Powders, diffraction

Since it is difficult to obtain a large, well formed crystal, grinding the sample to a fine powder is a preferred method of sample preparation and when the beam strikes the powder 

When the film is laid flat, the distance from the center of the hole to the diffraction line Si is measured. When the angle 20 is greater than 90°, this corresponds to the back reflections and S2 can be measured. The distance Si relates to a diffraction angle of 20, which is always the angle between the transmitted and diffracted beams. The distance between the centers of the holes (W) corresponds to a diffraction angle of 0 = jt. So can find 0 from  

For a cubic crystal system with interplanar spacing of d, 

Knowing 0, sin 0 can be obtained and multiplying by a selected constant, values for Qp- + k + P) can be obtained. By adjusting to an integer value, the values for h, k, and / can be found in the Miller Indices and hence, a can be calculated. 

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X-ray powder diffraction studies are perfonned both with films and with counter diffractometers. The powder photograph was developed by P Debye and P Scherrer and, independently, by A W Hull. The Debye-Scherrer camera has a cylindrical specimen surrounded by a cylindrical film. In another commonly used powder... 

Powder diffraction studies with neutrons are perfonned both at nuclear reactors and at spallation sources. In both cases a cylindrical sample is observed by multiple detectors or, in some cases, by a curved, position-sensitive detector. In a powder diffractometer at a reactor, collimators and detectors at many different 20 angles are scaimed over small angular ranges to fill in the pattern. At a spallation source, pulses of neutrons of different wavelengdis strike the sample at different times and detectors at different angles see the entire powder pattern, also at different times. These slightly displaced patterns are then time focused , either by electronic hardware or by software in the subsequent data analysis. 

The formation of such materials may be monitored by several techniques. One of the most useful methods is and C-nmr spectroscopy where stable complexes in solution may give rise to characteristic shifts of signals relative to the uncomplexed species (43). Solution nmr spectroscopy has also been used to detect the presence of soHd inclusion compound (after dissolution) and to determine composition (host guest ratio) of the material. Infrared spectroscopy (126) and combustion analysis are further methods to study inclusion formation. For general screening purposes of soHd inclusion stmctures, the x-ray powder diffraction method is suitable (123). However, if detailed stmctures are requited, the single crystal x-ray diffraction method (127) has to be used. 

Powder Diffraction File, Sets 1—29, CPDS International Center for Diffraction Data, Swarthmore, Pa., 1985. 

Analysis. Excellent reviews of phosphate analysis are available (28). SoHds characterization methods such as x-ray powder diffraction (xrd) and thermal gravimetric analysis (tga) are used for the identification of individual crystalline phosphates, either alone or in mixtures. These techniques, along with elemental analysis and phosphate species deterrnination, are used to identify unknown phosphates and their mixtures. Particle size analysis, surface area, microscopy, and other standard soHds characterizations are useful in relating soHds properties to performance. SoHd-state nmr is used with increasing frequency. 

Powder diffraction patterns have three main features that can be measured t5 -spacings, peak intensities, and peak shapes. Because these patterns ate a characteristic fingerprint for each crystalline phase, a computer can quickly compare the measured pattern with a standard pattern from its database and recommend the best match. Whereas the measurement of t5 -spacings is quite straightforward, the determination of peak intensities can be influenced by sample preparation. Any preferred orientation, or presence of several larger crystals in the sample, makes the interpretation of the intensity data difficult. 

Many of the procedures used for technical analysis of aluminum hydroxides are readily available from the major producers of aluminum hydroxides. Phase Composition. Weight loss on ignition (110°—1200°C) can differentiate between pure (34.5% Al(OH)2) ttihydroxides and oxide—hydroxides (15% Al(OH)2). However, distinction between individual ttihydroxides and oxide —hydroxides is not possible and the method is not useful when several phases are present together. X-ray powder diffraction is the most useful method for identifying and roughly quantifying the phase composition of hydroxide products. 

J. D. H. Doimay and H. M. Ondik, Crystal Data Determinative Tables, 3rd ed, U.S. Department of Commerce, National Bureau of Standards Joiut Committee on Powder Diffraction Standards, Washiagton, D.C., 1972, pp. 0-23, 0-73, 0-97, 0-106. 

Mighell, eds., Inorganic Compounds Vol. 4, National Bureau of Standards/Joint Committee on Powder Diffraction, Washington, D.C., 1978. 

Bragg-Brentano Powder Diffractometer. A powder diffraction experiment differs in several ways from a single-crystal diffraction experiment. The sample, instead of being a single crystal, usually consists of many small single crystals that have many different orientations. It may consist of one or more crystalline phases (components). The size of the crystaUites is usually about 1—50 p.m in diameter. The sample is usually prepared to have a fiat surface. If possible, the experimenter tries to produce a sample that has a random distribution of crystaUite orientations. 

Fig. 14. Focusing schemes in powder diffraction (a) conventional para-focusing Bragg-Brentano diffractometer (b) parallel-beam diffractometer using a...

Sea.rch-Ma.tch. The computer identifies which crystalline phases (components) match the unknown pattern by using a file of known powder patterns maintained by the International Center for Diffraction Data (ICDD). The Powder Diffraction File contains interplanar t5 -spacings d = A/(2sin0)] and intensities of the diffraction maxima for each crystalline powder pattern submitted to the ICDD. Currendy there are about 65,000 patterns in the file. Current search—match programs can successfully identify up to seven components in an unknown pattern. A typical diffraction pattern of an unknown sample and the components identified by the computer search-match program is shown in Figure 15. 

For further discussion of neutron sources, see R. B. Von Dreete. Reviews in Mineralogy. Volume 20 Modem Powder Diffraction. 333,20, 1990. 

The structure refinement program for disordered carbons, which was recently developed by Shi et al [14,15] is ideally suited to studies of the powder diffraction patterns of graphitic carbons. By performing a least squares fit between the measured diffraction pattern and a theoretical calculation, parameters of the model structure are optimized. For graphitic carbon, the structure is well described by the two-layer model which was carefully described in section 2.1.3. 

Doping of alkali-metals into CNTs has been examined [11]. The X-ray powder diffraction (XRD) patterns of the K- or Rb-doped CNTs show that alkali-metals are intercalated between the CNT layers. The hexagonal unit cell is essentially the same as that of the stage-1 alkali-metal intercalated graphite ACg (A=K, Rb). For a sample doped with Rb, the observed lattice parameter of the perpendicular... 

As already explained in the relevant section, the use of X-ray crystallography (Section V,D,2), the possibility to determine the molecular structure from powder diffraction without the need to obtain monocrystals, and the many variants of solid-state NMR (Section VI,F) have profoundly enhanced the study of tautomerism in the solid state. 

According to X-ray powder diffraction data, compounds RF NbOFs, Cs2NbOF5 [174] and Cs2TaOF5 [176] have similar type structure and are similar to K2GeF6, whereas (NFL,)2NbOF5 crystal structure is similar with Rb2Mo02F4 [184]. The above-mentioned compounds contain isolated NbOF52" complex ions [185]. 

Lastochkina et al. [216] reported on the preparation of KTaOi.5F3-H20, but the X-ray powder diffraction pattern obtained for the anhydrous product, KTaOi.5F3, does not correspond with the pattern given for K2Ta203F6 in [215]. 

The compounds characterized by X Me = 3.5 have a common formula of M2Me205F2 and crystallize either in a pyrochlore [192] or a veberite [229] type structure. According to X-ray powder diffraction patterns, the structure of Na2Nb205F2 can be regarded as a super-structure of pyrochlore, which is made up of octahedrons connected in layers and arranged in the (111) direction. The layers are linked via octahedrons so that each octahedron in one layer shares three vertexes with an octahedron in the adjacent layer. 

Fig. 43 shows fragments of X-ray powder diffraction patterns of compounds with rock-salt-type structures. 

Fig. 43. Fragments of X-ray powder diffraction patterns of compounds with rock-salt structures that underwent modification to a state of disordered ionic arrangement. 1 - Li3Ta04 2 - LiflbO 3 - Li4Ta04F 4 - Li3Ti03F 5 -LiiFeOiF 6 - LiNiOF (Reflections attributed to LiF are marked by an asterisk).

In all cases, broad diffuse reflections are observed in the high interface distance range of X-ray powder diffraction patterns. The presence of such diffuse reflection is related to a high-order distortion in the crystal structure. The intensity of the diffuse reflections drops, the closer the valencies of the cations contained in the compound are. Such compounds characterizing by similar type of crystal structure also have approximately the same type of IR absorption spectra [261]. Compounds with rock-salt-type structures with disordered ion distributions display a practically continuous absorption in the range of 900-400 cm 1 (see Fig. 44, curves 1 - 4). However, the transition into a tetragonal phase or cubic modification, characterized by the entry of the ions into certain positions in the compound, generates discrete bands in the IR absorption spectra (see Fig. 44, curves 5 - 8). 

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