Distribution coefficients of major and trace elements; fractional crystallization in the alkali basalt series of Chaîne des Puys (Massif Central,France)

Major and seventeen trace element distribution coefficients between main phenocrysts (olivine, clinopyroxene, amphibole, mica, feldspars and Fe-Ti oxides) and groundmass have been measured in the alkali basalt suite of Chaîne des Puys (Massif Central, France). The suite appears to be a well behaved crystal fractionation series. We pinpoint key elements whose behavior is closely related to the appearance or disappearance of specific crystal phases in the fractionation process. Ta, for instance, clearly indicates the role of hydrous silicates (amphiboles and micas). Distribution coefficients are shown to vary systematically along the differentiation trend. Significantly the hygromagmaphile tendency (Treuilet al., 1979) of U, Th, Ta and La is variable along the series.The mass balance equations,

$\text{D}{}^{\mathrm{i}}\text{=}\text{∑}\text{;}\text{x}{}_{\mathrm{j}}\text{D}{}_{\mathrm{j}}{}^{\mathrm{ii}}$

where Dⁱ and D_jⁱ are the bulk and mineral/liquid distribution coefficients respectively, and x_j the weight fractions of the fractionating phases, are solved by least square resolution of the overdetermined system, taking into account the analytical errors on data. The solution applied to the Chaîne des Puys suite leads to a coherent and quantitative model of the fractional crystallization process. The suite has apparently evolved in three stages. Each stage is characterized by constant bulk distribution coefficients and a specific mineral assemblage. Amphibole fractionation plays an important role in the early stages. Some intensive parameters (T, ? ?_O2, P_H2O) as well as f (weight fraction of residual liquid) are also estimated.     

Investigations of an intrusive contact,northwest Nelson,New Zealand—II. Diffusion of radiogenic and excess 40Ar in hornblende revealed by 40Ar39Ar age spectrum analysis

The Rameka Gabbro, emplaced 367 Ma ago, experienced a well documented reheating on intrusion of the Separation Point Batholith 114 Ma ago. ${}^{40}\text{Ar}{}^{39}\text{Ar}$ age spectrum analyses of hornblende from the Rameka Gabbro show diffusion gradients which provide information on the ⁴⁰Ar boundary concentration during reheating.Three samples of hornblende exhibit age spectra that conform to a model of ⁴⁰Ar loss by diffusion, implying a zero ⁴⁰Ar boundary concentration during heating. The calculated ⁴⁰Ar loss from these samples, together with a model of heat flow in the aureole, provide estimates of diffusion coefficients of ⁴⁰Ar in Mg-rich hornblende which correspond to an activation energy, E, of ~60 kcal-mol^?1 and a frequency factor. D₀, of ~ 10^?3 cm²-sec^?1. When combined with laboratory diffusion results, these data yield a well defined diffusion law (E = 63.3 ± 1.7 kcal-mol^?1, $\text{D}{}_0\text{= 0.022}{}^{\mathrm{+0.048}}{}_{\mathrm{?0.010}}\text{cm}{}^2\text{-}\text{sec}{}^{\mathrm{?1}}$).The age spectra of the eight other samples record steep gradients of excess ⁴⁰Ar over the first few percent of gas release. Although this effect causes high apparent conventional K-Ar ages, the plateau segments of many sampes still record the crystallization age of 367 ± 5 Ma. These measurements show that the excess ⁴⁰Ar phase developed locally in the intergranular regions of the gabbro, following intrusion of the batholith. on time scales that varied from 10⁴ to 10⁶years. The minimum average ${}^{40}\text{Ar}{}^{36}\text{Ar}$ ratio of this component was found to be 1300 ± 400. The partial pressure of Ar was at least 10^?2 bars in some places.A single ${}^{40}\text{Ar}{}^{39}\text{Ar}$ age spectrum analysis of plagioclase reveals a ‘saddle-shaped” release pattern with a minimum at 140 Ma.In conjunction with theoretical diffusion models and a diffusion law, ${}^{40}\text{Ar}{}^{39}\text{Ar}$ age spectrum analysis of hornblende that has experienced a post-crystallization heating can provide close estimates of the maximum temperature of the thermal event as well as both age of crystallization and reheating.     

The effect of pressure on the solubility of minerals in water and seawater

The effect of presure on the solubility of minerals in water and seawater can be estimated from In

$\text{(}\text{K}{}^{\mathrm{P}}{}_{\mathrm{sp}}\text{K}{}^0{}_{\mathrm{sp}}\text{) +}\text{(?ΔVP + 0.5ΔKP}{}^2\text{)}\text{RT}$

where the volume (ΔV) and compressibility (ΔK) changes at atmospheric pressure (P = 0) are given by

$\text{ΔV =}\text{V}\text{?}\text{(M}{}^{\mathrm{+}}\text{, X}{}^{\mathrm{?}}\text{) ?}\text{V}\text{?}\text{[MX(s)]ΔK =}\text{K}\text{?}\text{(M}{}^{\mathrm{+}}\text{, X}{}^{\mathrm{?}}\text{) ?}\text{K}\text{?}\text{[MX(s)]}$

Values of the partial molal volume ($\text{V}\text{?}$) and compressibilty ($\text{K}\text{?}$) in water and seawater have been tabulated for some ions from 0 to 50°C. The compressibility change is quite large (~10 × 10^?3 cm³ bar^?1 mol^?1) for the solubility of most minerals. This large compressibility change accounts for the large differences observed between values of ΔV obtained from linear plots of In K_sp versus P and molal volume data (Macdonald and North, 1974; North, 1974). Calculated values of $\text{K}{}^{\mathrm{P}}{}_{\mathrm{sp}}\text{K}{}^{\mathrm{o}}{}_{\mathrm{sp}}$ for the solubility of CaCO₃, SrSO₄ and CaF₂ in water were found to be in good agreement with direct measurements (Macdonald and North, 1974). Similar calculations for the solubility of minerals in seawater are also in good agreement with direct measurements (Ingle, 1975) providing that the surface of the solid phase is not appreciably altered.     

Distribution coefficients of Eu and Sr for plagioclase-liquid and clinopyroxene-liquid equilibria in oceanic ridge basalt: an experimental study

The distribution coefficients of Eu and Sr for plagioclase-liquid and clinopyroxene-liquid pairs as a function of temperature and oxygen fugacity were experimentally investigated using an oceanic ridge basalt enriched with Eu and Sr as the starting material. Experiments were conducted between 1190° and 1140°C over a range of oxygen fugacities between 10^?8 and 10^?14 atm.The molar distribution coefficients are given by the equations: log^PL_Sr = 7320/T ? 4.62logK^CPX_Sr = 18020/T ? 13.10. Similarly, the weight fraction distribution coefficients are given by the equations: logD^PL_Sr = 6570/T ? 4.30logD^CPX_Sr = 18434/T ? 13.62.Although the mole fraction distribution coefficients have a smaller dependence on bulk composition than do the weight fraction distribution coefficients, they are not independent of bulk composition, thereby restricting the application of these experimental results to rocks similar to oceanic ridge basalts in bulk composition.Because the Sr distribution coefficients are independent of oxygen fugacity, they may be used as geothermometers. If the temperature can be determined independently — for example, with the Sr distribution coefficients, the Eu distribution coefficients may be used as oxygen geobarometers. Throughout the range of oxygen fugacities ascribed to terrestrial and lunar basalts, plagioclase concentrates Eu but clinopyroxene rejects Eu.     

The ionization of acids in estuarine waters

The stoichiometric, $\text{K}{}_{\mathrm{HA}}{}^1$, and apparent, K'_HA, constants for the ionization of a number of weak acids (NH₄⁺, HSO₄^?, HF, H₂O, B(OH)₃, H₂CO₃, HCO₃^?, H₃PO₄, H₂PO₄^?, HPO₄², H₃AsO₄ H₂AsO₄^? and HAsO₄^2?) in seawater at 25°C diluted with water have been fitted to equations of the form (Millero, 1979). In $\text{K}{}_{\mathrm{HA}}{}^1\text{= In K}{}_{\mathrm{HA}}\text{+ AS}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{+ BS}$ where In K_HA is the thermodynamic constant in water, S is the salinity, A and B are adjustable parameters. The validity of this equation in estuarine waters has been examined by using an ion pairing model (Millero and Schreiber, 1981). The calculated values of $\text{K}{}_{\mathrm{HA}}{}^1$ and K'_HA at S = 35%. are in good agreement with the measured values for all the systems examined. The equation used to extrapolate the measured values to pure water K_HA predicted values that agreed with those determined by using the ion pairing model. The exception was the ionization of HPO₄^2? due to the strong interactions of Ca²⁺ and Mg²⁺ with PO₄^3?. The differences in the predicted values of $\text{K}{}_{\mathrm{HA}}{}^1$ in seawater diluted with pure water and average river water were very small for all the acids except HPO₄^2? (the maximum ΔpK = 0.96 in average river water). The larger difference in the $\text{K}{}_{\mathrm{HA}}{}^1$ for HPO₄^2? in river waters is due to the strong interactions of Ca²⁺ and PO₄^3?.     

Experimental hydrogen isotope studies—I. Systematics of hydrogen isotope fractionation in the systems epidote-H2O,zoisite-H2O and AlO(OH)-H2O

$\text{H}\text{D}$ Fractionation factors between epidote minerals and water, and between the AlO(OH) dimorphs boehmite and diaspore and water, have been determined between 150 and 650°C. Small water mineral ratios were used to minimise the effect of incongruent dissolution of epidote minerals. Waters were extracted and analysed directly by puncturing capsules under vacuum. Hydrogen diffusion effects were eliminated by using thick-walled capsules.$\text{H}\text{D}$ Exchange rates are very fast between epidote and water (and between boehmite and water), complete exchange taking only minutes above 450°C but several months at 250°C. Exchange between zoisite and water (and between diaspore and water) is very much slower, and an interpolation method was necessary to determine fractionation factors at 450 and below.For the temperature range 300–650°C, the $\text{H}\text{D}$ equilibrium fractionation factor (α^e) between epidote and water is independent of temperature and Fe content of the epidote, and is given by 1000 In α_epidote-H2O^e = ?35.9 ± 2.5, while below 300°C 1000 In , with a ‘cross-over’ estimated to occur at around 185°C. By contrast, zoisite-water fractionations fit the relationship 1000 In .All studied minerals have hydrogen bonding. Fractionations are consistent with the general relationship: the shorter the O-H -- O bridge, the more depleted is the mineral in D.On account of rapid exchange rates, natural epidotes probably acquired their H-isotope compositions at or below 200°C, where fractionations are near or above 0%.; this is in accord with the observation that natural epidotes tend to concentrate D relative to other coexisting hydrous minerals.     

The solubility of noble gases in water and in NaCl brine

A direct-sampling, mass-spectrometric technique has been used to measure simultaneously the solubilities of He, Ne, Ar, Kr, and Xe in fresh water and NaCl brine (0 to 5.2 molar) from 0° to 65 °C, and at 1 atm total pressure of moist air. The argon solubility in the most concentrated brines is 4 to 7 times less than in fresh water at 65 °C and 0°C, respectively. The salt effect is parameterized using the Setschenow equation.

$\text{ln}\text{[}\text{β}{}^{\mathrm{i}}{}_{\mathrm{o}}\text{(T)}\text{β}{}^{\mathrm{i}}\text{(T)}\text{= MK}{}^{\mathrm{i}}{}_{\mathrm{M}}\text{(T)}$

where M is NaCl moiarity, βⁱ_o(T) and βⁱ(T) the Bunsen solubility coefficients for gas i in fresh water and brine, and Kⁱ_M(T) the empirical salting coefficient. Values of Kⁱ_M(T) are calculated using volumetric concentration units for noble gas and NaCl content and are independent of NaCl molarity. Below about 40°C, temperature coefficients of all Kⁱ_M are negative. The value of K^He_M is a minimum at 40°C. K^Ar_M decreases from about 0.40 at 0°C to 0.28 at 65 °C. The absolute magnitudes of the differences in salting coefficients (relative to K^Ar_M) decrease from 0° to 65°C. Over the range of conditions studied, all noble gases are salted out, and K^He_M ? K^Ne_M < K^Ar_M < K^Kr_M < K^Xe_M.From the solubility data, we calculated $\text{Δ}\text{G}{}^0{}_{\mathrm{tr}}$, $\text{Δ}\text{S}{}^0{}_{\mathrm{tr}}$, $\text{Δ}\text{H}{}^0{}_{\mathrm{tr}}$ and $\text{Δ}\text{C}{}^{\mathrm{O}}{}_{\mathrm{p,tr}}$ for the transfer of noble gases from fresh water to 1 molar NaCl solutions. At low temperatures $\text{Δ}\text{S}{}^0{}_{\mathrm{tr}}$, is positive, but decreases and becomes negative at temperatures ranging from about 25°C for He to 45°C for Xe. At low temperatures, the dissolved electrolyte apparently interferes with the formation of a cage of solvent molecules about the noble gas atom. At higher temperatures, the local environment of the gas atom in the brine appears to be slightly more ordered than in pure water, possibly reflecting the longer effective range of the ionic fields at higher temperature.The measured solubilities can be used to model noble gas partitioning in two-phase geothermal systems at low temperatures. The data can also be used to estimate the temperature and concentration dependence of the salt effect for other alkali halides. Extrapolation of the measured data is not possible due to the incompletely-characterized minima in the temperature dependence of the salting coefficients. The regularities in the data observed at low temperatures suggest relatively few high-temperature data will be required to model the behavior of noble gases in high-temperature geothermal brines.     

Prediction of Gibbs free energies of calcite-type carbonates and the equilibrium distribution of trace elements between carbonates and aqueous solutions

A linear correlation exists between the standard Gibbs free energies of formation of calcite-type carbonates (MCO3) and the corresponding conventional standard Gibbs free energies of formation of the aqueous divalent cations (M2+) at 25 °C and 1 bar ΔGMCO30 = m(ΔGf,M2+0) ? 141,200 cal · mole?1 where m is equal to 0.9715. This relationship enables prediction of the standard free energies of formation of numerous hypothetical carbonates with the calcite structure. Associated uncertainties typically range from about ± 250 to 600 cal · mole?1. An important consequence of the above correlation is that the thermodynamic equilibrium constant for the distribution of two trace elements M and N between carbonate mineral and aqueous solution at 25 °C and 1 bar is proportional to the free energy difference between the corresponding two aqueous ions: In Combination of predicted standard free energies, entropies and volumes of carbonate minerals at 25°C and 1 bar with standard free energies of aqueous ions and the equation of state in Helgesonet al. (1981) enables prediction of the thermodynamic equilibrium constant for trace element distribution between carbonates and aqueous solutions at elevated temperatures and pressures. Interpretation of the thermodynamic equilibrium constant in terms of concentration ratios in the aqueous phase is considerably simplified if pairs of divalent trace elements are considered that have very similar ionic radii (e.g., $\text{Sr}{}^{\mathrm{2+}}\text{Pb}{}^{\mathrm{2+}}$, $\text{Mg}{}^{\mathrm{2+}}\text{Zn}{}^{\mathrm{2+}}$). In combination with data for the stabilities of complex ions in aqueous solutions, the above calculations enable useful limits to be placed on the concentrations of trace elements in hydrothermal solutions.     

The thermal significance of potassium feldspar K-Ar ages inferred from 40Ar39Ar age spectrum results

${}^{40}\text{Ar}{}^{39}\text{Ar}$ age spectrum analyses of three microcline separates from the Separation Point Batholith, northwest Nelson, New Zealand, which cooled slowly (~5°C-Ma^?1) through the temperature zone of partial radiogenic ⁴⁰Ar accumulation are characterized by a linear age increase over the first 65 percent of gas release with the lowest ages (~80 Ma) corresponding to the time that the samples cooled below about 100°C. The last 35 percent of ³⁹Ar released from the microclines yields plateau ages (103,99 and 93 Ma) which reflect the different bulk mineral ages, and correspond to cooling temperatures between about 130 to 160°C. Theoretical calculations confirm the likelihood of diffusion gradients in feldspars cooling at rates ≤5°C-Ma^?1. Diffusion parameters calculated from the ³⁹Ar release yield an activation energy, E = 28.8 ± 1.9 kcal-mol^?1, and a frequency factor/grain size parameter, $\text{D}{}_0\text{l}{}^2\text{= 5.6}{}_{\mathrm{?3.9}}{}^{\mathrm{+14}}\text{sec}{}^{\mathrm{?1}}$. This Arrhenius relationship corresponds to a closure temperature of 132 ± 13°C which is very similar to the independently estimated temperature. From the observed diffusion compensation correlation, this $\text{D}{}_0\text{l}{}^2$ implies an average diffusion half-width of about 3 μm, similar to the half-width of the perthite lamellae in the feldspars. The range in microcline K-Ar ages from the Separation Point Batholith is the result of relatively small temperature differences within the pluton during cooling. Comparison of the diffusion laws determined for microcline with those for anorthoclases and other homogeneous K-feldspars (E = 40 to 52 kcal-mol^?1) reveals that Ar diffusion is more highly temperature dependent in the disordered structural state than in the ordered structural state. Previously published U-shaped age spectra are probably the result of the superimposition of excess ⁴⁰Ar upon diffusion profiles of the kind described here.     

The effect of ionic interactions on the oxidation of metals in natural waters

The effect of ionic interactions of the major components of natural waters on the oxidation of Cu(I) and Fe(II) has been examined. The various ion pairs of these metals have been shown to have different rates of oxidation. For Fe(II), the chloride and sulfate ion pairs are not easily oxidized. The measured decrease in the rate constant at a fixed pH in chloride and sulfate solutions agrees very well with the values predicted. The effect of pH (6 to 8) on the oxidation of Fe(II) in water and seawater have been shown to follow the rate equation

$\text{-d in [Fe(II)]/dt = k}{}_1\text{β}{}_1\text{α}{}_{\mathrm{Fe}}\text{/[H}{}^{\mathrm{+}}\text{] + k}{}_2\text{β}{}_2\text{α}{}_{\mathrm{Fe}}\text{/[H}{}^{\mathrm{+}}\text{]}{}^2$

where k₁ and k₂ are the pseudo first order rate constants, β₁ and β₂ are the hydrolysis constants for Fe(OH)⁺ and Fe(OH)⁰. The value of α_FE is the fraction of free Fe²⁺. The value of k₁ (2.0 ±0.5 min^?1) in water and seawater are similar within experimental error. The value of k₂ (1.2 × 10⁵ min^?1) in seawater is 28% of its value in water in reasonable agreement with predictions using an ion pairing model.For the oxidation of Cu(I) a rate equation of the form

$\text{?d ln [Cu(I)]/dt = k}{}_0\text{α}{}_{\mathrm{Cu}}\text{+ k}{}_1\text{β}{}_1\text{α}{}_{\mathrm{Cu}}\text{[Cl]}$

was found where k₀ (14.1 sec^?1) and k₁ (3.9 sec^?1) are the pseudo first order rate constants for the oxidation of Cu⁺ and CuCl⁰, β₁ is the formation constant for CuCl⁰ and α_Cu is the fraction of free Cu⁺. Thus, unlike the results for Fe(II), Cu(I) chloride complexes have measurable rates of oxidation.     

Revised values for the Gibbs free energy of formation of [Al(OH)4 aq−], diaspore,boehmite and bayerite at 298.15 K and 1 bar,the thermodynamic properties of kaolinite to 800 K and 1 bar,and the heats of solution of several gibbsite samples

Solution calorimetric measurements compared with solubility determinations from the literature for the same samples of gibbsite have provided a direct thermochemical cycle through which the Gibbs free energy of formation of [Al(OH)_{4 aq}^?] can be determined. The Gibbs free energy of formation of [Al(OH)_{4 aq}^?] at 298.15 K is ?1305 ± 1 kJ/mol. These heat-of-solution results show no significant difference in the thermodynamic properties of gibbsite particles in the range from 50 to 0.05 μm.The Gibbs free energies of formation at 298.15 K and 1 bar pressure of diaspore, boehmite and bayerite are ?9210 ± 5.0, ?918.4 ± 2.1 and ?1153 ± 2 kJ/mol based upon the Gibbs free energy of [A1(OH)_{4 aq}^?] calculated in this paper and the acceptance of ?1582.2 ± 1.3 and ?1154.9 ± 1.2 kJ/mol for the Gibbs free energy of formation of corundum and gibbsite, respectively.Values for the Gibbs free energy formation of [Al(OH)_{2 aq}⁺] and [AlO_{2 aq}^?] were also calculated as ?914.2 ± 2.1 and ?830.9 ± 2.1 kJ/mol, respectively. The use of [AlC_{2 aq}^?] as a chemical species is discouraged.A revised Gibbs free energy of formation for [H₄SiO_4aq⁰] was recalculated from calorimetric data yielding a value of ?1307.5 ± 1.7 kJ/mol which is in good agreement with the results obtained from several solubility studies.Smoothed values for the thermodynamic functions C_P⁰, ($\text{H}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, $\text{(}\text{G}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, S_T⁰ - S₀⁰, $\text{ΔH}{}_{\mathrm{?,298}}{}^0$ kaolinite are listed at integral temperatures between 298.15 and 800 K. The heat capacity of kaolinite at temperatures between 250 and 800 K may be calculated from the following equation: C_P⁰ = 1430.26 ? 0.78850 T + 3.0340 × 10^?4T² ?1.85158 × 10^?4T²$\text{1}\text{2}\text{+ 8.3341 × 10}{}^6\text{T}{}^{\mathrm{?2}}$.The thermodynamic properties of most of the geologically important Al-bearing phases have been referenced to the same reference state for Al, namely gibbsite.     

Complex formation in the ternary system Mg(II)-CO2-H2O

The carbonato and hydrogencarbonato complexes of Mg²⁺ were investigated at 25 and 50° in solutions of the constant ClO₄^? molality (3 M) consisting preponderantly of NaClO₄. The experimental data could be explained assuming the following equilibria: Mg²⁺ + CO_2B + H₂O ag MgHCO⁺₃ + H⁺, $\text{log}{}^1\text{β}{}_1\text{= ?7.64}{}_4\text{± 0.01}{}_7\text{(25°), ?7.46}{}_2\text{± 0.01}{}_1\text{(50°)}$, Mg²⁺ + 2 CO_2g + 2 H₂Oag Mg(HCO₃)⁰₂ ± 2 H⁺, $\text{log}{}^1\text{β}{}_2\text{= ?15.00 ± 0.14 (25°)}$, ?15.37 ± 0.39 (50°), Mg²⁺ + CO_2g + H₂Oag MgCO⁰₃ + 2 H⁺, $\text{log}{}^1\text{k}{}_1\text{= ?15.64 ± 0.06 (25°)}$,?15.23 ± 0.02 (50°), with the assumption γ_MgCO3⁰ = γ_Mg(HCO3)⁰2, ΔG⁰(I = 0) for the reaction MgCO⁰₃ + CO_2g + H₂O = Mg(HCO₃)⁰₂ was estimated to be ?3.9₁ ± 0.8₆ and 0.6 ± 2.4 kJ/mol at 25 and 50°C, respectively. The abundance of carbonate linked Mg(II) species in fresh water systems is discussed.     

Kiglapait Geochemistry III: Potassium and Rubidium

The regular geometry and completeness of the Kiglapait intrusion permit its bulk composition to be obtained by summation, and the composition of successive liquids to be obtained by subtraction. The summations for K and Rb give 1806 and 1.08 ppm, yielding Rfrsol|K/Rb= 1670 for the intrusion, taken as equal to the parent magma. R increases slightly from this initial value to 2000 at the end of crystallization where MgO approaches zero in the rocks. K and Rb are therefore closely coherent and their distribution coefficients can differ only by a small amount in the Kiglapait system.Apparent feldspar/liquid distribution coefficients (D^F/L) can be estimated from detailed plots of feldspar and liquid compositions against F_L. The Kiglapait data imply that these coefficients are linear 1:1 functions of plagioclase composition within experimental error, having values given by D_KF/L = 1.42? X_AnD_RbF/L = 1.13? X_An with minimum values of 0.75 and 0.49, respectively. The ratio $\text{R}{}^{\mathrm{F}}\text{R}{}^{\mathrm{L}}$ lies in the range of 1.53± 0.03 for the plagioclase composition range X_An= 0.34 to 0.67 showing that high-R rocks such as anorthosite crystallized from high-R liquids.The apparent feldspar distribution coefficients are much closer to 1.0 than common literature values. They can be reduced by assuming that the cumulate pile was continuously recharged by the circulating magma until an advanced stage of differentiation was reached, and assuming that alkalies were exchanged to the feldspars from the magma. When such an ‘aquifer recharge’ model is calibrated using olivine-liquid equilibria as a time marker for the liquid, the inferred minimum equilibrium values of the distribution coefficients are $\text{D}{}_{\mathrm{K}}\text{F}\text{L}$= 0.42, $\text{D}{}_{\mathrm{Rb}}\text{F}\text{L}$ = 0.25 at the base of the intrusion. Their variation is given by $\text{D}{}_{\mathrm{K}}\text{F}\text{L}\text{= 1.66?1.88X}{}_{\mathrm{An}}$, $\text{D}{}_{\mathrm{Rb}}\text{F}\text{L}\text{= 1.17?1.41X}{}_{\mathrm{An}}$, The equilibrium values are considered to be appropriate for deducing liquid compositions in plutonic bodies where alkali exchange can be shown or inferred to have been inhibited, such as in small intrusions. The apparent values are considered to be appropriate, even though they may be artificial, for large intrusions similar to the Kiglapait.The bulk K and Rb concentrations in the Kiglapait intrusion are consistent with a plagioclase-rich abyssal tholeiite magma. Clinopyroxene and olivine fractionation in the mantle may contribute to the production of such high-Rmagmas.     

An experimental study of alkali metal distributions in feldspars and micas

K and Rb distributions between aqueous alkali chloride vapour phase (0.7 molar) and coexisting phlogopites and sanidines have been investigated in the range 500 to 800°C at 2000 kg/cm² total pressure.Complete solid solution of RbMg₃AlSi₃O₁₀(OH)₂ in KMg₃AlSi₃O₁₀(OH)₂ exists at and above 700°C. At 500°C a possible miscibility gap between approximately 0.2 and 0.6 mole fraction of the Rb end-member is indicated.Only limited solid solution of Rb AlSi₃O₈ in KAlSi₃O₈ has been found at all temperatures investigated.Distribution coefficients, expressed as $\text{K}{}_{\mathrm{d}}\text{= (}\text{Rb/K}\text{)}$ in solid/(Rb/K) in vapour, are appreciably temperature-dependent but at each temperature are independent of composition for low Rb end-member mole fractions in the solids. The determined $\text{K}{}_{\mathrm{D}}$ values and their approximate Rb end-member mole fraction ($\text{X}{}_{\mathrm{RM}}$) ranges of constancy are summarized as follows: (°C)$\text{T}$$\text{K}{}_{\mathrm{D}}{}^{\mathrm{Phlog/Vap.}}$$\text{X}{}_{\mathrm{RM}}$$\text{K}{}_{\mathrm{D}}{}^{\mathrm{Sandi/Vap.}}$$\text{X}{}_{\mathrm{rm}}$

     

17.

Gibbsite solubility and thermodynamic properties of hydroxy-aluminum ions in aqueous solution at 25°C     

Howard M. May  Philip A. Helmke  Marion L. Jackson 《Geochimica et cosmochimica acta》1979,43(6):861-868

Solubility curves were determined for a synthetic gibbsite and a natural gibbsite (Minas Gerais, Brazil) from pH 4 to 9, in 0.2% gibbsite suspensions in 0.01 M NaNO₃ that were buffered by low concentrations of non-complexing buffer agents. Equilibrium solubility was approached from oversaturation (in suspensions spiked with Al(NO₃)₃ solution), and also from undersaturation in some synthetic gibbsite suspensions. Mononuclear Al ion concentrations and pH values were periodically determined. Within 1 month or less, data from over-and undersaturated suspensions of synthetic gibbsite converged to describe an equilibrium solubility curve. A downward shift of the solubility curve, beginning at pH 6.7, indicates that a phase more stable than gibbsite controls Al solubility in alkaline systems. Extrapolation of the initial portion of the high-pH side of the synthetic gibbsite solubility curve provides the first unified equilibrium experimental model of Al ion speciation in waters from pH 4 to 9.The significant mononuclear ion species at equilibrium with gibbsite are Al³⁺, AlOH²⁺, Al(OH)⁺₂ and Al(OH)^?₄, and their ion activity products are $\text{1K}{}_{50}\text{= 1.29 × 10}{}^8$, $\text{1K}{}_{\mathrm{s1}}\text{= 1.33 × 10}{}^3$, $\text{1K}{}_{\mathrm{s2}}\text{= 9.49 × 10}{}^{\mathrm{?3}}$ and $\text{1K}{}_{\mathrm{s4}}\text{= 8.94 × 10}{}^{\mathrm{?15}}$. The calculated standard Gibbs free energies of formation (ΔG°_f) for the synthetic gibbsite and the A1OH²⁺, Al(OH)⁺₂ and Al(OH)^?₄ ions are ?276.0, ?166.9, ?216.5 and ?313.5 kcal mol^?1, respectively. These ΔG°_f values are based on the recently revised ΔG°_f value for Al³⁺ (?117.0 ± 0.3 kcal mol_?1) and carry the same uncertainty. The ΔG°_f of the natural gibbsite is ?275.1 ± 0.4 kcal mol^?, which suggests that a range of ΔG°_f values can exist even for relatively simple natural minerals.     

18.

Amorphous silica solubilities V. Predictions of solubility behavior in aqueous mixed electrolyte solutions to 300°C     

William L Marshall  Chen-Tung A Chen 《Geochimica et cosmochimica acta》1982,46(2):289-291

Solubilities of amorphous silica in several aqueous electrolyte solutions up to 300°C (Marshall, 1980a; Chen and Marshall, 1982) fitted the Setchénow equation, $\text{log(}\text{s}{}^0\text{s}\text{) = D·m}$ as described earlier (Marshall, 1980b) where s⁰ and s are molal solubilities of silica in pure water and salt solution, respectively, m is the molality of salt, and D is a proportionality constant related to the particular salt and temperature. It is now shown that, to a first approximation, the D parameters for various salts at the same temperature are additive. For instance, D(NaCl) ? D(KCl) = D(NaNO₃) ? D(KNO₃) or D(MgSO₄) = D(MgCl₂) + D(Na₂S0₄) ? 2D(NaCl). It also follows that $\text{(}\text{s}{}_0\text{s}\text{) =}\text{∑}\text{i}\text{(D}{}_{\mathrm{i}}\text{m}{}_{\mathrm{i}}\text{)}$.This additivity principle was used to estimate amorphous silica solubilities in mixed NaCl-Na₂SO₄, NaCl-MgCl₂, NaCl-MgSO₄, Na₂SO₄-MgCl₂, Na₂SO₄-MgSO₄, and MgCl₂-MgSO₄ aqueous solutions up to 300°C. The method produces results that agree reasonably well with experimental values and would be useful for predicting silica solubilities, for example, in seawater and its hydrothermal concentrates and in geothermal energy applications.     

19.

Constantes de formation des complexes hydroxydés de l'aluminium en solution aqueuse de 20 a 70°C     

Yves Couturier  Gil Michard  Gérard Sarazin 《Geochimica et cosmochimica acta》1984,48(4):649-659

Stability constants of hydroxocomplexes of Al(III):Al(OH)²⁺ and A1(OH)₄^? have been measured in the 20–70°C temperature range by reactions involving only dissolved species. The stability constant ${}^1\text{K}{}_1$ of the first complex ion is studied by measuring pH of solutions of aluminium salts at several concentrations. ${}^1\text{β}{}_4$ of aluminate ion is deduced from equilibrium constants of the reaction between the trioxalato aluminium (III) complex ion and Al³⁺ in acid medium, and between the same complex ion and A1(OH)₄^? in alkaline medium. The K values and the associated ΔH are ${}^1\text{K}{}_1\text{= 10}{}^{\mathrm{?5.00}}$ and ΔH₁ = 11.8 Kcal; ${}^1\text{β}{}_4\text{= 10}{}^{\mathrm{?22.20}}$ and ΔH₄ = 42.45 Kcal. These last results are not in agreement with the values of recent tables for $\text{ΔG}{}^0\text{?}$ and $\text{ΔH}{}^0\text{?}$ of Al³⁺ and Al(OH)₄^?. We suggest a consistent set of data for dissolved and solid Al species and for some aluminosilicates.     

20.

Settling velocities of particulate systems, 3. Power series expansion for the drag coefficient of a sphere and prediction of the settling velocity     

F. Concha  A. Barrientos 《International Journal of Mineral Processing》1982,9(2):167-172

The following equation has been previously developed for the drag coefficient of a sphere.

$\text{C}{}_{\mathrm{D}}\text{= C}{}_0\text{[1 + (σ}{}_0\text{/Re}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)]}{}^2$

In this work the authors propose a power series expansion for C₀ in terms of the Reynolds number:

$\text{C}{}_0\text{= 0 284153}\text{Σ}\text{α=0}\text{n}\text{B}{}_{\mathrm{\alpha }}\text{Re}{}^{\mathrm{\alpha }}$

A fifth-order polynomial permits obtaining the drag coefficient and the settling velocity of a sphere, up to a Reynolds number of 3 × 10⁵, with an average relative error of about 2%.     

(°C)T	$\text{K}{}_{\mathrm{D}}{}^{\mathrm{Phlog/Vap.}}$	$\text{X}{}_{\mathrm{RM}}$	$\text{K}{}_{\mathrm{D}}{}^{\mathrm{Sanid/Vap.}}$	$\text{X}{}_{\mathrm{RM}}$
500	$\text{0.64 ± 0.11}$	0–0.2	$\text{0.17 ± 0.04}$	0–0.07
700	$\text{1.11 ± 0.11}$	0–0.2	$\text{0.33 ± 0.04}$	0–0.1
800	$\text{1.28 ± 0.03}$	0–0.2	$\text{0.45 ± 0.06}$	0–0.1

Gibbsite solubility and thermodynamic properties of hydroxy-aluminum ions in aqueous solution at 25°C

Solubility curves were determined for a synthetic gibbsite and a natural gibbsite (Minas Gerais, Brazil) from pH 4 to 9, in 0.2% gibbsite suspensions in 0.01 M NaNO₃ that were buffered by low concentrations of non-complexing buffer agents. Equilibrium solubility was approached from oversaturation (in suspensions spiked with Al(NO₃)₃ solution), and also from undersaturation in some synthetic gibbsite suspensions. Mononuclear Al ion concentrations and pH values were periodically determined. Within 1 month or less, data from over-and undersaturated suspensions of synthetic gibbsite converged to describe an equilibrium solubility curve. A downward shift of the solubility curve, beginning at pH 6.7, indicates that a phase more stable than gibbsite controls Al solubility in alkaline systems. Extrapolation of the initial portion of the high-pH side of the synthetic gibbsite solubility curve provides the first unified equilibrium experimental model of Al ion speciation in waters from pH 4 to 9.The significant mononuclear ion species at equilibrium with gibbsite are Al³⁺, AlOH²⁺, Al(OH)⁺₂ and Al(OH)^?₄, and their ion activity products are $\text{1K}{}_{50}\text{= 1.29 × 10}{}^8$, $\text{1K}{}_{\mathrm{s1}}\text{= 1.33 × 10}{}^3$, $\text{1K}{}_{\mathrm{s2}}\text{= 9.49 × 10}{}^{\mathrm{?3}}$ and $\text{1K}{}_{\mathrm{s4}}\text{= 8.94 × 10}{}^{\mathrm{?15}}$. The calculated standard Gibbs free energies of formation (ΔG°_f) for the synthetic gibbsite and the A1OH²⁺, Al(OH)⁺₂ and Al(OH)^?₄ ions are ?276.0, ?166.9, ?216.5 and ?313.5 kcal mol^?1, respectively. These ΔG°_f values are based on the recently revised ΔG°_f value for Al³⁺ (?117.0 ± 0.3 kcal mol_?1) and carry the same uncertainty. The ΔG°_f of the natural gibbsite is ?275.1 ± 0.4 kcal mol^?, which suggests that a range of ΔG°_f values can exist even for relatively simple natural minerals.     

Amorphous silica solubilities V. Predictions of solubility behavior in aqueous mixed electrolyte solutions to 300°C

Solubilities of amorphous silica in several aqueous electrolyte solutions up to 300°C (Marshall, 1980a; Chen and Marshall, 1982) fitted the Setchénow equation, $\text{log(}\text{s}{}^0\text{s}\text{) = D·m}$ as described earlier (Marshall, 1980b) where s⁰ and s are molal solubilities of silica in pure water and salt solution, respectively, m is the molality of salt, and D is a proportionality constant related to the particular salt and temperature. It is now shown that, to a first approximation, the D parameters for various salts at the same temperature are additive. For instance, D(NaCl) ? D(KCl) = D(NaNO₃) ? D(KNO₃) or D(MgSO₄) = D(MgCl₂) + D(Na₂S0₄) ? 2D(NaCl). It also follows that $\text{(}\text{s}{}_0\text{s}\text{) =}\text{∑}\text{i}\text{(D}{}_{\mathrm{i}}\text{m}{}_{\mathrm{i}}\text{)}$.This additivity principle was used to estimate amorphous silica solubilities in mixed NaCl-Na₂SO₄, NaCl-MgCl₂, NaCl-MgSO₄, Na₂SO₄-MgCl₂, Na₂SO₄-MgSO₄, and MgCl₂-MgSO₄ aqueous solutions up to 300°C. The method produces results that agree reasonably well with experimental values and would be useful for predicting silica solubilities, for example, in seawater and its hydrothermal concentrates and in geothermal energy applications.     

Constantes de formation des complexes hydroxydés de l'aluminium en solution aqueuse de 20 a 70°C

Stability constants of hydroxocomplexes of Al(III):Al(OH)²⁺ and A1(OH)₄^? have been measured in the 20–70°C temperature range by reactions involving only dissolved species. The stability constant ${}^1\text{K}{}_1$ of the first complex ion is studied by measuring pH of solutions of aluminium salts at several concentrations. ${}^1\text{β}{}_4$ of aluminate ion is deduced from equilibrium constants of the reaction between the trioxalato aluminium (III) complex ion and Al³⁺ in acid medium, and between the same complex ion and A1(OH)₄^? in alkaline medium. The K values and the associated ΔH are ${}^1\text{K}{}_1\text{= 10}{}^{\mathrm{?5.00}}$ and ΔH₁ = 11.8 Kcal; ${}^1\text{β}{}_4\text{= 10}{}^{\mathrm{?22.20}}$ and ΔH₄ = 42.45 Kcal. These last results are not in agreement with the values of recent tables for $\text{ΔG}{}^0\text{?}$ and $\text{ΔH}{}^0\text{?}$ of Al³⁺ and Al(OH)₄^?. We suggest a consistent set of data for dissolved and solid Al species and for some aluminosilicates.     

Settling velocities of particulate systems, 3. Power series expansion for the drag coefficient of a sphere and prediction of the settling velocity

The following equation has been previously developed for the drag coefficient of a sphere.

$\text{C}{}_{\mathrm{D}}\text{= C}{}_0\text{[1 + (σ}{}_0\text{/Re}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)]}{}^2$

In this work the authors propose a power series expansion for C₀ in terms of the Reynolds number:

$\text{C}{}_0\text{= 0 284153}\text{Σ}\text{α=0}\text{n}\text{B}{}_{\mathrm{\alpha }}\text{Re}{}^{\mathrm{\alpha }}$

A fifth-order polynomial permits obtaining the drag coefficient and the settling velocity of a sphere, up to a Reynolds number of 3 × 10⁵, with an average relative error of about 2%.