The effect of intermolecular forces upon the vibrations of molecules in the crystalline state I. The out-of-plane bending of the carbonate ion in aragonite minerals

1963 ◽  
Vol 275 (1362) ◽  
pp. 295-309 ◽  
Keyword(s):  
Intermolecular Forces ◽  
Absolute Intensities ◽  
Carbonate Ion ◽  
Nearest Neighbours ◽  
Bending Mode ◽  
Infra Red ◽  
Out Of Plane ◽  
Plane Bending ◽  
Oxygen Bond ◽  
Dipole Energy

The infra-red absorption of polycrystalline BaCO 3 , SrCO 3 , and CaCO 3 , the latter in both the aragonite and calcite modifications, has been measured in the region 600 to 2000 cm -1 . Absolute intensities were determined for each of the three fundamental bands of the carbonate ion, by the method of extrapolation to infinite dilution of the carbonate in the alkali halide matrix. The band due to the out-of-plane bending mode was examined under high resolution, the samples employed having been enriched to a 50/50 ratio of 12 C/ 13 C. Intermolecular coupling in this band, which is revealed by the isotopic solid solution, has been interpreted as arising primarily from interaction of the dipoles produced during the vibration. The dipole derivatives calculated from this coupling agree fairly well with those estimated from the absolute intensities. Various sources of error are discussed, and in particular, an estimate is made of the dipole-dipole energy summed over the entire lattice, instead of merely for nearest neighbours. The carbon-oxygen bond moment during the vibration has an effective value of from 1.3 to 1.7 debyes.

Intensities in the infra-red spectrum of benzene

1956 ◽  
Vol 238 (1213) ◽  
pp. 245-255 ◽  
Keyword(s):  
Dipole Moment ◽  
Experimental Error ◽  
Carbon Skeleton ◽  
Absolute Intensities ◽  
Bond Stretching ◽  
Infra Red ◽  
Out Of Plane ◽  
Plane Bending ◽  
The Absolute

The absolute intensities of the infra-red active fundamental vibrations of benzene, mono-deuterobenzene, and para -dideuterobenzene have been measured and interpreted in terms of the dipole moment derivatives: ∂ μ z /∂ S 11 = -1·43 D/Å; ∂ μ y /∂ S 18 a = - 0·51 D/Å; ∂ μ y /∂ S 19 a = -0·32 D/Å; ∂ μ y /∂ S 20 a = -0·78 D/Å. All three spectra are consistent with these values. The ‘effective’ C—H bond moment for in-plane bending is 0·31 D and for out-of-plane bending 0·61 D. The value for the C—H bond-stretching dipole-moment derivative is 0·45 D/Å with the H atom becoming less positive as the bond stretches. In-plane distortions of the carbon skeleton which leave the C—H bond directions unchanged, produce zero dipole moment within the experimental error.

Large Amplitude Oscillations of Thin Circular Rings

1987 ◽  
Vol 54 (2) ◽  
pp. 315-322 ◽  
Author(s):  
S. P. Maganty ◽  
W. B. Bickford
Keyword(s):  
Large Amplitude ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Circular Ring ◽  
Bending Mode ◽  
Out Of Plane ◽  
Circular Rings ◽  
Linear Problems ◽  
Plane Bending ◽  
Nonlinear Equations Of Motion

Using an intrinsic formulation, an accurate set of geometrically nonlinear equations of motion is derived for the large amplitude oscillations of a thin circular ring. Non-dimensionalization of the equations of motion and the compatibility conditions indicates clearly that certain terms involving the extensional deformation, the shear deformation, and the rotatory inertia are relatively small and can be discarded. The resulting equations of motion are analyzed by the method of multiple scales with a single bending mode approximation to the linear problems indicating a softening type of nonlinearity for both the in-plane and the out-of-plane problems with the out-of-plane flexural motion experiencing a greater degree of softening when compared to that of the in-plane flexural motion. The results for the nonresonant case indicate that the frequency of an out-of-plane bending mode is significantly reduced by the presence of a nonzero in-plane bending amplitude, whereas the results for the resonant case indicate the presence of unsteady oscillations with an exchange of energy between the in-plane and the out-of-plane modes.

scholarly journals The electronic spectra of acetaldehyde-h4 and -d4

1992 ◽  
Vol 70 (3) ◽  
pp. 931-934 ◽  
Author(s):  
N. N. Yakovlev ◽  
I. A. Godunov
Keyword(s):  
Barrier Height ◽  
Room Temperature ◽  
Electronic Absorption Spectra ◽  
Energy Levels ◽  
Vapour Phase ◽  
Electronic Transitions ◽  
Torsional Barrier ◽  
Bending Mode ◽  
Out Of Plane ◽  
Plane Bending

The [Formula: see text] electronic absorption spectra of acetaldehyde-h4 and -d4 were recorded in the vapour phase at room temperature. The major experimental requirement was a high pressure × path length (650 Torr × 140 m). The vibrational structure of these electronic transitions was interpreted in terms of the torsional modes [Formula: see text] and [Formula: see text] attached to the [Formula: see text] out-of-plane bending mode. The main CH3CHO results agreed with those obtained earlier (Moule and Ng); the values of the [Formula: see text] transition and torsional barrier height were 27240.1 and 590 cm−1 respectively. Three inversion (out-of-plane bending) energy levels in the excited [Formula: see text] state were found and the inversion potential function was determined with a barrier height of 1110 cm−1. The CD3CDO spectrum confirmed the CH3CHO analysis. The values of the [Formula: see text] transition and torsional barrier height were equal to 27270 and 610 cm−1. Keywords: vibronic spectrum, acetaldehyde, molecular structure.

scholarly journals Microcrack Detection Using Spectral Response Data Alone

2021 ◽  
Vol 11 (8) ◽  
pp. 3655
Author(s):  
Gee-Soo Lee ◽  
Chan-Jung Kim
Keyword(s):  
Spectral Response ◽  
Coherence Function ◽  
Cold Forming ◽  
Response Data ◽  
Highly Sensitive ◽  
Bending Mode ◽  
Out Of Plane ◽  
Rectangular Specimen ◽  
Microcrack Detection ◽  
Impulse Force

Microcracks of depth less than 200 μm in mechanical components are difficult to detect because conventional methods such as X-ray or eddy current measurements are less sensitive to such depths. Nonetheless, an efficient microcrack detection method is required urgently in the mechanical industry because microcracks are produced frequently during cold-forming. The frequency response function (FRF) is known to be highly sensitive even to microcracks, and it can be obtained using both the input data of an impact hammer and the response data of an accelerometer. Under the assumption of an impulse force with a similar spectral impulse pattern, spectral response data alone could be used as a crack indicator because the dynamic characteristics of a microcrack may be dependent solely on these measured data. This study investigates the feasibility of microcrack detection using the response data alone through impact tests with a simple rectangular specimen. A simple rectangular specimen with a 200 μm microcrack at one face was prepared. The experimental modal analysis was conducted for the normal (uncracked) specimen and found-first bending mode about 1090 Hz at the X-Y plane (in-plane). Response accelerations were obtained in both at in-plane locations as well as X-Z plane (out-of-plane), and the crack was detected using the coherence function between a normal and a cracked specimen. A comparison of the crack inspection results obtained using the response data and the FRF data indicated the validity of the proposed method.

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