Rigid lattice limit

Experiments described in this section are suited to investigate ultraslow motion with correlation times in the millisecond-to-second range. Here, the NMR spectra are given by their rigid-lattice limit and one correlates the probability to find given NMR frequencies at two different times separated by the so-called mixing time tm [11,72]. A two-dimensional (2D) spectrum results, being a function of two NMR frequencies at t = 0 and t = tm, respectively. Since the NMR frequency reflects the orientation of the molecule, 2D spectra provide a visual representation of the reorientational process. Time- and frequency-domain... 

It has been usually argued that the NMR fine-shape reaches the solid-state, rigid-lattice limit at temperatures around Tg (cf. Fig. 38), and consequently no dynamical effects are expected when measuring solid-echo spectra. While such... 

In the first part of this introductory section, we summarize the main collective phenomena acquired by the dipolar exciton from the lattice-symmetry collectivization of molecular properties. The crystal is considered as an assembly of electrically neutral systems, the molecules, physically separated from each other and in electromagnetic interaction. This /V-body problem will be treated quantum-mechanically in the limit of low exciton densities. We redemonstrate the complete equivalence of this treatment with the theories of Lorentz and Ewald, as well as with the semiclassical approximation. In Section I.A, in a more compact but still gradual way, we establish the model of the rigid lattice of dipoles and the general theory of low-exciton-density systems in interaction with the radiation field. Coulombic excitons, photons,... 

One can describe this as the presence of a charge-density wave in the electronic system. In this case the charge-density wave follows from displacement of the atoms. One can ask the question whether in a rigid lattice the electron system itself can distort spontaneously to lower its symmetry, producing an effect that would then attempt to force the nuclei to follow suit. The driving force in this case would not be the movement of the atoms as in the Peierls instability but rather the inherent instability of the electron system itself. The answer to this question is yes. The study of these types of instabilities and associated instabilities in the spin system of the electrons has become an important part of the physics of limited dimensionality. 

The key structural feature of the molecular sieves is the narrow, uniform, continuous channel system that becomes available after the zeolitic water has been driven off by heating and evacuation. Great thermal stability after dehydration has been observed in the rigid lattices of X- and Y-type faujasites, zeolite A, mordenite, and chabazite. The geometry of the internal channel and cavity system is characteristic of the individual zeolite. Entrance to the intracrystalline volume is through orifices (ranging from 3 to 9 A in the various zeolites) located periodically throughout the structure. It is thus apparent that access to the intrazeolitic environment is limited to molecules whose dimensions are less than a certain critical size. 

Let A be the rigid-lattice chemical shift anisotropy. This is the separation between the divergence and the shoulder in the typical power pattern NMR line shape, as shown for example Figure 11. Also, let r be the correlation time of the slow-motion Brownian motion of the polymer chains. Then, with the onset of motion, it can be shown that the theory predicts that the two limiting powder pattern features, shoulder and divergence, will shift toward each other resulting in a narrowing of the powder pattern. The fractional shift is then found to be... 

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