Combined Analysis by Daniel Chateigner

By Daniel Chateigner

This ebook introduces and information the main points 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 method. The textual content begins with uncomplicated theories regarding diffraction by means of polycrystals and a few of the commonest mixed research instrumental set-ups are special. additionally mentioned are microstructures of powder diffraction profiles; quantitative part research from the Rietveld research; residual rigidity research for isotropic and anisotropic fabrics; specular x-ray reflectivity, and some of the linked models.

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Why do we need modeling? A central problem of powder diffraction is peak overlapping [SMI 77, SMI 89, WAG 66]. The increase in diffraction peak density with 2T results in strong peak overlaps, particularly for low crystal symmetries and low instrumental resolutions. This gives rise to a rapidly increasing jamming of the information at large 2Ts, and to an unusable diagram. The 2T limit value above which the diagram becomes unusable is never strictly defined and often prevents a careful determination of the necessary information.

2. 28] f with: E(t) E(t) Įȕ Įt e Įȕ Įȕ -ȕt e Įȕ for t d 0 for t ! 29] Basic Notions 21 with u, v, y and z as previously defined, and p and q taking the values: p Įx  iĮ 2ln2H q ȕx  iȕ 2ln2H and the pseudo-Voigt function admits Gaussian and Lorentzian components, the FWHMs of which are linked by the TCH relationship (see above). 30] The HGi and HLi coefficients are to be adjusted for a given instrument resolution, and the other sample-dependent parameters are: : Gaussian size contribution; h: anisotropic strain contribution; ]: Lorentzian strain fraction; : Lorentzian anisotropic size contribution.

E. to remove the instrumental broadening contribution. Direct Fourier deconvolution was first introduced by Stokes [STO 48], and is often used. However this method is subjected to biases when either the sample broadening contribution is weak compared to the instrumental one, or the background has not been removed satisfactorily [DEL 80]. Another approach is to use Bayesian deconvolution. Such an approach is used in the Richardson [RIC 72] iterative algorithm: ( n 1) fi (n ) fi ¦ k g ki h 'k ¦ g kj f j(n ) j in which the prime on h indicates that the background has been subtracted.

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