Tetrahedral bond length variations in sulfates

Observed S—O bond lengths for sulfate tetrahedral oxyanions isolated from crystalline solids correlate with the tetrahedral angles impressed upon these ions by their environments. An algorithm is presented which can account for more than 90 percent of the S—O bond length variations from a consideration only of the average of the three angles common to each bond. Extended Hückel molecular orbital theory serves to rationalize these correlations by relating changes in bond overlap population (i.e., bond strength) to angular distortions of sulfate ions observed in a large number of natural and synthetic compounds.     

Crystal structure refinement and electron density distribution in diaspore

Diaspore from Dilln, Hungary, AlOOH, is orthorhombic with space group Pbnm, a=4.4007(6), b=9.4253(13), c=2.8452(3) Å, and Z=4. The crystal structure and electron distribution have been refined from 791 graphite-monochromatized MoKα data (maximum 2θ=130°) to R=0.035 (R _w =0.029). Difference maps show substantial electron density ascribed to covalent bonding in the hydroxyl group, O(2)-H, but no residual density is observed along the Al-O(1,2) bonds. An analysis of the charge distribution implies net charges of +1.47(26), ?1.08(16), ?0.59(13) and +0.20(5) for Al, O(1), O(2) and H respectively. Semi-empirical molecular orbital calculations of the Hückel type agree with the experimentally determined atomic charge distribution and also allow a rationalization of the observed bond length variations.     

A theoretical approach to the magnetic flocculation of weakly magnetic minerals

Energy of interaction of a system of mineral paramagnetic and diamagnetic particles of colloidal dimensions is calculated under the influence of external magnetic field according to DLVO theory. Conditions of rapid flocculation into a potential well are derived in terms of threshold magnetic field as a function of particle size and magnetic susceptibility. The effect of surface potential, Debye-Hückel reciprocal length parameter and Hamaker constant is briefly discussed. The values of the flocculating magnetic field correspond more closely to reality than other theoretical models.     

Numerical estimation of effective diffusion coefficients for charged porous materials based on micro-scale analyses

In order to describe diffusive transport of solutes through a porous material, estimation of effective diffusion coefficients is required. It has been shown theoretically that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by the tortuosity (tensor) (Bear, 1988 [1]). Given detailed information of the pore geometry at the micro-scale the tortuosity of different materials can be accurately estimated using homogenization procedures. However, many engineering materials (e.g., clays and shales) are characterized by electrical surface charges on particles of the porous material which strongly affect the (diffusive) transport properties of ions. For these type of materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying micro-scale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters (Jougnot et al., 2009; Pivonka et al., 2009; Revil and Linde, 2006 2, 3 and 4). In this paper we employ a recently proposed up-scaled Poisson–Nernst–Planck type of equation (PNP) and its micro-scale counterpart to estimate effective ion diffusion coefficients in thin charged membranes. We investigate a variety of different pore geometries together with different surface charges on particles. Here, we show that independent of the charges on particles, a (generalized) tortuosity factor can be identified as function of the pore morphology only using the new PNP model. On the other hand, all electro-static interactions of ions and charges on particles can consistently be captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this formulation allows to consistently take into account electrochemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations.     

The stability of palladium(II) hydroxide and hydroxy–chloride complexes: an experimental solubility study at 25–85°C and 1 bar

Solubility methods were employed to determine conditional equilibrium constants for the formation of hydroxide and mixed hydroxy–chloride complexes of Pd(II). Measurements were made over a temperature range of 25–85°C, a pH range from 0 to 12, and ionic strengths of 0.1, 0.2, 0.5 and 1.0 molal in both KCl and NaClO₄ media. Several speciation models were fit to the data using nonlinear regression, and the model yielding the best fit with the fewest number of species was accepted for each temperature and ionic strength. The conditional equilibrium constants were then fit to a function of ionic strength and temperature (including a Debye–Hückel term) to facilitate interpolation and extrapolation to infinite dilution. The following species were found to be important in KCl solutions: PdCl₄²⁻, PdCl₃(OH)²⁻, and Pd(OH)₂⁰. The relative proportions of the species are dependent on pH and ionic strength (chloride concentration). In perchlorate media the predominant species were Pd(OH)₃⁻, Pd(OH)₂⁰, PdOH⁺ and Pd²⁺, depending on pH. Conditional stability constants determined in this study agree well with those reported in previous work for the simple chloride and hydroxide complexes, but our results suggest that mixed complexes may be more important than previously thought, and that PdCl₃(OH)²⁻ may be the dominant species in seawater, followed by Pd(OH)₂⁰.     

Thermal expansion of fayalite,Fe2SiO4

Thermal expansion of single-crystal fayalite has been measured by a dilatometric method at temperatures between 25 °C and 850 °C. The results show the presence of anomalous expansion in the b axis, which is correlated to the anomalous variation of elastic moduli with temperature. Grüneisen's parameter is 1.10 and the thermal Debye temperature is 565 K, which is close to the acoustic Debye temperature of 511 K.     

Hybrid Gaussian-cubic radial basis functions for scattered data interpolation

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent; however, for the datasets having insufficient observations, RBFs have the advantage over geostatistical methods as the latter requires variogram study and statistical expertise. Moreover, RBFs can be used for scattered data interpolation with very good convergence, which makes them desirable for shape function interpolation in meshless methods for numerical solution of partial differential equations. For interpolation of large datasets, however, RBFs in their usual form, lead to solving an ill-conditioned system of equations, for which, a small error in the data can cause a significantly large error in the interpolated solution. In order to reduce this limitation, we propose a hybrid kernel by using the conventional Gaussian and a shape parameter independent cubic kernel. Global particle swarm optimization method has been used to analyze the optimal values of the shape parameter as well as the weight coefficients controlling the Gaussian and the cubic part in the hybridization. Through a series of numerical tests, we demonstrate that such hybridization stabilizes the interpolation scheme by yielding a far superior implementation compared to those obtained by using only the Gaussian or cubic kernels. The proposed kernel maintains the accuracy and stability at small shape parameter as well as relatively large degrees of freedom, which exhibit its potential for scattered data interpolation and intrigues its application in global as well as local meshless methods for numerical solution of PDEs.     

Reply to Hüneke’s (2005) comment

Hüneke (Int J Earth Sci 2005) gives a new interpretation of the tectonic setting of five ⁴⁰K/⁴⁰Ar analyses published by Huckriede et al. (Int J Earth Sci 93: 414–431, 2004). In this context, Hüneke discusses the significance and provenance of Late Proterozoic ⁴⁰K/⁴⁰Ar-cooling ages of detrital muscovites from pre-flysch sediments of the Blankenburg and Harzgerode Zones (Harz Mountains). Hüneke’s reinterpretation is based on a wrong concept concerning the extend of the Blankenburg Zone. This wrong concept originates from the incorrect distinction between the greywackes of the Tanne Zone and the greywackes of the Gießen-Harz Nappe. These greywackes can be easily distinguished by petrographic methods. Hüneke additionally defends the assumption that large areas of the eastern Harz Mountains consist of Viséan olistostromes. There is no need for an extended discussion of this topic because Hüneke presents no arguments.     

Homogenization of a Darcy–Stokes system modeling vuggy porous media

We derive a macroscopic model for single-phase, incompressible, viscous fluid flow in a porous medium with small cavities called vugs. We model the vuggy medium on the microscopic scale using Stokes equations within the vugular inclusions, Darcy's law within the porous rock, and a Beavers–Joseph–Saffman boundary condition on the interface between the two regions. We assume periodicity of the medium and obtain uniform energy estimates independent of the period. Through a two-scale homogenization limit as the period tends to zero, we obtain a macroscopic Darcy's law governing the medium on larger scales. We also develop some needed generalizations of the two-scale convergence theory needed for our bimodal medium, including a two-scale convergence result on the Darcy–Stokes interface. The macroscopic Darcy permeability is computable from the solution of a cell problem. An analytic solution to this problem in a simple geometry suggests that: (1) flow along vug channels is primarily Poiseuille with a small perturbation related to the Beavers–Joseph slip, and (2) flow that alternates from vug to matrix behaves as if the vugs have infinite permeability.     

A three-scale model for pH-dependent steady flows in 1:1 clays

A new three-scale model to describe the coupling between electro-chemistry and hydrodynamics in non-swelling kaolinite clays in steady-state conditions is proposed. The medium is characterized by three separate nano-micro and macroscopic length scales. At the pore (micro)-scale the portrait of the clay consists of micro-pores saturated by an aqueous solution containing four monovalent ions (Na⁺, H⁺, Cl⁻, OH⁻) and charged solid particles surrounded by thin electrical double layers. The movement of the ions is governed by the Nernst–Planck equations and the influence of the double layers upon the hydrodynamics is modeled by a slip boundary condition in the tangential velocity governed by the Stokes problem. To capture the correct form of the interface condition we invoke the nanoscopic modeling of the thin electrical double layer based on Poisson–Boltzmann problem with varying surface charge density ruled by the protonation/deprotonation reactions which occur at the surface of the particles. The two-scale nano/micro model is homogenized to the macroscale leading to a precise derivation of effective governing equations. The macroscopic model is discretized by the finite volume method and applied to numerically simulate desalination of a clay sample induced by an external electrical field generated by the placement of electrodes. Numerical results indicate strong pH-dependence of the electrokinetics.     

Estimation of the dielectric constant of H2O from experimental solubilities of quartz,and calculation of the thermodynamic properties of aqueous species to 900°C at 2 kb

Experimental quartz solubilities in H₂O (Anderson and Burnham, 1965, 1967) were used together with equations of state for quartz and aqueous species (Helgesonet al., 1978; Walther and Helgeson, 1977) to calculate the dielectric constant of H₂O () at pressures and temperatures greater than those for which experimental measurements (Heger, 1969; Lukashovet al., 1975) are available ($\text{0.001 ? P ? 5}\text{kb}$ and $\text{0 ? T ? 600°C}$). Estimates of computed in this way for 2 kb (which are the most reliable) range from 9.6 at 600°C to 5.6 at 800°C. These values are 0.5 and 0.8 units greater, respectively, than corresponding values estimated by Quist and Marshall (1965), but they differ by <0.3 units from extrapolated values computed from Pitzer's (1983) adaptation of the Kirkwood (1939) equation. The estimates of generated from quartz solubilities at 2 kb were fit with a power function of temperature, which was then used together with equations and data given by Helgeson and Kirkham (1974a,b, 1976) Helgesonet al. (1981), and Helgeson (1982b, 1984) to calculate Born functions, Debye Hückel parameters, and the thermodynamic properties of Na⁺, K⁺, Mg⁺⁺, Ca⁺⁺, and other aqueous species of geologic interest at temperatures to 900°C.     

Radiative transfer in relativistic plasma outflows and comptonization of photons near the photosphere

We study radiative transfer in plasma by numerical solution of kinetic Boltzmann equations for all particles. We are interested in the thermalization of photons. We considered three cases: 1. The calculations of the timescales of the thermalization in the uniform isotropic plasma. 2. The expansion of the mildly relativistic pair plasma for the mini fireball in the frame of the kinetic approach. 3. The case of ultra relativistically expanding outflow from the surface of the compact object with the Fokker-Planck approximation to the Boltzmann equation for photons. The last case gives the generalized Kompaneets equation which takes into account anisotropic distribution of photons developed near the photosphere. For the electron temperature dependence from radius T ∝ r ^?2 and thermal electrons spectrum we found the low-energy photon index can be ?0.5 as typically observed in GRB.     

盐溶液的渗透吸力计算方法

膨润土垫层在高放废料处置库环境中与围岩接触,力学性能会受到围岩裂隙中所含盐溶液的影响。盐溶液的渗透吸力会在膨润土上产生类似于竖向荷载作用的附加应力,量化盐溶液对膨润土力学性能的影响对评估地下处置库的安全性具有重要意义。溶液渗透吸力系数作为计算渗透吸力的关键,目前需要通过较为复杂的实验测得,对工程实际应用造成了阻碍。通过引入Debye-Hückel公式,提出含单价离子电解质、2-2型电解质及混合电解质溶液的渗透吸力系数及渗透吸力的计算方法。基于Debye-Hückel公式,分析溶剂种类和温度对渗透吸力系数的影响,结果表明:溶剂极性越大,渗透吸力系数越大;温度越高,渗透吸力系数越小。      

Thermal expansion and crystal structure of FeSi between 4 and 1173 K determined by time-of-flight neutron powder diffraction

The thermal expansion and crystal structure of FeSi has been determined by neutron powder diffraction between 4 and 1173?K. No evidence was seen of any structural or magnetic transitions at low temperatures. The average volumetric thermal expansion coefficient above room temperature was found to be 4.85(5)?×?10^?5?K^?1. The cell volume was fitted over the complete temperature range using Grüneisen approximations to the zero pressure equation of state, with the internal energy calculated via a Debye model; a Grüneisen second-order approximation gave the following parameters: θ_D=445(11)?K, V ₀=89.596(8)?ų, K ₀′=4.4(4) and γ′=2.33(3), where θ_D is the Debye temperature, V ₀ is V at T=0?K, K ₀′ is the first derivative with respect to pressure of the incompressibility and γ′ is a Grüneisen parameter. The thermodynamic Grüneisen parameter, γ_th, has been calculated from experimental data in the range 4–400?K. The crystal structure was found to be almost invariant with temperature. The thermal vibrations of the Fe atoms are almost isotropic at all temperatures; those of the Si atoms become more anisotropic as the temperature increases.     

An alternative use of Kieffer’s lattice dynamics model using vibrational density of states for constructing thermodynamic databases

We use Kieffer’s model to represent the vibrational density of states (VDoS) and thermodynamic properties of pure substances in pressure–temperature space. We show that this model can be simplified to a vibrational model in which the VDoS is represented by multiple Einstein frequencies without significant loss of accuracy in thermodynamic properties relative to experimental data. The resulting analytical expressions for thermodynamic properties, including the Gibbs energy, are mathematically simple and easily accommodated in existing computational software for making thermodynamic databases. We show for aluminium, platinum, orthoenstatite and forsterite that thermodynamic properties can be represented with comparable accuracy as with Kieffer’s model with the same number of fitting parameters as in the Mie–Grüneisen–Debye model. We demonstrate that the method enables to achieve thermodynamic properties with superior accuracy relative to the Mie–Grüneisen–Debye method. The method is versatile in the sense that it allows incorporating dispersion of Grüneisen parameters. It is possible to extend the formalism to include other physical effects, such as intrinsic anharmonicity in the same way as in vibrational models based on Kieffer’s formalism.     

A single numerically efficient equation for approximating the Mohr–Coulomb and the Matsuoka–Nakai failure criteria with rounded edges and apex

This paper presents a novel formulation for defining soil failure. It plots in the principal stress space as a surface with the shape ranging between an approximation of the Matsuoka–Nakai and of the Mohr–Coulomb criteria depending on the value of a single parameter. The new function can be used as a replacement of the original equations of these well‐established criteria for implementing in a program for numerical analyses, and it is particularly effective for approximating the Matsuoka–Nakai criterion. Both the Mohr–Coulomb and the Matsuoka–Nakai failure criteria present numerical difficulties during implementation and also at run‐time. In the case of the Matsuoka–Nakai, the new formulation plots in the first octant only, whereas the original criterion plots in all octants, which causes severe convergence problems particularly for those Gauss points with low stress state, such as those on the side of a shallow footing. When the shape parameter is set to reproduce the Mohr–Coulomb failure criterion, on the other hand, the new formulation plots as a pyramid with rounded edges. Moreover, as the new function is at least of class C², the second derivatives are continuous, thus ensuring quadratic convergence of the Newton's method used within the integration scheme of the constitutive law. The proposed formulation can also provide both sharp and rounded apex of the surface at the origin of the stress space by setting accordingly one additional parameter. Copyright © 2013 John Wiley & Sons, Ltd.     

P-V-T equation of state of magnesiowüstite (Mg0.6Fe0.4)O

The lattice parameter of magnesiowüstite (Mg_0.6Fe_0.4)O has been measured up to a pressure of 30 GPa and a temperature of 800 K, using an external heated diamond anvil cell and diffraction using X-rays from a synchrotron source. The experiments were conducted under quasi-hydrostatic condition, using neon as a pressure transmitting medium. The experimental P-V-T data were fitted to a thermal-pressure model with the isothermal bulk modulus at room temperature K _T0 = 157 GPa, (?K _TO /?P) _T =4, (?K _T /?T) _P =-2.7(3) × 10^-2 GPa/K, (?K _T /?T) _v =-0.2(2) × 10^-2 GPa/K and the Anderson-Grüneisen parameter δ _T =4.3(5) above the Debye temperature. The data were also fitted to the Mie-Grüneisen thermal equation of state. The least-squares fit yields the Debye temperature θ _DO = 500(20) K, the Grüneisen parameter γ ₀=1.50(5), and the volume dependence q=1.1(5). Both thermal-pressure models give consistent P-V-T relations for magnesiowüstite to 140 GPa and 4000 K. The P-V-T relations for magnesiowüstite were also calculate by using a modified high-temperature Birch-Murnaghan equation of state with a δ _t of 4.3. The results are consistent with those calculated by using the thermal-pressure model and the Mie-Grüneisen relation to 140 GPa and 3000 K.     

P–V–T equations of state of MgO and thermodynamics

A simplest equation within the framework of the Mie-Grüneisen–Einstein approach is considered. Pressure estimation values are presented that are derived by conventional arithmetic and algebraic calculations as a function of temperature and volume. The equation under consideration complies with the Mie-Grüneisen–Debye model at high temperature. Different versions of an equation of state (EoS) of MgO proposed by Speziale et al. (J Geophys Res 106B:515–528, 2001) as a pressure standard at high temperatures are subject to analyses. In the literature, at least four versions of Speziale et al. EoS of MgO are discussed; the discrepancy between them reaching a few GPa at T > 2,000 K and P > 100 GPa. Our analyses of these equations suggest that the volume dependence of the Debye temperature is accepted arbitrarily and does not agree with the definition of the Grüneisen parameter, γ = −(∂lnΘ/∂lnV) _T . Pressure as a function of temperature and volume in the Mie-Grüneisen–Einstein approach or the Gao pressure calculator can be used to estimate true pressure at compression x = V/V ₀ < 1 with the Speziale et al. EoS of MgO.     

Appearance of the nonlinearity from the nonlocality in diffusion through multiscale fractured porous media

We shall consider diffusion or single-phase flow in a multiscale porous medium which represents an infinite set of self-similar double-porosity media. At each scale, the medium consists of a highly permeable network of connected channels and low-permeable blocks. The characteristic scale of heterogeneity is ε at the highest level of hierarchy, wherein ε is a small parameter. The ratio between the channel and block permeability at each scale is ε ². The process analyzed is described using a diffusion equation with an oscillating multiscale diffusion parameter. The macroscale behavior is of interest. The transition to the macroscale is performed by means of the two-scale homogenization procedure. One step of averaging at each level of hierarchy leads to the appearance of the memory terms in the averaged equation. The successive averaging steps lead to progressive memory accumulation, so at each step of averaging, the macroscale model changes its type, and even the result of the second step is unknown a priori. The objective was to determine the macroscopic limit model for the infinite number of scales. By the method of induction, we obtained the macroscale model for an arbitrary number of scales and its limit for the infinite hierarchy. The limit model represents the system of two equations with memory terms. The kernel of the memory operator is the solution of a nonlinear integro-differential equation. Its solution is obtained through Laplace transform.     

Nonlinear two-point flux approximation for modeling full-tensor effects in subsurface flow simulations

Subsurface flow models can exhibit strong full-tensor anisotropy due to either permeability or grid nonorthogonality effects. Upscaling procedures, for example, generate full-tensor effects on the coarse scale even for cases in which the underlying fine-scale permeability is isotropic. A multipoint flux approximation (MPFA) is often needed to accurately simulate flow for such systems. In this paper, we present and apply a different approach, nonlinear two-point flux approximation (NTPFA), for modeling systems with full-tensor effects. In NTPFA, transmissibility (which provides interblock connections) is determined from reference global flux and pressure fields for a specific flow problem. These fields can be generated using either fully resolved or approximate global simulations. The use of fully resolved simulations leads to an NTPFA method that corresponds to global upscaling procedures, while the use of approximate simulations gives a method corresponding to recently developed local–global techniques. For both approaches, NTPFA algorithms applicable to both single-scale full-tensor permeability systems and two-scale systems are described. A unified framework is introduced, which enables single-scale and two-scale problems to be viewed in a consistent manner. Extensive numerical results demonstrate that the global and local–global NTPFA techniques provide accurate flow predictions over wide parameter ranges for both single-scale and two-scale systems, though the global procedure is more accurate overall. The applicability of NTPFA to the simulation of two-phase flow in upscaled models is also demonstrated.