Orthorhombic system

The problem of indexing increases manifold as these systems involve four and six independent constants and there are sometimes more than himdred lines found in the diffraction patterns. Solving and indexing the lines manually then turns out to be almost impossible and so, they are generally done with the aid of computer. Standard programs are now available and therefore indexing of the lines belonging to any system is seldom done manually. 

Different X-ray diffraction techniques for single crystal starting from Laue techniques to rotation/oscillation and finally to Weissenberg techniques are discussed along with the interpretation and the advantages and limitations. These techniques which are systematically introduced and discussed are essential for imderstanding the inside of structure and their arrangements in a crystal. 

CuUity, Elements of X-Ray Diffraction (Addison Wesley, Reading, MA, 

Woolfson, An Introduction to X-Ray Crystallography, 2nd edn. (Cambridge University Press, Cambridge, 1997) 

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Physical Properties. The absorption of x-rays by iodine has been studied and the iodine crystal stmcture deterrnined (12,13). Iodine crystallizes in the orthorhombic system and has a unit cell of eight atoms arranged as a symmetrical bipyramid. The cell constants at 18°C (14) are given in Table 1, along with other physical properties. Prom the interatomic distances of many iodine compounds, the calculated effective radius of the covalently bound iodine atom is 184 pm (15). 

The PVC crystaUites are smaU, average 0.7 nm (3 monomer units), in the PVC chain direction, and are packed lateraUy to a somewhat greater extent (4.1 nm) (21,33). A model of the crystaUite is shown in Figure 6. The crystalline stmcture of PVC is found to be an orthorhombic system, made of syndiotactic stmctures, having two monomer units per unit cell and 1.44—1.53 specific gravity (34—37). 

In contrast to single-crystal work, a fiber-diffraction pattern contains much fewer reflections going up to about 3 A resolution. This is a major drawback and it arises either as a result of accidental overlap of reflections that have the same / value and the same Bragg angle 0, or because of systematic superposition of hkl and its counterparts (-h-kl, h-kl, and -hkl, as in an orthorhombic system, for example). Sometimes, two or more adjacent reflections might be too close to separate analytically. Under such circumstances, these reflections have to be considered individually in structure-factor calculation and compounded properly for comparison with the observed composite reflection. Unobserved reflections that are too weak to see are assigned threshold values, based on the lowest measured intensities. Nevertheless, the number of available X-ray data is far fewer than the number of atomic coordinates in a repeat of the helix. Thus, X-ray data alone is inadequate to solve a fiber structure. 

Over the last few years the DCA and ACA compounds have been the subject of a number of interesting chemical developments including their use as templates in polymerisation 23,24), and as media for stereospecific chemical reactions 98 100). This work has been carried out on the orthorhombic systems and is therefore outside the scope of this review. 

CsTeFs also crystallizes in the orthorhombic system (97, 98). An infrared and Raman study (97) further confirmed the lowering of the symmetry of the TeF, ions to Cs, in accordance with the strong quad-... 

During the tilt about the main axes, 90° angles were preserved and the tilt series turned out to be symmetrical, which implies an orthorhombic system in each case. The third axes were calculated as 23.5 A and 25.3 A, respectively. These preliminary cell parameters have been refined according to the ratio of the axes in every measured zone leading to a higher cell parameter precision for both modifications (Mod I a=23.83 A, b=9.10 A, c=5.03 A Mod II a=10.22 A, b=25.43 A, c=4.I8 A). With the refined cell parameters it was possible to index the two-phase diffraction diagram. 

Pyroxenes are poly silicates ( inosilicates in the mineralogical classification), crystallizing, respectively, in the monoclinic clinopyroxenes spatial groups C2lc, Pljlc, P2ln) and orthorhombic systems orthopyroxenes spatial groups... 

The X-ray powder patterns were reported for the XFg type (34, 64, 246) and the BF4 (64) adduct and were tentatively indexed in the orthorhombic system. 

The determination of the molecular structures of SOF and SOPHi did not present any particular difficulties, SOF crystallizing in the Pljc monoclinic space group (Z = 4 Fig. 44) and SOPHi in the P2j2j2j orthorhombic system (Z = 4 Fig. 45) It may again be noted that these two structures differ from those of SOAz and MYKO 63 by the spatial arrangement of their aziridinyl wings. 

Potassium hexacyanochromate(III) is a yellow solid, highly soluble in water, that crystallizes as large square platelets. It crystallizes in the orthorhombic system, with the space group Pcan. The unit parameters are a = 8.53, b = 10.60, c = 13.68 A. Because of its disorder behavior, it presents a complex crystallographic problem. The compound shows a j/cn band at 2131 cm. The molar extinction coefficients in aqueous solution of the two observable d d bands at 376 nm ( A2g —> 72) and 309 nm (4 2 T l ) are 93 and 62 L mol ... 

It is sometimes useful to be able to calculate the perpendicular distance dhu between parallel planes (Miller indices hkl). When the axes are at right angles to one another (orthogonal) the geometry is simple and for an orthorhombic system where a b i c and... 

Mercury fulminate consists of octahedral crystals, belonging to the orthorhombic system with the axial relationship a b c=0.712 1 1.353 (Miles [13]). The pure substance crystallizes into the form of white, silky needles. 

Fig. 34. Orthorhombic system. (See also Fig. 25.) a. Unit cell type.. (H.COO),Sr.2HsO. Cla8s222. Left-and right-handed crystals, c. 1-Brom, 2-hydroxy-naphthalene. Class 222. d. Picric acid, Class mm. e. Oxalic acid. Class mmm. /. C,Br. Class mmm.

The same type of unit cell is appropriate for classes 222 and mmm (= 2jm 2jm 2/m) the cell edges, lie along the twofold axes. Donnay (1943) recommends that the longest shall be called b and the shortest c. When axes are chosen on morphological grounds the axis of the principal prism zone is labelled c, while b is the longer of the other two. The three classes mm, 222, and mmm constitute the orthorhombic system (Fig. 34). 

The urea molecule 0--C(NHa)a has two planes of symmetry intersecting in a single twofold axis—the symmetry found in crystals belonging to the polar class of the orthorhombic system (Kendricks, 1.928 a) the point-group symbol is mm2. 

Sodium nitrite, NaN02, forms orthorhombic crystals of the shape of Fig. 179. This shape has holohedral symmetry mmm the internal symmetry might, however, be lower than this (see p. 269), and therefore atomic arrangements in all three classes of the orthorhombic system (mmm, 222, and mm2) may be considered. 

According to Mathieu, trinitrocellulose crystals belong to the orthorhombic system, the dimensions of the crystal cell being a = 12.40 A,b — 25.4 A, c = 9.0 A, angle (S = 90°. Similar figures have been reported by Happey [15]. 

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