Lattice discontinuity

The distribution of these impurities or minor alloy constituents near lattice discontinuities is known to affect the chemical and mechanical properties of the contaminated materials for example the presence of sulfur on a metal surface can promote ) or retard - o) corrosion, modify the surface energy ) or cause considerable increase in the surface self-diffusion coefficient ). Sulfur accumulation along grain boundaries may induce intergranular weakness and render otherwise ductile materials brittle ), either by formation of precipitates " ) or by enhancement of hydrogen adsorption >227)... 

As in crystals, defects in liquid crystals can be classified as point, line or wall defects. Dislocations are a feature of liquid crystal phases where tliere is translational order, since tliese are line defects in tliis lattice order. Unlike crystals, tliere is a type of line defect unique to liquid crystals tenned disclination [39]. A disclination is a discontinuity of orientation of tire director field. 

Clearly Fig. 7 must actually have a maximum at high asymmetry since this corresponds to negligible anchor block size and therefore to no adsorption (ct = 0). The lattice theory of Evers et al. predicts this quantitatively [78] and is, on preliminary examination, also able to explain some aspects of these data. From these data, the deviation from power law behavior occurs at a number density of chains where the number of segments in the PVP blocks are insufficient to cover the surface completely, making the idea of a continuous wetting anchor layer untenable. Discontinuous adsorbed layers and surface micelles have been studied theoretically but to date have not been directly observed experimentally [79]. 

The thermodynamic transition between different forms as the above described is formally discontinuous. The difference between polymorphs is shown in general also by a different metrical description of the corresponding lattices. 

An alloy is said to be of Type II if neither the AC nor the BC component has the structure a as its stable crystal form at the temperature range T]. Instead, another phase (P) is stable at T, whereas the a-phase does exist in the phase diagram of the constituents at some different temperature range. It then appears that the alloy environment stabilizes the high-temperature phase of the constituent binary systems. Type II alloys exhibit a a P phase transition at some critical composition Xc, which generally depends on the preparation conditions and temperature. Correspondingly, the alloy properties (e.g., lattice constant, band gaps) often show a derivative discontinuity at Xc. 

The ionic conductivities of most solid crystalline salts and oxides are extremely low (an exception are the solid electrolytes, which are discussed in Section 8.4). The ions are rigidly held in the crystal lattices of these compounds and cannot move under the effect of applied electric fields. When melting, the ionic crystals break down, forming free ions the conductivities rise drastically and discontinuously, in some cases up to values of over 100 S/m (i.e., values higher than those of the most highly conducting electrolyte solutions). 

Proton NMR relaxation parameters have also been determined for polyethylene ( ) and polyethylene oxide (39) in the melting region. The apparent contradiction between the proton spin-lattice relaxation parameter for a high molecular weight linear polyethylene sample at its melting point, with the relaxation measurements, has previously been pointed out. (17) This discrepancy is still maintained with the more detailed results reported here for both types of polyethylene. For the proton relaxation a small, but distinct, discontinuity is reported at the melting teirperature. (38)... 

Using the self-consistently obtained solutions of Eq. 19, the calculated chemical shift (Jiso = (To + a(T) is calculated and compared to the experimental data in Fig. 4. Even though the experimentally observed transition is broader than the calculated one, the agreement between theory and experiment is good. As the discontinuity in the lattice-related mode is small at Tc, where Tc corresponds to a = 0, the chemical shift does not show a discontinuity at Tc within numerical accuracy. It is important to note here that the S-shape in the cf T) data is a direct consequence of using the renormalized frequencies as defined in Eq. 19. 

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