Intensity powder diffraction

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. 

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. 

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). 

In the powder diffraction technique, a monochromatic (single-frequency) beam of x-rays is directed at a powdered sample spread on a support, and the diffraction intensity is measured as the detector is moved to different angles (Fig. 1). The pattern obtained is characteristic of the material in the sample, and it can be identified by comparison with a database of patterns. In effect, powder x-ray diffraction takes a fingerprint of the sample. It can also be used to identify the size and shape of the unit cell by measuring the spacing of the lines in the diffraction pattern. The central equation for analyzing the results of a powder diffraction experiment is the Bragg equation... 

In addition, an interesting, although negative, result has come from powder diffraction studies of the hexachloro compounds. We have examined Debye—Scherrer photographs of several samples known to contain predominantly hexachlorodibenzo-p-dioxins and have identified the patterns of at least three crystalline phases therein. (There are 10 possible isomers of hexachlorodibenzo-p-dioxin.) These patterns have been checked carefully against the calculated d-spacings and intensities of the 1,2,3,7,8,9-hexa isomer described by Cantrell, Webb, and Mabis (I) and also against an observed pattern supplied by Cantrell and believed to be from the low temperature phase of the same material. Yet to date we... 

The X-ray powder diffraction pattern of miconazole was performed using a Simmons XRD-5000 diffractometer. Figure 1 shows the X-ray powder diffraction pattern of miconazole nitrate, which was obtained on a pure sample of the drug substance. Table 1 shows the values for the scattering angles (26 (°)), the interplanar <7-spacing (A), and the relative intensities (%) observed for the major diffraction peaks of miconazole. 

The X-ray powder diffraction pattern of niclosamide has been measured using a Philips PW-1050 diffractometer, equipped with a single-channel analyzer and using a copper Ka radiation. The pattern obtained is shown in Fig. 1, and the data of scattering angle (degrees 20) and the relative intensities (///max) are found in Table 1. 

Table 1. Scattering angles and relative intensities in the X-ray powder diffraction pattern of niclosamide...

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

One big problem, which arises mainly in crystals with rather large unit cells, is the overlapping of reflections. This prevents an accurate measurement of the local integrated intensities of a large number of reflections. A solution to this problem can be the 2D pattern decomposition method, which is based on the same principles as in X-ray powder diffraction. This method takes into account the dependence of intensities on the particle orientation function and the size of microcrystals. It is therefore necessary to establish the mathematical formalism that describes the dififiaction pattern taking into account these parameters. 

The X-ray and neutron powder diffraction methods successfully use two approaches connected to extraction of intensities (see [14]) ... 

Most of the unknown structures is determined from single crystal diffraction and refined from powder diffraction. Refinement is done with the Rietveld method, which is a least square fitting of the computed pattern to the measured one, while structure parameters are treated as the primary fitting parameters. This is in contrast to the procedure in pattern decomposition, which is outlined above (where not the structure parameters, but the peak intensities were the primary fitting parameters). Beside the... 

One application of powder diffraction is phase identification. Since zeolites of the same structure type give similar powder patterns, the powder pattern can be used as a fingerprint to identify the zeolite type. Furthermore, when multiple phases are present, the powder pattern is a superposition of the patterns for each of the separate phases and the relative overall intensities of the peaks is related to the amount of each phase. Thus patterns from mixtures of phases can be analyzed to determine the identity and relative amount of each phase. 

Recently, the PDF method was extended to describe the local dynamics of disordered materials (Dmowski W, Vakhrushev SB, Jeong I-K, Hehlen M, Trouw F, Egami T (2006) Abstracts American conference on neutron scattering, St. Charles, IL, 18-22 June 2006, unpublished). The total PDF is obtained by the powder diffraction method so that S(Q) includes both elastic and inelastic intensities. To determine the dynamics we have to use an inelastic neutron scattering spectrometer and measure the dynamic structure factor, S(Q,a>), over a large Q and co space, and Fourier-transform along Q to obtain the dynamic PDF (DPDF). While the interpretation of the DPDF is a little... 

All patterns showed a sharp decay in intensities at about 20 to 22 A. Thus we were misled into believing that 20 A was the actual resolution limit. Only much later, when crystals grew larger and measuring facilities were further improved, did we discover that the crystals are ordered internally to much higher level, close to that indicated by the powder diffraction. 

The x-ray powder diffraction pattern of cortisone acetate was obtained using a Siemens D 5000 x-ray diffractometer system. The incident radiation was provided by a copper tube, yielding X = 1.5480 A. The powder pattern thusly obtained is presented in Figure 1, and the scattering angles, interplanar distances, and peak relative intensities are collected in Table 2 for diffraction lines whose relative intensity exceeds 4%. 

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