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An efficient ab initio calculation of powder diffraction intensity using Debye's equation.

The Debye equation gives the spherically averaged diffracted intensity from a group of atoms and is exact under the first Born, or kinematic, approximation. Algebraic simplifications are developed for calculating multiplicities in the double summation and are used in a new algorithm for implementing this equation. The results for cubic, body-centred cubic and face-centred cubic systems agree exactly with previous methods while achieving substantial computational advantage.

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Time-resolved X-ray powder diffraction on a three-way catalyst at the GILDA beamline.

Time-resolved X-ray diffraction experiments carried out at the beamline BM08-GILDA of ESRF allowed a study of the structural modifications taking place in a Pt/ceria-zirconia catalyst while the CO oxidation reaction was in progress. The capillary tube in which the sample is stored acts effectively as a chemical microreactor that ensures homogeneity of the sample treatments and minimization of diffusion effects. During the flowing of the reactant CO/He mixture, the investigated catalyst undergoes a fast Ce(IV)-Ce(III) partial reduction that involves the release of one O atom for every two reduced Ce cations. Because Ce(III) has a larger ionic radius than Ce(IV), the structural modification produces an increase of the lattice constant of the ceria-zirconia mixed oxide, and this increase is monitored by the translating imaging-plate device implemented at GILDA. The CO(2) resulting from the oxidation of the fluxed CO is monitored by a quadrupole mass spectrometer during the recording of the time-resolved X-ray diffraction pattern. The chemical and structural information was combined to show that the CO(2) yield is nearly constant until the catalytic system can provide oxygen for the reaction, while the structural rearrangement of the catalyst is delayed with respect to the switching on of the CO/He flux. After this induction time, during which CO(2) is produced with no structural modification of the catalyst, a fast increase of the lattice constant takes place.

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