Combined refinement using different diffraction data

8 Combined refinement using different diffraction data 

in our case when we have two sets of diffraction data and one crystalline phase, two scale factors K and A mo Ka) have been refined independently (see Eq. 7.10, below). 

When more than one set of experimental diffraction data is employed in the combined Rietveld refinement, the minimized function (in the simplest case of Eq. 7.3) becomes 

/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 

As expected, adding the contribution from the impurity phase (again as Le Bail s approximation) results in further reduction of the profile residuals, see row six in Table 7.7. The final model of this crystal structure, as determined using the combined Rietveld refinement in the two-phase approximation, is found in the data file Ch7Ex01k.inp on the CD. Structural parameters are listed in Table 7.8. 

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Displacement parameters of atoms are also expected to be different as the temperature of the powder diffraction experiment varies. Furthermore, it is also feasible that atomic positions may change due to generally anisotropic thermal expansion of crystal lattices. These considerations are in addition to the most obvious cause (different lattice parameters) preventing combined refinement using powder diffraction data collected at different temperatures. In general, material may also be polymorphic but this is not the case here, as was established in Chapter 6, sections 6.10 and 6.11. 

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. 

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. 

A Quench D5niamics protocol (a combination of high temperature Molecular Dynamics and Energy Minimization techniques) is used for predicting the location of triethylmethylammonium (TEMA) cations in zeolite MFI. Rietveld refinement of the high-resolution synchrotron X-ray diffraction data confirms these predictions. The TEMA cations are located at the channels intersections in two different conformations with two ethyl groups located in the linear channel. 

Chapter 1, p. 18) r° if the parameters were derived from electron-diffraction intensities alone rz if they were derived from rotational constants alone r v if they were derived utilizing a combination of both types of data. The method includes a way of converting rg to r ° distances, but it does not provide a procedure for converting r to r , the isotope-substitution distance from microwave spectroscopy. The first structures to be refined by the above workers using these methods were those of butadiene, acrolein, and glyoxal. The principal results for these planar molecules, in which the double bonds are situated trans to each other, are listed in Table 2. This work establishes with certainty for the first time the differences between the C-C bond lengths in these three molecules. 

The structure of BioHu has been restudied using low-temperature X-my and neutron diffraction data. By the use of combined difference syntheses, the distribution of bonding electrons has been determined. Electrons in the terminal B-H and bridging B-H-B bonds were very distinct. Towards the end of the refinement process, the framework electrons were also found. These are smeared out over the whole framework but some distinct centres... 

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