Cage rattling

Therefore, in glass formers, the spatial aspect of the dynamic heterogeneity of the alpha relaxation may be described as a consequence of a mobility contrast between an island of high mobility [65] (where local mobility persists even below Tg as described previously in characterizing the beta process cage-rattling motions)... 

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. 

In solids, atoms rattle around — vibrate—in the cages formed by the surrounding atoms. In liquids, atoms or molecules move past one another continuously, like minnows in a stream endlessly changing positions. In gases, atoms or molecules are free to move over large distances. Figure 2 is a schematic illustration of motion of a monatomic substance in these three phases. 

The susceptibility minimum observed in the DS and LS relaxation spectra is a consequence of the interplay of the high-frequency tail of the a-relaxation peak and the contribution from certain fast dynamics dominating at frequencies close to but above the minimum. As was demonstrated by several experimental studies as well as by molecular dynamics simulations (cf. Fig. 13a), in addition to the vibrational contribution a fast relaxation process has to be taken into account for describing correctly the susceptibility minimum [5,9,19,55,64, 133,134,136,147]. This spectral contribution may usually be described by a power law with a positive exponent less than unity. In fact, the search for this fast relaxation process was mostly inspired by MCT, where it naturally appears in the solutions and is interpreted as rattling in the cage type of dynamics. Some authors discussed in addition a constant loss contribution [10,138,222,... 

---