Density calculations for silicate liquids. I. Revised method for aluminosilicate compositions

Equations are developed for calculating the density of aluminosilicate liquids as a function of composition and temperature. The mean molar volume at reference temperature T_r, is given by $\text{V}{}_{\mathrm{r}}\text{= ∑X}{}_{\mathrm{i}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{i}}\text{+ X}{}_{\mathrm{A}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$, where the summation is taken over all oxide components except A1₂O₃, X stands for mole fraction, terms are constants derived independently from an analysis of volume-composition relations in alumina-free silicate liquids, and $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is the composition-dependent apparent partial molar volume of Al₂O₃. The thermal expansion coefficient of aluminosilicate liquids is given by $\text{α = ∑X}{}_{\mathrm{i}}\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}\text{+ X}{}_{\mathrm{A}}\text{}\text{?}\text{ga}{}_{\mathrm{A}}{}^{\mathrm{o}}$, where $\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}$ terms are constants independent of temperature and composition, and $\text{}\text{?}\text{ga}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is a composition-dependent term representing the effect of Al₂O₃ on the thermal expansion. Parameters necessary to calculate the volume of silicate liquids at any temperature T according to V(T) = V_rexp[α(T-T_r)], where T_r = 1400°C have been evaluated by least-square analysis of selected density measurements in aluminosilicate melts. Mean molar volumes of aluminosilicate liquids calculated according to the model equation conform to experimentally measured volumes with a root mean square difference of 0.28 $\text{cc}\text{mole}$ and an average absolute difference of 0.90% for 248 experimental observations. The compositional dependence of $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is discussed in terms of several possible interpretations of the structural role of Al³⁺ in aluminosilicate melts.     

Transfer and exchange equilibria in a portion of the pyroxene quadrilateral as deduced from natural and experimental data

Differences in the chemical composition of metamorphic and igneous pyroxene minerals may be attributed to a transfer reaction, which determines the Ca content of the minerals, and an exchange reaction, which determines the relative Mg:Fe²⁺ ratios. Natural data for associated Ca pyroxene (Cpx) and orthopyroxene (Opx) or pigeonite are combined with experimental data for Fe-free pyroxenes, to produce the following equations for the Cpx slope of the solvus surface: $\text{> 1080°C: T =}\text{1000}\text{(0.468 + 0.246X}{}^{\mathrm{Cpx}}\text{? 0.123 ln (1–2 [Ca]))}$$\text{< 1080°C: T =}\text{1000}\text{(0.054 + 0.608X}{}^{\mathrm{Cpx}}\text{? 0.304 ln (1–2 [Ca]))}$, and the following equation for the temperature-dependence of the Mg-Fe distribution coefficient: $\text{T =}\text{1130}\text{(}\text{ln}\text{K}{}_{\mathrm{p}}\text{+ 0.505)}$, where T is absolute temperature, X is $\text{Fe}{}^{\mathrm{2+}}\text{(Mg + Fe}{}^{\mathrm{2+}}\text{))}$, [Ca] is $\text{Ca}\text{(Ca + Mg + Fe}{}^{\mathrm{2+}}\text{)}$ in Cpx, and K_D is the distribution coefficient, defined as $\text{X}{}^{\mathrm{Opx}}\text{/(1 ? X}{}^{\mathrm{Opx}}\text{) ÷ X}{}_{\mathrm{Cpx}}\text{/(1 ?}{}^{\mathrm{Cpx}}\text{)}$.The transfer and exchange equations form useful temperature indicators, and when applied to 9 sets of well-studied rocks, yield pairs of temperatures that are in good agreement. For example, temperatures obtained for the Bushveld Complex are 1020°C (solvus equation) and 980°C (exchange equation), based on 7 specimens. The uncertainty in these numbers, due to precision and accuracy errors, is estimated to be ±60°.     

The system pargasite-H2O-CO2: a model for melting of a hydrous mineral with a mixed-volatile fluid—I. Experimental results to 8 kbar

The stability of the amphibole pargasite [NaCa₂Mg₄Al(Al₂Si₆))O₂₂(OH)₂] in the melting range has been determined at total pressures (P) of 1.2 to 8 kbar. The activity of H₂O was controlled independently of P by using mixtures of H₂O + CO₂ in the fluid phase. The mole fraction of H₂O in the fluid ($\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$) ranged from 1.0 to 0.2.At P < 4 kbar the stability temperature (T) of pargasite decreases with decreasing $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ at constant P. Above P ? 4 kbar stability T increases as $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ is decreased below one, passes through a T maximum and then decreases with a further decrease in $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$. This behavior is due to a decrease in the H₂O content of the silicate liquid as $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ decreases. The magnitude of the T maximum increases from about 10°C (relative to the stability T for $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{= 1}$) at P = 5 kbar to about 30°C at P = 8 kbar, and the position of the maximum shifts from $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{? 0.6}$ at P = 5 kbar to $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{? 0.4}$ at P = 8 kbar.The H₂O content of liquid coexisting with pargasite has been estimated as a function of at 5 and 8 kbar P, and can be used to estimate the H₂O content of magmas. Because pargasite is stable at low values of $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ at high P and T, hornblende can be an important phase in igneous processes even at relatively low H₂O fugacities.     

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.     

Light hydrocarbons in Red Sea brines and sediments

Light hydrocarbon (C₁-C₃) concentrations in the water from four Red Sea brine basins (Atlantis II, Suakin, Nereus and Valdivia Deeps) and in sediment pore waters from two of these areas (Atlantis II and Suakin Deeps) are reported. The hydrocarbon gases in the Suakin Deep brine (T = ~ 25°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 85‰}$, $\text{CH}{}_4\text{=}\text{~ 71}\text{1}$) are apparently of biogenic origin as evidenced by $\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3$) ratios of ~ 1000. Methane concentrations (6–8 μl/l) in Suakin Deep sediments are nearly equal to those in the brine, suggesting sedimentary interstitial waters may be the source of the brine and associated methane.The Atlantis II Deep has two brine layers with significantly different light hydrocarbon concentrations indicating separate sources. The upper brine (T = ~ 50°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 73‰}$, CH₄ = ~ 155 μl/l) gas seems to be of biogenic origin [$\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3\text{) = ~1100}$], whereas the lower brine (T = ~ 61°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 155‰}$, CH₄ = ~ 120μl/l) gas is apparently of thermogenic origin [$\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3\text{) = ~ 50}$]. The thermogenic gas resulting from thermal cracking of organic matter in the sedimentary column apparently migrates into the basin with the brine, whereas the biogenic gas is produced in situ or at the seawater-brine interface. Methane concentrations in Atlantis II interstitial waters underlying the lower brine are about one half brine concentrations; this difference possibly reflects the known temporal variations of hydrothermal activity in the basin.     

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.     

Etude des inclusions fluides du système N2-CO2 de dolomites et de quartz de Tunisie septentrionale. Données de la microcryoscopie et de l'analyse à la microsonde à effet Raman

Optical and analytical studies were performed on 400 N₂ + CO₂ gas bearing inclusions in dolomites and quartz from Triassic outcrops in northern Tunisia. Other fluids present include brines (NaCl and KCl bearing inclusions) and rare liquid hydrocarbons. At the time of trapping, such fluids were heterogeneous gas + brine mixtures. In hydrocarbon free inclusions the $\text{N}{}_2\text{(N}{}_2\text{+ CO}{}_2\text{)}$ mole ratio was determined using two different non-destructive and punctual techniques: Raman microprobe analysis, and optical estimation of the volume ratios of the different phases selected at low temperatures. In the observed range of compositions, the two methods agree reasonably well.The N₂ + CO₂ inclusions are divided into three classes of composition: (a) $\text{N}{}_2\text{(N}{}_2\text{+ CO}{}_2\text{)}\text{> 0,57}$: Liquid nitrogen is always visible at very low temperature and homogenisation occurs in the range ?151°C to ? 147°C (nitrogen critical temperature) dry ice (solid CO₂) sublimates between ?75°C and ?60°C; (b) $\text{0,20 <}\text{N}{}_2\text{(N}{}_2\text{+ CO}{}_2\text{)}\text{? 0,57}$: liquid nitrogen is visible at very low temperature but dry ice melts on heating; liquid and gas CO₂ homogenise to liquid phase between ?51°C to ?22°C; (c) $\text{N}{}_2\text{(N}{}_2\text{+ CO}{}_2\text{)}\text{? 0,20}$: liquid nitrogen is not visible even at very low temperature (?195°C) and liquid and gas CO₂ homogenise to liquid phase between ?22°C and ?15°C. The observed phases changes are used to propose a preliminary phase diagram for the system CO₂-N₂ at low temperatures.Assuming additivity of partial pressures, isochores for the CO₂-N₂ inclusions have been computed. The intersection of these isochores with those for brine inclusions in the same samples may give the P and T of trapping of the fluids.     

The solubilities of calcite,aragonite and vaterite in CO2-H2O solutions between 0 and 90°C,and an evaluation of the aqueous model for the system CaCO3-CO2-H2O

Calculations based on approximately 350 new measurements (Ca_T-PCO₂) of the solubilities of calcite, aragonite and vaterite in CO₂-H₂O solutions between 0 and 90°C indicate the following values for the log of the equilibrium constants K_C, K_A, and K_V respectively, for the reaction CaCO₃(s) = Ca²⁺ + CO^2?₃: $\text{Log K}{}_{\mathrm{C}}\text{= ?171.9065 ? 0.077993T +}\text{2839.319}\text{T}\text{+ 71.595 log T}$$\text{Log K}{}_{\mathrm{A}}\text{= ?171.9773 ? 0.077993T +}\text{2903.293}\text{T}\text{+71.595 log T}$$\text{Log K}{}_{\mathrm{V}}\text{= ?172.1295 ? 0.077993T +}\text{3074.688}\text{T}\text{+ 71.595 log T}$ where T is in ^oK. At 25°C the logarithms of the equilibrium constants are ?8.480 ± 0.020, ?8.336 ± 0.020 and ?7.913 ± 0.020 for calcite, aragonite and vaterite, respectively.The equilibrium constants are internally consistent with an aqueous model that includes the CaHCO⁺₃ and CaCO⁰₃ ion pairs, revised analytical expressions for CO₂-H₂O equilibria, and extended Debye-Hückel individual ion activity coefficients. Using this aqueous model, the equilibrium constant of aragonite shows no PCO₂-dependence if the CaHCO⁺₃ association constant is between 0 and 90°C, corresponding to the value logK_Cahco⁺3 = 1.11 ± 0.07 at 25°C. The CaCO⁰₃ association constant was measured potentiometrically to be between 5 and 80°C, yielding logK_CaCO⁰3 = 3.22 ± 0.14 at 25°C.The CO₂-H₂O equilibria have been critically evaluated and new empirical expressions for the temperature dependence of K_H, K₁ and K₂ are $\text{log K}{}_{\mathrm{H}}\text{= 108.3865 + 0.01985076T ?}\text{6919.53}\text{T}\text{? 40.45154 log T +}\text{669365.}\text{T}{}^2$, $\text{log K}{}_1\text{= ?356.3094 ? 0.06091964T +}\text{21834.37}\text{T}\text{+ 126.8339 log T —}\text{1684915.}\text{T}{}^2$ and logK₂ = ?107.8871 ? 0.03252849T + 5151.79/T + 38.92561 logT ? 563713.9/T² which may be used to at least 250°C. These expressions hold for 1 atm. total pressure between 0 and 100°C and follow the vapor pressure curve of water at higher temperatures.Extensive measurements of the pH of Ca-HCO₃ solutions at 25°C and 0.956 atm PCO₂ using different compositions of the reference electrode filling solution show that measured differences in pH are closely approximated by differences in liquid-junction potential as calculated by the Henderson equation. Liquid-junction corrected pH measurements agree with the calculated pH within 0.003-0.011 pH.Earlier arguments suggesting that the CaHCO⁺₃ ion pair should not be included in the CaCO₃-CO₂-H₂O aqueous model were based on less accurate calcite solubility data. The CaHCO⁺₃ ion pair must be included in the aqueous model to account for the observed PCO₂-dependence of aragonite solubility between 317 ppm CO₂ and 100% CO₂.Previous literature on the solubility of CaCO₃ polymorphs have been critically evaluated using the aqueous model and the results are compared.     

Phase relations in the system NaCl-KCl-H2O II: Differential thermal analysis of the halite liquidus in the NaCl-H2O binary above 450°c

Thermal analysis of the halite liquidus in the system NaCl-H₂O has been conducted for NaCl mole fractions (X_NaCl) greater than 0.25 (i.e., > 50 wt. % NaCl) at pressures between 0.3 and 4.1 kb and temperatures greater than 450°C. The position of the liquidus was located by differential thermal analysis (DTA) of cooling scans only, as heating scans did not produce definitive DTA peaks. The dP/dT slope of the liquidus is positive and steep at high pressures, but at high X_NaCl, and pressures below 0.5 kb it appears to reverse slope and intersects the three-phase curve (liquid-halite-vapour) at a shallow angle. However, due to the complex nature of the DTA signal when P <- 0.5 kb, there is considerable doubt about exactly what event has been recorded in the experiments conducted at these low pressures.The solubility of halite can be expressed as a function of the mole-fractional-based activity of NaCl in the liquid phase (L) in temperature (T, °K) and pressure (P, bars) In $\text{α}{}_{\mathrm{NaCl(L.T.P)}}\text{=}\text{?19.884 ? 0.001275T ? 1388}\text{T + 3.2305 In (T) ? 0.07574PT}$ Our liquidus data (based on 10 compositions) above 500 bars for these brines were combined with this equation to generate activity coefficients of NaCl which were fit within their experimental uncertainties to the following one parameter Margules equation In $\text{γ}{}_{\mathrm{NaCl(L.T.P)}}\text{=}\text{(0.7268 ? 695.7}\text{T ? 0.1217PT)}\text{(1 ? X}{}_{\mathrm{NaCl}}\text{)}{}^2$. Concentrated solutions of NaCl show negative deviations from ideality which rapidly increase in magnitude with decreasing X_NaCl.     

On calculating activity coefficients and other excess functions from the intracrystalline exchange properties of a double-site phase

For a phase at equilibrium in which two cation species are partitioned ideally between two sub-lattice sites, the excess functions of mixing (free energy, enthalpy and entropy) are directly related to the bulk composition of the phase and ΔG_E°(T, P), the standard-state intra- crystalline exchange free energy. If the phase is not at equilibrium internally, an additional ordering parameter is necessary to fix the excess free energy of mixing, G_mix^EX, unambiguously. Conversely, for any fixed G_mix^EX there exists an infinity of possible intracrystalline cation dis- tributions, only one of which is the equilibrium distribution for the specified temperature and pressure. As ideal intraphase cation ordering becomes more pronounced, G_mix^EX decreases. In response, the total free energy of mixing for the phase decreases progressively for non-end member compositions, approaching, at the limits of ordering, values appropriate for stabilizing compounds of intermediate composition.The model-dependent activity coefficient for component A in the phase, γ_A^T, can be calculated for any bulk composition, X_A^T, either from G_mix^EX directly or from more basic equations involving the interrelation of chemical potentials at equilibrium. A general form for γ_A^T is ln $\text{γ}{}_{\mathrm{A}}{}^{\mathrm{T}}\text{= 1n[}\text{2(X}{}_{\mathrm{A}}{}^{\mathrm{\alpha }}\text{X}{}_{\mathrm{A}}{}^{\mathrm{\beta }}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/}\text{(X}{}_{\mathrm{A}}{}^{\mathrm{\alpha }}\text{+X}{}_{\mathrm{A}}{}^{\mathrm{\beta }}\text{)}\text{]+Y}$, where Xj^κ denotes the mole fraction of species j in site κ. The first term on the right-hand side of this equation is the contribution to γ_A^T from ideal intracrystalline partitioning, and is common to the several theories lately presented to model intraphase cation partitioning. It can be shown rigorously that this term contributes to a negative deviation from ideality for the bulk phase. The second term is the contribution to the macroscopic activity coefficient from non-ideal intraphase partitioning, and is related to an enthalpy of mixing, H_mix^N in excess of that resulting from ideal inter-site cation ordering. While the expression represented by Y can take several functional forms, the additional enthalpy can be evaluated explicitly for specific non-ideal partitioning models from the relation $\text{H}{}_{\mathrm{mix}}{}^{\mathrm{N}}\text{= 2RT(1? X}{}_{\mathrm{A}}{}^{\mathrm{T}}\text{) ∝}\text{Y}\text{(1 ? X}{}_{\mathrm{A}}{}^{\mathrm{T}}\text{)}{}^2\text{dX}{}_{\mathrm{A}}{}^{\mathrm{T}}$.In those cases, G_mix^EX can also be determined exactly.     

The kinetics of silica-water reactions

A differential rate equation for silica-water reactions from 0–300°C has been derived based on stoichiometry and activities of the reactants in the reaction SiO₂(s) + 2H₂O(l) = H₄SiO₄(aq)

where ($\text{A}\text{M}$) = (the relative interfacial area between the solid and aqueous phases/the relative mass of water in the system), and k₊ and k_? are the rate constants for, respectively, dissolution and precipitation. The rate constant for precipitation of all silica phases is $\text{log k}{}_{\mathrm{?}}\text{= ? 0.707 ?}\text{2598}\text{T}\text{(T, K)}$ and E_act for this reaction is 49.8 kJ mol^?1. Corresponding equilibrium constants for this reaction with quartz, cristobalite, or amorphous silica were expressed as $\text{log K = a + bT +}\text{c}\text{T}$. Using $\text{K =}\text{k}{}_{\mathrm{+}}\text{k}{}_{\mathrm{?}}$, k was expressed as $\text{log k}{}_{\mathrm{+}}\text{= a + bT +}\text{c}\text{T}$ and a corresponding activation energy calculated:

     

13.

Thermochemistry of the high structural state plagioclases     

R.C. Newton  T.V. Charlu  O.J. Kleppa 《Geochimica et cosmochimica acta》1980,44(7):933-941

The enthalpies of solution of a suite of 19 high-structural state synthetic plagioclases were measured in a Pb₂B₂O₅ melt at 970 K. The samples were crystallized from analyzed glasses at 1200°C and 20 kbar pressure in a piston-cylinder apparatus. A number of runs were also made on Amelia albite and Amelia albite synthetically disordered at 1050–1080°C and one bar for one month and at 1200°C and 20 kbar for 10 hr. The component oxides of anorthite, CaO, Al₂O₃ and SiO₂, were remeasured.The ΔH of disorder of albite inferred in the present study from albite crystallized from glass is 3.23 kcal, which agrees with the 3.4 found by Holm and Kleppa (1968). It is not certain whether this value includes the ΔH of a reversible displacive transition to monoclinic symmetry, as suggested by Helgesonet al. (1978) for the Holm-Kleppa results. The enthalpy of solution value for albite accepted for the solid solution series is based on the heat-treated Amelia albite and is 2.86 kcal less than for untreated Amelia albite.The enthalpy of formation from the oxides at 970 K of synthetic anorthite is ?24.06 ± 0.31 kcal, significantly higher than the ?23.16 kcal found by Charluet al. (1978), and in good agreement with the value of ?23.89 ± 0.82 given by Robieet al. (1979), based on acid calorimetry.The excess enthalpy of mixing in high plagioclase can be represented by the expression, valid at 970 K: ΔH^ex(±0.16 kcal) = 6.7461 X_abX²_An + 2.0247 X_AnX²_Ab where X_Ab and X_An are, respectively, the mole fractions of NaAlSi₃O₈ and CaAl₂Si₂O₈. This ΔH^ex, together with the mixing entropy of Kerrick and Darken's (1975) Al-avoidance model, reproduces almost perfectly the free energy of mixing found by Orville (1972) in aqueous cation-exchange experiments at 700°C. It is likely that Al-avoidance is the significant stabilizing factor in the high plagioclase series, at least for X_An≥ 0.3. At high temperatures the plagioclases have nearly the free energies of ideal one-site solid solutions. The Al-avoidance model leads to the following Gibbs energy of mixing for the high plagioclase series: $\text{ΔG}{}^{\mathrm{mix}}\text{= ΔH}{}^{\mathrm{ex}}\text{+ RT X}{}_{\mathrm{Ab}}\text{ln[X}{}^2{}_{\mathrm{Ab}}\text{(2 ? X}{}_{\mathrm{Ab}}\text{)]+ X}{}_{\mathrm{An}}\text{ln}\text{[X}{}_{\mathrm{An}}\text{(1+X}{}_{\mathrm{An}}\text{)}{}^2\text{]}\text{4}$. The entropy and enthalpy of mixing should be very nearly independent of temperature because of the unlikelihood of excess heat capacity in the albite-anorthite join.     

14.

Calcium diffusion in a simple silicate melt to 30 kbar     

E.Bruce Watson 《Geochimica et cosmochimica acta》1979,43(3):313-322

Calcium-45 was used as a radiotracer to measure self-diffusion coefficients for Ca in a sodium-calcium-aluminosilicate melt (29% Na₂O, 5% CaO, 10% Al₂O₃, 56% SiO₂) at temperatures in the range 1100–1400°C and pressures to 30 kbar. Calcium diffusivity (D_Ca) was found to depend upon both temperature and pressure in a complex but systematic manner: $\text{(}\text{?D}{}_{\mathrm{Ca}}\text{?P}\text{)}{}_{\mathrm{T}}$ is always negative and has a larger absolute value at lower temperatures; $\text{(}\text{?D}{}_{\mathrm{Ca}}\text{?T}\text{)}{}_{\mathrm{P}}$ is positive and increases with increasing pressure. The overall dependence of D_Ca upon T and P is given approximately by $\text{D}{}_{\mathrm{caT.P}}\text{= [0.0025 exp(}\text{-23,107}\text{RT}\text{)] exp [P}\text{(0.7297T ? 1261.32)}\text{RT}\text{]}$. When expressed in terms of volume (V_a) and energy (E) of activation, the results are as follows: V_a ranges from 2.2 cm³/mole at 1400°C to 11.9 cm³/mole at 1100°C. and E ranges from 25.4 kcal/mole (1 kban to 49.8 kcal/mole (20 kbar).From the systematic dependence of D_Ca upon T and P, it is concluded that diffusion of Ca²⁺ in silicate melts does not take place by means of a vacant site mechanism, but is controlled instead by the amount and distribution of free volume in the melt structure.If it is assumed that the viscosity of the melt used in this study decreases with increasing pressure (Kushiro, 1976, J. Geophys. Res.81, 6351–6356) as D_Ca does, then the Stokes-Einstein inverse relation between viscosity and diffusivity is clearly violated, and its validity for silicate melts must be questioned. Thus, it appears that in silicate melts, unlike many liquids, viscous flow and diffusion are fundamentally different transport processes, involving different structural units.The effect of pressure on calcium diffusion is too small to invalidate kinetic models of upper mantle processes that have been based upon diffusivity values measured at 1 atm. Pressure may, however, induce significant reductions in the diffusion rates of large ions such as Rb⁺ or SiO^4?₄ in silicate melts.     

15.

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

Walter Riesen  Heinz Gamsjäger  Paul W. Schindler 《Geochimica et cosmochimica acta》1977,41(9):1193-1200

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.     

16.

The partial molal volume of silicic acid in 0.725 M NaCl at 1°C determined by the neutralization of Na₂SiO₃     

J.Peter Hershey  Iver W Duedall 《Geochimica et cosmochimica acta》1983,47(11):1931-1936

The partial molal volume of silicic acid ($\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$) in 0.725 M NaCl at 1°C was calculated from the measured volume change (Δ$\text{V}\text{?}{}_{\mathrm{n}}$) due to the neutralization of anhydrous sodium metasilicate with HCl and the $\text{V}\text{?}\text{(HCl)}$ and $\text{V}\text{?}\text{(NaCl)}$ obtained from the literature. $\text{V}\text{?}\text{(Si(OH)}{}_4\text{) = 59.0 cm}{}^3\text{mol}\text{? 1}$, determined under experimental conditions of pH = 2.2, compares favorably with $\text{V}\text{?}\text{(Si(OH)}{}_4\text{) = 58.9 cm}{}^3\text{mol}{}^{\mathrm{?1}}$ calculated from the measured volume change due to the hydrolysis of the meta-silicate salt at pH = 11 and from the partial molal volume due to electrostriction ($\text{V}\text{?}{}_{\mathrm{elect}}$) of water by charged Si species present in the solution at the high pH. This agreement lends support to a semiempirical model for calculating $\text{V}\text{?}{}_{\mathrm{elect}}$ in developed by Millero (1969). $\text{V}\text{?}\text{(NaOH) = ? 5.45 cm}{}^3\text{mol}{}^{\mathrm{?1}}$ in 0.725 M NaCl needed for this calculation was also determined in this work. The rate of polymerization of Si(OH)₄ at 1°C was monitored to insure that the monomer Si(OH)₄ was the main Si species present during the determination of $\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$ by neutralization of the alkali silicate. $\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$ determined in this study compares favorably with the value calculated from high pressure solubility measurements.     

17.

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

Richard J. Williams 《Geochimica et cosmochimica acta》1974,38(9):1415-1433

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.     

18.

Dissociation constants for alkali earth and sodium borate ion pairs from 10 to 50°C     

E.J. Reardon 《Chemical Geology》1976,18(4):309-325

Potentiometric measurements in dilute sodium borate solutions with added alkali earth chlordie salts yield the following expressions for the dissociation constants of alkali earth borate ion pairs from 10 to 50°C:

$\text{p}\text{K(}\text{MgH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.266+0.001204 T}$

$\text{p}\text{K(}\text{CaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.154+0.002170 T}$

$\text{p}\text{K(}\text{SrH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.033+0.001738 T}$

$\text{p}\text{K(}\text{BaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.942+0.001850 T}$

where T is in °K. Enthalpies for the dissociation reactions at 25°C are less than 1 kcal./mole for all the alkali earth borate ion pairs.Values for pK(NaH₂BO₃°) from 5 to 55°C computed from the experimental data of Owen and King are in good agreement with those determined potentiometrically. The average value from both methods is 0.22 ± 0.1 at 25°C.Application to seawater of computed pK's for MgH₂BO₃⁺, CaH₂BO₃⁺ and NaH₂BO₃⁰ yields an apparent dissociation constant for boric acid of 8.73 vs. 8.70 measured by Lyman, 8.68 by Buch and 8.73 by Byrne and Kester.     

19.

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

Dimitri A Sverjensky 《Geochimica et cosmochimica acta》1984,48(5):1127-1134

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.     

20.

Effet de la température sur les distributions de Na,Rb et Cs entre la sanidine,la muscovite,la phlogopite et une solution hydrothermale sous une pression de 1 kbar     

Marcel Volfinger 《Geochimica et cosmochimica acta》1976,40(3):267-282

The distribution of trace amounts of Na, Rb and Cs, between muscovite, phlogopite, sanidine and hydrothermal solution have been studied by ion exchange in a temperature range from 400 to 800°C.These distributions have been expressed with a partition ratio P^aq?m_x = $\text{(}\text{X}\text{K}\text{)}{}^{\mathrm{aq}}\text{(}\text{X}\text{K}\text{)}{}^{\mathrm{m}}$ (where X is Na, Rb or Cs).In the case of Na and Cs in muscovite, even for the dilute solutions, the ratio P^aq?m_x is not the equilibrium constant k_x of exchange reactions. In other cases, P^aq?m_x does not depend on the trace alkali ion concentration in silicates (X) and is equal to k_x. Variations of P_x or k_x with T are greater for Na and Cs than for Rb. Generally, k_x decreases with increase in T. The function log $\text{P}{}_{\mathrm{x}}\text{= f(}\text{1}\text{T}\text{)}$ is not linear for Na or Cs, but in the case of Rb, $\text{f(}\text{1}\text{T}\text{)}$ is linear and the standard enthalpy and entropy of exchange reactions have been estimated by applying the Arrhenius relation.The distribution relations obtained between silicate and vapour phase permit the determination of distributions of Na, Rb and Cs between two minerals mI and mII, relative to K. These have been expressed with the partition ratio Q_x =$\text{(}\text{X}\text{K}\text{)}{}^{\mathrm{mI}}\text{(}\text{X}\text{K}\text{)}{}^{\mathrm{mII}}$. Variations of Q_x with T are not remarkable, and even for Rb between phlogopite and feldspar are negligible. Nevertheless, one may use the distributions of Rb and Cs between muscovite and feldspar for geothermometry. Experimental results have been applied to some rocks by effecting corrections from the major element composition of the natural minerals. Estimated temperatures are near to 400°C in the granites and pegmatite studied here.     

	a	b	c	Eact(kJ mol -1)
Quarts	1.174	-2.028 x 103	-4158	67.4–76.6
α-Cristobalite	-0.739	0	-3586	68.7
β-Cristobalite	-0.936	0	-3392	65.0
Amorphous silica	-0.369	-7.890 x 10-4	3438	60.9–64.9

Thermochemistry of the high structural state plagioclases

The enthalpies of solution of a suite of 19 high-structural state synthetic plagioclases were measured in a Pb₂B₂O₅ melt at 970 K. The samples were crystallized from analyzed glasses at 1200°C and 20 kbar pressure in a piston-cylinder apparatus. A number of runs were also made on Amelia albite and Amelia albite synthetically disordered at 1050–1080°C and one bar for one month and at 1200°C and 20 kbar for 10 hr. The component oxides of anorthite, CaO, Al₂O₃ and SiO₂, were remeasured.The ΔH of disorder of albite inferred in the present study from albite crystallized from glass is 3.23 kcal, which agrees with the 3.4 found by Holm and Kleppa (1968). It is not certain whether this value includes the ΔH of a reversible displacive transition to monoclinic symmetry, as suggested by Helgesonet al. (1978) for the Holm-Kleppa results. The enthalpy of solution value for albite accepted for the solid solution series is based on the heat-treated Amelia albite and is 2.86 kcal less than for untreated Amelia albite.The enthalpy of formation from the oxides at 970 K of synthetic anorthite is ?24.06 ± 0.31 kcal, significantly higher than the ?23.16 kcal found by Charluet al. (1978), and in good agreement with the value of ?23.89 ± 0.82 given by Robieet al. (1979), based on acid calorimetry.The excess enthalpy of mixing in high plagioclase can be represented by the expression, valid at 970 K: ΔH^ex(±0.16 kcal) = 6.7461 X_abX²_An + 2.0247 X_AnX²_Ab where X_Ab and X_An are, respectively, the mole fractions of NaAlSi₃O₈ and CaAl₂Si₂O₈. This ΔH^ex, together with the mixing entropy of Kerrick and Darken's (1975) Al-avoidance model, reproduces almost perfectly the free energy of mixing found by Orville (1972) in aqueous cation-exchange experiments at 700°C. It is likely that Al-avoidance is the significant stabilizing factor in the high plagioclase series, at least for X_An≥ 0.3. At high temperatures the plagioclases have nearly the free energies of ideal one-site solid solutions. The Al-avoidance model leads to the following Gibbs energy of mixing for the high plagioclase series: $\text{ΔG}{}^{\mathrm{mix}}\text{= ΔH}{}^{\mathrm{ex}}\text{+ RT X}{}_{\mathrm{Ab}}\text{ln[X}{}^2{}_{\mathrm{Ab}}\text{(2 ? X}{}_{\mathrm{Ab}}\text{)]+ X}{}_{\mathrm{An}}\text{ln}\text{[X}{}_{\mathrm{An}}\text{(1+X}{}_{\mathrm{An}}\text{)}{}^2\text{]}\text{4}$. The entropy and enthalpy of mixing should be very nearly independent of temperature because of the unlikelihood of excess heat capacity in the albite-anorthite join.     

Calcium diffusion in a simple silicate melt to 30 kbar

Calcium-45 was used as a radiotracer to measure self-diffusion coefficients for Ca in a sodium-calcium-aluminosilicate melt (29% Na₂O, 5% CaO, 10% Al₂O₃, 56% SiO₂) at temperatures in the range 1100–1400°C and pressures to 30 kbar. Calcium diffusivity (D_Ca) was found to depend upon both temperature and pressure in a complex but systematic manner: $\text{(}\text{?D}{}_{\mathrm{Ca}}\text{?P}\text{)}{}_{\mathrm{T}}$ is always negative and has a larger absolute value at lower temperatures; $\text{(}\text{?D}{}_{\mathrm{Ca}}\text{?T}\text{)}{}_{\mathrm{P}}$ is positive and increases with increasing pressure. The overall dependence of D_Ca upon T and P is given approximately by $\text{D}{}_{\mathrm{caT.P}}\text{= [0.0025 exp(}\text{-23,107}\text{RT}\text{)] exp [P}\text{(0.7297T ? 1261.32)}\text{RT}\text{]}$. When expressed in terms of volume (V_a) and energy (E) of activation, the results are as follows: V_a ranges from 2.2 cm³/mole at 1400°C to 11.9 cm³/mole at 1100°C. and E ranges from 25.4 kcal/mole (1 kban to 49.8 kcal/mole (20 kbar).From the systematic dependence of D_Ca upon T and P, it is concluded that diffusion of Ca²⁺ in silicate melts does not take place by means of a vacant site mechanism, but is controlled instead by the amount and distribution of free volume in the melt structure.If it is assumed that the viscosity of the melt used in this study decreases with increasing pressure (Kushiro, 1976, J. Geophys. Res.81, 6351–6356) as D_Ca does, then the Stokes-Einstein inverse relation between viscosity and diffusivity is clearly violated, and its validity for silicate melts must be questioned. Thus, it appears that in silicate melts, unlike many liquids, viscous flow and diffusion are fundamentally different transport processes, involving different structural units.The effect of pressure on calcium diffusion is too small to invalidate kinetic models of upper mantle processes that have been based upon diffusivity values measured at 1 atm. Pressure may, however, induce significant reductions in the diffusion rates of large ions such as Rb⁺ or SiO^4?₄ in silicate melts.     

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.     

The partial molal volume of silicic acid in 0.725 M NaCl at 1°C determined by the neutralization of Na2SiO3

The partial molal volume of silicic acid ($\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$) in 0.725 M NaCl at 1°C was calculated from the measured volume change (Δ$\text{V}\text{?}{}_{\mathrm{n}}$) due to the neutralization of anhydrous sodium metasilicate with HCl and the $\text{V}\text{?}\text{(HCl)}$ and $\text{V}\text{?}\text{(NaCl)}$ obtained from the literature. $\text{V}\text{?}\text{(Si(OH)}{}_4\text{) = 59.0 cm}{}^3\text{mol}\text{? 1}$, determined under experimental conditions of pH = 2.2, compares favorably with $\text{V}\text{?}\text{(Si(OH)}{}_4\text{) = 58.9 cm}{}^3\text{mol}{}^{\mathrm{?1}}$ calculated from the measured volume change due to the hydrolysis of the meta-silicate salt at pH = 11 and from the partial molal volume due to electrostriction ($\text{V}\text{?}{}_{\mathrm{elect}}$) of water by charged Si species present in the solution at the high pH. This agreement lends support to a semiempirical model for calculating $\text{V}\text{?}{}_{\mathrm{elect}}$ in developed by Millero (1969). $\text{V}\text{?}\text{(NaOH) = ? 5.45 cm}{}^3\text{mol}{}^{\mathrm{?1}}$ in 0.725 M NaCl needed for this calculation was also determined in this work. The rate of polymerization of Si(OH)₄ at 1°C was monitored to insure that the monomer Si(OH)₄ was the main Si species present during the determination of $\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$ by neutralization of the alkali silicate. $\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$ determined in this study compares favorably with the value calculated from high pressure solubility measurements.     

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.     

Dissociation constants for alkali earth and sodium borate ion pairs from 10 to 50°C

Potentiometric measurements in dilute sodium borate solutions with added alkali earth chlordie salts yield the following expressions for the dissociation constants of alkali earth borate ion pairs from 10 to 50°C:

$\text{p}\text{K(}\text{MgH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.266+0.001204 T}$

$\text{p}\text{K(}\text{CaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.154+0.002170 T}$

$\text{p}\text{K(}\text{SrH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.033+0.001738 T}$

$\text{p}\text{K(}\text{BaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.942+0.001850 T}$

where T is in °K. Enthalpies for the dissociation reactions at 25°C are less than 1 kcal./mole for all the alkali earth borate ion pairs.Values for pK(NaH₂BO₃°) from 5 to 55°C computed from the experimental data of Owen and King are in good agreement with those determined potentiometrically. The average value from both methods is 0.22 ± 0.1 at 25°C.Application to seawater of computed pK's for MgH₂BO₃⁺, CaH₂BO₃⁺ and NaH₂BO₃⁰ yields an apparent dissociation constant for boric acid of 8.73 vs. 8.70 measured by Lyman, 8.68 by Buch and 8.73 by Byrne and Kester.     

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.     

Effet de la température sur les distributions de Na,Rb et Cs entre la sanidine,la muscovite,la phlogopite et une solution hydrothermale sous une pression de 1 kbar

The distribution of trace amounts of Na, Rb and Cs, between muscovite, phlogopite, sanidine and hydrothermal solution have been studied by ion exchange in a temperature range from 400 to 800°C.These distributions have been expressed with a partition ratio P^aq?m_x = $\text{(}\text{X}\text{K}\text{)}{}^{\mathrm{aq}}\text{(}\text{X}\text{K}\text{)}{}^{\mathrm{m}}$ (where X is Na, Rb or Cs).In the case of Na and Cs in muscovite, even for the dilute solutions, the ratio P^aq?m_x is not the equilibrium constant k_x of exchange reactions. In other cases, P^aq?m_x does not depend on the trace alkali ion concentration in silicates (X) and is equal to k_x. Variations of P_x or k_x with T are greater for Na and Cs than for Rb. Generally, k_x decreases with increase in T. The function log $\text{P}{}_{\mathrm{x}}\text{= f(}\text{1}\text{T}\text{)}$ is not linear for Na or Cs, but in the case of Rb, $\text{f(}\text{1}\text{T}\text{)}$ is linear and the standard enthalpy and entropy of exchange reactions have been estimated by applying the Arrhenius relation.The distribution relations obtained between silicate and vapour phase permit the determination of distributions of Na, Rb and Cs between two minerals mI and mII, relative to K. These have been expressed with the partition ratio Q_x =$\text{(}\text{X}\text{K}\text{)}{}^{\mathrm{mI}}\text{(}\text{X}\text{K}\text{)}{}^{\mathrm{mII}}$. Variations of Q_x with T are not remarkable, and even for Rb between phlogopite and feldspar are negligible. Nevertheless, one may use the distributions of Rb and Cs between muscovite and feldspar for geothermometry. Experimental results have been applied to some rocks by effecting corrections from the major element composition of the natural minerals. Estimated temperatures are near to 400°C in the granites and pegmatite studied here.