Diffractometer absorption factor

In the case of testing a powdered sample in a Bragg-Brentano diffractometer, the sample has the shape of a flat plate located parallel to the reflecting plane, making equal angles with the incident and diffracted beams then, if we have a single phase in the sample, the absorption factor is given by [21]... 

The absorption factor for a sample in the form of a plate located in the sample holder of a Bragg-Brentano geometry powder diffractometer is given by [4]... 

Derive an expression for the absorption factor of a diffractometer specimen in the form of a flat plate of finite thickness t. (Note that the absorption factor now depends on 0.)... 

First, a polyciystalline sample usually has a size that ranges in millimeters and the beam irradiating this sample is partially absoibed. This means that a crystal located in a given area of the sample sees an incident intensity 1 that is different from the initial beam s intensity lo. Furthermore, the diffracted beams are also partially absoibed. As a result, the actual intensity that is measured is attenuated by an absorption factor which we will denote by A. The form of this factor depends on the geometric characteristics of the diffractometer used for the experiment. This point will be detailed later on, in particular when describing the diffractometers designed for the study of thin films. 

For each Bragg reflection, the raw data normally consist of the Miller indices (h,k,l), the integrated intensity I(hkl), and its standard deviation [ a[I) ]. In Equation 7.2 (earlier), the relationship between the measured intensity / [hkl] and the required structure factor amplitude F[hkl) is shown. This conversion of I hkl) to F hkl) involves the application of corrections for X-ray background intensity, Lorentz and polarization factors, absorption effects, and radiation damage. This process is known as data reduction.The corrections for photographic and diffractometer data are slightly different, but the principles behind the application of these corrections are the same for both. 

Intensity data were collected on the diffractometer by using the w —26 scanning mode and a scan rate of 4° /min. Stationary background counts of 5 s were taken at both limits of each scan. Four reference reflections were monitored periodically and showed no significant intensity deterioration. Corrections were made for Lorentz and polarization factors, but not for absorption effects. A total of 2024 unique reflections, of which 24 had no net intensities, were measured to the limit 20=130°. ... 

The single-crystal study of the a-Ni(NCS) (4-ViPy), structure was performed by using a Siemens AED aut omated three-circle diffractometer (filtered MoKa). 5029 independent reflections were measured within 27° of 0 by using the 0) - 20 scan mode, but as little as 950 reflections having 2a(I) have been used for structure analysis. The intensities were corrected for Lorentz-polarization effects but not for absorption. The structure was solved by direct methods, SHELX was used (ref. 5). Full-matrix refinement was made but, in view of low data/parameters ratio, only Ni, thiocyanates and pyridine N atoms were given anisotropic temperature factors. H atoms were included in the refinement at calculated positions. The final R value is 0.056 the weighted = 0.046 (w = 1.7/(a (F) + 0.0002(F) ). 

The RIR method derives from the fact the diffraction peak intensity from a particular constituent in a mixture is proportional to weight fractirMi of that cmistit-uent, in addition to factors related to the particular instrumental setup (incident beam intensity, cross-sectional area of the incident beam, radiation wavelength, diffractometer radius, etc.) and parameters intrinsic to that particular material (structure factor, multiplicity factor, temperature factor, linear absorption coefficient, etc.). Since the RIR method uses ratio of intensities observed in the same pattern, several instrumental contributions are assumed to the same for each phase... 

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