Powder diffraction geometries

The use of Equation (22) is very general, but it is also possible, with accurate measurements and data treatment, to perform the quantitative phase analysis in semi-crystalline materials without using any internal standard. This procedure is possible only if the chemical compositions of all the phases, including the amorphous one, are known. If the composition of the amorphous phase is unknown, the quantitative analysis without using any internal standard can still be used provided that the chemical composition of the whole sample is available [51]. This approach, until now, has been developed only for the XRD with Bragg-Brentano geometry that is one of the most diffused techniques in powder diffraction laboratories. 

Two common geometries are used for collecting powder diffraction data, either the reflection or Bragg-Brentano method (Figure 8.29a) which uses a flat plate sample holder made either of glass or, ideally, of an... 

The factors that are included when calculating the intensity of a powder diffraction peak in a Bragg-Brentano geometry for a pure sample, composed of three-dimensional crystallites with a parallelepiped form, are the structure factor Fhkl 2=l/ TS )l2, the multiplicity factor, mm, the Lorentz polarization factor, LP(0), the absorption factor, A, the temperature factor, D(0), and the particle-size broadening factor, Bp(0). Then, the line intensity of a powder x-ray diffraction pattern is given by [20-22,24-26]... 

Figure 13. Effect of diffraction geometry on XRD powder patterns.

At one point, Ca, Sr, and Ba were believed to adopt monohalides as well. Their geometries, based upon X-ray powder diffraction, suggested a distortion of the rocksalt structure, but without significant metal-metal bonding. With nine valence electrons per formula unit, simple models... 

Figure 12 Three different monochromator/sample geometries used in powder diffraction (a) flat diffracted beam monochromator, parallel arrangement, (b) curved diffracted beam monochromator, angular arrangement, and (c) flat primary beam monochromator, parallel arrangement...

Powder diffraction data were taken on a Philips PW 1710 X-ray powder diffractometer (XRPD) with Bragg Brentano geometry (vertical goniometer) in 0.025 ° step from 5 to 90 29 with 20 s per step. 

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