The ionic model: Extension to spatial charge distributions

In this paper the validity of the classical ionic model, using a Madelung term and a Born-Mayer repulsive term, is investigated quantatively for systems with a considerable overlap of the electron clouds of neighbouring ions, such as silicates with a high degree of polymerisation. A modified ionic model is presented which takes into account the spatial extent of the ions within the approximation of spherical atoms. Both models are tested against quantum mechanical electron densities and energies for SiO ₄ ^4- -clusters. The data demonstrate the validity of the spherical atom approximation, producing a fit of 99.995%, and the importance of manybody effects maintaining the spherical symmetry of the electron clouds as contraction/expansion of the ions and charge transfer between ions. Although the new interaction potential is physically more plausible than the classical Born-Mayer model, both models reproduce the quantum mechanical potential surface with numerical accuracies of the same order of magnitude. The new model provides an improved tool for judging between ionic and non-ionic effects and for analysis of the quantum mechanical electron densities and interaction energies.     

The solubility of olivine in basaltic liquids: an ionic model

A simple ionic model which describes the solution of the forsterite component of olivine in silicate liquids is reported. The melting relation is represented: (Mg₂SiO₄)_ol = 2(Mg²⁺)_L + (SiO₄^4?_L and is extended to all silicate liquids by normalizing their compositions to 4 oxygens. At 1 bar, the temperature at which olivine is in equilibrium with any alkali-depleted basaltic composition can be calculated to within ±30°C. This error is increased considerably when applied to terrestrial basalts which contain several weight percent alkalis. Alkalis interfere with the equilibrium by generating strongly repulsive interionic forces which can be crudely modelled in a manner consistent with constraints imposed by regular solution theory.The model quantifies the reduced activity of SiO₄^4? monomers due to increasing SiO₂ concentrations in the melt. This is a consequence of polymerization which does not appear to operate gradually over the entire spectrum of mafic and ultramafic compositions. The coordination of alumina in melts which precipitate olivine only appears to be dominantly octahedral. Titanium acts as a polymerizing agent by interconnecting previously isolated SiO₄^4? monomers. Calcium associated with normative diopside tends to exhibit small but perceptible repulsive forces involving Mg²⁺.     

A mapping of the electron localization function for the silica polymorphs: evidence for domains of electron pairs and sites of potential electrophilic attack

The electron localization function, η, evaluated for first-principles geometry optimized model structures generated for quartz and coesite, reveals that the oxide anions are coordinated by two hemispherically shaped η-isosurfaces located along each of the SiO bond vectors comprising the SiOSi angles. With one exception, they are also coordinated by larger banana-shaped isosurfaces oriented perpendicular to the plane centered in the vicinity of the apex of each angle. The hemispherical isosurfaces, ascribed to domains of localized bond-pair electrons, are centered ～0.70 Å along the bond vectors from the oxide anions and the banana-shaped isosurfaces, ascribed to domains of localized nonbonding lone-pair electrons, are centered ～0.60 Å from the apex of the angle. The oxide anion comprising the straight SiOSi angle in coesite is the one exception in that the banana-shaped isosurface is missing; however, it is coordinated by two hemispherically shaped isosurfaces that lie along the bond vectors. In the case of a first-principles model structure generated for stishovite, the oxide anion is coordinated by five hemispherically shaped η-isosurfaces, one located along each of the three SiO bond vectors (ascribed to domains of bonding-electron pairs) that are linked to the anion with the remaining two (ascribed to domains of nonbonding-electron pairs) located on opposite sides of the plane defined by three vectors, each isosurface at a distance of ～0.5 Å from the anion. The distribution of the five isosurfaces is in a one-to-one correspondence with the distribution of the maxima displayed by experimental Δρ and theoretical ??²ρ maps. Isosurface η maps calculated for quartz and the (HO) ₃ SiOSi(OH) ₃ molecule also exhibit maxima that correspond with the (3,?3) maxima displayed by distributions of ??²ρ. Deformation maps observed for the SiOSi bridges for the silica polymorphs and a number of silicates are similar to that calculated for the molecule but, for the majority, the maxima ascribed to lone-pair features are absent. The domains of localized nonbonding-electron pair coordinating the oxide anions of quartz and coesite provide a basis for explaining the flexibility and the wide range of the SiOSi angles exhibited by the silica polymorphs with four-coordinate Si. They also provide a basis for explaining why the SiO bond length in coesite decreases with increasing angle. As found in studies of the interactions of solute molecules with a solvent, a mapping of η-isosurfaces for geometry-optimized silicates is expected to become a powerful tool for deducing potential sites of electrophilic attack and reactivity for Earth materials. The positions of the features ascribed to the lone pairs in coesite correspond with the positions of the H atoms recently reported for an H-doped coesite crystal.     

Extension of the specific interaction model to include gas solubilities in high temperature brines

A semi-empirical model for gas solubilities in high temperature brines was developed by modification of the Pitzer interaction model (Pitzer, 1973) and evaluated by least-squares fitting to available P-T-X data for carbon dioxide, hydrogen sulfide, and methane in pure water and in aqueous sodium chloride solutions. Over the range of experimental data used (25°–350°C, NaCl concentration 0–6 m, P_CO2 1–150 atm. P_CH4 1–30 atm, P_CH4 1–1700 atm), standard deviations of fit in the natural logarithm of the Henry's law ratio were 0.096 for CO₂, 0.093 for H₂S and 0.116 for CH₄.The model has several advantages. First, it has a theoretical basis which can easily be extended for the inclusion of more than one salt or gas. Second, the equations simplify to the empirically derived equation of Setschenow, in the limit of infinite dilution. Finally, the model is easily integrated into a framework of equations which can yield all of the thermodynamic properties of the system.An example in which values of the model parameters for interaction of gas with salt may be used to estimate the effect of dissolved gas or salt solubility is given.     

Solubility of silica polymorphs in electrolyte solutions, I. Activity coefficient of aqueous silica from 25° to 250°C, Pitzer''s parameterisation

Within the framework of Pitzer's specific interaction model, interaction parameters for aqueous silica in concentrated electrolyte solutions have been derived from Marshall and co-authors amorphous silica solubility measurements. The values, at 25°C, of the Pitzer interaction parameter (λ_SiO2(aq)−i) determined in this study are the following: 0.092 (i = Na⁺), 0.032 (K⁺), 0.165 (Li⁺), 0.292 (Ca²⁺, Mg²⁺), −0.139 (SO₄²⁻), and −0.009 (NO₃⁻). A set of polynomial equations has been derived which can be used to calculate λ_SiO2(aq)−i for these ions at any temperature up to 250°C. A linear relationship between the aqueous silica-ion interaction parameters (λ_SiO2(aq)−i) and the surface electrostatic field (Z_i/r_e,i) of ions was obtained. This empirical equation can be used to estimate, in first approximation, λ_SiO2(aq)−i if no measurements are available. From this parameterisation, the calculated activity coefficient of aqueous silica is 2.52 at 25°C and 1.45 at 250°C in 5 m NaCl solution. At lower concentrations, e.g. 2 m NaCl, the activity coefficient of silica is 1.45 at 25°C and 1.2 at 250°C. Hence, in practice, it is necessary to take into account the activity coefficient of aqueous silica (λ_SiO2(aq)≠1) in hydrothermal solutions and basinal brines where the ionic strength exceeds 1. A comparison of measured [Marshall, W.L., Chen, C.-T.A., 1982. Amorphous silica solubilities, V. Prediction of solubility behaviour in aqueous mixed electrolyte solutions to 300°C. Geochim. Cosmochim. Acta 46, 289–291.] and computed amorphous silica solubility, using this parameterisation, shows a good agreement. Because the effect of individual ions on silicate and silica polymorph solubilities are additive, the present study has permitted to derive Pitzer interaction parameters that allow a precise computation of γ_SiO2(aq) in the Na---K---Ca---Mg---Cl---SO₄---HCO₃---SiO₂---H₂O system, over a large range of salt concentrations and up to temperatures of 250°C.     

A dynamic spatial diffusion model: an application to the kibbutz industry in Israel

A simple dynamic spatial diffusion model is suggested using the hitherto unreferred to concept ofinnovation adoption disparity between adoption units. Such disparity is an outcome of spatial variations in information flow caused by differential distances. The model is structured around the relationship between adoption disparity and distance in a temporal context. An application of the model to the diffusion of industrialization among Kibbutzim in Israel demonstrates its usefulness as a basic conceptual framework for understanding spatial difcesses. A possible extension of the model to inncorporate elements of the logistic curve is also proposed. *** DIRECT SUPPORT *** ABI02060 00004     

A surface structural model for ferrihydrite I: Sites related to primary charge, molar mass, and mass density

A multisite surface complexation (MUSIC) model for ferrihydrite (Fh) has been developed. The surface structure and composition of Fh nanoparticles are described in relation to ion binding and surface charge development. The site densities of the various reactive surface groups, the molar mass, the mass density, the specific surface area, and the particle size are quantified. As derived theoretically, molecular mass and mass density of nanoparticles will depend on the types of surface groups and the corresponding site densities and will vary with particle size and surface area because of a relatively large contribution of the surface groups in comparison to the mineral core of nanoparticles. The nano-sized (∼2.6 nm) particles of freshly prepared 2-line Fh as a whole have an increased molar mass of M ∼ 101 ± 2 g/mol Fe, a reduced mass density of ∼3.5 ± 0.1 g/cm³, both relatively to the mineral core. The specific surface area is ∼650 m²/g. Six-line Fh (5-6 nm) has a molar mass of M ∼ 94 ± 2 g/mol, a mass density of ∼3.9 ± 0.1 g/cm³, and a surface area of ∼280 ± 30 m²/g. Data analysis shows that the mineral core of Fh has an average chemical composition very close to FeOOH with M ∼ 89 g/mol. The mineral core has a mass density around ∼4.15 ± 0.1 g/cm³, which is between that of feroxyhyte, goethite, and lepidocrocite. These results can be used to constrain structural models for Fh. Singly-coordinated surface groups dominate the surface of ferrihydrite (∼6.0 ± 0.5 nm⁻²). These groups can be present in two structural configurations. In pairs, the groups either form the edge of a single Fe-octahedron (∼2.5 nm⁻²) or are present at a single corner (∼3.5 nm⁻²) of two adjacent Fe octahedra. These configurations can form bidentate surface complexes by edge- and double-corner sharing, respectively, and may therefore respond differently to the binding of ions such as uranyl, carbonate, arsenite, phosphate, and others. The relatively low PZC of ferrihydrite can be rationalized based on the estimated proton affinity constant for singly-coordinated surface groups. Nanoparticles have an enhanced surface charge. The charging behavior of Fh nanoparticles can be described satisfactory using the capacitance of a spherical Stern layer condenser in combination with a diffuse double layer for flat plates.     

Rare earth element diffusion in diopside: influence of temperature, pressure, and ionic radius, and an elastic model for diffusion in silicates

Volume diffusion rates for five rare earth elements (La, Ce, Nd, Dy, and Yb) have been measured in single crystals of natural diopside at pressures of 0.1 MPa to 2.5 GPa and temperatures of 1,050 to1,450 °C. Polished, pre-annealed crystals were coated with a thin film of rare earth element oxides, then held at constant temperature and pressure for times ranging from 20 to 882 h. Diffusion profiles in quenched samples were measured by SIMS (secondary ion mass spectrometry) depth profiling. At 1 atm pressure, with the oxygen fugacity controlled near the quartz-fayalite-magnetite buffer, the following Arrhenius relations were obtained for diffusion normal to (001) (diffusion coefficient D in m²/s): log₁₀D_Yb=(-4.64ǂ.42)-(411ᆠ kJ/mol/2.303RT); log₁₀D_Dy=(-3.31ǃ.44)-(461ᆽ kJ/mol/2.303RT); log₁₀D_Nd=(-2.95DŽ.64)-(496ᇡ kJ/mol/2.303RT); log₁₀D_Ce=(-4.10ǃ.08)-(463ᆳ kJ/mol/2.303RT); log₁₀D_Lu=(-4.22DŽ.66)-(466ᇢ kJ/mol/2.303RT). Diffusion rates decrease significantly with increasing ionic radius, with La a factor of ~35 slower than Yb. The relationship between diffusivity and ionic radius is consistent with a model in which elastic strain plays a critical role in governing the motion of an ion through the crystal lattice. Activation volumes for Yb and Ce diffusion, at constant temperature and oxygen fugacity, are 9.0DŽ.0 cm³/mol and 8.9Dž.2 cm³/mol, respectively, corresponding to an order of magnitude decrease in diffusivity as pressure is increased from 0 to 3 GPa at 1,200 °C. Diffusion of Nd is such that grain-scale isotopic equilibrium in the mantle can be achieved in ~1 My under conditions near the peridotite solidus (~1,450 °C at 2.5 GPa). The equilibration time is much longer under P, T conditions of the lithospheric mantle or at the eclogite solidus (~1 Gy at 1.5 GPa and 1,150 °C). Because of the relatively strong decrease in diffusivity with pressure (two orders of magnitude between 2.5 and 15 GPa along an adiabatic temperature gradient), Nd transport in clinopyroxene will be effectively frozen at pressures approaching the transition zone, on time scales less than 100 My. Rare earth element diffusion rates are slow enough that significant disequilibrium uptake of REE by growing clinopyroxene phenocrysts may be preserved under natural conditions of basalt crystallization. The relative abundances and spatial distributions of REE in such crystals may provide a sensitive record of the cooling and crystallization history of the host lava.     

B NMR investigation of boron interaction with mineral surfaces: Results for boehmite, silica gel and illite

Boron is an important micronutrient for plants but is toxic at high pore solution concentrations. Its mobility and migration in many geochemical environments is often controlled by reactions with mineral surfaces, and thus its speciation on mineral surfaces has been extensively investigated. Most previous studies have used IR spectroscopy to characterize the surface B-environments. We present here the first ¹¹B MAS NMR study of surface sorbed boron on minerals. The results demonstrate the capability of this method to effectively probe the local structure of the sorption sites at total B-concentrations in the samples as small as 0.03 wt% and to provide insight into the mechanisms of sorption. Signal is readily resolved for both trigonal (B(3)) and tetrahedral (B(4)) boron exchanged onto boehmite, silica gel and illite, and the resonances are readily assigned on the basis of chemical shift and quadrupole coupling constant. Boron surface densities on illite are approximately order of magnitude greater than on silica gel or boehmite. For boehmite, both B(3) and B(4) occur dominantly as inner-sphere complexes formed by ligand exchange reaction with surface aluminol sites. The B(3)/[B(3) + B(4)] ratio of approximately 0.87 does not vary significantly with pH from 3 to 11, with solution B-concentration, or with washing. The occurrence of B(3) and B(4) as inner-sphere complexes is in agreement with previous suggestions from IR studies of B-sorption on iron hydroxide, allophone, kaolinite, and hydrous ferric oxide. For silica gel, B(3) and B(4) occur principally as outer-sphere complexes or as residual precipitate from un-removed solution. The B(3)/B(4) ratio decreases with increasing pH paralleling the speciation in solution, but the relative abundance of B(4) is greater than in solution. A small fraction of the B(4) occurs as inner-sphere complexes with B(4)-O-Si linkages formed by ligand exchange reaction with silanol sites. For illite, surface boron occurs as outer-sphere B(3) and B(4), as for silica gel, and as inner-sphere B(3) and B(4), as for boehmite. Outer-sphere B(3) and B(4) are dominant at pH 3 and 5, whereas inner-sphere B(3) and B(4) are dominant at pH 9 and 11. The inner-sphere complexes probably form dominantly by ligand exchange reactions involving sites on the broken edges of illite layers.     

A methodology to assess the spatial configuration of urban systems in Iran from an interaction perspective

The aim of this paper is to develop a methodology for identifying various dimensions of the spatial configuration of urban systems in Iran from an interaction perspective. Through the provision of empirical evidence of different types of flows of people including air passenger flows, passenger flows by bus and car, this paper compares the resulting spatial constellations of these flows through the innovative use of indices to systematically describe and measure five dimensions of an urban system’s spatial configuration that include: (1) centrality and dominance of vertices, (2) network cohesion, (3) network strength, (4) network symmetry, and (5) communities and levels. The findings show that although the spatial configurations of different flows are not the same, all were characterized by having a significant distance within a polycentric urban system due to the primacy of the Tehran metropolis. In regard to passenger flows by car and bus, it was found that for various functional regions, there was a balanced distribution of centrality and urban hierarchy evident in Iran. By contrast, air passenger flows were not able to determine centrality within a national urban hierarchy because of the limited distribution of centers for air travel in Iran at higher levels of spatial organization.     

Computation of surface energies in an electrostatic point charge model: I. Theory

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and Ψ(x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy (γ ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy γ is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Computation of surface energies in an electrostatic point charge model: II. Application to zircon (ZrSiO4)

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and (x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy ( ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Variational stabilization of the ionic charge densities in the electron-gas theory of crystals: Applications to MgO and CaO

The electron-gas theory of crystals is extended to include the effects of many-body forces that arise from both electrostatic and overlap interactions. These effects are incorporated through a self-consistent spherical relaxation of the ionic charge distributions such that the crystal binding energy is minimized. This variational model is used to compute the elastic constants and equations of state of MgO and CaO, and we compare its results to those derived from earlier electron-gas models. In the variational model, the anion charge distributions are markedly more sensitive to the local crystal environment than they are in the PIB or other electron-gas models. We find that for these oxides the variational model gives the best overall agreement with experiment for lattice constants, equations of state, dissociation energies, and elastic moduli.     

A new procedure to best-fit earthquake magnitude probability distributions: including an example for Taiwan

Since the year 1973, more than 54,000 M _w ≥ 3.0 earthquakes have occurred around Taiwan, and their magnitude–frequency relationship was found following with the Gutenberg–Richter recurrence law with b value equal to 0.923 from the least-square calculation. However, using this b value with the McGuire–Arabasz algorithm results in some disagreement between observations and expectations in magnitude probability. This study introduces a simple approach to optimize the b value for better modeling of the magnitude probability, and its effectiveness is demonstrated in this paper. The result shows that the optimal b value can better model the observed magnitude distribution, compared with two customary methods. For example, given magnitude threshold = 5.0 and maximum magnitude = 8.0, the optimal b value of 0.835 is better than 0.923 from the least-square calculation and 0.913 from maximum likelihood estimation for simulating the earthquake’s magnitude probability distribution around Taiwan.     

The north-eastern Polish anorthosite massifs: petrological, geochemical and isotopic evidence for a crustal derivation

ABSTRACT Deeply buried 1.5 Ga Polish anorthosites, accessible only by bore holes, reveal diagnostic features of some massif-type anorthosites (polybarism, jotunitic parent magma), diapirically emplaced in the mid crust together with the rapakivi granites of the EW-trending Mazury complex, intruded along a major crustal discontinuity. Geochemical modelling and isotope data corroborate recent experimental work on the basaltic system in dry conditions: the source rock of the parental magma is a gabbronorite, necessarily lying in the lower crust. Since no Archaean crust is known in the region, high initial ¹⁸⁸Os/¹⁸⁷Os ratios for sulphide-oxide isochrons and negative ε_Nd values are best accounted for by melting a ∼ 2.0 Ga mafic crust.     

Dynamic phytoclimatology,an aid to spatial generalisation of external geodynamical studies

Abstract

The statistics and mechanical studies of the spatial variability of rainfall do not seem to be entirely satisfactory for brief events, such as the showers generating gullying. Thus, indirect indications of vegetation may be useful. Botanical continuums do reflect some climatic changes that may be linked to the distribution of these events. As an example, the analyses of some floristic transects, located at the transition of Mediterranean and oceanic, and Mediterranean and arid climates are presented. Conducted in parallel with the dynamic interpretation of climatic fields, these analyses have, for instance, allowed to state more precisely the spatial extension of several features of rains such as their cumulated values and their regime. The floristic ‘signal’ mainly concerns the climatic variations of the cumulated value of rainfall, but, in a subtler way, vegetation may signal the variations of regime. These features are linked with the strength of showers, and, as a consequence with the erosive capacity of rainfall. Dynamic phytoclimatology is then liable to give an aid to the spatialization of external geodynamic studies. © 2000 Éditions scientifiques et médicales Elsevier SAS     

The application of ionic equilibria to metamorphic differentiation: An example

Mineral segregations formed by metamorphic differentiation are an important source of information on diffusion processes in metamorphism. Segregations consisting of andalusite-biotite-quartz cores surrounded by a quartz-feldspar mantle in sillimanite-biotitefeldspar-quartz gneiss near Västervik, Sweden (Loberg, 1963) formed by core-to-mantle migration of K, and mantle-to-core migration of Fe, Mg and Ca. These migrations can be represented by a set of interconnected ionic equilibria involving reaction of microcline and Fe(OH)⁺ in the core to form andalusite plus biotite, and reaction of K⁺, sillimanite and biotite in the mantle to form microcline. Equilibrium constants for these reactions, calculated for conditions inferred from the mineral assemblage and biotite composition, indicate gradients of K⁺ activity (higher in core) and Fe(OH)⁺ activity (higher in mantle). These gradients result simply from the free energy difference between andalusite and sillimanite, without invoking pre-existing megascopic inhomogeneities in the rock or surface energy effects. Although small, these gradients appear to be capable of driving the segregation process.     

An ecosystem-based composite spatial model for floodplain vulnerability assessment: a case study of Artigas,Uruguay

Floods are natural processes that constitute a hazard to society when associated to improper land use. Anthropic activities in floodplains are a factor of vulnerability that converts a natural hazard into a threat factor, eventually leading to disaster. Nowadays, natural and social complex processes demand integrated assessments in order to improve their understanding, helping decision making over sustainable use of territory, as well as integrating society’s activity in ecosystems and potentials, restrictions and benefits that society obtain from them. In this context, the objective of this work was to build a composite vulnerability model for a floodplain under urban influence, using an integrated assessment approach. This model was based on three dimensions; threat, fragility and an ecosystem services provision. These dimensions were calculated using both primary and secondary information, and weights by specialists. Main results show that the area presents high vulnerability with an increasing gradient towards high and urbanized areas, associated with an important number and relevant ecosystem services. Also, a spatial heterogeneity of the three dimensions emerged, making evident this area’s complexity and the need of integrated assessments to approach it. The composite vulnerability model proposed presents an elevated potential for natural and social processes analysis in floodplains, which is crucial for these territory management. Moreover, these integrated dimensions could contribute to decision making in different levels, as well as generating important supplies for environmental management and land planning.