Neutron powder diffraction, Rietveld

The Rietveld method was originally devised for the refinement of crystal structures using neutron powder diffraction (Rietveld 1969) and was later extended to XRD (Young et al. 1977) and eventually to QPA (Bish and Howard 1988 Hill and Howard 1987). For an in-depth description of the various aspects and applications of the Rietveld method, the reader is referred to Dinnebier and Billinge (2008) and Young (1993). The following notes will focus on the application of the Rietveld method to QPA. 

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

The technique of Rietveld profile analysis has already been mentioned in the context of X-ray powder diffraction, but it was with neutron powder diffraction that this technique originated. The fact that the neutron scattering factors are almost invariant with smOA means that the intensity of the data does not drop off at high angles of 6 as is the case with X-ray patterns, and so a neutron powder pattern tends to yield up considerably more data. 

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). 

The program just described, for Rietveld analyses using generalized coordinates, has been used in the structural analysis of isotactic polypropylene recently undertaken both with x-ray and with neutron powder diffraction data. We believe this analysis (Immirzi, in preparation) to be the first Rietveld analysis of a polymer done from x-ray data. Rietveld analyses of polymers from neutron data have been done but, at least in the polyethylene case reported by Willis and co-workers (15), there was no use of generalized coordinates. 

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. 

Because no single crystal of any binary rare-earth oxide fluoride has been obtained to date, computational efforts such as Rietveld analysis have been carried out to determine the crystal structure by means of X-ray and neutron powder diffraction. While... 

Hill, R. J., and Howard, C. J. Quantitative ph2ise analysis from neutron powder diffraction data using the Rietveld method. J. Appl. Cryst. 20, 467-474 (1987). Franklin, R. E., and Gosling, R. G. Molecular configuration in sodium thymonu-cleate. Nature (London) 171, 740-741 (1953). 

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.)...

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 =...

Early data analysis attempted to extract values of the individual structure factors from peak envelopes and then apply standard single crystal methods to obtain structural information. This approach was severely limited because the relatively broad peaks in a powder pattern resulted in substantial reflection overlap and the number of usable structure factors that could be obtained in this way was very small. Consequently, only very simple crystal structures could be examined by this method. For example, the neutron diffraction study of defects in CaF2-YF3 fluorite solid solutions used 20 reflection intensities to determine values for eight structural parameters. To overcome this limitation, H. M. Rietveld realized that a neutron powder diffraction pattern is a smooth curve that consists of Gaussian peaks on top of a smooth background... 

LHPM a Computer Program for Rietveld Analysis of X ray and Neutron Powder Diffraction Patterns, R. J. Hill, and C. J. Howard (1986) AAEC Report No. Ml 12 and QPDA A User Friendly, Interactive Program for Quantitative Phase and Crystal Size/Strain Analysis of Powder Diffraction Data, I. C. Madsen and R. J. Hill, Powder Diffr., 1990, 5, 195 199 A Rietveld analysis program RIETAN 98 and its applications to zeolites, F. Izumi and T. Ikeda, Mater. Sci. Forum, 2000, 321-324, 198 203 and F. Izumi, Development and Applications of the Pioneering Technology of Structure Refinement from Powder Diffraction Data, J. Ceram. Soc. Jpn., 2003, 111, 617 623... 

LHPM a Computer Program for Rietveld Analysis of X ray and Neutron Powder Diffraction Patterns, B. A. Hunter and C. J. Howard (February 2000), Lucas Heights Research Laboratories, Australian Nuclear Science and Technology Organisation and Rietica A visual Rietveld program, Brett Hunter, Int. Union Crystallogr., Commission Powder Diffr. Newsletter, 1998, No. 20, p. 21... 

At very low temperature (5 K), the positions of D2 molecules in the MOFs are relatively static, which allows use of neutron powder diffraction techniques to determine the positions of D2 molecules. The Rietveld profile analysis of... 

The binding of H2 to exposed metal sites has also been probed for [Cu3(BTC)2]oo (HKUST-1 in Section 11.2.4). Rietveld analysis of the neutron powder diffraction data for D2-loaded samples of [Cu3(BTC)2] 00 reveals that there are six possible adsorption sites, the most favourable being the unsaturated axial site of the binuclear Cu fragment (Peterson et al., 2006). The CU-D2 distance of 2.39 A suggests significant interaction between H2 and Cu(II), but this is much weaker than that observed for molecular o-bonded t -H2 complexes. Interestingly, the heat of adsorption of H2 binding in HKUST-1... 

The structures of the yet determined phases come all from neutron powder diffraction experiments and exhibit the best fits in the Rietveld refinements [21]. The refined models were extracted from ideas outlined in the next section. Fig. 3-4 presents the structures so far determined in a (211)ir-projection which in all cases corresponds to the common [100]-direction for almost all the phases. The locations for defects are marked by vacancy centred tetrahedra (yellow). 

Figure 3.5 High resolution time-of-flight neutron powder diffraction collected on deuterated AlMePO-p (Al2(CD3P03)3) at station HRPD at the pulsed neutron source ISIS, Oxfordshire, UK. The diffraction is measured at detectors at scattering angles of 168° (above left and, expanded, below) and 90° (above right). The profile has been fitted using Rietveld profile analysis in which the positions of 49 atoms were refined. [Reproduced from reference 43 with permission. Copyright 1999 Elsevier.] ""...

Figure 7.8 The minimum energy configuration of C5D5N pyridine coordinated to potassium cations in the channels of zeolite K-L, as determined from neutron powder diffraction data by Rietveld refinement.

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