Temperature-jump induced cation exchange kinetics in (Co<Subscript>0.1</Subscript>Mg<Subscript>0.9</Subscript>)<Subscript>2</Subscript>SiO<Subscript>4</Subscript> olivine: an in situ optical spectroscopic study

In the olivine crystal structure, cations are distributed over two inequivalent octahedral sites, M1 and M2. Kinetics of cation exchange between the two octahedral sites in (Co_0.1Mg_0.9)₂SiO₄ single crystal have been studied in the temperature range from 600 to 800°C by monitoring the time evolution of the absorbance of Co²⁺ ions in M1 or M2 sites using optical spectroscopy after rapid temperature jumps. It was found from such temperature-jump induced relaxation experiments that with increasing temperature the absorbance of Co²⁺ ions in the M1 site decreases while that in the M2 site increases. This indicates a tendency of Co²⁺ cations to populate the M2 site with increasing temperatures and vice versa. The experimental relaxation data can be modeled using a triple exponential equation based on theoretical analysis. Activation energies of 221 ± 4 and 213 ± 10 kJ/mol were derived from relaxation experiments on the M2 site and M1 site, respectively, for the cation exchange processes in (Co_0.1Mg_0.9)₂SiO₄ olivine. Implications for cation diffusion at low temperatures are discussed.     

Structure energies of the alkali feldspars

Structural energetics of the alkali feldspars have been studied using a “lattice” or structure energy model. Electrostatic energies, U _e,for 20 well-refined, non-intergrown alkali feldspars were calculated using Bertaut's (1952) summation procedure and average about ?13,400 kcal/mol; the repulsive energies of the alkali site in each structure (～15 kcal/mol) were calculated using repulsive parameters for K-O and Na-O interactions estimated from bulk modulus data for NaF and KF and the exponential form of the repulsive potential. Using a procedure in which the position of the alkali cation was varied while the oxygen cage was kept fixed, structure energy gradients for the alkali sites of high albite and a hypersolvus Ab₄₂Or₅₈ structure were computed. In both cases, a broad structure energy well, elongated approximately parallel to c and subparallel to the observed split Na positions, was found. In both structures there is a single energy minimum corresponding closely with the observed single alkali positions. Comparison of U _e values for the alkali feldspars with different K/Na ratios shows that intermediate compositions are predicted to be less “stable” than either endmember and that the potassic end-member is predicted to be less “stable” than the sodic one, assuming that all other factors contributiong to the free energies of each phase are approximately the same. Comparison of U _e values for the high albite and low sanidine structures with different Al/Si distributions and a fixed tetrahedral framework indicates that the ordered charge distributions are 63.0 and 54.8 kcal/mol, respectively, more “stable” than the disordered distributions. Smaller, more realistic energy differences were obtained by using U _evalues averaged from four separate calculations with a +3 charge on a different T site in each and with +4 charges on the other T sites. If, in addition, the charges on cations and oxygen are reduced to half their nominal formal charges, in agreement with Pauling's electroneutrality principle and the results of recent molecular orbital calculations on silicates, the predicted electrostatic energy differences are reduced to 3.6 and 1.6 kcal/mol, respectively. These calculations also indicate that the T₁O site in the high albite structure energetically favors Al and that the Al/Si distribution determines the Na position within the alkali site.     

Prediction of Gibbs free energies of formation of minerals of the alunite supergroup

A method for the prediction of Gibbs free energies of formation for minerals belonging to the alunite family is proposed, based on an empirical parameter Δ_GO⁼ M^z+(c) characterizing the oxygen affinity of the cation M^z+. The Gibbs free energy of formation from constituent oxides is considered as the sum of the products of the molar fraction of an oxygen atom bound to any two cations, multiplied by the difference of oxygen affinity Δ_GO⁼ M^z+(c) between any two consecutive cations. The Δ_GO⁼ M^z+(c) value, using a weighing scheme involving the electronegativity of a cation in a specific site (12-fold coordination site, octahedral and tetrahedral) is assumed to be constant. It can be calculated by minimizing the difference between experimental Gibbs free energies (determined from solubility measurements) and calculated Gibbs free energies of formation from constituent oxides. Results indicate that this prediction method gives values within 0.5% of the experimentally measured values. The relationships between Δ_GO⁼ M^z+(alunite) corresponding to the electronegativity of a cation in either dodecahedral sites, octahedral sites or tetrahedral sites and known as Δ_GO⁼ M^z+(aq) were determined, thereby allowing the prediction of the electronegativity of rare earth metal ions and trivalent ions in dodecahedral sites and highly charged ions in tetrahedral sites. This allows the prediction of Gibbs free energies of formation of any minerals of the alunite supergroup (bearing various ions located in the dodecahedral and tetrahedral sites). Examples are given for hydronium jarosite and hindsalite, and the results appear excellent when compared to experimental values.     

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.     

Refinements in a site-mixing model for illites: local electrostatic balance and the quasi-chemical approximation

A quasi-chemical model for illites has been derived, and local electrostatic balance has been added to a random regular solution site-mixing model for illites (Stoessell, 1979). Each model assumes similar order-disorder conditions for both the end-members micas and the solid solution. Thermodynamic properties of illites predicted by the random, electrostatic, and quasi-chemical models are compared as a function of composition. For natural illite compositions, molar entropies of mixing in the electrostatic model are about 1 entropy unit less than those in the random model. Intermediate values are given by the quasi-chemical model. Each model predicts an increased entropy of mixing in dominantly trioctahedral illites as compared to dioctahedral illites. Each model also predicts destabilization of trioctahedral illites using absolute molar exchange energies greater than 2 RT/Z_x, where Z_x is the number of adjacent cation interactions per site in the Xth site class. The most negative free energies of mixing are predicted by the quasi-chemical model. Intermediate values predicted by the random model are apparently the result of error cancellation due to overestimation of both the entropy and enthalpy of mixing.     

Modelling the sorption of Mn(II), Co(II), Ni(II), Zn(II), Cd(II), Eu(III), Am(III), Sn(IV), Th(IV), Np(V) and U(VI) on montmorillonite: Linear free energy relationships and estimates of surface binding constants for some selected heavy metals and actinides

In solution thermodynamics, and more recently in surface chemistry, it is well established that relationships can be found between the free energies of formation of aqueous or surface metal complexes and thermodynamic properties of the metal ions or ligands. Such systematic dependencies are commonly termed linear free energy relationships (LFER). A 2 site protolysis non-electrostatic surface complexation and cation exchange (2SPNE SC/CE) model has been used to model “in house” and literature sorption edge data for eleven elements: Mn(II), Co(II), Ni(II), Zn(II), Cd(II), Eu(III), Am(III), Sn(IV), Th(IV), Np(V) and U(VI) to provide surface complexation constants for the strong sites on montmorillonite. Modelling a further 4 sets of sorption isotherms for Ni(II), Zn(II), Eu(III) and U(VI) provided complexation constants for the weak sites. The protolysis constants and site capacities derived for the 2SPNE SC/CE model in previous work were fixed in all of the calculations. Cation exchange was modelled simultaneously to provide selectivity coefficients. Good correlations between the logarithms of strong ^SK_x−1 and weak ^W1K_x−1 site binding constants on montmorillonite and the logarithm of the aqueous hydrolysis constants ^OHK_x were found which could be described by the following equations: Strong (≡S^SOH) sites:

SlogKX−1=8.1±0.3+(0.90±0.02)log^OHKX     

Application of a new approach to the calculation of electrostatic energies of expanded Di- and trioctahedral micas

The electrostatic lattice energies of expanded and unexpanded micas are calculated starting from a “generic” structure the ionic charges of which are varied. The mode of expansion is to move the layers apart perpendicular to (001), the K⁺ ions remaining midway between the layers. The energy required for expansion is a quadratic function of the layer charge. It is larger when the layer charge is in the octahedral sites (K _x Al_2?x Mg _x Si₄O₁₀(OH)₂) than when it is in the tetrahedral sites (K _x Mg₃Si_4?x Al _x O₁₀(OH)₂). Fluormicas have a slightly larger expansion energy than OH-micas. With the tetrahedral layer charge, dioctahedral micas have a slightly larger expansion energy than trioctahedral micas. This mode of expansion is less favourable than the mode usually adopted, viz. an expansion whereby the K ions divide themselves between the layers. The energy difference increases with the separation distance and is about 60 kJ mol^?1 at 2.5 Å expansion. An intercalated water layer would be necessary to stabilize the K ions in positions midway between the layers.     

Effect of solution saturation state and temperature on diopside dissolution

Steady-state dissolution rates of diopside are measured as a function of solution saturation state using a titanium flow-through reactor at pH 7.5 and temperature ranging from 125 to 175°C. Diopside dissolved stoichiometrically under all experimental conditions and rates were not dependent on sample history. At each temperature, rates continuously decreased by two orders of magnitude as equilibrium was approached and did not exhibit a dissolution plateau of constant rates at high degrees of undersaturation. The variation of diopside dissolution rates with solution saturation can be described equally well with a ion exchange model based on transition state theory or pit nucleation model based on crystal growth/dissolution theory from 125 to 175°C. At 175°C, both models over predict dissolution rates by two orders of magnitude indicating that a secondary phase precipitated in the experiments. The ion exchange model assumes the formation of a Si-rich, Mg-deficient precursor complex. Lack of dependence of rates on steady-state aqueous calcium concentration supports the formation of such a complex, which is formed by exchange of protons for magnesium ions at the surface. Fit to the experimental data yields where the Mg-H exchange coefficient, n = 1.39, the apparent activation energy, E _a = 332 kJ mol^-1, and the apparent rate constant, k = 10^41.2 mol diopside cm^-2 s^-1. Fits to the data with the pit nucleation model suggest that diopside dissolution proceeds through retreat of steps developed by nucleation of pits created homogeneously at the mineral surface or at defect sites, where homogeneous nucleation occurs at lower degrees of saturation than defect-assisted nucleation. Rate expressions for each mechanism (i) were fit to where the step edge energy (α) for homogeneously nucleated pits were higher (275 to 65 mJ m^-2) than the pits nucleated at defects (39 to 65 mJ m^-2) and the activation energy associated with the temperature dependence of site density and the kinetic coefficient for homogeneously nucleated pits (E_{b-homogeneous} = 2.59 × 10^-16 mJ K^-1) were lower than the pits nucleated at defects (E_{b-defect assisted} = 8.44 × 10^-16 mJ K^-1).     

A tabulation and evaluation of ion exchange data on smectites

An extensive search of the literature was made for ion exchange data on smectites. The data, in the form of ion exchange equilibrium constants and free energies of exchange, have been tabulated and evaluated. Equilibrium constants describing monovalent-monovalent and monovalent-divalent types of exchange for the same reaction on the same type of smectite were found to differ by as much as an order of magnitude. While some of the difference can be attributed to variance in experimental procedures, much of the difference appears due to differences in charge densities and effective field strengths of the smectites, which are in turn related to the amount and type of substitution on intercrystalline octahedral and tetrahedral sites.     

Mechanisms of radiation damage of zircons deduced from computer simulation

The radiation resistance of zircon (ZrSiO₄) was comparatively tested with computer simulations of four different sets of parameters of interatomic potentials. The energies of Frenkel pairs (FP) for Zr, Si, and O atoms were calculated using the Mott-Littleton method in approximation of isolated defects. The difference between the FP energies calculated for four potentials and the FP energies obtained ab initio is the least in the one of the four calculated potentials that takes into account the ab initio data for Zircon 3. The formation of an atomic displacement cascade (ADC) after the passage of the initially knocked-out Th atom with energy of 20 keV was investigated using the molecular dynamics method. The number of FP in ADC reaches 5300 to 61 900, depending on the chosen potential. The number of FP at the end of the simulation varies from 480 to 4970. The distribution of internodal oxygen atoms in zircon has been studied. It is shown that within a time (t) interval of 0?C0.1 ps (ballistic stage), the internodal oxygen atoms knocked-out from the initial equilibrium site are predominant (O1 defects). Thereby the Si-O bond is ruptured. The mean displacement of those defects is 2?C3 ?. The probability of their survival is 34?C73% depending on the chosen potential. After t = 0.1 ps (onset of the thermal stage), many SiO₄ tetrahedra in zircon are displaced with formation of a great amount of internodal oxygen atoms, because the Si-O bond is not ruptured. The mean displacement of those O2 defects is 1 ?; the probability of their survival is insignificant: 1.5?C3.0% depending on the chosen potential. The total amount of internodal oxygen atoms consists of O2 defects (19?C25%) and largely of O1 defects. A parameter characterizing that part of the energy of the initially knocked-out atom, which is consumed for FP, has been introduced. The physically acceptable values of this parameter (<1) are obtained only for Zircon 3 potential. The results show that a substantial discrepancy in relative amounts of Si and O atoms with displacements for 0.3?C0.5 ? from the equilibrium site exists for different potentials. In particular, the number of FP in zircon diminishes with decrease in mobility of atoms. It has been established that the lower the mobility of atoms, the lower the number of FP, and the most reasonable consistency with the preset conditions of the computer simulation is provided by Zircon 3 potential.     

Etude des solutions solides des néphélines (Na,K)AlSiO4 et (Na,Rb)AlSiO4

Ion exchange equilibrium of nepheline solid solutions (Na, K)AlSiO₄ and (Na, Rb)AlSiO₄ with hydrothermal solutions has been studied at 600°C and 2000 bars. The behaviour of dilute solid solutions was specially investigated.Na-Rb ion exchange data can be represented satisfactorily by a model taking into account the existence of two different sites in the structure of nepheline. At 600°C Rb atoms substitute almost exclusively for Na atoms situated in the larger sites. On the other hand, this model only partially applies to Na-K ion exchange equilibrium.Finally, the importance of the ion exchange data concerning extremely dilute solutions to calculate activity-composition diagrams is emphasized with special reference to the nepheline solid solutions.     

Ion migration in MgSiO3-perovskite and olivine by molecular dynamics calculations

We applied molecular dynamics (MD) simulations to finding likely paths of atomic migration of the Mg ion in forsterite (Mg₂SiO₄) and the oxygen ion in MgSiO₃-perovskite to better understand atomic diffusion in minerals. Our simulations show that there exist two routes of Mg migration in the forsterite structure, that is, paths between the M1 and M2 sites and between the M1 and M1 sites. In the MgSiO₃-perovskite structure, some oxygen ions migrate to the next sites all together through the O1 vacant site showing co-operative movements. The O ions are relatively mobile mainly along the b axis in the perovskite structure. Meta-stable sites are often present between a stable site and another stable site on atomic migration. In spite of many assumptions, our MD simulations may show likely paths of atomic migration in crystal.     

Ligand field theory and inter- and intracrystalline cation distribution of transition elements in minerals and related inorganic compounds

Many independent investigations have shown, that the ligand field stabilization energy LFSE has, in addition to other factors such as ionic size, site distortion, covalency, respectively, an important influence on the distribution of transition elements between different coexisting minerals as well as between different, crystallographic sites within the same mineral. A transition element prefers or is enriched in that mineral or that lattice position within a mineral, in which its LFSE has its maximum value. Principally, the LFSE of transition metal ions can be evaluated from the absorption spectra in the visible and near infrared parts of the electromagnetic spectrum. In the present paper, the influence of the LFSE on the polyhedral distortion, the phase stability, the intra-as well as the intercrystalline cation distribution of transition metal ions in some well established examples is presented and discussed. The Gibbs free energies of the exchange reactions can be evaluated from the site occupancies and used as a measure for the site preference. Deviations from a pure ionic model are explained on the basis of MO-theory and covalent bonding and other crystal chemical effects.     

Strong site preference of Co2+ in olivine,Co1.10Mg0.90SiO4

The crystal structure and site preference of Co²⁺ in a synthetic Co_1.10Mg_0.90SiO₄ olivine have been determined from single crystal X-ray diffraction data collected on an automatic diffractometer. The R factor is 0.044 for 612 reflections. The site occupancies are: Ml site: Co 0.730±0.006; Mg 0.270; M2 site: Co 0.370, Mg 0.630. The Gibbs free energy change, ΔG° for the ion-exchange reaction between M1 and M2 sites is ?4.06 kcals/mole, assuming ideal mixing at each set of sites. This energy may be called ‘site preference energy’ of Co²⁺ in olivine. The strong preference of Co²⁺ for the M1 site can be quantitatively explained by two competing forces: preference of ions larger than Mg²⁺ for the M2 site and stronger covalent bonding of transition metal ions at the M1 site. For Fe²⁺, Mg²⁺, these two effects nearly neutralize each other, explaining the lack of considerable cation-ordering in Fe-Mg olivines.     

莱河矿的超结构和低温穆斯堡尔谱的对比研究

本文进行了莱河矿3C超结构和4.2K穆斯堡尔谱的对比研究。研究表明。莱河矿的非等效位置M2A+M2C,M2B,M1B,M1A和VB能够分别与Kan等(1985)测定的莱河矿穆斯堡尔谱的吸收双峰A,B,C,D和E对应,不仅解决了超结构位置和吸收双峰之间的对应,而且圆满解释了吸收双峰A:B和C:D的强度比为2:1的关系。另外,还利用莱河矿超结构的资料讨论了莱河矿的反铁磁性内部作用。     

Dissolution of silica from montmorillonite: effect of solution chemistry

The rate of silica removal from two montmorillonites (Chambers and Polkville) has been measured as a function of time, temperature, solution composition, and exchange ion on the clay. Silica removal rate increased with temperature from 200 to 350°C, decreased with time, and could be approximated initially by a parabolic rate law. Solution composition influenced silica removal rate by determining the exchange population of the clay; silica removal is most rapid when K-exchange ions are present. Thus increasing the concentration of K⁺ accelerated silica removal, whereas increasing the concentration of Na⁺, Ca²⁺, and Mg²⁺ inhibited silica removal. Activation energies for silica removal range from 5 to 10 kcal/mol. The largest values are associated with the largest concentrations of inhibitor ions in solution. Activation energies of this magnitude suggest that the rate-limiting step for silica removal is transport through a hydrated, expanded interlayer space. Application of experimental results to diagenesis in moderately to deeply buried sediments suggests that K⁺ uptake by montmorillonite may precede and accelerate illite formation.     

Acceleration of multiply charged ions of the anomalous cosmic-ray component at the heliosphere boundary

The formation of the energy spectra of heavy ions at the front of a parallel shock is considered taking into account ionization and recombination during the acceleration. An analytic solution for ions with three possible charge states is obtained and applied to the acceleration of the anomalous cosmic-ray component at the boundary of the heliosphere. In addition, a more general numerical model for such acceleration at a spherical shock front is developed and used to obtain the energy dependence of the mean charges for C, N, O, Ne, Si, S, Ar, and Fe ions. The model implies that highly excited ions begin to dominate over ions with low charges at energies above 1 MeV/nucleon, in agreement with observational data.     

Optical absorption and electron spin resonance in blue and green natural beryl

A comparative study of blue and green beryl crystals (from the region of Governador Valadares, Minas Gerais, Brazil) using electron paramagnetic resonance (EPR) and optical absorption (OA) spectroscopy is reported. The EPR spectra show that Fe³⁺ in blue beryl occupies a substitutional Al³⁺ site and in green beryl is localized in the structural channels between two O₆ planes. On the other hand the infrared spectra show that the alkali content in the blue beryl is mostly at substitutional and/or interstitial sites and in green beryl is mostly in the structural channels. The OA spectra show two types of Fe²⁺. Thermal treatments above 200° C in green beryl cause the reduction of Fe³⁺ into Fe²⁺ accompanied by a change of color to blue. The blue beryl color does not change on heating. The kinetics of the thermal conversion of Fe³⁺ into Fe²⁺ is composed of two first order processes; the first one has an activation energy ΔE ₁=0.30 eV and the second one has an activation energy ΔE ₂=0.46 eV.