Rietveld refinement method

Figure 57.14. The wt.% of Ni fee, Ni/Al bcc and Ni2Al3 as Al was leached from the CA53 as calculated by the Rietveld refinement method.

Of the 15 experimentally known phases of the higher oxides only five of them have been determined by X-ray and neutron diffraction using the Rietveld refinements method. To understand the thermodynamic behavior and phase reactions it is helpful to have a model of the undetermined structures. Using the experimental electron diffraction data it is possible to determine the symmetry of the unit cell and develops a transformation matrix between the fluorite and ten of the intermediate phases as shown in Table 2. The module theory provides a method for modeling the unknown structures of the homologous series of the lanthanide... 

Figure 17. Temperature dependence of the mean Si-O bond length, determined from the T(r) fanctions, (Si-O), compared with the distance between the mean positions of the Si and O atoms, (Si)-<0), determined by Rietveld refinement methods.

In order to obtain a more quantitative picture of the mechanochemical reaction, we performed a quantitative XRD phase analysis using the Rietveld refinement method. In addition to the amount of the crystalline phases, i.e., Na2CC, Nb20s and NaNbCh, we determined also the contribution from the XRD background, which we denoted as "XRD-amorphous" phase. This was done using an internal standard method details of the method can be found in Kuscer et al. (2006) and Rojac et al. (2008b). 

The XRD measurements were performed on a Philips PW1800 diffiactometer using Cu radiation at 40KV/30mA. Scans were done with a step size of 0.02 over a range of 10 to 70 . The counting time was ten hours. Upon collection of the diffraction patterns, the Powder Diffraction File of the International Centre for Diffraction Data was used to identify the crystalline phases. The Rietveld Refinement Method was used to determine the quantitative phase data[14,15]. 

Sometimes it is difficult to obtain a good quality single crystal of sufficient size for structure determination using the single crystal X-ray diffraction method. In that case, the crystal structure of the material of interest can be determined from its powder x-ray diffraction data using the Rietveld refinement method (Rietveld 1969). The methodology involves four stages (Docherty and Meenan... 

H.M. Rietveld developed a practical method to analyze powder diffraction data. The Rietveld refinement method [6] is based on modeling a diffraction pattern according to structural information available for the phases previously identified in the pattern. This model is calculated by computer software after introduction of some crystallographic data space group symmetry, atomic species and positions within the cell, occupancies, lattice parameters, line broadening parameters, and experimental conditions. The term refinement refers to the cyclic improvement process used in the estimation of the set of parameters that can model the diffraction pattern as close as possible to the observed pattern. Usually, the Rietveld refinement is accomplished by minimizing the sum of the differences of calculated and observed intensities for each angular step of the diffraction pattern and by a... 

Table 6.1 Mineral phase identification by JCPDS data files and quantification by Rietveld refinement method...

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