Powder Diffraction Suites

Suites for powder diffraction that can span a moderately comprehensive range of powder diffraction analysis are relatively uncommon, but some do exist and are listed in Table 17.21. 

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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. 

Currently, techniques for analyzing powder diffraction that involve the analytical dissection of measured Bragg reflection shapes " " can be used to derive a data set similar to that for a single crystal. As a result, crystal structures may be determined, and in some cases, refined anisotropically using powder diffraction data for X rays or neutrons. Powder diffraction methods can be used at a wide variety of temperatures and pressures and are well suited for studies of phase transformations. 

A crystal structure is described by a collection of parameters that give the arrangement of the atoms, their motions and the probability that each atom occupies a given location. These parameters are the atomic fractional coordinates, atomic displacement or thermal parameters, and occupancy factors. A scale factor then relates the calculated structure factors to the observed values. This is the suite of parameters usually encountered in a single crystal structure refinement. In the case of a Rietveld refinement an additional set of parameters describes the powder diffraction profile via lattice parameters, profile parameters and background coefficients. Occasionally other parameters are used these describe preferred orientation or texture, absorption and other effects. These parameters may be directly related to other parameters via space group symmetry or by relations that are presumed to hold by the experimenter. These relations can be described in the refinement as constraints and as they relate the shifts, Ap,-, in the parameters, they can be represented by... 

The crystal structures of proteins represent an extreme in the number of atom positions needed to describe them compared to those structures more commonly studied by powder diffraction. For example, the well-known tetragonal crystal structure of hen egg white lysozyme has 1001 nonhydrogen atoms within the protein molecule another 100 or so water molecules and salt ions are also present. This gives over 3000 atomic x,j,z coordinates. Nonetheless, a Rietveld refinement of these structures from powder diffraction data can be performed by extending the suite of restraints to include all stereochemical features that show characteristic values.The suite of restraints given in Equation (24) is then ... 

Powder diffraction is very well suited for studies at non-ambient conditions. Naturally, one of the early applications of powder diffraction was high temperature studies of phase transformations. Development of equipment for low temperature and high-pressure studies quickly followed. Later, application of powder diffraction for in situ, time-resolved and in operando studies were successfully pursued. 

Pioneering development of a capillary based micro reaction cell was published by Clausen et al., for studies of catalysts under real operating conditions. The reaction cell was suited for both in situ EXAFS and transmission geometry powder diffraction studies (and was also used for combined... 

Fullprof Suite/ Winplotr WinPFOTR A Windows tool for powder diffraction pattern analysis, T. Roisnel and J. Rodriguez Carvajal, EPDIC 7 Yes Yes X Y, Old DIA, DIB, Brookhaven Synchrotron, G4.1, D2B, RX (Socabim), VCT, GSAS, CPI, Panalytical, normalized ISIS... 

Single Crystal Suites useful to Powder Diffraction... 

Fullprof Suite FULLPROF. A Program for Rietveld Refinement and Pattern Matching Analysis, J. Rodriguez Carvajal, Abstracts of the Satellite Meeting on Powder Diffraction of the XV Congress of lUCr, (1990) Toulouse, France, p. 127 Direct space for magnetic structures... 

Na and H) in the solid state over a large timescale without the requirement for single crystal substrates or even homogeneous samples. Thus, not only is SSNMR spectroscopy well suited for identifying polymorphs and solvates in bulk APIs, but this teehnique ean also provide detailed struetural information useful for both rationalizing material properties in terms of molecular and crystal structure and eonfirming structure solutions obtained by powder diffraction. ... 

Because x-rays are particularly penetrating, they are very usefiil in probing solids, but are not as well suited for the analysis of surfaces. X-ray diffraction (XRD) methods are nevertheless used routinely in the characterization of powders and of supported catalysts to extract infomration about the degree of crystallinity and the nature and crystallographic phases of oxides, nitrides and carbides [, ]. Particle size and dispersion data are often acquired with XRD as well. 

Holve, D.J. Using ensemble diffraction to measure particle size distribution. Powder Bulk Eng. 1991, 5 June (6), 15-19. See also trade literature of INSITEC, 2110 Omega Road, Suite D, San Ramon, CA 94583. 

There is no doubt that single crystal X-ray diffraction is a powerful technique for the study of polymorphs and solvatomorphs, but it is equally apparent that this methodology is not well suited for the routine evaluation of the crystalline state of powdered solids. It is definitely not a technique that one would want to use in the determination of polymorphic phase impurities in a sample, since by definition only a single crystal is studied at one time. That crystal would certainly be phase-pure, and its quantitative analysis not... 

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