Intersecting crystals

Figure 3.25. Phase diagram of a binary polymer blend with miscibihty gap (UCST) and intersecting crystal/melt coexistence curve. The curve is extrapolated into the miscibility gap. Quenching routes A to D are explained in the text. For routes B and C, the quenching-induced phase...

Photograph 7-18 Clinker thin section (approximately 15 pm thick) showing relatively large angular alite smaller, round belite and normal ferrite with its short slender intersecting crystals, between which the aluminate occurs (not visible at this magnification). (S A6638)... 

FIGURE 7.6. A Wulff construction for a hypothetical, two-dimensional crystal with surface energies X and IX, from which the ideal geometric shape of the crystal can be predicted. The arrows emanating from the common point are proportional to the surface free energy of the intersecting crystal faces. 

It can be rightly said that The reciprocal lattice is as important in crystal structure analysis as the walking stick of a blind man moving in a narrow lane having frequent turns. It is extremely difficult if not impossible to picture the different intersecting crystal planes satisfying the Bragg s reflection in three-dimensional lattice from the two-dimensional array of spots or lines. 

Figure 3.29 Two intersecting crystals of polyethylene grown at 80°C from 0.05% xylene solution. The top crystal has the longer a-axis pointing to about 10 o clock, while the bottom crystal has the fe-axis oriented at 4 o clock. Two oppositely directed steps of thickness k are evident on a line near 11 o clock. Two coincident giant screw dislocations, each left handed, have been created at common the tip of the notches. Transmission electron micrograph of unspecified magnification by Hirai [45] with permission from John Wiley Sons, Inc.

The density of dislocations is usually stated in terms of the number of dislocation lines intersecting unit area in the crystal it ranges from 10 cm for good crystals to 10 cm" in cold-worked metals. Thus, dislocations are separated by 10 -10 A, or every crystal grain larger than about 100 A will have dislocations on its surface one surface atom in a thousand is apt to be near a dislocation. By elastic theory, the increased potential energy of the lattice near... 

Several studies have concerned the microstnicture of lamellae in materials such as the block copolymers polystyrene-h/oc/r-poly-l-vinylpyridine [139] and polystyrene-h/oc/r-polybutadiene [140], as well as single crystals of poly-para-xylylene [139], and reveal features (such as intersecting lamellae (figure Bl.19.29)) that had not been previously observed. 

Figure B3.3.13. Intersecting stacking faults in a fee crystal at the impact plane induced by collision with a momentum mirror for a square cross section of side 100 unit cells. The shock wave has advanced half way to the rear ( 250 planes). Atom shading indicates potential energy. Thanks are due to B Holian for tliis figure.

Crystallizers with Fines Removal In Example 3, the product was from a forced-circulation crystallizer of the MSMPR type. In many cases, the product produced by such machines is too small for commercial use therefore, a separation baffle is added within the crystallizer to permit the removal of unwanted fine crystalline material from the magma, thereby controlling the population density in the machine so as to produce a coarser ciystal product. When this is done, the product sample plots on a graph of In n versus L as shown in hne P, Fig. 18-62. The line of steepest ope, line F, represents the particle-size distribution of the fine material, and samples which show this distribution can be taken from the liquid leaving the fines-separation baffle. The product crystals have a slope of lower value, and typically there should be little or no material present smaller than Lj, the size which the baffle is designed to separate. The effective nucleation rate for the product material is the intersection of the extension of line P to zero size. 

When crystals yield, dislocations move through them. Most crystals have several slip planes the f.c.c. structure, which slips on 111) planes (Chapter 5), has four, for example. Dislocations on these intersecting planes interact, and obstruct each other, and accumulate in the material. 

By their nature, dislocations cannot end suddenly in the interior of a crystal a dislocation line can only end at a free surface or a grain boundary (or form a closed loop). Where a screw dislocation intersects a free surface there is inevitably a step or ledge in the surface, one atomic layer high, as shown in Fig. 20.30c. Furthermore, the step need not necessarily be straight and will, in fact, almost certainly contain kinks. 

In the as-synthesized MFI-crystals the tetrapropylammonium (TPA) ions are occupying the intersections between the straight (parallel) and the sinusoidal channels of the zeolite, thus providing an efficient pore filling. The detailed structure of as-synthesized MFI-TPA has been elucidated by X-ray single crystal analysis (ref. 3). Also the combination tetrabutyl-Ztetraethylammonium can be applied as template in MFI-synthesis. A 1 1 build-in is found then (Fig. 1). When only tetrabutylammonium is available as template, the MEL (ZSM-11) lattice is formed with another distance between the channel intersections. 

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