Precise age determinations and petrogenetic studies using the KCa method

High precision mass spectrometric determination of calcium isotope ratios allows the ⁴⁰K → ⁴⁰Ca radioactive decay to be used for dating a much broader range of geologic materials than is suggested by previous work. ${}^{40}\text{Ca}{}^{42}\text{Ca}$ is used to monitor enrichments in ⁴⁰Ca and can be measured to ±0.01% (2σ) using an exponential mass discrimination correction (Russell et al., 1978) and large ion currents. The earth's mantle has such a low $\text{K}\text{Ca}$ (～0.01) that it has retained “primordial” ${}^{40}\text{Ca}{}^{42}\text{Ca}\text{= 151.016}$ ± 0.011 (normalized to ${}^{42}\text{Ca}{}^{44}\text{Ca}\text{= 0.31221}$), as determined by measurements on two meteorites, pyroxene from an ultramafic nodule, metabasalt, and carbonatite. ${}^{40}\text{Ca}{}^{42}\text{Ca}$ ratios can be conveniently expressed relative to this value as ?_Ca in units of 10^?4. To test the method for age dating, a mineral isochron has been obtained on a sample of Pikes Peak granite, which has been shown to have concordant KAr, RbSr, and UPb ages. Plagioclase, K-feldspar, biotite, and whole rock yield an age of 1041 ± 32 m.y. (2σ) in agreement with previous age determinations (λ_K = 0.5543 b.y.^?1, $\text{λ}{}_{\mathrm{\beta ?}}\text{λ}{}_{\mathrm{<mtext>K</mtext>}}\text{= 0.8952}$, ⁴⁰K = 0.01167%). The initial ${}^{40}\text{Ca}{}^{42}\text{Ca}$ of 151.024 ± 0.016 (?_Ca = +0.5 ± 1.0), indicates that assimilation of high K/Ca crust was insufficient to affect calcium isotopes. Measurements on two-mica granite from eastern Nevada indicate that the magma sources had K/Ca ≈ 1, similar to intermediate-composition crustal rocks. These results show that the KCa system can be used as a precise geochromometer for common felsic igneous and metamorphic rocks, and may prove applicable to sedimentary rocks containing authigenic K minerals. The relatively short half-life of ⁴⁰K, the non-volatile daughter, and the fact that potassium and calcium are stoichiometric constituents of many minerals, make the KCa system complementary to other dating methods, and potentially applicable to a variety of geologic problems.     

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 incorporation of Mg2+ and Sr2+ into calcite overgrowths: influences of growth rate and solution composition

The concentrations of Mg²⁺ and Sr²⁺ incorporated within calcite overgrowths precipitated from seawater and related solutions, determined at 25°C, were independent of the precipitation rate over approximately an order of magnitude. The saturation states used to produce this range of precipitation rates varied from 3 to 17 depending on the composition of the solution.The amount of Mg²⁺ incorporated in the overgrowths was not directly proportional to $\text{Mg}{}^{\mathrm{2+}}\text{Ca}{}^{\mathrm{2+}}$ in solution over the entire range (1–20) of ratios studied. Below a ratio of 7.5, the overgrowth was enriched in MgCO₃ relative to what is predicted by the constant distribution coefficient measured above a ratio of 7.5. This increased MgCO₃ correlates with the relative enrichment of adsorbed Mg²⁺. Above a ratio of 7.5 the concentration of MgCO₃ in the calcite overgrowths followed a classical thermodynamic behavior characterized by a constant distribution coefficient of 0.0123 (±0.008 std dev).The concentration of SrCO₃ incorporated in the overgrowths was linearly related to the MgCO₃ content of the overgrowths, and is attributed to increased solubility of SrCO₃ in calcite due to the incorporation of the smaller Mg²⁺ ions.The kinetic data indicate that the growth mechanism involves the adsorption of the cations on the surface of the calcite prior to dehydration and final incorporation. It is suggested that dehydration of cations at the surface is the rate controlling step.     

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.     

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.     

Kinetic and thermodynamic factors controlling the distribution of SO32− and Na+ in calcites and selected aragonites

Significant amounts of SO₄^2?, Na⁺, and OH^? are incorporated in marine biogenic calcites. Biogenic high Mg-calcites average about 1 mole percent SO₄^2?. Aragonites and most biogenic low Mg-calcites contain significant amounts of Na⁺, but very low concentrations of SO₄^2?. The SO₄^2? content of non-biogenic calcites and aragonites investigated was below 100 ppm. The presence of Na⁺ and SO₄^2? increases the unit cell size of calcites. The solid-solutions show a solubility minimum at about 0.5 mole percent SO₄^2? beyond which the solubility rapidly increases. The solubility product of calcites containing 3 mole percent SO₄^2? is the same as that of aragonite. Na⁺ appears to have very little effect on the solubility product of calcites. The amounts of Na⁺ and SO₄^2? incorporated in calcites vary as a function of the rate of crystal growth. The variation of the distribution coefficient ($\text{D}$) of SO₄^2? in calcite at 25.0°C and 0.50 molal NaCl is described by the equation $\text{D = k}{}_0\text{+ k}{}_1\text{R}$ where $\text{k}{}_0$ and $\text{k}{}_1$ are constants equal to $\text{6.16 × 10}{}^{\mathrm{?6}}$ and $\text{3.941 × 10}{}^{\mathrm{?6}}$, respectively, and $\text{R}$ is the rate of crystal growth of calcite in mg·min^?1·g^?1 of seed. The data on Na⁺ are consistent with the hypothesis that a significant amount of Na⁺ occupies interstitial positions in the calcite structure. The distribution of Na⁺ follows a Freundlich isotherm and not the Berthelot-Nernst distribution law. The numerical value of the Na⁺ distribution coefficient in calcite is probably dependent on the number of defects in the calcite structure. The Na⁺ contents of calcites are not very accurate indicators of environmental salinities.     

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 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?.     

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.     

A fundamental equation for calcite dissolution kinetics

A fundamental rate equation for the dissolution of calcite in a pure 0.7 M KC1 solution has been determined. Between pH 8.0 and 10.1 the kinetics of the dissolution reaction can be expressed by the equation

$\text{d[Ca}{}^{\mathrm{2+}}\text{]/dt = kA(C-[Ca}{}^{\mathrm{2+}}\text{]}\text{1}\text{2}\text{[CO}{}_3{}^{\mathrm{2?}}\text{]}\text{1}\text{2}\text{)}$

, where d[Ca²⁺]/dt is the rate in mole cm^?3s^?1, k is the apparent rate constant in s^?1 cm^?2, A is the calcite surface area and C is the square root of the calcite solubility constant. The apparent rate constant at 20°C is 9.5 × 10^?6s^?1cm^?2. The apparent activation energy for the reaction between 5 and 50°C is 8.4 kcal mole^?1.The reaction rate is pH independent above pH = 7.5. At pH values less than 8, [CO₃^2?] becomes negligible, and the rate becomes fast and should be dependent on the calcite surface area alone, if there is no change in mechanism.The stirring coefficient between 2.8 and 11.1 rev s^?1 is 0.33. This, together with the relatively high activation energy, indicates that the reaction is mainly chemically controlled.Interpolation of the experimental results into seawater systems gives a computed rate several magnitudes greater than the observed rate, but considerably less than that calculated for a diffusion-controlled reaction.     

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.     

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 dissolution kinetics of biogenic calcium carbonates in seawater

Dissolution rate as a function of degree of undersaturation was measured on shells of individual species of coccoliths and foraminifera, various size fractions of sediment from the Ontong-Java Plateau and the Rio Grande Rise, a collection of large pteropods, and on synthetic calcite and aragonite powder.Results of the study indicate that all biogenic and synthetic calcium carbonate follows the rate law $\text{R\% = k\%(1 ? Ω)}{}^{\mathrm{n}}$ where $\text{Ω  [Ca}{}^{\mathrm{2+}}\text{][CO}{}_3{}^{\mathrm{2?}}\text{]/K'}{}_{\mathrm{sp}}$ and K'_sp is the apparent solubility product of calcite or aragonitic seawater. In the case of all calcite samples, n_c = 4.5, while for aragonitic samples n_a = 4.2. The ‘rate constant’, k%, varies widely between samples and in many cases is inversely correlated with grain size. However, the individual species of coccoliths, E. huxleyi and C. neohelis, which were cultured in the laboratory appear not to follow this rule, with dissolution rates an order to magnitude lower than expected.     

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.     

A corundum-rich inclusion in the Murchison carbonaceous chondrite

A corundum-hibonite inclusion, BB-5, has been found in the Murchison carbonaceous chondrite. This is the first reported occurrence of corundum as a major phase in any refractory inclusion, even though this mineral is predicted by thermodynamic calculations to be the first condensate from a cooling gas of solar composition. Ion microprobe measurements of Mg isotopic compositions yield the unexpected result for such an early condensate that ²⁶Mg excesses are small: δ_N²⁶Mg = 7.0 ± 1.6%. for hibonite and 5.0 ± 4.8%. for corundum, despite very large ${}^{27}\text{Al}{}^{24}\text{Mg}$ ratios, 130 and 2.74 × 10⁴, respectively. Within the errors, δ_N²⁶Mg does not vary over this exceedingly large range of ${}^{27}\text{Al}{}^{24}\text{Mg}$ ratios. The extreme temperature required to melt this inclusion makes a liquid origin unlikely, except possibly by hypervelocity impact involving refractory bodies. If, instead, BB-5 is a direct gas-solid condensate, textural evidence implies that corundum formed first and later reacted to produce hibonite. In this model, BB-5's uniform enrichment in ²⁶Mg must be a characteristic of the reservoir from which it condensed. Because severe difficulties are encountered in making such a reservoir by prior decay of ²⁶Al, nebular heterogeneity in magnesium isotopic composition is a preferred explanation.     

Importance of alteration of volcanic material in the sediments of deep sea drilling site 323: chemistry, 18O16O and 87Sr86Sr

A downhole decrease in ¹⁸O, Mg²⁺ and K⁺, an increase in Ca²⁺ and a low ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratio of 0.7067 in the pore fluids of DSDP site 323 were caused principally by the alteration of volcanic material. These chemical and isotopic patterns were produced by the alteration, in order of decreasing importance of: a 60-m thick basal layer of volcanic ash; the underlying basalts; and igneous components in the 640-m thick upper sequence composed largely of terrigenous material. A significant portion of the alteration of the ash in the basal sequence must have occurred before the deposition of the upper sediments, perhaps under the influence of advecting solutions. The rest of the alteration occurred during the deposition of the thick upper sediments. Mass balance considerations and the low δ¹⁸O values of most of the alteration products suggest that much of the later alteration occurred progressively over the last 13 Myr. The principal alteration products were smectite, potassium feldspar, clinoptilolite and calcite.     

Kiglapait geochemistry V: Strontium

The Kiglapait intrusion contains 330 ppm Sr and has $\text{Sr}\text{Ca}\text{= 5 × 10}{}^{\mathrm{?3}}$ and $\text{Rb}\text{Sr}\text{= 3 × 10}{}^{\mathrm{?3}}$, as determined by summation over the Layered Group of the intrusion. Wholerocks in the Lower Zone contain 403 F_L^0.141 ppm Sr, where F_L is the fraction of liquid remaining; Sr drops to 180 ppm at the peak of augite production (F_L = 0.11) and rises to a maximum of 430 ppm in the Upper Zone before decreasing to 172 ppm at the end of crystallization. Feldspars in the Lower Zone contain 532 F_L^0.090 ppm Sr, increasing to 680 ppm in the Upper Zone before decreasing to 310 ppm at the end. Clinopyroxenes contain 15 to 30 ppm Sr and have a mineral-melt distribution coefficient D = 0.06 except near the top of the intrusion where D = 0.10.The calculated feldspar-liquid distribution coefficient has an average value near 1.75 but shows four distinct trends when plotted against X_An of feldspar. The first two of these are strongly correlated with the modal augite content of the liquid, on average by the relation D = 1.4 + 0.02 Aug^L. The third (decreasing) trend is due to co-crystallization of apatite, and the fourth (increasing) trend can best be attributed to a triclinic-monoclinic symmetry change in the feldspar at An₂₆, 1030°C. The compound feldspar-liquid distribution coefficient K_D for $\text{Sr}\text{Ca}$ bears out these deductions in detail and yields ΔG_r for the Sr-Ca exchange ranging from nearly zero at the base of the Lower Zone to ?26 kJ/gramatom at the end of crystallization. The compound feldspar-liquid distribution coefficient K_D for $\text{Rb}\text{Sr}$ varies from 0.3 in the Lower Zone to 1.1 at the end of crystallization.The ratio $\text{Ca}{}^{\mathrm{F}}\text{Ca}{}^{\mathrm{L}}$ is about 1.45 for troctolitic liquids containing 5% augite, for which K_D (Sr-Ca) = 1.0 and D_Ca = D_Sr. For common basaltic liquids containing 20% augite, the Kiglapait data predict $\text{solSr}{}^{\mathrm{F}}\text{Sr}{}^{\mathrm{L}}\text{= 1.8}$, as commonly found elsewhere. The strong dependence of D_sr on augite content of the liquid illuminates the role of liquid composition and structure in determining the feldspar-liquid distribution coefficient. Conversely, a discontinuous change in the trend of D_Sr when apatite arrives shows that the effect is due to apatite crystallization itself, not to the continuous variation of the liquid as it becomes enriched in apatite component.