectra. A number of deficiencies of e. the potential energy distribution PED analysis is discussed. a 1998 John Wiley & Sons, Inc. Int J Quant Chem 67 :4 1 a55, 1998

水素結合における構造物性と機能 ラマン散乱による水素結合系混晶におけるＨ結合とＤ結合の相互作用の解明

In K3H (SO4) 2-K3D (SO4) 2 mixed crystals, internal v2 mode frequencies of DSO4 show abrupt splitting at the phase transition temperature, while those of HSO4 split continuously. The length of D-hydrogen bond is concluded to be independent of the D concentration. This conclusion is supported by the measurement of the characteristic time τc-1 of deuteron motion; gradients of the temperature dependence of τc-1 are almost the same for any concentration of D studied.

Differential scanning calorimetric and electrical conductivity measurement on superionic Rb 4H 2(SeO 4) 3

Differential Scanning Calorimetry (DSC), a.c. electrical conductivity and infrared spectroscopic measurements on crystalline Rb 4H 2(SeO 4) 3 have been performed. A large endothermic peak in the DSC at 377 K supported by a sudden jump in the conductivity plot, confirms the presence of a phase transition at this temperature. Infrared spectra at various temperatures show a change in the internal mode frequencies on heating.

Raman study of pressure-induced structural transitions in CsIO 4 to 12 GPa

High pressure Raman scattering studies have been carried out on cesium periodate (CsIO 4) using the diamond anvil cell. Three pressure-induced phase transitions occur in the range 0.1–12 GPa as indicated by abrupt changes in the Raman spectra, and pressure dependence of the phonon frequencies. The transitions are observed at 1.5, 4.5 and 6.2 GPa in the increasing pressure cycle. A large hysteresis is noticed for the reverse transition when releasing the pressure. The high pressure phase is nearly quenchable to ambient pressure. The nature of the pressure-induced transitions are discussed in terms of the sequence of pressure-induced transitions expected for scheelite-pseudoscheelite structure ABO 4 compounds from crystal chemical considerations. For the softening of the two high frequency internal modes, a pressure-induced electronic change involving the 5 d states of cesium and 5 p states of iodine is invoked.