Diffraction data analysis

Practical aspects of powder diffraction data analysis, Stud. Surf Sd. Catal., vol. 85, Elsevier, Amsterdam, pp. 391 28. 

CAR can be observed microscopically on double-sided PWBs using back lighting (Rig. 12). Subsequent scanning electron microscopy with energy dispersive x-ray spectroscopy (SEM/EDS) analysis shows that it contains copper and chloride (Fig. 13). A CAR sample was extracted and transmission electron microscopy (TEM) analysis was used to obtain electron diffraction data. Analysis of these results identify CAR as atacamite, Cu2(OH)3Cl (Ref 24). The Pourbaix diagram (Ref 25) (Fig. 14) of the cop-... 

Powder diffraction studies with neutrons are perfonned both at nuclear reactors and at spallation sources. In both cases a cylindrical sample is observed by multiple detectors or, in some cases, by a curved, position-sensitive detector. In a powder diffractometer at a reactor, collimators and detectors at many different 20 angles are scaimed over small angular ranges to fill in the pattern. At a spallation source, pulses of neutrons of different wavelengdis strike the sample at different times and detectors at different angles see the entire powder pattern, also at different times. These slightly displaced patterns are then time focused , either by electronic hardware or by software in the subsequent data analysis. 

The two major databases containing information obtained from X-ray structure analysis of small molecules are the Cambridge Structural Database (CSD) [25] and the Inorganic Crystal Structure Database (ICSD) [26] both are available as in-house versions. CSD provides access to organic and organometallic structures (mainly X-ray structures, with some structures from neutron diffraction), data which are mostly unpublished. The ICSD contains inorganic structures. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Another major difference between the use of X rays and neutrons used as solid state probes is the difference in their penetration depths. This is illustrated by the thickness of materials required to reduce the intensity of a beam by 50%. For an aluminum absorber and wavelengths of about 1.5 A (a common laboratory X-ray wavelength), the figures are 0.02 mm for X rays and 55 mm for neutrons. An obvious consequence of the difference in absorbance is the depth of analysis of bulk materials. X-ray diffraction analysis of materials thicker than 20—50 pm will yield results that are severely surface weighted unless special conditions are employed, whereas internal characteristics of physically large pieces are routinely probed with neutrons. The greater penetration of neutrons also allows one to use thick ancillary devices, such as furnaces or pressure cells, without seriously affecting the quality of diffraction data. Thick-walled devices will absorb most of the X-ray flux, while neutron fluxes hardly will be affected. For this reason, neutron diffraction is better suited than X-ray diffraction for in-situ studies. 

Figure 6 Site occupancies for two of the oxygen atoms (01 and 05) in the YBa2Cu307 x superconductor as a function of temperature. The site occupancies resulted from an analysis of insitu neutron diffraction data. Reprinted by permission from Jorgensen and Hinks. ...

Sakata, M., Uno, T., Takata, M. and Howard, C. (1993) Maximum-entropy-method analysis of neutron diffraction data, J. Appl. Cryst., 26, 159-165. 

We originally proposed NNM to be present in metallic beryllium [30] based on analysis of the X-ray diffraction data measured by Larsen and Hansen [24], Based on Fourier maps and elaborate multipole least-squares modeling, indisputable evidence... 

An important lesson learned from the studies of naphtazarin [2], benzoylacetone [8] and nitromalonamide has been that the detailed structure of these types of compounds can only be reliably determined by introducing results of low-temperature neutron diffraction studies in the analysis of the low-temperature X-ray diffraction data. Furthermore it has been found that information about the bonding of the enol hydrogen can be extracted from the thermal parameters of the enol hydrogen. This underlines the importance of the neutron diffraction study in these cases. 

Koritzansky, T., Howard, S., Mallison, P.R., Su, Z., Richter, T. and Hansen, N.K. (1995) XD, a computer program package for multipole refinement and analysis of charge densities from diffraction data, Institute for Crystallography, Berlin. 

The structure of alumina on NiAl(l 1 0) was the subject of a surface X-ray diffraction study by Stierle et al. [46]. The model derived by Stierle et al. from the analysis of the X-ray diffraction data was based on a strongly distorted double layer of hexagonal oxygen ions, where the Al ions are hosted with equal probability on octahedral- and tetrahedral-coordinated sites the resulting film structure was closely related to bulk k-A1203. An attractive feature of Stierle s model was that it provided a natural explanation of the domain structure of the alumina overlayer, which is induced by a periodic row matching between film and substrate lattices. However, as pointed out recently by Kresse et al. [47], this structure model has two bonds with... 

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