Diffraction patterns from orthorhombic crystals

The first attempt to establish the crystal and molecular structure of CTA I was made by Stipanovic and Sarko, who suggested the occurrence of parallel-arranged cellulosic chains within an orthorhombic unit-cell. Later, the structural analysis of the diffraction pattern from an acetylated material derived from the green alga Cladophora sp. established it as a one-chain unit cell crystallizing in the P2i space group (fl = 5.94 A, = 11.43 A, c = 10.46 A, y = 95.4°, density = 1.375). 

Figure 27. Schematic diffraction pattern from the orthorhombic untilted crystal E phase, with herringbone packing of the molecules.

A possible economically attractive alternative would be the production of acrylic acid in a single step process starting from the cheaper base material propane. In the nineteen nineties the Mitsubishi Chemical cooperation published a MoVTeNb-oxide, which could directly oxidise propane to acrylic acid in one step [6], Own preparations of this material yielded a highly crystalline substance. Careful analysis of single crystal electron diffraction patterns revealed that the MoVTeNb-oxide consists of two crystalline phases- a hexagonal so called K-Phase and an orthorhombic I-phase, which is the actual active catalyst phase, as could be shown by preparing the pure phases and testing them separately. 

If no external evidence is available, it is still possible to determine the unit cell dimensions of crystals of low symmetry from powder diffraction patterns, provided that sharp patterns with high resolution are avail able. Hesse (1948) and Lipson (1949) have used numerical methods successfully for orthorhombic crystals. (Sec also Henry, Lipson, and Wooster, 1951 Bunn 1955.) Ito (1950) has devised a method which in principle will lead to a possible unit cell for a crystal of any symmetry. It may not be the true unit cell appropriate to the crystal symmetry, but when a possible cell satisfying all the diffraction peaks on a powder pattern lias been obtained by Ito s method, the true unit cell can be obtained by a reduction process first devised by Delaunay (1933). Ito applies the reduction process to the reciprocal lattice (see p. 185), but International Tables (1952) recommend that the procedure should be applied to the direct space lattice. 

A previous examination of a synthetic calcium mordenite 15) revealed an orthorhombic cell. A synthetic strontium mordenite 16) had a C-centered orthorhombic cell although Kerr 12) reported that a few crystals giving electron diffraction patterns corresponding approximately to the body-centered structure Immm) have been synthesized hydro-thermally from aluminosilicate gels containing strontium similar to those gels which yielded a strontium-mordenite. ... 

Fig. 15 Diffraction patterns of ethylene-1-octene copolymer (5.2 mol %) shown from 100 °C to 25 °C while cooling at 10 °C/min recorded during crystallization from melt at 3.8 kbar. The open-orthorhombic phase appears at 80 °C, intensity and position of this reflection remains unchanged. The open-orthorhombic phase is followed by the incoming of the (100) monoclinic reflection concomitant with a shift to higher angles and drop in the intensity of the (110) dense-orthorhombic reflection. The X-ray wavelength used for these experiments is 0.744 A...

The diffraction pattern of the scattered x-rays, including intensities, can be calculated from the electron density distribution of the sample by means of Fourier transforms. Equation 1 shows the calculation of the structure factors F(hkl) for an orthorhombic unit cell of dimensions axbxc from the electron density p(x,y,z) and the exponential phase-factor term. The integers h, k, and / specify the order of the diffraction peaks and are related to the Miller indices that specify the reflecting planes within the crystal producing the diffraction spots (vide infra). An observed intensity I is calculated from I = F hkl)F hkl) = F hkl) where... 

Fig. 5.3. Protein structure determination by X-ray diffraction. A. Crystals of porcine heart aconitase composed of 754 amino acids. The orthorhombic crystals shown are about 0.5 mm in the longest dimension. B. Film showing the diffraction pattern obtained from the above crystal. These data were used to obtain a 2.7 A resolution structure shown in two representations in panels C and D. Panel C shows the tracing of the protein backbone, with the small molecule (in red and yellow) in the central region depicting the iron-containing cofactor of the enzyme. Panel D shows the space-filling representation. (Courtesy of Dr Arthur H. Robbins, Miles Pharmaceuticals Inc. For details see A.H.Robbins and C.D.Stout (1989). Proteins Structure, Function, and Genetics 5, 289 312.)...

The similarity of the two crystal structures leads to very similar X-ray powder diffraction patterns (Fig. 9.3), reminiscent of the situation in terephthalic acid (Section 4.4). Careful inspection reveals that the orthorhombic modification can be distinguished by a peak (the 511 reflection in the Golovina et al. (1994) cell) at 29 = 27.24°, while the monoclinic modification can be distinguished peak (from 211) at 20 = 19.26°. 

The maximum size of the unit cell edges can be estimated from the d-spacing of the first Bragg peak (t/max) observed in the diffraction pattern. In the majority of low symmetry cases (triclinic through orthorhombic crystal systems), the maximum size of the unit cell edge should not exceed... 

Consider the powder diffraction pattern collected from a ground Hf2Ni3Si4 powder, which is shown in Figure 6.46. The pattern has been indexed in the orthorhombic crystal system and the unit cell dimensions are a = 5.18, b = 13.65 and c = 6.85 A. An analysis of the systematic absences indicates that the following groups of reflections have non-zero intensity ... 

ZSM-5 has a crystal density of 1.77 g/cm3. Its crystals have orthorhombic symmetry, as synthesized, and can vary widely in size. Compositionally ZSM-5 is unusual, in comparison with the preceding examples given above, in that it can be prepared in the absence of aluminum. Organics can be removed from ZSM-5 samples by careful oxidative calcination at about 500°. Alkali metal cations, if present, can be exchanged by ammonium ion, for example, to produce NH4ZSM-5. Calcined samples of NH4ZSM-5 will sorb about 11% hexane (25°, 20 torr). The X-ray diffraction pattern of ZSM-5 is characterized by the... 

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