Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

This paper presents an original method for the analysis of multicomponent spectral data sets. The proposed algorithm is based on Bayesian estimation theory and Markov Chain Monte Carlo (MCMC) methods. Resolving spectral mixture analysis aims at recovering the unknown component spectra and at assessing the concentrations of the underlying species in the mixtures. In addition to non-negativity constraint, further assumptions are generally needed to get a unique resolution. The proposed statistical approach assumes mutually independent spectra and accounts for the non-negativity and the sparsity of both the pure component spectra and the concentration profiles. Gamma distribution priors are used to translate all these information in a probabilistic framework. The estimation is performed using MCMC methods which lead to an unsupervised algorithm, whose performances are assessed in a simulation study with a synthetic data set

Bayesian separation of spectral sources under non-negativity and full additivity constraints

This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and non-negativity of sources and mixing coefficients. A Bayesian estimation approach based on Gamma priors was recently proposed to handle the non-negativity constraints in a linear mixture model. However, incorporating the full additivity constraint requires further developments. This paper studies a new hierarchical Bayesian model appropriate to the non-negativity and sum-to-one constraints associated to the regressors and regression coefficients of linear mixtures. The estimation of the unknown parameters of this model is performed using samples generated using an appropriate Gibbs sampler. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture models. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy.Comment: v4: minor grammatical changes; Signal Processing, 200

The Raman spectrum of CaCO3 polymorphs calcite and aragonite: A combined experimental and computational study

Powder and single crystal Raman spectra of the two most common phases of calcium carbonate are calculated with ab initio techniques (using a “hybrid” functional and a Gaussian-type basis set) and measured both at 80 K and room temperature. Frequencies of the Raman modes are in very good agreement between calculations and experiments: the mean absolute deviation at 80 K is 4 and 8 cm−1 for calcite and aragonite, respectively. As regards intensities, the agreement is in general good, although the computed values overestimate the measured ones in many cases. The combined analysis permits to identify almost all the fundamental experimental Raman peaks of the two compounds, with the exception of either modes with zero computed intensity or modes overlapping with more intense peaks. Additional peaks have been identified in both calcite and aragonite, which have been assigned to 18O satellite modes or overtones. The agreement between the computed and measured spectra is quite satisfactory; in particular, simulation permits to clearly distinguish between calcite and aragonite in the case of powder spectra, and among different polarization directions of each compound in the case of single crystal spectra

The vibrational spectrum of CaCO3 aragonite: A combined experimental and quantum-mechanical investigation

The vibrational properties of CaCO3 aragonite have been investigated both theoretically, by using a quantum mechanical approach (all electron Gaussian type basis set and B3LYP HF-DFT hybrid functional, as implemented in the CRYSTAL code) and experimentally, by collecting polarized infrared (IR) reflectance and Raman spectra. The combined use of theory and experiment permits on the one hand to analyze the many subtle features of the measured spectra, on the other hand to evidentiate limits and deficiencies of both approaches. The full set of TO and LO IR active modes, their intensities, the dielectric tensor (in its static and high frequency components), and the optical indices have been determined, as well as the Raman frequencies. Tools such as isotopic substitution and graphical animation of the modes are available, that complement the analysis of the spectrum

Relation Composition-Structure des Hydroxydes Doubles Lamellaires (Effets de la charge du feuillet et de la nature de l'anion interfoliaire)

Ce travail de thèse s'intéresse à la relation entre la composition des phases Hydroxydes Doubles Lamellaires (HDL) et leurs propriétés structurales. La première partie de ce manuscrit est consacrée à la formation et aux propriétés structurales de ces matériaux. L'effet de la nature des cations (MgII, NiII, CoII ; AlIII, FeIII) et de leur stoechiométrie dans le feuillet (MII/MIII E [2 ; 10]) constitue les axes principaux de ces travaux. L'étude du comportement hydrolytique d'un mélange de cations divalents et trivalents en fonction de leurs proportions en solution a permis de proposer un mécanisme topotactique de formation de ces phases HDL. Il a aussi été montré que la variabilité stoechiométrique du feuillet ne dépend que de la nature des cations. Ainsi, des modèles électrostatiques ont été proposés afin de rationaliser et prédire la gamme de composition de ces phases HDL en fonction de la nature des cations. La seconde partie est dédiée aux propriétés du milieu interfoliaire. Une étude couplant des analyses par spectroscopies vibrationnelles infrarouge et Raman et par diffraction des Rayons X a permis d'apporter une description précise de l'influence de la nature des cations, et de leurs stoechiométries sur l'organisation des anions dans le milieu interfoliaire (Cl-, CO32-, NO3-, ClO4-, acides aminés). Le rôle de l'eau dans ces phases a également été étudié. Dans le cas des hybrides organo-minéraux, il a été montré que la charge dicte l'orientation des acides aminés intercalées et par conséquent, leur réactivité envers la formation de la liaison peptidique. Également, les propriétés énantioselectives du domaine interfeuillet sont mises en avant pour la formation de peptidesThis manuscript is devoted to the comprehension of the relationship between the composition of Layered Double Hydroxides (LDH) and their structural properties. The first part of this manuscript is focalized on the formation and the structural properties of these materials. The influence of the cationic nature (MgII, NiII, CoII ; AlIII, FeIII) and their stoichiometries within the layer (MII/MIII E [2 ; 10]) constitutes the main axis of these investigations. The study of the hydrolytic behavior of a solution containing a mixture of divalent and trivalent cations as a function of their relative proportion allowed to propose a topotactic mechanism of formation of LDH phases. Moreover, it has been showed that the composition range is solely dependent on the nature of the cations. Thus, electrostatic models were designed to rationalize and predict the composition range as a function of the cationic nature. The second part is concerned with the properties of the interlayer domain. A joint study, coupling vibrational spectroscopies (Infrared and Raman) and X-ray diffraction allowed a detailed description of the influence of the cations and their stoichiometries on the organization of the interlayer anions (Cl-, CO32-, NO3-, ClO4-, aminoacids). The role of the interlayer water has also been investigated. Concerning hybrid organo-minerals, it has been showed that the layer charge dictates the orientation of the interlayered aminoacids, and consequently, their reactivity toward the formation of the peptide bonds. The enantioselective properties of the interlayer domain are highlighted toward the formation of peptidesMETZ-SCD (574632105) / SudocNANCY1-Bib. numérique (543959902) / SudocNANCY2-Bibliotheque electronique (543959901) / SudocNANCY-INPL-Bib. électronique (545479901) / SudocSudocFranceF

Séparation de sources non-négatives par l'approche du maximum de vraisemblance

Ce papier traite du problème de la séparation de sources non-négatives en utilisant l'approche du maximum de vraisemblance. Il est montré que cette approche peut être appliquée avec succès si on utilise une fonction non-linéaire dérivée de la modélisation des distributions des signaux sources par des densités à support positif. Dans le cas des signaux de spectroscopie, qui est notre application principale, une bonne loi candidate est la distribution gamma qui permet de prendre en compte conjointement la non-négativité et la parcimonie des signaux sources. Un exemple synthétique est présenté afin d'étudier les performances de l'algorithme résultant

Modelling the Structure and Vibrational Properties of Layered Double Hydroxides

International audienceA model structure is proposed for the layered double hydroxide [Mg2Al(OH)6]+ · Cl- (Mg/Al ratio R = 2). The structural parameters of this model have been optimized by DFT calculations and both PXRD and vibrational spectra have been simulated. The comparison with experimental data confirms the validity of the model. Thanks to the synergy between experiment and theory it is now possible to analyze in detail the vibrational signals and understand the interactions between the different components of this material

Far- and mid-infrared examination of nontronite-1 clay mineral – Redox and cation saturation effects

Infrared Spectroscopy is a very useful tool studying clay minerals in a structural level as well as interactions on their surfaces. In this study, middle- and far- infrared spectroscopy was utilised to better understand how iron-bearing smectites and more specifically the nontronite-1 (NAu1) alters upon iron reduction. Changes in the middle-infrared spectral range have been studied extensively, such as the 3570 cm−1, 1020 cm−1 and 823 cm−1, while far-infrared spectral range changes have not drawn much attention. In this study, NAu1 spectra of oxidised, partially, and fully reduced state are presented noting the differences that occur on different vibration bands at this low frequency infrared range. Key changes took place at the region of 430–494 cm−1, as well as the 145 cm−1 band. From the 175 cm−1 to the 380 cm−1 region, vibrating bands disappeared or convoluted in a wider spectral envelope, upon full iron reduction. At the same time, NAu1 is saturated with different cations, such as Na+, Ca2+, K+, isolating effects on vibrating bands, depending on these cations, across the oxidation states and infrared range examined. These effects are more prominent at the region of 1620–1650 cm−1, where adsorbed H2O bending vibration takes place, for the middle-infrared range. Far-infrared range changes, due to the cation present, are less prominent, but recorded and discussed in detail. Eventually, the redox state of iron-bearing clay minerals controls the structural configuration of the lattice and consequently the interaction strength of clay mineral/saturating cations. The increasing interaction strength observed was Ca2+ < Na+ < K+, which will govern clay mineral hydration and cation exchange processes taking place on the clay mineral surface, as demonstrated, and discussed in this study. These outcomes can be useful in agriculture, waste disposal, and the oil & gas industry

Enhanced photocatalytic ability of Cu, Co doped ZnAl based mixed metal oxides derived from layered double hydroxides

International audienc