Crystal structure refinement using

The lack of crystalline order in polymers such as cellulose or silk significantly reduces the number of interference spots in diffraction investigations hence the patterns often cannot be analysed unambiguously. In these cases a crystal structure refinement using NMR chemical shifts will be of great value, because NMR spectroscopy does not require long-range crystalline order. In our second example of cellulose, the situation occurred that the C4 values in BPT C chemical shift calculations deviated seriously from... 

Although simple intensity correction techniques can be used to develop very adequate XRPD methods of quantitative analysis, the introduction of more sophisticated data acquisition and handling techniques can greatly improve the quality of the developed method. For instance, improvement of the powder pattern quality through the use of the Rietveld method has been used to evaluate mixtures of two anhydrous polymorphs of carbamazepine and the dihydrate solvatomorph [43]. The method of whole pattern analysis developed by Rietveld [44] has found widespread use in crystal structure refinement and in the quantitative analysis of complex mixtures. Using this approach, the detection of analyte species was possible even when their concentration was less than 1% in the sample matrix. It was reported that good quantitation of analytes could be obtained in complex mixtures even without the requirement of calibration curves. 

Crystal structure refinement of a polysaccharide requires not only definition of the conformation of the backbone but also substituent orientation with respect to the backbone. For example, different dispositions of the hydroxymethyl group are possible by a rotation about the C-5-C-6 bond.10-17 A convenient notation28 for denoting this torsion angle by use of the terms tg, gt, and gg, as shown in Fig. 1, has been adopted. 

In the pharmaceutical community, quantitative analyses has conventionally been based on the intensity of a characteristic peak of the analyte. It is now recognized that phase quantification will be more accurate if it is based on the entire powder pattern.This forms the basis for the whole-powder-pattern analyses method developed in the last few decades. Of the available methods, the Rietveld method is deemed the most powerful since it is based on structural parameters. This is a whole-pattern fitting least-squares refinement technique that has also been extensively used for crystal structure refinement and to determine the size and strain of crystallites. 

The difference electron density distribution also finds an interesting application when the fully refined model of the crystal structure is used to compute a Fourier transformation. Although it may seem that such a Fourier map should result in zero electron density throughout the unit cell (since the differences in Eq. 2.135 are expected to approach zero), this is true only if electron shells of atoms in the crystal structure were not deformed. In reality, atoms do interact and form chemical bonds with their neighbors. This causes a redistribution of the electron density when compared to isolated atoms, for which atomic scattering functions are known. 

The end angle should be selected as high as possible when experimental data will be used for precise unit cell or crystal structure refinement. This usually can be established by a quick scan (5 to 10 deg/min) with 20s ... 

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... 

Application of total pattern fitting to X ray powder diffraction data, H. Toraya and F. Marumo, Rep. Res. Lab. Engin. Mat., Tokyo Inst. Tech., 1980, 5, 55 64 and Crystal structure refinement of alpha 813X4 using synchrotron radiation powder diffraction data unbiased refinement strategy, H. Toraya,... 

C. Rietveld performs crystal structure refinement and quantitative phase analysis using powder diffraction data and the Rietveld method. Combining refinement programs and advanced modeling tools allows a faster route to determining the structures of both inorganic and molecular crystals. An effective way to know the atomic structure is by means of diffraction techniques using neutrons from nuclear reactors and particle accelerators or X-rays from... 

Much has been said (see chapters by Tukey, Andrews, and Nicholson, this volume) concerning the Gaussian method of least squares (characterized repeatedly during discussion as the method of ill repute ) and possible modifications or replacements of it. Nevertheless, it is by far the most frequently used method for crystal structure refinement and will continue to be for some time to come. 

The trouble with this method of least squares is that the result of the refinement may be a local rather than global minimum. Therefore it is common to refine a protein crystal structure by use of molecular dynamics. This means that each atom is assigned a velocity, and equations of motion are solved under the restraints of X-ray information. The assigned velocities, while initially corres-... 

The RMC methods that are described in detail below have so far been successfully used for crystal structure refinement. There have been some attempts at ab initio structure determination, i.e. starting the model from random atomic positions within the unit cells that make up the configuration. Best results are found (for simple structures) if g(r) is modelled first. However, it... 

Liang J-J, Hawthorne FC, Novak M, Cemy P, Ottolini L (1995) Crystal-structure refinement of boromuscovite polytypes using a coupled Rietvelt-static-stracture energy-minimization method. Can Mineral 33 859-865... 

In contrast, Haselton et al. (1995) assert that comparison of previous and new results from precise heat capacity and heat contents measurements with previous experimental work and new experimental work by them, supports the suggestion of low configurational entropy in Ms, and hence, significant ordering in the IV sitesAn direct contradiction with the results of crystal structure refinement work (and the IR work on IV ordering cited below). However, the Ms used in their experiments is quite impure (having... 

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