Rietveld refinement, neutron powder

There have been many powder neutron diffraction structural studies of coordination compounds and only a few will be mentioned here. Because of the presence of an unrefmable preferred orientation, it was not possible to solve the structure of the polymeric coordination complex, Ni(l,3-thiazole)2Br2, by powder X-ray diffraction." In contrast, a Rietveld refinement of powder neutron diffraction data did yield a pseudooctahedral structure doubly linked by bridging bromide ions into infinite linear chains. 

Rietveld, H.M. (1967) line profiles of neutron powder-diffraction peaks for structure refinement. Acta Crystallogr.,... 

The structural determination of Ba CugO for 6.8 < x < 7.0, was completed in several laboratories by Rietveld analysis of powder neutron d iffraction data (10-15). The neutron diffraction experiments confirmed the space group Pmmm and the main structural features found by x-rays by Siegriest et al. (7), but revealed that some of the oxygen assignments made in the x-ray studies were not entirely correct. The refined structural parameters obtained in four of these... 

During the last five years, a powerful new method of getting crystal structural information from powder diffraction patterns has become widely used. Known variously as the Rietveld method, profile refinement1, or, more descriptively, whole-pattern-fitting structure refinement, the method was first introduced by Rietveld (X, 2) for use with neutron powder diffraction patterns. It has now been successfully used with neutron data to determine crystal structural details of more than 200 different materials in polycrystalline powder form. Later modified to work with x-ray powder patterns (3, X) the method has now been used for the refinement of more than 30 crystal structures, in 15 space groups, from x-ray powder data. Neutron applications have been reviewed by Cheetham and Taylor (5) and those for x-ray by Young (6). 

A complete understanding of the structure of the material under study or application is a sine qua non condition for the successful research or use of the material. In the case of powders, the best way to decipher the structure of new materials is the Rietveld method. This methodology was initially developed by Hugo M. Rietveld in 1969 [23] as a procedure for refining crystal structures using neutron powder diffraction data. To implement the method in practice, certain information about the estimated crystal structure of the phase or phases of interest in the diffraction profile under test is necessary. 

A perfect crystal structure model is very helpful for theoretical calculations, reaction mechanism analysis, and some physical property analysis such as conductivity, magnetic susceptibility, chemical potential, etc. Powder XRD (or neutron diffraction) Rietveld refinement is one of the most popular methods used to characterize crystal structure. 

Results of Rietveld refinement of neutron powder data for Na-A zeolite at various temperatures above and below the cubic-rhombohedral transition. The space group used in each refinement is as shown. In the rhombohedral refinements, the positional parameters were constrained to satisfy Fm3c symmetry as discussed in text, f is the fractional occupancy and N the number of reflections included in this refinement. Also shown in columns I and II are the X-ray single crystal results of Pluth and Smith(t), but with their anisotropic temperature factors converted to the average isotropic values. Neutron... 

H.M. Rietveld, Line profiles of neutron powder-dififraction peaks for structure refinement, Acta Cryst. 22, 151 (1967) H.M. Rietveld, A profile refinement method for nuclear and magnetic structures, J. Appl. Cryst. 2, 65 (1969). 

In this section, we are concerned with a powder diffraction experiment, which consists of a single pattern (profile). The Rietveld technique may also be used to conduct refinement of the crystal structure employing multiple patterns collected from the same material. For example, powder diffraction data collected using conventional x-ray sources with different wavelengths, conventional and synchrotron x-rays, conventional or synchrotron x-rays and neutron source may be used simultaneously in a combined Rietveld refinement. The fundamentals of the combined Rietveld refinement are briefly considered in section 7.3.8. 

In Eq. 7.10, /t is the number of different sets of powder diffraction data, is the number of data points collected in the 5" set, and is the scale factor for the x diffraction pattern, which appears because scattered intensity is measured on a relative scale. Other notations are identical to Eq. 7.3. Different scale factors, and K, are simple multipliers. Hence, they strongly correlate, and usually are not refined simultaneously. Constraining one of the scale factors (usually k, for the first diffraction data set) at 1 enables successful refinement of the phase scale K) and scale factors of all remaining sets of diffraction data ki, k, . .., k/,). Equations 7.4, 7.6 and 7.7 are modified in the same way as Eq. 7.3 for a combined Rietveld refinement. Furthermore, it is often the case that x-ray and neutron, or conventional x-ray and synchrotron data are used in combined refinements, therefore, the... 

This crystal structure was solved earlier (see sections 6.10 and 6.11), first using x-ray and then using neutron powder diffraction data. The x-ray data (Mo Ka radiation) were collected at room temperature, while the neutron scattering experiment (K = 1.494 A) was conducted at 200 K. Hence, combined Rietveld refinement is not feasible because of the differences in the lattice and structural parameters of the alloy due to thermal expansion, and we will use the two sets of data independently. 

Table 7.12. The progress of Rietveld refinement of the crystal structure of CeRhGes using neutron powder diffraction data collected at T = 200 K. The wavelength used X = 1.494 A.

Figure 7.16. The observed and calculated neutron powder diffraction patterns of CeRhGes after the completion of Rietveld refinement. The region 35.2 < 20 < 39.1 ° was excluded from the refinement. (Data courtesy of Dr. O. Zaharko.)...

Figure 7.23. The observed and calculated powder diffraction patterns of NiMn02(0H) after the completion of combined Rietveld refinement using neutron (a) and x-ray (b) powder diffraetion data.

Table 7.18. Atomic parameters and interatomic distances (in A) after the completion of the combined Rietveld refinement based on both the x-ray and neutron powder diffraction data collected from NiMn02(0H) powder. The refined chemical composition is NiMnOs (OH)j where 8 = 0.62(5). The unit cell parameters are a = 2.86112(4), b = 14.6516(1), c =...

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