Incoherent lattice

The concept of a superlattice can also be applied to regular overlayers of foreign adsorbed atoms (see Section 2.2). If the coupling forces between atoms exceed the atom-surface interaction forces, they can form a structure which is not related to the symmetry of the substrate surface incommensurate structure or incoherent lattice). In such a case det C is an irrational number (Fig. 2.2c). 

Here, we show three differences in the interface between the nucleus, N, and the original crystal, A. We find that in the first case, the lattices match fairly closely and are coherent. In the second case, there is some correspondence between the lattices. But the incoherent case shows little matching of the two lattices. 

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

In the theory of deuteron spin-lattice relaxation we apply a simple model to describe the relaxation of the magnetizations T and (A+E), for symmetry species of four coupled deuterons in CD4 free rotators. Expressions are derived for their direct relaxation rate via the intra and external quadrupole couplings. The jump motion between the equilibrium positions averages the relaxation rate within the same symmetry species. Spin conversion transitions couple the relaxation of T and (A+E). This mixing is included in the calculations by reapplying the simple model under somewhat different conditions. The results compare favorably with the experimental data for the zeolites HY, NaA and NaMordenite [6] and NaY presented here. Incoherent tunnelling is believed to dominate the relaxation process at lowest temperatures as soon as CD4 molecules become localized. 

Fig. 4.10 Coethite twinning. Upper left Twins grown at pH 4 and 25 °C consist of two (a) or three armed (b) twin pieces (Schwertmann. Murad, 1983,with permission). Upperright Multidomainic star-like twin grown at [OH] = 0.3 ML" and 70°C with stirring (courtesy P. Weidler).Lower/ejt Schematic drawing of a twin-zone in a singly-branched goethite twin showing the lattice planes and the coherent and incoherent boundary (Maeda. Hirono, 1981, with permission).

The study of molecular dynamics in polymers is of great interest because the structural changes of the crystal lattice are intimately related to the onset of molecular motions which generate a special type of dynamical disorder within the crystals [101-104]. In this final section, we prerent an experimental account of the molecular dynamics of copolymers with 60/40 and 80/20 VF2/F3E mole fraction composition using incoherent quasielastic neutron scattering. 

So far, we have tacitly assumed that the stresses were applied externally. However, stresses which are induced by local changes in component concentrations and the corresponding changes in the lattice parameters during transport and reaction are equally important. These self-stresses can strongly influence the course of a solid state reaction. Similarly, coherent, semicoherent, and even incoherent interfaces during heterogeneous solid state reactions are sources of (local and nonlocal) stress. The... 

Incoherent Clusters. As described in Section B.l, for incoherent interfaces all of the lattice registry characteristic of the reference structure (usually taken as the crystal structure of the matrix in the case of phase transformations) is absent and the interface s core structure consists of all bad material. It is generally assumed that any shear stresses applied across such an interface can then be quickly relaxed by interface sliding (see Section 16.2) and that such an interface can therefore sustain only normal stresses. Material inside an enclosed, truly incoherent inclusion therefore behaves like a fluid under hydrostatic pressure. Nabarro used isotropic elasticity to find the elastic strain energy of an incoherent inclusion as a function of its shape [8]. The transformation strain was taken to be purely, dilational, the particle was assumed incompressible, and the shape was generalized to that of an... 

For an incoherent nucleus, the jump rate across the cluster/matrix interface will be much faster than the lattice jump rate. Therefore, the /3C frequency factor is controlled by the lattice-replacement jumping and Eq. 19.34 holds. 

In some cases of localised adsorption the adsorbate is ordered into a two-dimensional lattice or net in a particular range of surface coverage and temperature. If the net of the ordered adsorbed phase is in registry with the lattice of the adsorbent the structure is called coherent, if not it is called incoherent (see also 1.2.4). 

For crystalline-crystalline interfaces we further discriminate between homophase and heterophase interfaces. At a homophase interface, composition and lattice type are identical on both sides, only the relative orientation of the lattices differ. At a heterophase interface two phases with different composition or/and Bravias lattice structure meet. Heterophase interfaces are further classified according to the degree of atomic matching. If the atomic lattice is continuous across the interface, we talk about a fully coherent interface. At a semicoherent interface, the lattices only partially fit. This is compensated for by periodic dislocations. At an incoherent interface there is no matching of lattice structure across the interface. 

Fig. 8. All the partial RDFs for ASW, HGW, and LDA agree within the experimental error, which suggests that ASW, HGW, and LDA all represent the same structural state at 77 K and 1 bar. The basic short-range order structural motif is the Walrafen pentamer (i.e., a central oxygen atom, which is surrounded tetrahedrally by four oxygen atoms c.f. inset Fig. 8.). However, whereas their structures appear identical, it was suggested from inelastic incoherent neutron scattering that the dynamics of lattice and internal vibrations of water molecules differ significantly in HGW and LDA [176].

Section IV is devoted to excitons in a disordered lattice. In the first subsection, restricted to the 2D radiant exciton, we study how the coherent emission is hampered by such disorder as thermal fluctuation, static disorder, or surface annihilation by surface-molecule photodimerization. A sharp transition is shown to take place between coherent emission at low temperature (or weak extended disorder) and incoherent emission of small excitonic coherence domains at high temperature (strong extended disorder). Whereas a mean-field theory correctly deals with the long-range forces involved in emission, these approximations are reviewed and tested on a simple model case the nondipolar triplet naphthalene exciton. The very strong disorder then makes the inclusion of aggregates in the theory compulsory. From all this study, our conclusion is that an effective-medium theory needs an effective interaction as well as an effective potential, as shown by the comparison of our theoretical results with exact numerical calculations, with very satisfactory agreement at all concentrations. Lastly, the 3D case of a dipolar exciton with disorder is discussed qualitatively. 

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