Powder diffraction pattern reduced

Fig. 7.13. X-ray powder diffraction pattern of digoxin, whose degree of crystallinity was reduced to 40% by ball-milling. The figure was adapted from data contained in Ref. [32],...

Information content in a powder diffraction pattern is reduced as compared to that in single crystal diffraction, due to the collapse of the three dimensional reciprocal space into a one dimensional space where the only independent variable is the scattering angle. The poorer the resolution of the diffraction method, the less the information content in the pattern (Altomare et al. 1995 David 1999). As a consequence, structure of less complex phases can be determined from power diffraction alone (fewer atoms in the asymmetric unit of the unit cell). However, refinement of the structure is not limited so seriously with resolution issues, so powder diffraction data are used in Rietveld refinement more frequently than in structure determination. Electron powder diffraction patterns can be processed and refined using public domain computer programs. The first successful applications of electron diffraction in this field were demonstrated on fairly simple structures. 

Some sophisticated cells now make possible diffraction experiments at pressures higher than 400 GPa, thus approaching those at the earth s center, but this has a cost in terms of reduced sample size, nonhydrostaticity, and so on [92]. At such high pressures only powder diffraction patterns can be obtained, while the unrestricted three-dimensional collection of single-crystal diffraction data is possible only up to a few gigapascal. Fortunately,... 

Thermal decomposition of R—NiF3 at 356 K yields a red-brown solid which has the same X-ray powder diffraction pattern as the product obtained when dry R—NiF3 is reduced by xenon in the presence of aHF vapours. This compound is probably Ni2F5 and still possesses some oxidizing power in aHF. 

Figure 3.34. The set of x-ray powder diffraction patterns collected from the nearly spherical LaNi4 gsSno.is powder (see Figure 3.32, inset) on a Rigaku TTRAX rotating anode powder diffractometer using Mo Ka radiation. Goniometer radius R = 285 mm receiving slit RS = 0.03° flat specimen diameter d = 20 mm. Incident beam apertures were 0.05, 0.17, 0.25, 0.38, 0.5, 0.75, 1, 1.5, 2° and completely opened ( 5°), respectively. An automatic variable scatter slit was used to reduce the background. The data were collected with a fixed step A20 = 0.01°, and the sample was continuously spun during the data collection.

Figure 7.25. The observed and calculated powder diffraction patterns of tmaWiOq after the initial Rietveld least squares with only the scale factor and shifted-Chebyshev polynomial background refined. The difference Y° - is shown using the same scale as both the observed and calculated data but the plot is trancated to fit within the range [-1500,1500] for clarity. The ordinate is reduced to l/3 of the maximum intensity to better illustrate low intensity Bragg peaks. The inset clarifies the range between 34 and 50° 20.

The inverse matrix, B, is normalized by the reduced [Equation (13)] to give the variance-covariance matrix. The square roots of the diagonal elements of this normalized matrix are the estimated errors in the values of the shifts and, thus, those for the parameters themselves. These error estimates are based solely on the statistical errors in the original powder diffraction pattern intensities and can not accommodate the possible discrepancies arising from systematic flaws in the model. Consequently, the models used to describe the powder diffraction profile must accurately represent a close correspondence to... 

The X-ray powder diffraction patterns are shown in Fig. 2. The X-ray diffraction pattern of alumina precipitated from gel shows two broad maxima at 20=46 and 67° characteristic of Y-AI2O3. Introduction of small amounts of titania markedly reduces the intensity of these peaks. Accordingly, the sample with 15% appears to be virtually amorphous to X-rays. This result is in agreement with the data of Ramirez [15]. Amorphisation of AI2O3 by Ti02 also explains the increase in Sbet (see above). 

The advantage of the crystal structure solution from powder diffraction data over the ab initio crystal structure prediction method is that in the former approach the accuracy of prediction can be validated by matching the simulated powder pattern with the experimental powder diffraction pattern. In retrospect, concerns over global minimization algorithms, force field, and charge distribution accuracies are reduced with this method. 

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