University of Rennes

About: University of Rennes is a education organization based out in Rennes, France. It is known for research contribution in the topics: Population & Catalysis. The organization has 18404 authors who have published 40374 publications receiving 995327 citations.

Nb-Ta fractionation in peraluminous granites: A marker of the magmatic-hydrothermal transition

Abstract: In their late stages of evolution, peraluminous granitic melts exsolve large amounts of fluidswhich can modify the chemical composition of granitic whole-rock samples. The niobium/tantalum (Nb/Ta) ratio is expected to decrease during the magmatic differentiation of graniticmelts, but the behavior of both elements at the magmatic-hydrothermal transition remainsunclear. Using a compilation of whole-rock geochemical data available in the literature, wedemonstrate that fractional crystallization alone is not sufficient to explain the distribution ofNb-Ta in most peraluminous granites. However, we notice that most of the granitic samplesdisplaying evidence of interactions with fluids have Nb/Ta < 5. We propose that the decreaseof the Nb/Ta ratio in evolved melts is the consequence of both fractional crystallization andsub-solidus hydrothermal alteration. We suggest that the Nb/Ta value of ~5 fingerprints themagmatic-hydrothermal transition in peraluminous granites. Furthermore, a Nb/Ta ratio of ~5appears to be a good marker to discriminate mineralized from barren peraluminous granites.

Banach spaces adapted to Anosov systems

Abstract: We study the spectral properties of the Ruelle-Perron-Frobenius operator associated to an Anosov map on classes of functions with high smoothness. To this end we construct anisotropic Banach spaces of distributions on which the transfer operator has a small essential spectrum. In the C ∞ case, the essential spectral radius is arbitrarily small, which yieldsa descriptionof the correlationswith arbitraryprecision. Moreover,we obtain sharp spectral stability results for deterministic and random perturbations. In particular, we obtain differentiability results for spectral data (which imply differentiability of the Sinai-Ruelle-Bowenmeasure, the variancefor the centrallimit theorem, the rates of decay for smooth observable, etc.).

Effect of a crystallite size distribution on X‐ray diffraction line profiles and whole‐powder‐pattern fitting

Abstract: A distribution of crystallite size reduces the width of a powder diffraction line profile, relative to that for a single crystallite, and lengthens its tails. It is shown that estimates of size from the integral breadth or Fourier methods differ from the arithmetic mean of the distribution by an amount which depends on its dispersion. It is also shown that the form of `size' line profiles for a unimodal distribution is generally not Lorentzian. A powder pattern can be simulated for a given distribution of sizes, if it is assumed that on average the crystallites have a regular shape, and this can then be compared with experimental data to give refined parameters defining the distribution. Unlike `traditional' methods of line-profile analysis, this entirely physical approach can be applied to powder patterns with severe overlap of reflections, as is demonstrated by using data for nanocrystalline ceria. The procedure is compared with alternative powder-pattern fitting methods, by using pseudo-Voigt and Pearson VII functions to model individual line profiles, and with transmission electron microscopy (TEM) data.