Crystalline unit cells

Re-organization of amorphous chain segments adjacent to crystallite surfaces leads to crystallite thickening. These segments align themselves to form additional crystalline unit cells that increase the c dimensions of the crystallites. 

Fig. 4. A model for the possible relationship between crystalline and disordered regions within a collagen fibril. The cross-sectional model of a 50-nm diameter fibril shows regions of crystallinity interfaced by grain boundaries. The individual crystalline unit cells are shown and the gap region is represented by a darker color. The axial projection of a single microfibrillar unit is also shown. Based on die structures developed by Hulmes et al. (1995) and adapted with permission from Hulmes et al (2002).

Phonon dispersion expresses the phase relationship between different molecules in the lattice as they participate in the same mode. The repeat distance between molecules which vibrate totally in-phase is the phonon (deBroglie) wavelength, it is written in terms of the crystalline unit-cell dimensions and defines the characteristic momentum of the phonon, q. The... 

These unexplored forms of matter contain innumerable surprises, as we know from the many extraordinary compounds that are among the ten million already studied. Furthermore there is as yet no known maximum size either of a molecule, or crystalline unit cell, i.e. no maximum size above which matter is guaranteed to be repetitive. Hence even centimeter3 size chunks might contain new surprises. ... 

If we define three vectors a, b and c, as in Problem 5.9, the expression a (6 X c), known as the scalar triple product, yields a scalar quantity, the magnitude of which provides the formula for the volume, F, of a parallelepiped with adjacent edges defined by vectors a, b and c (an example in chemistry being a crystalline unit cell). If the determinantal representation of A x c is used, then, on expanding the determinant from the first row, and evaluating the three scalar products, we obtain ... 

Fig. 2. Pictorial representation of crystalline unit cell in space showing the relation of the orientation of the crystalline axes to that of a cartesian coordinate system where the stretch axis (machine direction) lies along the z axis...

The salt-free crystalline polysaccharides reviewed by Bluhm et al. [15] are stabilized in characteristic crystalline unit cells by specific amounts of water. Two kinds of locations have been proposed for the water molecules one is unique, i.e., the water lies clustered in an existing interstitial cavity between double helices of B-starch. The other has water bound at specific sites within each unit cell. Additional water in this second type expands one or more unit cell dimension. This almost continuous expansion of the unit cell with increasing content of water may represent a more ordered aspect of the same interaction that occurs between water and accessible, disordered surfaces of celluloses crystallites (and other imperfectly crystalline polysaccharides). 

Isomorphous substitution of the framework aluminium of ZSM-5 for zinc The gas-solid reaction of anhydrous ZnClz vapor with HZSM-5 was studied at 773 K. The retention of the crystallinity of the zeolite after the reaction was confirmed by XRD results. Figure 1 shows the change in the volume of the crystalline unit cell, Vu.c., and the frequency of the framework-sensitive IR absorption near 1100 cm during the reaction. The result that the product zeolite of the reaction has an Vu.c. value greater than that for the initial HZSM-5 indicates that the zinc atom is inserted into the zeolite framework since the bond of Zn-0(1.96 A) is longer than Al-0(1.75 A) and Si-0(1.61 A). The linear relationship between Vu.c. and the reaction time suggests that the insertion of zinc is proportional to the reaction period. The continuous shift in the framework-sensitive IR absorption frequency towards lower wavenumbers provides further evidence... 

Figure 12.11 Distribution of coordination numbers of Rb sites for simulated Na Rbi xSi02.5. Na08Rb means that we have ONa and 8Rb atoms in the starting crystalline unit cell for the simulation of the alkalisilicate glass etc.

By collecting the integrated intensities of diffraction peaks and subjecting them to a sequence of analyses, it is possible to determine the positions of the atoms packed in the crystalline unit cell. Such an endeavor constitutes the traditional process of crystal structure analysis, and much of the information that is available today about the shape of polymer molecules and their arrangement in crystals was derived by this method. 

The a-form is the most common form of PLLA. It expands under normal crystallization conditions, such as crystallization from molten, glassy state, or in solution [54]. The a-form is characterized by two antiparallel chains in a left-handed IO3 helix conformation [54, 55]. As shown in Table 8.3, the chains are stacked in an orthorhombic or pseudo-orthorhombic crystalline unit cell. A notable structural feature of the a-form is the distortion of the helix conformation and the crystal structure change. According to the authors named in Table 8.3 the interactions between closest neighbour chains, that is to say the electrostatic dipole-dipole interactions, are the cause of these changing data. 

The hypothesis (1-3) that all native celluloses are a composite of two crystalline allomorphs, designated and Ig, has been further tested using C solid state NMR. In particular, two alternate origins of sharp resonance features were considered in addition to the usual origin, the crystalline unit cell. The first source is ordered layers on crystal surfaces the second is possible anistropic bulk magnetic susceptibility (ABMS) shifts associated with well defined fibril patterns (tertiary morphology). 

Crystalline unit cell parameters depend on crystallite thickness. The comonomer amount, comonomer type, and crystallization conditions determine the crystallite thickness in ethylene copolymers. The major cause of lattice expansion in ethylene copolymers is due to decrease in lamellae thickness by exclusion of branch points from the lamellar crystals coupled with surface stress on thin lamellae (see references 24 and 25 for details). The table below is for butene-1 mLLDPE (My, = 122,000, Mw/M = 2), crystallized from the melt at a cooling rate of 7°Cmin . ... 

The crystalline allomorphs of cellulose differ from each other also by the shapes of the crystalline unit cells. The projection of the Cl-unit cell has a parallelepiped shape, CIV-unit cell has a square shape, while unit cells of Cll and CIII have a rhombic shape. 

Table 9.2 Parameters of Crystalline Unit Cells of Various Allomorphs...

Other frequently used characterization parameters include surface area and pore size distribution. X-ray crystallinity, unit cell size, and chemical composition (especially rare earth loadings). Surface areas can range from 100... 

Micromorphology discussed in terms of submicron-sized crystalline unit cells Thus, macromolecular Configuration belongs to the sub-nanometer structures... 

Structural constitution on a submicron scale as related to crystallinity, viz., crystalline unit cells, lamellae shape and size, and stress-induced shish kebab crystals. Computer system that stores, analyzes, and adjusts the controls of a machine based on the parameters established during the operation of the machine it is controlling. It continuously analyzes output data to adjust and maintain the machine s cycle within programmed limits. Can also store data and output it as directed by programming. 

Less organized (amorphous) cellulose is also present along with the crystalline cellulose. The crystalline forms la and 1(3 differ by their crystalline unit cell structure and overall hydrogen bonding pattern, but the main intermolecular hydrogen bond is the same for both, i.e., 06-H 03 (Fig. 21.2). The intramolecular hydrogen bond of 03-H 05, which is partly responsible for the cellulose chain stiffness and contributes to load transfer along the chain, is also shown in Fig. 21.2. Other crystalline forms of cellulose include cellulose 11, cellulose 111, and cellulose... 

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