Compliance Constants Research Articles

Vibration of fiber-reinforced spherical shells

The extensional vibrations of different fiber-reinforced spherical shells in vacuo were studied. The shells' materials are made of filament wound fiberglass in epoxy. The equivalent elastic orthotropic compliance constants are evaluated and as a result the natural frequencies and corresponding mode shapes are obtained by a closed form solution as well as by an infinite series approximation.

The orientation dependence of the elastic moduli of crystalline mercury

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Potential Constants of the Hexacyanocobaltate Ion

The infrared and Raman spectra of Co(12C14N)63−, Co(13C14N)63−, and Co(12C15N)63− have been studied in aqueous solution and in the solid state. Fundamental frequencies have been assigned for all but the F2u vibrations. Force constants and compliance constants have been calculated and compared with isoelectronic Cr(CO)6 and with Au(CN)2−.

Compliance constants and interaction coordinates of the hexacarbonyls of chromium, molybdenum, and tungsten

Compliance constants and interaction coordinates have been calculated for the hexacarbonyls of chromium, molybdenum, and tungsten in the vapor phase and in solution. A statistical analysis shows that most of the constants are not significantly different, at the 95% confidence level, among the three molecules and two phases. A brief discussion is given pointing out that many of the interaction compliance constants should be suitable for transfer to other metal carbonyls.

The influence of alloying and temperature on the elastic constants of tantalum

The elastic compliance constants of TaRe, TaW, TaMo and TaNb single crystals have been determined over the temperature range 80 °–1400 °K. These constants were then used to derive the bulk modulus, shear moduli C 44, and C′ = 1 2 (C 11−C 12 ) and the anisotropy factor. The results were also used to interpret solid solution hardening in tantalum-base alloys.

Study of Defect Reactions in Crystals by Means of Anelastic and Dielectric Relaxation

A general theory of anelastic and dielectric relaxation processes has previously been developed for a single defect species which can exist in several crystallographically equivalent orientations. In the present paper, the occurrence of a reaction between different defect species is considered. It is shown that the existence of such a reaction introduces a mode of relaxation, called the “reaction mode”, which involves a net change in the concentration of each species, but no reorientations. This mode gives rise to relaxation of those compliance (or susceptibility) constants associated with stress- (or electric-) field components which are invariant under the symmetry operations of the crystal. A table of these components and the corresponding material constants is presented. The thermodynamic and kinetic theory for such relaxation processes is developed in general, and then considered for important special cases. The few examples in which the reaction mode has been studied are reviewed. Finally, an example (the Al–Na defect in α quartz) is given to demonstrate the value of studying the reaction mode.

Potential constants of nitrous oxide

Least squares estimates of compliance constants, force constants, and interaction coordinates have been calculated for nitrous oxide from recent literature values of vibrational frequencies and centrifugal distortion constants of isotopic species. Mean square amplitudes and Coriolis coupling constants have also been calculated. Observed amplitudes have not been reported; however, the observed Coriolis values for 14N 14N 16O are in reasonable agreement with the calculated values. It is shown that for mean square amplitudes to be useful in the least square calculations of the potential constants they would have to be known within a few per cent, which is not likely with present-day electron diffraction techniques. The interaction coordinates tell us that if the NO bond length is constrained in a configuration longer than its equilibrium length, the resulting electron rearrangement would lead to a shortening of the NN bond, for minimum energy, equal to 6% of the NO displacement [that is, (NN) NO = −0.06]. Similarly, (NO) NN = −0.096. The average of (NN) NO and (NO) NN is equal to the interaction coordinate of CO 2, in accord with the similarity in bonding.

Interaction Coordinates and Compliance Constants

It is shown that interaction coordinates are closely related to compliance constants. Also it is emphasized, using a vibrational analysis of H2O as an example, that compliance constants are invariant with the force field and thus are more unique quantities than are force constants.

Extremal Compliance Constants for Molecular Vibrations

Abstract The occurrence of a stationary or extremal diagonal compliance constant in the general secular equation for molecular vibrations leads to pecularities in the normal coordinates, in the distribution of potential energy among the compliance constants, and in the secular determinant which then possesses a linear factor.

The infrared spectrum of ammonium thiocyanate from 90 to 300°K

The infrared absorption spectra of NH 4NCS, ND 4NCS, and of a mixture of partially deuterated species has been studied between 300–4000 cm −1 in the form of polycrystalline films at temperatures ranging from about 90–300°K. Initially amorphous films were annealed, and after crystallization exhibited splittings of all the degenerate modes of the ammonium and thiocyanate ions. A previously unknown phase (II) was observed which transformed irreversibly into the room temperature phase (I) at about 207°K in NH 4NCS and 189°K in ND 4NCS. Approximate compliance constants were evaluated and used to predict the frequencies of the partially deuterated species of ammonium ion. A crystalline solid solution containing a mixture of these species revealed extensive fine structure, which is attributed to the fact that in addition to the site group splittings of the degenerate species of NH 3D + and NH 2D 2 +, the isotopic C 3 υ molecules occupy their sites in four distinguishable ways and NH 2D 2 + occupies its site in six distinguishable orientations.

Mean Amplitudes of Vibration, and Related Quantities for Tetrahedral XY4Molecules

AbstractSpectroscopic calculations for 38 tetrahedral XY4molecules have been performed, assuming small harmonic vibrations. The results of following quantities are reported: (a) force constants, (b) compliance constants, (c) mean‐square amplitude matrices, (d) parallel and perpendicular mean‐square amplitudes, (e) mean amplitudes of vibration, and (f) Bastiansen‐Morino's shrinkage effects.One arithmetic error in previous work on this molecular model is corrected.

Elastic Constants of Bismuth

The six adiabatic elastic stiffness constants of bismuth have been determined at 301°K by an ultrasonic pulse echo technique. The results are: c11 = 63.5, c33 = 38.1, c44 = 11.30, c66 = 19.4, c14 = +7.23, and c13 = 24.5, all in units of 1010 d/cm2. These values were redundantly determined by the measurement of 14 different velocities in four different single crystals of zone-purified bismuth. The velocities are believed accurate to better than 1%, the principal error arising from the uncertainty of the transducer transit time correction. The moduli are in poor agreement with the previously determined static elastic compliance constants reported by Bridgman. Some data on the velocity of sound in bismuth at 98° and at 4.2°K are also presented.