Proximity effects on semiconducting mineral surfaces II:: Distance dependence of indirect interactions

In a previous study, we described proximity effects on surfaces of the semiconducting minerals galena and pyrite, whereby a chemical reaction at one surface site modifies the reactivity of a remote surface site several Ångstroms or even nanometers away (Becker et al., 2001). The modification of interest does not arise because of a direct “through space” interaction between the two sites, but rather an indirect interaction via the electronic structure of the substrate. Here we investigate the distance and direction dependence of proximity effects using quantum mechanical modeling. The direct and indirect interactions between co-adsorbed oxygen atoms and between adsorbed oxygen atoms and point defects on vacuum-terminated galena (100) surfaces were modeled. Density functional theory cluster and plane wave pseudopotential calculations were used to calculate the modifications to the adsorption energy as a function of separation. Energy-distance plots indicate that the proximity effect energy can become very strong at separations decreasing below about 5 to 6 Å, and persist at increasing separations up to 12 Å in a slowly decaying form. A strong attractive indirect interaction out-competes direct electrostatic repulsion for O-vacancy interactions. An oscillatory asymptotic behavior is found for co-adsorbed O-O indirect interactions, which indicates that the proximity effect energy can vary with surface crystallographic direction. It implies the presence of a strong organizing force on like adatoms that may explain the progressive oxidation of certain sulfide minerals by patchwork growth. These findings begin to pave the way for improved adsorption isotherms and extended surface complexation models that will include the specific influence of semiconductor-type proximity effects.     

Complexity–entropy analysis of daily stream flow time series in the continental United States

Complexity–entropy causality plane (CECP) is a diagnostic diagram plotting normalized Shannon entropy \({\cal H}_S\) versus Jensen–Shannon complexity \({\cal C}_{JS}\) that has been introduced in nonlinear dynamics analysis to classify signals according to their degrees of randomness and complexity. In this study, we explore the applicability of CECP in hydrological studies by analyzing 80 daily stream flow time series recorded in the continental United States during a period of 75 years, surrogate sequences simulated by autoregressive models (with independent or long-range memory innovations), Theiler amplitude adjusted Fourier transform and Theiler phase randomization, and a set of signals drawn from nonlinear dynamic systems. The effect of seasonality, and the relationships between the CECP quantifiers and several physical and statistical properties of the observed time series are also studied. The results point out that: (1) the CECP can discriminate chaotic and stochastic signals in presence of moderate observational noise; (2) the signal classification depends on the sampling frequency and aggregation time scales; (3) both chaotic and stochastic systems can be compatible with the daily stream flow dynamics, when the focus is on the information content, thus setting these results in the context of the debate on observational equivalence; (4) the empirical relationships between \({\mathcal H}_S\) and \({\mathcal C}_{JS}\) and Hurst parameter H, base flow index, basin drainage area and stream flow quantiles highlight that the CECP quantifiers can be considered as proxies of the long-term low-frequency groundwater processes rather than proxies of the short-term high-frequency surface processes; (6) the joint application of linear and nonlinear diagnostics allows for a more comprehensive characterization of the stream flow time series.     

Alternative stable states in mountain forest ecosystems: the case of European larch (<Emphasis Type="Italic">Larix decidua</Emphasis>) forests in the western Alps

European larch (Larix decidua) forests of the western Alps form extensive cultural landscapes whose resilience to global changes is currently unknown. Resilience describes the capacity of ecological systems to maintain the same state, i.e., the same function, processes, structure, and composition despite disturbances, environmental changes and internal fluctuations. Our aim is to explore the resilience of larch forests to changes in climate and land use in the western Italian Alps. To do so, we examined whether larch forests can be described as an alternative stable state in mountain forest ecosystems. We used tree basal area data obtained from field forest inventories in combination with topography, forest structure, land use, and climate information. We applied three different probabilistic methods: frequency distributions, logistic regressions, and potential analyses to infer the resilience of larch forests relative to that of other forest types. We found patters indicative of alternative stable states: bimodality in the frequency distribution of the percent of larch basal area, and the presence of an unstable state, i.e., mixed larch forests, in the potential analyses. We also found: (1) high frequency of pure larch forests at high elevation, (2) the probability of pure larch forests increased mostly with elevation, and (3) pure larch forests were a stable state in the upper montane and subalpine belts. Our study shows that the resilience of larch forests may increase with elevation, most likely due to the altitudinal effect on climate. Under the same climate conditions, land use seems to be the main factor governing the dominance of larch forests. In fact, subalpine larch forests may be more resilient, and natural succession after land abandonment, e.g., towards Pinus cembra forests, seems slower than in montane larch forests. In contrast, in the upper montane belt only intense land use regimes characterized by open canopies and forest grazing may maintain larch forests. We conclude that similar approaches could be applied in other forest ecosystems to infer the resilience of tree species.     

Adatom Fe(III) on the hematite surface: Observation of a key reactive surface species

The reactivity of a mineral surface is determined by the variety and population of different types of surface sites (e.g., step, kink, adatom, and defect sites). The concept of "adsorbed nutrient" has been built into crystal growth theories, and many other studies of mineral surface reactivity appeal to ill-defined "active sites." Despite their theoretical importance, there has been little direct experimental or analytical investigation of the structure and properties of such species. Here, we use ex-situ and in-situ scanning tunneling microcopy (STM) combined with calculated images based on a resonant tunneling model to show that observed nonperiodic protrusions and depressions on the hematite (001) surface can be explained as Fe in an adsorbed or adatom state occupying sites different from those that result from simple termination of the bulk mineral. The number of such sites varies with sample preparation history, consistent with their removal from the surface in low pH solutions.     

A mapping of the electron localization function for earth materials

The electron localization function, ELF, generated for a number of geometry-optimized earth materials, provides a graphical representation of the spatial localization of the probability electron density distribution as embodied in domains ascribed to localized bond and lone pair electrons. The lone pair domains, displayed by the silica polymorphs quartz, coesite and cristobalite, are typically banana-shaped and oriented perpendicular to the plane of the SiOSi angle at ~0.60 Å from the O atom on the reflex side of the angle. With decreasing angle, the domains increase in magnitude, indicating an increase in the nucleophilic character of the O atom, rendering it more susceptible to potential electrophilic attack. The Laplacian isosurface maps of the experimental and theoretical electron density distribution for coesite substantiates the increase in the size of the domain with decreasing angle. Bond pair domains are displayed along each of the SiO bond vectors as discrete concave hemispherically-shaped domains at ~0.70 Å from the O atom. For more closed-shell ionic bonded interactions, the bond and lone pair domains are often coalesced, resulting in concave hemispherical toroidal-shaped domains with local maxima centered along the bond vectors. As the shared covalent character of the bonded interactions increases, the bond and lone pair domains are better developed as discrete domains. ELF isosurface maps generated for the earth materials tremolite, diopside, talc and dickite display banana-shaped lone pair domains associated with the bridging O atoms of SiOSi angles and concave hemispherical toroidal bond pair domains associated with the nonbridging ones. The lone pair domains in dickite and talc provide a basis for understanding the bonded interactions between the adjacent neutral layers. Maps were also generated for beryl, cordierite, quartz, low albite, forsterite, wadeite, åkermanite, pectolite, periclase, hurlbutite, thortveitite and vanthoffite. Strategies are reviewed for finding potential H docking sites in the silica polymorphs and related materials. As observed in an earlier study, the ELF is capable of generating bond and lone pair domains that are similar in number and arrangement to those provided by Laplacian and deformation electron density distributions. The formation of the bond and lone pair domains in the silica polymorphs and the progressive decrease in the SiO length as the value of the electron density at the bond critical point increases indicates that the SiO bonded interaction has a substantial component of covalent character.     

Computer simulation of electron transfer at hematite surfaces

Molecular dynamics simulations in combination with ab initio calculations were carried out to determine the rate of electron transfer at room temperature in bulk hematite (α-Fe₂O₃) and at two low-index surfaces, namely the (012) and (001) surfaces. The electron transfer reactions considered here involve the II/III valence interchange between nearest-neighbor iron atoms. Two electron transfer directions were investigated, namely the basal plane and c direction electron transfers. Electron transfer rates obtained in bulk hematite were in good agreement with ab initio electronic structure calculations thus validating the potential model. The surfaces were considered both in vacuum and in contact with an equilibrated aqueous solution. The reorganization energy is found to increase significantly at the first surface layer and this value is little affected by the presence of water. In addition, in the case of the (012) surface, the electronic coupling matrix element for the topmost basal plane transfer was calculated at the Hartree-Fock level and was found to be weak compared to the corresponding electron transfer in the bulk. Therefore, most surfaces show a decrease in the rate of electron transfer at the surface. However, where iron atoms involved in the electron transfer reaction are directly coordinated to water molecules, water lowers the free energy of activation to a great extent and provides a large driving force for electrons to diffuse toward the bulk thus opposing the intrinsic surface effect. The surfaces considered in this work show different electron transfer properties. Hematite has been shown to exhibit anisotropic conductivity and thus different surfaces will show different intra- and inter-layer rates depending on their orientation. Moreover, the calculations of electron transfers at the hydroxyl- and iron-terminated (001) surfaces revealed that surface termination has a significant effect on the electron transfer parameters in the vicinity of the surface. Finally, our findings indicate that undercoordinated terminal iron atoms could act as electron traps at the surface.     

New energy and helicity bounds for knotted and braided magnetic fields

In this article we present a review of some of the author's most recent results in topological magnetohydrodynamics (MHD), with an eye to possible applications to astrophysical flows and solar coronal structures. First, we briefly review basic work on magnetic helicity and linking numbers, and fundamental relations with magnetic energy and average crossing numbers of magnetic systems in ideal conditions. In the case of magnetic knots, we focus on the relation between their groundstate energy and topology, discussing the energy spectrum of tight knots in terms of ropelength. We compare this spectrum with the one given by considering the bending energy of such idealized knots, showing that curvature information provides a rather good indicator of magnetic energy contents. For loose knots far from equilibrium we show that inflexional states determine the transition to braid form. New lower bounds for tight knots and braids are then established. We conclude with results on energy-complexity relations for systems in presence of dissipation.     

Structure, charge distribution, and electron hopping dynamics in magnetite (Fe3O4) (1 0 0) surfaces from first principles

For the purpose of improving fundamental understanding of the redox reactivity of magnetite, quantum-mechanical calculations were applied to predict Fe²⁺ availability and electron hopping rates at magnetite (1 0 0) surfaces, with and without the presence of adsorbed water. Using a low free energy surface reconstruction (½-Fe_tet layer relaxed into the Fe_oct (1 0 0) plane), the relaxed outermost layer of both the hydrated and vacuum-terminated surfaces were found to be predominantly enriched in Fe²⁺ within the octahedral sublattice, irrespective of the presence of adsorbed water. At room temperature, mobile electrons move through the octahedral sublattice by Fe²⁺-Fe³⁺ valence interchange small polaron hopping, calculated at 10¹⁰-10¹² hops/s for bulk and bulk-like (i.e., near-surface) environments. This process is envisioned to control sustainable overall rates of interfacial redox reactions. These rates decrease by up to three orders of magnitude (10⁹ hops/s) at the (1 0 0) surface, and no significant difference is observed for vacuum-terminated versus hydrated cases. Slower hopping rates at the surface appear to arise primarily from larger reorganization energies associated with octahedral Fe²⁺-Fe³⁺ valence interchange in relaxed surface configurations, and secondarily on local charge distribution patterns surrounding Fe²⁺-Fe³⁺ valence interchange pairs. These results suggest that, with respect to the possibility that the rate and extent of surface redox reactions depend on Fe²⁺ availability and its replenishment rate, bulk electron hopping mobility is an upper-limit for magnetite and slower surface rates may need to be considered as potentially rate-limiting. They also suggest that slower hopping mobilities calculated for surface environments may be amenable to Fe²⁺-Fe³⁺ site discrimination by conventional spectroscopic probes.