Quantitative analysis preferred orientation

The Rietveld analysis is mainly used for refining the structures of crystalline phases and to perform quantitative analysis of multiphase samples. The quantitative analysis is possible since the Rietveld method can easily deal with diffraction patterns with strongly overlapped peaks, while preferred orientation can be quantitatively treated. 

Frequently, polycrystalline specimens exhibit a preferred orientation of the crystallites or polycrystalline texture. In addition, many manufacturing processes of technological materials can induce texture. In comparison with specimens having randomly oriented crystallites, the relative intensities of the diffraction lines of textured samples are modified. As a consequence the structural and quantitative phase analysis of polycrystalline samples becomes impossible without proper modeling of the texture. 

A preferred orientation that favors the intensity of some line or lines of the diffraction spectrum due to deviations of the ideal random orientation of crystallites is perhaps the most serious problem limiting the quantitative analysis of complex mixtures. Although it is possible to accommodate preferred orientation during data analysis, it is preferable to utilize a procedure that minimizes or eliminates preferred orientation during sample preparation. 

For a physical mixture, the powder diffraction pattern is the sum of the patterns of the individual materials. The diffraction pattern can therefore be used to identify the crystalline phases in a mixture. The concentrations of the crystalline phases can be determined by methods based on comparing the intensities of the diffraction peaks with standards (6-8). If the crystal structures of the phases are known, the concentration of each phase can be detamined by Rietveld analysis (20,21). In the Rietveld method, a theoretical diffraction pattern is computed and the difference between the theoretical and observed patterns is minimized. For quantitative analysis, some care should be taken with specimen preparation if accurate and reliable results are to be obtained. The effects of factors such as preferred orientation, texturing, and particle size broadening must be minimized. 

The inherent specificity and quantitative power towards the crystalline state make pXRD as the technique of choice for studying crystallization from amorphous systems (Ochsenbein and Schenk 2006). Also, the instrumental flexibility allows in situ monitoring of crystallization as function of time, temperature, pressure, RH, or combinations. An API can crystallize to different polymorphs from ASD (Guns et al. 2011). The reference powder pattern enables the identification/quantification of the polymorphs developing in ASD (Ivanisevic et al. 2010). Preferred orientation of crystalline faces is a major source of error. Generally, analysis in transmission mode reduces the preferred orientation and avoid other instrumentally induced distortions and anisotropic shifts (Moore et al. 2009). 

According to the above discussion a quantitative evaluation of the absorption spectra in oriented solvents is much simpler than an analysis of magnetic resonance spectra of partially oriented molecules. However, this is only valid if the axes of preferred solute orientation (or the principal axes of the order matrix) coincide with the directions of the optical transition moments. The situation may be much more complicated if molecules of lower than Cjv symmetry are considered. In these cases the principal axes system of the order matrix and the directions of the OO-transitions moments do not coincide. An example for such a molecule is chrysene [7]. In these cases the liquid crystal method yields only the relative polarization directions. A way out of these difficulties could be a systematic study of substituted molecules. It is well known that the substituents such as methyl groups do not shift the polarization direction appreciably but such groups may have large effects on the average orientation of the molecule in the liquid crystal. 

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