Interpretation of powder diffraction data

Given the nature of the powder diffraction method, the resultant experimental data can be employed to obtain and/or confirm the following information  

The first four items in this list represent the most common goals that are usually achieved during characterization of polycrystalline materials using 

For example, the range 10 20 90° scanned with a step A20 = 0.02° results in 4001 measured data points. 

In the context of this book, structure solution from first principles (also referred to as the ab initio structure determination) means that all crystallographic data, including lattice parameters and symmetry, and the distribution of atoms in the unit cell, are inferred from the analysis of the scattered intensity as a function of Bragg angle, collected during a powder diffraction experiment. Additional information, such as the gravimetric density of a material, its chemical composition, basic physical and chemical properties, may be used as well, when available. 

a fast experiment is routinely suitable for evaluation of the specimen and phase identification, i.e. qualitative analysis. When needed, it should be followed by a weekend experiment for a complete structural determination. An overnight experiment is required for indexing and accurate lattice parameters refinement, and a weekend-long experiment is needed for crystal structure determination and refinement. In some instances, e.g. when a specimen has exceptional quality and its crystal structure is known or very simple, all relevant parameters can be determined using data collected in an overnight experiment. Similarly, fast experiment(s) may be suitable for unit cell determination in addition to phase identification. In any case, one should use his/her own judgment and experience to assess both the suitability of the experimental data and the reliability of the result. 

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Our experience with applications of the powder method in diffraction analysis was for the most part, conceptual, and in the remainder of this book, we will discuss key issues that arise during the processing and interpretation of powder diffraction data. Despite the apparent simplicity of onedimensional diffraction patterns, which are observed as series of constructive interference peaks (both resolved and partially or completely overlapped), created by elastically scattered waves and placed on top of a nonlinear background noise, the complexity of their interpretation originates from the complexity of events involved in converting the underlying structure into the experimentally observed data. Thus, nearly every component of data processing in powder diffraction is computationally intense. 

X-Ray powder diffraction patterns are catalogued in the JCPDS data file,7 and can be used to identify crystalline solids, either as pure phases or as mixtures. Again, both the positions and the relative intensities of the features are important in interpretation of powder diffraction patterns, although it should be borne in mind that diffraction peak heights in the readout from the photon counter are somewhat dependent on particle size. For example, a solid deposit accumulating in a heat exchanger can be quickly identified from its X-ray powder diffraction pattern, and its source or mechanism of formation may be deduced—for instance, is it a corrosion product (if so, what is it, and where does it come from) or a contaminant introduced with the feedwater ... 

Abstract. - High-resolution powder neutron diffraction has been used to study the crystal structure of the fullerene Cm in the temperature range 5 K to 320 K. Solid Cm adopts a cubic structure at all temperatures. The experimental data provide clear evidence of a continuous phase transition at ca. 90 K and confirm the existence of a first-order phase transition at 260 K. In the high-temperature face-centred-cubic phase (T > 260 K), the Cm molecules are completely orientation-ally disordered, undergoing continuous reorientation. Below 260 K, interpretation of the diffraction data is consistent with uniaxial jump reorientation principally about a single (111) direction. In the lowest-temperature phase (T < 90 K), rotational motion is frozen although a small amount of static disorder still persists. 

The cell constants for stage-1 compounds have been more precisely determined over the years. It must be emphasized here, as it has been before and certainly will be again later, that the availability of oriented polyacetylene has been crucial for the progress made in the interpretation of the diffraction data. For the quantitative comparison of intensities, Shirakawa polyacetylene is still used because its isotropic diffraction can be compared with powder calculations and does not need the tricky Lorentz corrections of fibre symmetries. Moreover, Shirakawa polyacetylene is known for its relatively high crystallographic coherence and the absence of impurity reflections. 

Powder diffraction patterns have three main features that can be measured t5 -spacings, peak intensities, and peak shapes. Because these patterns ate a characteristic fingerprint for each crystalline phase, a computer can quickly compare the measured pattern with a standard pattern from its database and recommend the best match. Whereas the measurement of t5 -spacings is quite straightforward, the determination of peak intensities can be influenced by sample preparation. Any preferred orientation, or presence of several larger crystals in the sample, makes the interpretation of the intensity data difficult. 

A method known as Rietveld analysis has been developed for solving crystal structures from powder diffraction data. The Rietveld method involves an interpretation of not only the line position but also of the line intensities, and because there is so much overlap of the reflections in the powder patterns, the method developed by Rietveld involves analysing the overall line profiles. Rietveld formulated a method of assigning each peak a gaussian shape and then allowing the gaussians to overlap so that an overall... 

X-ray powder diffraction data may be helpful but are often hard to interpret for complex mixtures use of computer data file search programs (6) and microcamera methods for single particle analysis (7) may be useful for identification. Comparative sample identification is generally less often possible than for metals since the latter are manufactured while the nonmetallic inorganic solids are often unprocessed materials with large property variations. However, where applicable, the following are some examples of determinations which might be made (a) particle size by microscopy (b) microstructure and sub-microstructure characterization... 

It is shown that both the Bragg and the diffuse scattering parts of neutron powder diffraction data on ice Ih can be interpreted simultaneously by constructing large models of the structure that are consistent with the measured total scattering functions within errors. The RMCPOW algorithm proved to be readily applicable for the purpose. 

To further prove the interpretation of the XRD data, and to obtain more quantitative information concerning the core-shell structures, the powder diffraction patterns were simulated [7, 69]. Nanocrystals were built by stacking planes along the (111) axis of the cubic lattice, and the sum of the specified core radius, r, and shell thickness, tj, was used to carve out the nanocrystal, assuming a spherical shape. 

Another interpretation of the LT structural behaviom of Pr AIO3 was given by Moussa et al. (2001) and Carpenter et al. (2005). Based on a combination of high-resolution neutron and s)mchrotron powder diffraction data, Moussa et al. (2001) showed that the RT rhombohedral structure of PrAlOs transforms into an orthorhombic Imma structure on cooling to about 205 K than to a monoclinic dim structure near 150 K. The structure tends towards tetragonal symmetry as the sample is further cooled however, the symmetry remains monoclinic down to 10 K. The authors proposed the following transition scheme in PrAlOs ... 

The MEM is a powerful new method which is especially useful in cases with limited data sets (powder diffraction). Monte Carlo simulations have shown that the MEM introduces systematic features into the reconstructed density and caution should be exercised when interpreting fine details of an MEM density. It must be emphasized that because the present MEM algorithms do not contain any models, they cannot filter out inconsistencies in the data stemming from systematic errors. The MEM densities may therefore contain non-physical features not only because of systematic bias in the calculation but also because of systematic errors in the data. 

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