By Daniel Chateigner
This publication introduces and information the foremost elements of mixed research - an x-ray and/or neutron scattering method which mixes structural, textural, pressure, microstructural, part, layer, or different correct variable or estate analyses in one procedure. The textual content starts off with simple theories concerning diffraction through polycrystals and a few of the commonest mixed research instrumental set-ups are particular. additionally mentioned are microstructures of powder diffraction profiles; quantitative part research from the Rietveld research; residual pressure research for isotropic and anisotropic fabrics; specular x-ray reflectivity, and a number of the linked models.
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Refinable parameters: U11 , U 22 , U 33 , U12 , U13 , U 23 ; and Vij ' s , Wij ' s , pU ij ' s , pVij ' s , pWij ' s . This means that 36 parameters are refined at maximum. This formulation is actually not linked to either the Popa-like parameters for microstructure (see Chapter 5 on QMA) or the tensor components intended to physically represent crystallite sizes or microstrains. 9. Anisotropic variable Pearson VII [LEB 97] This function is defined in a similar way to the previous variable pseudo-Voigt, within the same goal.
2] implies that the measurements are independent and that the variations of the observations obey a normal frequency distribution. The second weighting scheme is then preferred for diagrams with low counting levels where normal distributions are not satisfied. P P B B B B B B B B B B B B The sum extends to all the measured points of the pattern. 4] Structure Refinement 43 with [SAB 80]: – U’: effective density of ) in the sample; – U: theoretical density of the phase; – X: volume of ) in the sample; – Vc: unit cell volume of ) – ): incident flux; – h, w: height and width of the detecting slit; – t: counting time; – r: sample to detector distance; – j)k is the multiplicity factor of the peak for phase ) – Lp)k is the Lorentz-polarisation factor; – P)k is a correction factor describing preferred orientations of phase ) – |F)k| is the modulus of the structure factor (including thermal vibrations) of phase ) – :i)k describes the profile function of the peaks of phase ), which represents instrumental and potential sample broadenings; – Ai is an absorption factor which takes into account the experimental and sample geometries.
6] yisi is the sample contribution to the background, associated with incoherent scattering from crystalline defects, fluorescence, etc. yisc is the independent coherent scattering contribution of the sample, coming from thermal atomic vibrations and lattice imperfections. yin is the noise contribution, with