Cage motion

The result given here may also be extended to rotation in space. As far as the cage motion is concerned, the complex susceptibility will still be governed by the Rocard equation because the equations of motion factorize. However, the solution for the dipole correlation function is much more complicated because of the difficulty of handling differential recurrence relations pertaining to rotation in space in the presence of a potential. 

Fig. 6.21 Cage motion of Fe at interstitial equivalent positions. Fitting parameters for Mossbauer spectra of Fe in a-Zr as functions of temperature, and a possible model to explain the temperature dependence a resonance areas, b quadrupole splitting AEq, and c center shifts 5 [31]...

In the case of Sc in Fig. 6.20b, there seems to be a similar cage motion accompanied by both a quadrupole relaxation and a strong decrease of the area on the doublet at the right hand side at 300 and 450 K. In the case of Pb, on the other hand, the singlet shows a shght line broadening above 250 K, which could be due... 

The sternoclavicular joint, one of the true joints of the shoulder girdle, may affect rib cage motion either primarily, via the manubrium and ligamentous attachments to the costal cartilage, or secondarily, because of the position of the upper extremity. 

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

Figure 7.6. A filled. skutterudite antimonide crystal structure. A transition niclal atom (Fc or Co) at the centre of each octahedron is bonded to antimony atoms at each corner. The rare earth atoms (small spheres) are located in cages made by eight octahedra. The large thermal motion of rattling of the rare earth atoms in their cages is believed be responsible for the strikingly low thermal conductivity of these materials (Sales 1997).

Dynamic information such as reorientational correlation functions and diffusion constants for the ions can readily be obtained. Collective properties such as viscosity can also be calculated in principle, but it is difficult to obtain accurate results in reasonable simulation times. Single-particle properties such as diffusion constants can be determined more easily from simulations. Figure 4.3-4 shows the mean square displacements of cations and anions in dimethylimidazolium chloride at 400 K. The rapid rise at short times is due to rattling of the ions in the cages of neighbors. The amplitude of this motion is about 0.5 A. After a few picoseconds the mean square displacement in all three directions is a linear function of time and the slope of this portion of the curve gives the diffusion constant. These diffusion constants are about a factor of 10 lower than those in normal molecular liquids at room temperature. 

BIrd-cagIng or core-popping. Sudden unloading of line such as hitting fluid with excessive speed. Improper drilling motion or jar action. Use of sheaves of too small diameter or passing line around sharp bend. 

Because this is a friction-driven motion, the cage turns much slower than the inner race of the bearing. Generally, the rate of rotation is slightly less than one-half of the shaft speed. FTF is calculated by the following equation ... 

The function 0(7) is again defined by Eq. 10 and represents the contributions due to translational motion and internal degrees of freedom of the solute molecule.t The second term is related to the potential energy w o) of the solute molecule at the center of its cage referred to the perfect gas, and the integral is the Tree volume of the solute molecule wandering in the cavity. In order to conform with the customary notation of the L-J-D theory we shall further write the free volume as... 

Here the vector rj represents the centre of mass position, and D is usually averaged over several time origins to to improve statistics. Values for D can be resolved parallel and perpendicular to the director to give two components (D//, Dj ), and actual values are summarised for a range of studies in Table 3 of [45]. Most studies have found diffusion coefficients in the 10 m s range with the ratio D///Dj between 1.59 and 3.73 for calamitic liquid crystals. Yakovenko and co-workers have carried out a detailed study of the reorientational motion in the molecule PCH5 [101]. Their results show that conformational molecular flexibility plays an important role in the dynamics of the molecule. They also show that cage models can be used to fit the reorientational correlation functions of the molecule. 

---