Axes of crystals

A further increase in extension leads to irreversible changes which immediately precede the transition of the polymer into the oriented state. During this transition, the spherulites undergo considerable structural changes and are thus converted qualitatively into different structural elements i.e. macrofibrils4). After a certain critical elongation has been attained, the initial crystallites collapse and melt and a new oriented structure is formed in which the c axes of crystals are oriented in the direction of extension. 

A crystal plane has intercepts on the three axes of crystal in the ratio of 2 2 1. The Miller indices of the plane are ... 

The A-axes of crystals XIII and XIV are twice the length of those of X (and XI and xn), as shown in Figures 4.10 and 4.11. This means that there are two CTABs and one dibenzofuran or carbazole molecule in the asymmetric unit, respectively. Although the two crystal structures are isostructural, the dibenzofuran molecule is ordered whereas... 

P) handed helical long-range orientational order of cholesteric and smectic C phase and the left (M) or right (P) handed screw axes of crystals. 

Axes of symmetry. An axis about which rotation of the body through an angle of 2njn (where n is an integer) gives an identical pattern 2-fold, 3-fold, 4-fold and 6-fold axes are known in crystals 5-fold axes are known in molecules. In a lattice the rotation may be accompanied by a lateral movement parallel to the axis (screw axis). 

Austenitic Steel weld has a well defined transcrystalline (oriented) macrostructure with continuously changing orientation of the crystal axis - from the periphery towards the centre the angle between the axis of the crystal and the axis of the weld is changed from 90 to 0 degrees. Weld metal eould be possible to approximate in the form of a discrete combination of crystals with parallel axes of the crystallites. 

The direction of the alignment of magnetic moments within a magnetic domain is related to the axes of the crystal lattice by crystalline electric fields and spin-orbit interaction of transition-metal t5 -ions (24). The dependency is given by the magnetocrystalline anisotropy energy expression for a cubic lattice (33) ... 

Fig. 2. SolubiHty diagram for a hypothetical system. The curves AB and BC represent solution compositions that are in equiHbrium with soHds whose compositions are given by the lines AD and CE. If AD and CE are vertical along the respective axes, the crystals are pure R and S, respectively. Crystallization from any solution whose composition is to the left of the vertical line through point B produces crystals of pure R, whereas solutions to the right of the line produce crystals of pure S. A solution whose composition falls on the line through B produces a soHd mixture that has a composition...

Figure 7. 5. Time evolution of crystallographic texture [(0002) pole figures] along the axis of an explosively driven, hemispherical, titanium liner [66]. A high density of contours near the center of the circle indicate the c-axes of individual crystals are all normal to liner surface.

Metallurgists originally, and now materials scientists (as well as solid-state chemists) have used erystallographic methods, certainly, for the determination of the structures of intermetallic compounds, but also for such subsidiary parepistemes as the study of the orientation relationships involved in phase transformations, and the study of preferred orientations, alias texture (statistically preferential alignment of the crystal axes of the individual grains in a polycrystalline assembly) however, those who pursue such concerns are not members of the aristocracy The study of texture both by X-ray diffraction and by computer simulation has become a huge sub-subsidiary field, very recently marked by the publication of a major book (Kocks el al. 1998). 

As an example of the second case, we may have conformationally disordered chains, but long-range order in the positions of the chain axes (condis crystals [5]). Fiber spectrum features are the occurrence of sharp reflections on the equator only and diffuse reflections on the other layer lines. 

A typical liquid-crystal molecule, such as p-azoxyanisole, is long and rodlike (14). Their rodlike shape enables the molecules to stack together like dry, uncooked spaghetti they lie parallel to one another but are free to slide past one another along their long axes. Liquid crystals are anisotropic because of this ordering. Anisotropic materials have properties that depend on the direction of measurement. The viscosity of liquid crystals is least in the direction parallel to the long... 

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