Europium retention onto clay minerals from 25 to 150 °C: Experimental measurements, spectroscopic features and sorption modelling

The sorption of Eu(III) onto kaolinite and montmorillonite was investigated up to 150 °C. The clays were purified samples, saturated with Na in the case of montmorillonite. Batch experiments were conducted at 25, 40, 80 and 150 °C in 0.5 M NaClO4 solutions to measure the distribution coefficients (Kd) of Eu as a trace element (<10−6 mol/L) between the solution and kaolinite. For the Na-montmorillonite, we used Kd results from a previous study [Tertre, E., Berger, G., Castet, S., Loubet, M., Giffaut, E., 2005. Experimental study of adsorption of Ni2+, Cs+ and Ln3+ onto Na-montmorillonite up to 150 °C. Geochim. Cosmochim. Acta 69, 4937–4948] obtained under exactly the same conditions. The number and nature of the Eu species sorbed onto both clay minerals were investigated by time resolved laser fluorescence spectroscopy (TRLFS) in specific experiments in the same temperature range. We identified a unique inner-sphere complex linked to the aluminol sites in both clays, assumed to be double bond; length as m-dashAlOEu2+ at the edge of the particles, and a second exchangeable outer-sphere complex for montmorillonite, probably in an interlayer position. The Kd values were used to adjust the parameters of a surface complexation model (DLM: diffuse layer model) from 25 to 150 °C. The number of Eu complexes and the stoichiometry of reactions were constrained by TRLFS. The acidity constants of the amphoteric aluminol sites were taken from another study [Tertre, E., Castet, S., Berger, G., Loubet, M., Giffaut, E. Acid/base surface chemistry of kaolinite and Na-montmorillonite at 25 and 60 °C: experimental study and modelling. Geochim. Cosmochim. Acta, in press], which integrates the influence of the negative structural charge of clays on the acid/base properties of edge sites as a function of temperature and ionic strength. The results of the modelling show that the observed shift of the sorption edge towards low pH with increasing temperature results solely from the contribution of the double bond; length as m-dashAlOEu2+ edge complexes. Finally, we successfully tested the performance of our model by confronting the predictions with experimental Kd data. We used our own data obtained at lower ionic strength (previous study) or higher suspension density and higher starting concentration (TRLFS runs, this study), as well as published data from other experimental studies [Bradbury, M.H., Baeyens, B., 2002. Sorption of Eu on Na and Ca-montmorillonite: experimental investigations and modeling with cation exchange and surface complexation. Geochim. Cosmochim. Acta 66, 2325–2334; Kowal-Fouchard, A., 2002. Etude des mécanismes de rétention des ions U(IV) et Eu(III) sur les argiles: influence des silicates. Ph.D. Thesis, Université Paris Sud, France, 330p]

Antiferromagnetic Phases of One-Dimensional Quarter-Filled Organic Conductors

The magnetic structure of antiferromagnetically ordered phases of quasi-one-dimensional organic conductors is studied theoretically at absolute zero based on the mean field approximation to the quarter-filled band with on-site and nearest-neighbor Coulomb interaction. The differences in magnetic properties between the antiferromagnetic phase of (TMTTF)$_2$X and the spin density wave phase in (TMTSF)$_2$X are seen to be due to a varying degrees of roles played by the on-site Coulomb interaction. The nearest-neighbor Coulomb interaction introduces charge disproportionation, which has the same spatial periodicity as the Wigner crystal, accompanied by a modified antiferromagnetic phase. This is in accordance with the results of experiments on (TMTTF)$_2$Br and (TMTTF)$_2$SCN. Moreover, the antiferromagnetic phase of (DI-DCNQI)$_2$Ag is predicted to have a similar antiferromagnetic spin structure.Comment: 8 pages, LaTeX, 4 figures, uses jpsj.sty, to be published in J. Phys. Soc. Jpn. 66 No. 5 (1997

Optical properties of perovskite alkaline earth titanates : a formulation

In this communication we suggest a formulation of the optical conductivity as a convolution of an energy resolved joint density of states and an energy-frequency labelled transition rate. Our final aim is to develop a scheme based on the augmented space recursion for random systems. In order to gain confidence in our formulation, we apply the formulation to three alkaline earth titanates CaTiO_3, SrTiO_3 and BaTiO_3 and compare our results with available data on optical properties of these systems.Comment: 19 pages, 9 figures, Submitted to Journal of Physics: Condensed Matte

Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2_2CuCl4_4 and to the layered organic superconductors κ\kappa-(BEDT-TTF)2_2X

We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials $\kappa$-(BEDT-TTF)$_2$X. The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs$_2$CuCl$_4$. We find rich phase diagrams for each model. The Sp(N) antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finite-N are also discussed. For parameters relevant to Cs$_2$CuCl$_4$ the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase with deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform phase. The uniform and SFP phases exhibit a pseudogap. A metal-insulator transition occurs at intermediate values of the interaction strength.Comment: Typos corrected, one reference added. 20 pages, 17 figures, RevTeX 3.

Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type

We consider the electronic properties of layered molecular crystals of the type theta-D$_2$A, where A is an anion and D is a donor molecule such as BEDT-TTF [where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene)] which is arranged in the theta type pattern within the layers. We argue that the simplest strongly correlated electron model that can describe the rich phase diagram of these materials is the extended Hubbard model on the square lattice at a quarter filling. In the limit where the Coulomb repulsion on a single site is large, the nearest-neighbour Coulomb repulsion, V, plays a crucial role. When V is much larger than the intermolecular hopping integral t the ground state is an insulator with charge ordering. In this phase antiferromagnetism arises due to a novel fourth-order superexchange process around a plaquette on the square lattice. We argue that the charge ordered phase is destroyed below a critical non-zero value V, of the order of t. Slave boson theory is used to explicitly demonstrate this for the SU(N) generalisation of the model, in the large N limit. We also discuss the relevance of the model to the all-organic family beta''-(BEDT-TTF)$_2$SF$_5$YSO$_3$ where Y = CH$_2$CF$_2$, CH$_2$, CHF.Comment: 15 pages, 6 eps figure

Charge Ordering in Organic ET Compounds

The charge ordering phenomena in quasi two-dimensional 1/4-filled organic compounds (ET)_2X (ET=BEDT-TTF) are investigated theoretically for the $\theta$ and $\alpha$-type structures, based on the Hartree approximation for the extended Hubbard models with both on-site and intersite Coulomb interactions. It is found that charge ordered states of stripe-type are stabilized for the relevant values of Coulomb energies, while the spatial pattern of the stripes sensitively depends on the anisotropy of the models. By comparing the results of calculations with the experimental facts, where the effects of quantum fluctuation is incorporated by mapping the stripe-type charge ordered states to the S=1/2 Heisenberg Hamiltonians, the actual charge patterns in the insulating phases of $\theta$-(ET)_2MM'(SCN)_4 and $\alpha$-(ET)_2I_3 are deduced. Furthermore, to obtain a unified view among the $\theta$, $\alpha$ and $\kappa$-(ET)_2X families, the stability of the charge ordered state in competition with the dimeric antiferromagnetic state viewed as the Mott insulating state, which is typically realized in $\kappa$-type compounds, and with the paramagnetic metallic state, is also pursued by extracting essential parameters.Comment: 35 pages, 27 figures, submitted to J. Phys. Soc. Jp

Superconductivity and Density Wave in the Quasi-One-Dimensional Systems: Renormalization Group Study

The anisotropic superconductivity and the density wave have been investigated by applying the Kadanoff-Wilson renormalization group technique to the quasi-one-dimensional system with finite-range interactions. It is found that a temperature (T) dependence of response functions is proportional to exp(1/T) in a wide region of temperature even within the one-loop approximation. Transition temperatures are calculated to obtain the phase diagram of the quasi-one-dimensional system, which is compared with that of the pure-one-dimensional system. Next-nearest neighbor interactions (V_2) induce large charge fluctuations, which suppress the d_{x^2 -y^2}-wave singlet superconducting (dSS) state and enhance the f-wave triplet superconducting (fTS) state. From this effect, the transition temperature of fTS becomes comparable to that of dSS for large V_2, so that field-induced f-wave triplet pairing could be possible. These features are discussed to comprehend the experiments on the (TMTSF)_2PF_6 salt.Comment: 8 pages, 4 figures, submitted to J. Phys. Soc. Jp

Effect of nearest- and next-nearest neighbor interactions on the spin-wave velocity of one-dimensional quarter-filled spin-density-wave conductors

We study spin fluctuations in quarter-filled one-dimensional spin-density-wave systems in presence of short-range Coulomb interactions. By applying a path integral method, the spin-wave velocity is calculated as a function of on-site (U), nearest (V) and next-nearest (V_2) neighbor-site interactions. With increasing V or V_2, the pure spin-density-wave state evolves into a state with coexisting spin- and charge-density waves. The spin-wave velocity is reduced when several density waves coexist in the ground state, and may even vanish at large V. The effect of dimerization along the chain is also considered.Comment: REVTeX, 11 pages, 9 figure

Dielectric response of charge induced correlated state in the quasi-one-dimensional conductor (TMTTF)2PF6

Conductivity and permittivity of the quasi-one-dimensionsional organic transfer salt (TMTTF)2PF6 have been measured at low frequencies (10^3-10^7 Hz) between room temperature down to below the temperature of transition into the spin-Peierls state. We interpret the huge real part of the dielectric permittivity (up to 10^6) in the localized state as the realization in this compound of a charge ordered state of Wigner crystal type due to long range Coulomb interaction.Comment: 11 pages, 3 .eps figure

Theoretical Aspects of Charge Ordering in Molecular Conductors

Theoretical studies on charge ordering phenomena in quarter-filled molecular (organic) conductors are reviewed. Extended Hubbard models including not only the on-site but also the inter-site Coulomb repulsion are constructed in a straightforward way from the crystal structures, which serve for individual study on each material as well as for their systematic understandings. In general the inter-site Coulomb interaction stabilizes Wigner crystal-type charge ordered states, where the charge localizes in an arranged manner avoiding each other, and can drive the system insulating. The variety in the lattice structures, represented by anisotropic networks in not only the electron hopping but also in the inter-site Coulomb repulsion, brings about diverse problems in low-dimensional strongly correlated systems. Competitions and/or co-existences between the charge ordered state and other states are discussed, such as metal, superconductor, and the dimer-type Mott insulating state which is another typical insulating state in molecular conductors. Interplay with magnetism, e.g., antiferromagnetic state and spin gapped state for example due to the spin-Peierls transition, is considered as well. Distinct situations are pointed out: influences of the coupling to the lattice degree of freedom and effects of geometrical frustration which exists in many molecular crystals. Some related topics, such as charge order in transition metal oxides and its role in new molecular conductors, are briefly remarked.Comment: 21 pages, 19 figures, to be published in J. Phys. Soc. Jpn. special issue on "Organic Conductors"; figs. 4 and 11 replaced with smaller sized fil