Combined Analysis by Daniel Chateigner
By Daniel Chateigner
This e-book introduces and info the foremost elements of mixed research - an x-ray and/or neutron scattering method which mixes structural, textural, pressure, microstructural, section, layer, or different proper variable or estate analyses in one strategy. The textual content starts off with uncomplicated theories concerning diffraction through polycrystals and a few of the commonest mixed research instrumental set-ups are distinctive. additionally mentioned are microstructures of powder diffraction profiles; quantitative section research from the Rietveld research; residual pressure research for isotropic and anisotropic fabrics; specular x-ray reflectivity, and some of the linked models.
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Extra info for Combined Analysis
35]: P(0) μ 0 e μ 0! 05 or P = 3. The detection limit is then at Adl = 3 counts with a 95% confidence. This will have consequences on the minimum percentage of detectable phase in a diagram, as will be seen in quantitative phase analysis. 4. Presence of background under peaks In real practice of course, background is present on the whole measured range. We will need to extract the net intensity of the peak before its analysis, then to subtract background. For a total measured number of counts Nt, a net number of counts Nn and a background giving Nb counts, simple relationships exist between the mean values (PNt = PNn + PNb) and standard deviations (VNt = (Nn + Nb)1/2) of the components.
Peak profile parameters The parameters used to define the peak profiles are: i) positions of the individual contributions; ii) their angular or energetic dispersions (FWHM); iii) their surface under profile (intensity); iiii) their shape. 9] These parameters play a role in the identification of solid substances, pattern indexing, etc. It is then of prior importance to operate to a careful calibration of the instrument to avoid systematic errors as far as possible. Also, some structural defects or states like stacking faults or residual stresses can shift the diffraction peaks, which have to be taken into account before any result can be given.
3. 14] Refinable parameters: U, V, W, P, m. 4. 15] 16 Combined Analysis K is the mixing parameter of the linear combination which varies between 0 and 1; L(2Ti) is the pure Lorentzian function and G(2Ti) the pure Gaussian function. 5. 17] for 2Ti > 2Tk with C1 2 1 / L0 1 and C 2 2 1 / H 0 1 As(ș k ) As(1) As(2)/sinș k As(3)/sin 2 ș k L 0 (ș k ) L 0 (1) L 0 (2)/sinș k L 0 (3)/sin 2 ș k H 0 (ș k ) H 0 (1) H 0 (2)/sinș k H 0 (3)/sin 2 ș k Q is a function of As, L0 and H0. Refinable parameters: U, V, W, P, As(13), Lo(13), Ho(13).