Disordered phases, structural coordination

When B-site ions can take on a variety of oxidation states, a change in the external oxygen partial pressure can lead to an oxygen composition range for the brownmillerite phase. This additional oxygen has a number of structural consequences. The oxygen can occupy the vacancies in the brownmillerite phase and lead to new ordered phases, new coordination polyhedra such as trigonal prisms or square pyramids, discussed below (Section 2.5), or result in a disordered cubic perovskite phase. 

It took 8 years to publish another structure. In 1976 K. J. Palmer et al. reported two conformers of another resorcin[4] arene derivative, i.e. cis- and trans-C-para-bromophenyl-4,6,10,12,16,18,22,24-0-octaacetylcalix[4]resorcinarene [3]. Than in next 3 years G. D. Andreetti et al. published the first crystal structure of inclusion compound formed by para-ferf-butylcalix[4] arene with toluene [4]. The calixarene molecule was found in cone conformation and the guest molecule could not be located within the host cavity due to its disorder (the molecular complex was located on a crystallographic fourfold axis). The Authors also noticed that the structure undergoes the order-disorder phase transition at 248 K. In 1996 the disorder high temperature phase was resolved with the aid of solid-state NMR data by E. B. Brouwer et al. [5] (unfortunately, the atoms coordinates are not deposited in CSD) and in 1998 the low temperature ordered phase was reported by A. Arduini et al. [6] (Fig. 38.2). The inclusion complex is stabilized by week interaction. The crystal and molecular structure of this... 

Solid state NMR is a relatively recent spectroscopic technique that can be used to uniquely identify and quantitate crystalline phases in bulk materials and at surfaces and interfaces. While NMR resembles X-ray diffraction in this capacity, it has the additional advantage of being element-selective and inherently quantitative. Since the signal observed is a direct reflection of the local environment of the element under smdy, NMR can also provide structural insights on a molecularlevel. Thus, information about coordination numbers, local symmetry, and internuclear bond distances is readily available. This feature is particularly usefrd in the structural analysis of highly disordered, amorphous, and compositionally complex systems, where diffraction techniques and other spectroscopies (IR, Raman, EXAFS) often fail. 

By Fourier transforming the EXAFS oscillations, a radial structure function is obtained (2U). The peaks in the Fourier transform correspond to the different coordination shells and the position of these peaks gives the absorber-scatterer distances, but shifted to lower values due to the effect of the phase shift. The height of the peaks is related to the coordination number and to thermal (Debye-Waller smearing), as well as static disorder, and for systems, which contain only one kind of atoms at a given distance, the Fourier transform method may give reliable information on the local environment. However, for more accurate determinations of the coordination number N and the bond distance R, a more sophisticated curve-fitting analysis is required. 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

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