For a molecule to be considered stable in a mechanical sense means that when its component parts, nuclei or electrons, are displaced from their equilibrium positions, there are internal attractive forces in the molecule that tend to restore the particles to their initial positions. If that were true for all displacements of the particles no matter how large in magni- [Pg.212]

From the frequency of the transverse optical mode in a simple AB lattice with k = Q a force constant can be derived which is a measure of the restoring forces experienced by the atoms as they are distorted from the equilibrium position. This force constant, Fflattice), is a linear combination of internal force constants, since in a lattice a linear combination of equilibrium distances and angles yields a coordinate of this vibration. Based on this assumption, the GF method (Wilson et al, 1955) can be applied. For diamond (or zinc blende), the following relation is obtained [Pg.248]

This analysis may be extended to formally achiral molecules that are composed of four or more atoms. The motions in such polyatomic molecules are restricted by the restoring forces imposed by bonding, and stochastic achirality is here the result of internal vibrations. Thus, for example, molecular deformations in some vibrational states impart chirality to the methane molecule, but the sense of chirality averages to zero under the conditions of measurement. As this discussion makes clear, the conventional symmetry of methane is a property solely of the model. [Pg.67]

The solution of (8 81) for b can be obtained easily. The two terms on the right-hand side of this equation represent the stretching of the drop that is due to the strain rate E, and the restoring force that is due to interfacial tension. The dimensionless relaxation rate, for return to a spherical shape in the absence of a flow, is (5/6)(l/Ca) when the viscosity ratio is small, and (20/19k)(l/Ca) for X 1. Hence, for a relatively inviscid drop, the relaxation rate is determined by the external fluid viscosity, whereas the relaxation rate for a very viscous drop is determined by the internal fluid viscosity. The steady-state solution of (8-81) is [Pg.542]

Hysteretic whirl. This type of whirl occurs in flexible rotors and results from shrink fits. When a radial deflection is imposed on a shaft, a neutralstrain axis is induced normal to the direction of flexure. From first-order considerations, the neutral-stress axis is coincident with the neutral-strain axis, and a restoring force is developed perpendicular to the neutral-stress axis. The restoring force is then parallel to and opposing the induced force. In actuality, internal friction exists in the shaft, which causes a phase shift in the stress. The result is that the neutral-strain axis and neutral-stress axis are displaced so that the resultant force is not parallel to the deflection. The [Pg.206]

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