Nomenclature of the hydrotalcite supergroup: Natural layered double hydroxides

Layered double hydroxide (LDH) compounds are characterized by structures in which layers with a brucite-like structure carry a net positive charge, usually due to the partial substitution of trivalent octahedrally coordinated cations for divalent cations, giving a general layer formula [( M 2+ 1-x M 3+ x )(OH)2] x +. This positive charge is balanced by anions which are intercalated between the layers. Intercalated molecular water typically provides hydrogen bonding between the brucite layers. In addition to synthetic compounds, some of which have significant industrial applications, more than 40 mineral species conform to this description. Hydrotalcite, Mg6Al2(OH) 16[CO3]•4H2O, as the longest-known example, is the archetype of this supergroup of minerals. We review the history, chemistry, crystal structure, polytypic variation and status of all hydrotalcite-supergroup species reported to date. The dominant divalent cations, M 2+, that have been reported in hydrotalcite supergroup minerals are Mg, Ca, Mn, Fe, Ni, Cu and Zn; the dominant trivalent cations, M 3+, are Al, Mn, Fe, Co and Ni. The most common intercalated anions are (CO3)2-, (SO4)2- and Cl -; and OH-, S2- and [Sb(OH)6] - have also been reported. Some species contain intercalated cationic or neutral complexes such as [Na(H2O)6]+ or [MgSO4]0. We define eight groups within the supergroup on the basis of a combination of criteria. These are (1) the hydrotalcite group, with M 2+:M 3+ = 3:1 (layer spacing ∼7.8 Å); (2) the quintinite group, with M 2+:M 3+ = 2:1 (layer spacing ∼7.8 Å); (3) the fougèrite group, with M 2+ = Fe2+, M 3+ = Fe3+ in a range of ratios, and with O2- replacing OH- in the brucite module to maintain charge balance (layer spacing ∼7.8 Å); (4) the woodwardite group, with variable M 2+:M 3+ and interlayer [SO4] 2-, leading to an expanded layer spacing of ∼8.9 Å; (5) the cualstibite group, with interlayer [Sb(OH)6]- and a layer spacing of ∼9.7 Å; (6) the glaucocerinite group, with interlayer [SO4]2- as in the woodwardite group, and with additional interlayer H2O molecules that further expand the layer spacing to ∼11 Å; (7) the wermlandite group, with a layer spacing of ∼11 Å, in which cationic complexes occur with anions between the brucite-like layers; and (8) the hydrocalumite group, with M 2+ = Ca2+ and M 3+ = Al, which contains brucite-like layers in which the Ca:Al ratio is 2:1 and the large cation, Ca2+, is coordinated to a seventh ligand of 'interlayer' water. The principal mineral status changes are as follows. (1) The names manasseite, sjögrenite and barbertonite are discredited; these minerals are the 2H polytypes of hydrotalcite, pyroaurite and stichtite, respectively. Cyanophyllite is discredited as it is the 1M polytype of cualstibite. (2) The mineral formerly described as fougèrite has been found to be an intimate intergrowth of two phases with distinct Fe 2+:Fe3+ ratios. The phase with Fe2+:Fe 3+ = 2:1 retains the name fougèrite; that with Fe 2+:Fe3+ = 1:2 is defined as the new species trébeurdenite. (3) The new minerals omsite (IMA2012-025), Ni 2Fe3+(OH)6[Sb(OH)6], and mössbauerite (IMA2012-049), Fe3+ 6O 4(OH)8[CO3]•3H2O, which are both in the hydrotalcite supergroup are included in the discussion. (4) Jamborite, carrboydite, zincaluminite, motukoreaite, natroglaucocerinite, brugnatellite and muskoxite are identified as questionable species which need further investigation in order to verify their structure and composition. (5) The ranges of compositions currently ascribed to motukoreaite and muskoxite may each represent more than one species. The same applies to the approved species hydrowoodwardite and hydrocalumite. (6) Several unnamed minerals have been reported which are likely to represent additional species within the supergroup. This report has been approved by the Commission on New Minerals, Nomenclature and Classification (CNMNC) of the International Mineralogical Association, voting proposal 12-B. We also propose a compact notation for identifying synthetic LDH phases, for use by chemists as a preferred alternative to the current widespread misuse of mineral names. © 2012 Mineralogical Society.Fil: Mills, S.J.. Museum Victoria; AustraliaFil: Christy, A.G.. Australian National University. Centre for Advanced Microscopy; AustraliaFil: Génin, J. M. R.. CNRS-Université de Lorraine; FranciaFil: Kameda, T.. Tohoku University. Graduate School of Environmental Studies; JapónFil: Colombo, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Ciencias de la Tierra. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Centro de Investigaciones en Ciencias de la Tierra; Argentin

Thermodynamics of beta-amyloid fibril formation

Amyloid fibers are aggregates of proteins. They are built out of a peptide called $\beta$--amyloid (A$\beta$) containing between 41 and 43 residues, produced by the action of an enzyme which cleaves a much larger protein known as the Amyloid Precursor Protein (APP). X-ray diffraction experiments have shown that these fibrils are rich in $\beta$--structures, whereas the shape of the peptide displays an $\alpha$--helix structure within the APP in its biologically active conformation. A realistic model of fibril formation is developed based on the seventeen residues A$\beta$12--28 amyloid peptide, which has been shown to form fibrils structurally similar to those of the whole A$\beta$ peptide. With the help of physical arguments and in keeping with experimental findings, the A$\beta$12--28 monomer is assumed to be in four possible states (i.e., native helix conformation, $\beta$--hairpin, globular low--energy state and unfolded state). Making use of these monomeric states, oligomers (dimers, tertramers and octamers) were constructed. With the help of short, detailed Molecular Dynamics (MD) calculations of the three monomers and of a variety of oligomers, energies for these structures were obtained. Making use of these results within the framework of a simple yet realistic model to describe the entropic terms associated with the variety of amyloid conformations, a phase diagram can be calculated of the whole many--body system, leading to a thermodynamical picture in overall agreement with the experimental findings. In particular, the existence of micellar metastable states seem to be a key issue to determine the thermodynamical properties of the system

Schur functions and their realizations in the slice hyperholomorphic setting

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space

Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling

In this paper, we design a supervisor to prevent vehicle collisions at intersections. An intersection is modeled as an area containing multiple conflict points where vehicle paths cross in the future. At every time step, the supervisor determines whether there will be more than one vehicle in the vicinity of a conflict point at the same time. If there is, then an impending collision is detected, and the supervisor overrides the drivers to avoid collision. A major challenge in the design of a supervisor as opposed to an autonomous vehicle controller is to verify whether future collisions will occur based on the current drivers choices. This verification problem is particularly hard due to the large number of vehicles often involved in intersection collision, to the multitude of conflict points, and to the vehicles dynamics. In order to solve the verification problem, we translate the problem to a job-shop scheduling problem that yields equivalent answers. The job-shop scheduling problem can, in turn, be transformed into a mixed-integer linear program when the vehicle dynamics are first-order dynamics, and can thus be solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201

An Analytical Framework to Describe the Interactions Between Individuals and a Continuum

We consider a discrete set of individual agents interacting with a continuum. Examples might be a predator facing a huge group of preys, or a few shepherd dogs driving a herd of sheeps. Analytically, these situations can be described through a system of ordinary differential equations coupled with a scalar conservation law in several space dimensions. This paper provides a complete well posedness theory for the resulting Cauchy problem. A few applications are considered in detail and numerical integrations are provided

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations suggest that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By mean of molecular dynamics simulations around the native conformation, which simulate the protein and the surrounding solvent at full--atom level, we generate an energetic map of the equilibrium state of the protein and simplify it with an Eigenvalue decomposition. The components of the Eigenvector associated with the lowest Eigenvalue indicate which are the "hot" sites responsible for the stability and for the fast folding of the protein. Comparison of these predictions with the results of mutatgenesis experiments, performed for five small proteins, provide an excellent agreement

On the stability of the standard Riemann semigroup

We consider the dependence of the entropic solution of a hyperbolic system of conservation laws {ut + f(u)x = 0, u(0, \ub7) = u0 on the flux function f. We prove that the solution is Lipschitz continuous w.r.t, the C0 norm of the derivative of the perturbation of f. We apply this result to prove the convergence of the solution of the relativistic Euler equation to the classical limit

Micro-to-macro: astrodynamics at extremes of lengths-scale

This paper investigates astrodynamics at extremes of length-scale, ranging from swarms of future `smart dust' devices to the capture and utilisation of small near Earth asteroids. At the smallest length-scales families of orbits are found which balance the energy gain from solar radiation pressure with energy dissipation due to air drag. This results in long orbit lifetimes for high area-to-mass ratio `smart dust' devices. High area-to-mass hybrid spacecraft, using both solar sail and electric propulsion, are then considered to enable `pole-sitter' orbits providing a polar-stationary vantage point for Earth observation. These spacecraft are also considered to enable displaced geostationary orbits. Finally, the potential material resource available from captured near Earth asteroids is considered which can underpin future large-scale space engineering ventures. The use of such material for geo-engineering is investigated using a cloud of unprocessed dust in the vicinity of the Earth-Sun $L_1$ point to fractionally reduce solar insolation