Unique diffraction data example

When the space group symmetry is unknown, i.e. when reflection conditions are analyzed from diffraction data, the answer may not be unique. For example, the combination of systematic absences listed above also... 

Preliminary models of the surface topography, for example, can be determined by atomic-probe methods, ion-scattering, electron diffraction, or Auger spectroscopy. The chemical bonds of adsorbates can be estimated from infrared spectroscopy. The surface electronic structure is accessible by photoelectron emission techniques. In case the surface structure is known, its electronic structure has to be computed with sophisticated methods, where existing codes more and more rely on first principles density functional theory (DFT) [16-18], or, in case of tight-binding models [19], they obtain their parameters from a fit to DFT data [20]. The fit is not without ambiguities, since it is unknown whether the density of states used for the fit is really unique. 

Chapter six is dedicated to the solution of materials structures, i.e. here we learn how to find the distribution of atoms in the unit cell and create a complete or partial model of the crystal structure. The problem is generally far from trivial and many structure solution cases in powder diffi action remain unique. Although structure determination from powder data is not a wide open and straight highway, knowing where to enter, how to proceed, and where and when to exit is equally vital. Hence, in this chapter both direct and reciprocal space approaches and some practical applications of the theory of kinematical diffraction to solving crystal structures from powder data will be explained and broadly illustrated. Practical examples start fi-om simple, nearly transparent cases and end with quite complex inorganic structures. 

To show that a co-crystal has formed, it is typical to show comparative data that indicate the existence of the co-crystal. For example, a comparison of the XRPD pattern or the SSNMR spectra of the API, the co-former, and the co-crystal can show the differences or changes that have occurred upon cocrystal formation. These differences can then be used to claim the co-crystal as a unique composition of matter based upon its characteristic peaks. Figure 14.2 is an example of such a comparison using a stack plot of X-ray powder diffraction (XRPD) patterns. The differences in peaks can be seen. For a patent, a unique set of peaks differentiating the co-crystal from the API and co-former could be used to form the basis of a patent claim for the co-crystal. 

The spectrometry method also outperforms the diffraction technique both in precision and accuracy, perhaps by a factor of two to six. The diffraction technique is at best a rather insensitive, slow technique, giving somewhat poor quantitative accuracy. On the other hand, it will be realized that the information given by the X-ray diffraction method is unique, and no other technique is able to provide such data. This is not true of the X-ray fluorescence method, since there are many other techniques available to the analytical chemist today for the quantitation of elements. Atomic absorption, inductively coupled plasma emission, and solid-source mass spectrometry are all examples of competing methods. 

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