Aqueous oxidation-reduction kinetics associated with coupled electron-cation transfer from iron-containing silicates at 25°C

Mechanisms and kinetics of aqueous $\text{Fe}{}^{\mathrm{+2}}\text{Fe}{}^{\mathrm{+3}}$ oxidation-reduction and dissolved O₂ interaction in the presence of augite, biotite and hornblende were studied in oxic and anoxic solutions at pH 1–9 at 25°C. Oxidation of surface iron on the minerals coincided with both surface release of Fe⁺² and by reduction of Fe⁺³ in solution. Reaction with iron silicates consumed dissolved oxygen at a rate that increased with decreasing pH. Both Fe⁺³ and O₂ consumption were shown to be controlled by coupled electron-cation transfer reactions of the form;

$\text{[}\text{Fe}{}^{\mathrm{+2}}\text{,}\text{1}\text{zM}{}^{\mathrm{+z}}\text{]}{}_{\mathrm{silicate}}\text{+}\text{Fe}{}^{\mathrm{+3}}\text{→ [}\text{Fe}{}^{\mathrm{+3}}\text{]}{}_{\mathrm{silicate}}\text{+}\text{Fe}{}^{\mathrm{+2}}\text{+}\text{1}\text{zM}{}^{\mathrm{+z}}$

and

$\text{[}\text{Fe}{}^{\mathrm{+2}}\text{,}\text{1}\text{zM}{}^{\mathrm{+z}}\text{]}{}_{\mathrm{silicate}}\text{+}\text{H}{}^{\mathrm{+}}\text{+}\text{1}\text{4}\text{O}{}_2\text{→ [}\text{Fe}{}^{\mathrm{+3}}\text{]}{}_{\mathrm{silicate}}\text{+}\text{1}\text{zM}{}^{\mathrm{+z}}\text{+}\text{1}\text{2}\text{H}{}_2\text{O}$

where M is a cation of charge +z. The spontaneous reduction of aqueous Fe⁺³in the presence of precipitated Fe(OH)₃bracketed the surface oxidation standard half cell between +0.33 and +0.52 volts. Concurrent hydrolysis reactions involving cation release from the iron silicates were suppressed by the above reactions. Calculated oxidation depths in the minerals varied between 12 and 80Å and were apparently controlled by rates of solid-state cation diffusion.     

Rutile solubility and titanium coordination in silicate melts

The solubility of rutile has been determined in a series of compositions in the K₂O-Al₂O₃-SiO₂ system ($\text{K}{}^1\text{=}\text{K}{}_2\text{O}\text{(K}{}_2\text{O}$ + Al₂O₃) = 0.38–0.90), and the CaO-Al₂O₃-SiO₂ system ($\text{C}{}^1\text{=}\text{CaO}\text{(CaO + Al}{}_2\text{O}{}_3\text{)}\text{= 0.47–0.59}$). Isothermal results in the KAS system at 1325°C, 1400°C, and 1475°C show rutile solubility to be a strong function of the $\text{K}{}^1$ ratio. For example, at 1475°C the amount of TiO₂ required for rutile saturation varies from 9.5 wt% ($\text{K}{}^1\text{= 0.38}$) to 11.5 wt% ($\text{K}{}^1\text{= 0.48}$) to 41.2 wt% ($\text{K}{}^1\text{= 0.90}$). In the CAS system at 1475°C, rutile solubility is not a strong function of $\text{C}{}^1$. The amount of TiO₂ required for saturation varies from 14 wt% ($\text{C}{}^1\text{= 0.48}$) to 16.2 wt% ($\text{C}{}^1\text{= 0.59}$).The solubility changes in KAS melts are interpreted to be due to the formation of strong complexes between Ti and K⁺ in excess of that needed to charge balance Al³⁺. The suggested stoichiometry of this complex is K₂Ti₂O₅ or K₂Ti₃O₇. In CAS melts, the data suggest that Ca²⁺ in excess of A1³⁺ is not as effective at complexing with Ti as is K⁺. The greater solubility of rutile in CAS melts when $\text{C}{}^1$ is less than 0.54 compared to KAS melts of equal $\text{K}{}^1$ ratio results primarily from competition between Ti and Al for complexing cations (Ca vs. K).TiK_β x-ray emission spectra of KAS glasses ($\text{K}{}^1\text{= 0.43–0.60}$) with 7 mole% added TiO₂, rutile, and Ba₂TiO₄, demonstrate that the average Ti-O bond length in these glasses is equal to that of rutile rather than Ba₂TiO₄, implying that Ti in these compositions is 6-fold rather than 4-fold coordinated. Re-examination of published spectroscopic data in light of these results and the solubility data, suggests that the 6-fold coordination polyhedron of Ti is highly distorted, with at least one Ti-O bond grossly undersatisfied in terms of Pauling's rules.     

Rates of reaction of pyrite and marcasite with ferric iron at pH 2

The relative reactivities of pulverized samples (100–200 mesh) of 3 marcasite and 7 pyrite specimens from various sources were determined at 25°C and pH 2.0 in ferric chloride solutions with initial ferric iron concentrations of 10^?3 molal. The rate of the reaction:

$\text{FeS}{}_2\text{+ 14}\text{Fe}{}^{\mathrm{3+}}\text{+ 8}\text{H}{}_2\text{O}\text{= 15}\text{Fe}{}^{\mathrm{2+}}\text{+ 2}\text{SO}{}^{\mathrm{2?}}{}_4\text{+ 16}\text{H}{}^{\mathrm{+}}$

was determined by calculating the rate of reduction of aqueous ferric ion from measured oxidation-reduction potentials. The reaction follows the rate law:

where m_Fe³⁺ is the molal concentration of uncomplexed ferric iron, k is the rate constant and $\text{A}\text{M}$ is the surface area of reacting solid to mass of solution ratio. The measured rate constants, k, range from 1.0 × 10^?4 to 2.7 × 10^?4 sec^?1 ± 5%, with lower-temperature/early diagenetic pyrite having the smallest rate constants, marcasite intermediate, and pyrite of higher-temperature hydrothermal and metamorphic origin having the greatest rate constants. Geologically, these small relative differences between the rate constants are not significant, so the fundamental reactivities of marcasite and pyrite are not appreciably different.The activation energy of the reaction for a hydrothermal pyrite in the temperature interval of 25 to 50°C is 92 kJ mol^?1. This relatively high activation energy indicates that a surface reaction controls the rate over this temperature range. The BET-measured specific surface area for lower-temperature/early diagenetic pyrite is an order of magnitude greater than that for pyrite of higher-temperature origin. Consequently, since the lower-temperature types have a much greater $\text{A}\text{M}$ ratio, they appear to be more reactive per unit mass than the higher temperature types.     

Concentration of Mn and separation from Fe in sediments—I. Kinetics and stoichiometry of the reaction between birnessite and dissolved Fe(II) at 10°C

Redox reactions between Fe²⁺ in solution and Mn-oxides are proposed as a mechanism for concentration of Mn in sediments both during weathering and diagenesis in marine sediments, e.g. the formation of Mn-nodules.If such a mechanism is to be effective, then reaction rates between Fe²⁺ and Mn-oxides should be fast. The kinetics and stoichiometry of the reaction between dissolved Fe²⁺ and synthetically prepared birnessite (Mn₇O₁₃·5H₂O) were studied experimentally in the pH range 3–6.Results show a stoichiometry which at pH < 4 conforms to a simple reaction between Fe²⁺ and birnessite, releasing Mn²⁺ and Fe³⁺ to the solution. At pH > 4 FeOOH is precipitated and excess Fe²⁺ consumption compared to the theoretical stoichiometry is observed. The excess Fe²⁺ consumption is not due to a formation of a quantitative MnOOH layer but rather to adsorption.Reaction kinetics are very fast at pH < 4 and change at pH 4 to a slower mechanism. At pH > 4 the reaction is fast initially until 17% of the bimessite has dissolved and changes then to a slower stage. The later stage can be described by the equation: $\text{J = km}{}_0\text{(H}{}^{\mathrm{+}}\text{)}{}^{\mathrm{?0.45}}\text{[Fe}{}^{\mathrm{2+}}\text{]}{}^{\mathrm{\gamma }}\text{(}\text{m}\text{m}{}_0\text{)}{}^{\mathrm{\beta }}$ where J is the overall rate of Mn²⁺ release, m₀ and m the mass of birnessite at time t = 0 and t > 0, β = 6.76?0.94 pH and γ has values of 0.76 at pH 5 and 0.39 at pH 6. The rate constant k is 7.2·10^?7 moles s^?1 g^?1 (moles/1)^?0.31 at pH 5 and 9.6·10^?8 moles s^?1 g^?1 (moles/1)^0.06 at pH 6.Diffusion calculations show that the rate is controlled by surface reaction and it is tentatively proposed that the availability of vacancies in octahedral [MnO₆]sheets of the birnessite surface could be rate controlling. It is concluded that reactions between Fe(II) and birnessite, and probably other Mn-oxides, are fast enough to be important in natural environments at the earth surface.     

M and Mg values in igneous rocks: proposed usage and a comment on currently employed Fe2O3 corrections

It is proposed that the ‘M value’ of an igneous rock should be 100Mg/(Mg + ΣFe) and that the ‘Mg value’ should be 100Mg/(Mg + Fe²⁺). A plea is made to standardize any necessary corrections for Fe₂O₃ so that $\text{Fe}{}_2\text{O}{}_3\text{(Fe}{}_2\text{O}{}_3\text{+ FeO)}\text{= 02}$ for basic rocks.     

Liquidus relationships in the system CaCO3Ca(OH)2CaS and the solubility of sulfur in carbonatite magmas

CaCO₃Ca(OH)₂CaS serves as a model system for sulfide solubility in carbonatite magmas. Experiments at 1 kbar delineate fields for primary crystallization of CaCO₃, Ca(OH)₂ and CaS. The three fields meet at a ternary eutectic at 652°C with liquid composition (wt%): CaCO₃ = 46.1%, Ca(OH)₂ = 51.9%, CaS = 2.0%. Two crystallization sequences are possible for liquids that precipitate calcite, depending upon whether the liquid is on the low-CaS side, or the high-CaS side of the line connecting CaCO₃ to the eutectic liquid. Low-CaS liquids precipitate no sulfide until the eutectic temperature is reached leading to sulfide enrichment. The higher-CaS liquids precipitate some sulfide above the eutectic temperature, but the sulfide content of the melt is not greatly depleted as the eutectic temperature is approached. Theoretical considerations indicate that sulfide solubility in carbonate melts will be directly proportional to and inversely proportional to ; it also is likely to be directly proportional to melt basicity, defined here by . A strong similarity exists in the processes which control sulfide solubility in carbonate and in silicate melts. By analogy with silicates, ferrous iron, which was absent in our experiments, may also exert an important influence on sulfide solubility in natural carbonatite magmas.     

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?.     

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.     

Sorption of noble gases by solids,with reference to meteorites. I. Magnetite and carbon

To simulate trapping of meteoritic noble gases by solids, 18 samples of Fe₃O₄ were synthesized in a noble gas atmosphere at 350–720 K by the reactions: 3Fe + 4H₂O → Fe₃O₄ + 4H₂ (Ne, Ar, Kr, Xe) 3Fe + 4CO → Fe₃O₃ + 4C + carbides (Xe only) Phases were separated by selective solvents (HgCl₂, HCl). Noble gas contents were analyzed by mass spectrometry, or, in runs where 36 d Xe¹²⁷ tracer was used, by γ-counting. Surface areas, as measured by the BET method, ranged from 1 to 400 m²/g. Isotopic fractionations were below the detection limit of 0.5%/m.u.Sorption of Xe on Fe₃O₄ and C obeys Henry's Law between $\text{1 × 10}{}^{\mathrm{?8}}$ and $\text{4 × 10}{}^{\mathrm{?5}}$ atm, but shows only a slight temperature dependence between 650 and 720 K ($\text{ΔH}{}_{\mathrm{sol}}\text{= ?4 ± 2}\text{kcal/mole}$). The mean distribution coefficient K_Xe is $\text{0.28 ± 0.09}$ cc STP/g atm for Fe₃O₄ and only a factor of $\text{1.2 ± 0.4}$ greater for C; such similarity for two cogenetic phases was predicted by Lewis et al. (1977). Stepped heating and etching experiments show that 20–50% of the total Xe is physically adsorbed and about 20% is trapped in the solid. The rest is chemisorbed with $\text{ΔH}{}_{\mathrm{s}}\text{? ?13}\text{kcal/mole}$. The desorption or exchange half-time for the last two components is >10² yr at room temperature.Etching experiments showed a possible analogy to “Phase $\text{Q}$” in meteorites. A typical carbon + carbide sample, when etched with HNO₃, lost 47% of its Xe but only 0.9% of its mass, corresponding to a ~0.6 Å layer. Though this etchable, surficial gas component was more thermolabile than $\text{Q}$ (release $\text{T}$ below 1000°C, compared to 1200–1600°C), another experiment shows that the proportion of chemisorbed Xe increases upon moderate heating (1 hr at 450°C). Apparently adsorbed gases can become “fixed” to the crystal, by processes not involving volume diffusion (recrystallization, chemical reaction, migration to traps, etc.). Such mechanisms may have acted in the solar nebula, to strengthen the binding of adsorbed gases.Adsorbed atmospheric noble gases are present in all samples, and dominate whenever the noble gas partial pressure in the atmosphere is greater than that in the synthesis. Many of the results of Lancet and Anders (1973) seem to have been dominated by such an atmospheric component; others are suspect for other reasons, whereas still others seem reliable. When the doubtful samples of Lancet and Anders are eliminated or corrected, the fractionation pattern—as in our samples—no longer peaks at Ar, but rises monotonically from Ne to Xe. No clear evidence remains for the strong temperature dependence claimed by these authors.     

Changes in the content and composition of pedogenic iron oxyhydroxides in a chronosequence of soils in southern California

Studies of the pedogenic iron oxyhydroxides in suites of latest Holocene to middle Pleistocene soils formed on fluvial deposits of the transverse ranges, southern California, indicate that the content and composition of iron oxyhydroxide change in a systematic manner. Analysis of total secondary free iron oxides (dithionite extractable, Fe₂O₃d) and ferrihydrite (oxalate extractable, Fe₂O₃o) shows that (1) a single-logarithmic model (Y = a + b log X) or double logarithmic model (log Y = a + b log X), where Y is the total mass of pedogenic Fe oxides (g/cm²-soil column) and X is soil age, describes the rate of increase in Fe₂O₃d with time; (2) the Fe₂O₃d content correlates linearly with soil reddening and clay content; (3) the $\text{Fe}{}_2\text{O}{}_3\text{o}\text{Fe}{}_2\text{O}{}_3\text{d}$ ratio, which indicates the degree of Fe oxide crystallinity, is moderately high to very high (0.22–0.58) in middle Holocene to latest Pleistocene soils and progressively decreases to less than 0.10 in older soils; (4) the value of the $\text{Fe}{}_2\text{O}{}_3\text{o}\text{Fe}{}_2\text{O}{}_3\text{d}$ ratio also appears to be infuenced by climate; and (5) temporal changes in Fe oxide content and mineralogy are accompanied by related, systematic changes in clay mineralogy and organic matter content. These relationships are attributed to a soil environment that must initially favor ferrihydrite precipitation and/or organic matter-Fe complexation. Subsequent transformation to hematite causes increasingly intense reddening and a concomitant decrease in the $\text{Fe}{}_2\text{O}{}_3\text{o}\text{Fe}{}_2\text{O}{}_3\text{d}$ ratio. The results demonstrate that iron oxide analysis is useful for numerical age studies of noncalcic soils and shows potential as an indicator of paleoclimates.     

Use of Pitzer's equations to determine the media effect on the formation of lead chloro complexes

The spectrophotometric measurements of chloro complexes of lead in aqueous HCl, NaCl, MgCl₂ and CaCl₂ solutions at 25°C have been analyzed using Pitzer's specific interaction equations. Parameters for activity coefficients of the complexes PbCl⁺, PbCl₂⁰ and PbCl₃^? have been determined for the various media. Values of $\text{K}{}_1\text{= 30.0 ± 0.6}$, $\text{K}{}_2\text{= 106.7 ± 2.1}$ and $\text{K}{}_3\text{= 73.0 ± 1.5}$ were obtained for the cumulative formation constants. [$\text{Pb}{}^{\mathrm{2+}}\text{+ nCl}{}^{\mathrm{?}}\text{→ PbCl}{}_{\mathrm{n}}{}^{\mathrm{2?n}}\text{)}$]. These values are in reasonable agreement with literature data. The Pitzer parameters for the PbCl ion pairs in various media were used to calculate the speciation of Pb²⁺ in an artificial seawater solution.     

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.     

Medium pressure crystallization of a monchiquitic magma — evidence from megacrysts of Drever''s block, Ubekendt Ejland, West Greenland

Megacrysts and polymineralic fragments of extraordinary diversity from a Tertiary monchiquitic dyke of Ubekendt Ejland comprise three groups: (1) Cr-diopside-fassaitic diopside + olivine, Fo_90.5?81.5 + CrAl spinels. (II) Fassaitic salite-ferrisalite + KTi-pargasite-ferropargasite + apatite + AlTi-magnetite, (III) Scapolite + hyalophane + potassium feldspar + nepheline + analcime. By comparison with mineralogy and phase relations in the host rock and experimental data from alkaline rocks the megacrysts are related to a sequence of crystallization from primitive monchiquitic to potassic phonolitic magmas rich in H₂O and CO₂ at 5–11 kb. Group I megacrysts formed at temperatures of 1300-1150°C and group II between ? bar at the latter temperature. High P_co2 may have stabilized the scapolite in the more evolved liquid and K-feldspar and nepheline began to crystallize at ca. 800°C possibly together with the ferrisalite.     

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.     

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.     

Luna 20: mineral chemistry of spinel,pleonaste, chromite,ulvöspinel,ilmenite and rutile

Electron microprobe analyses of the spinel mineral group, ilmenite and rutile have been carried out on part of the Luna 20 soil sample. The spinel group shows an almost continuous trend from MgAl₈O₄ to FeCr₂O₄ and a discontinuous trend from FeCr₂O₄ to Fe₂TiO₄. Well defined non-linear relationships exist within the spinel group for Fe-Mg substitution, for divalent ($\text{FeO}\text{FeO + MgO}$) versus trivalent ($\text{Cr}{}_2\text{O}{}_3\text{Cr}{}_2\text{O}{}_3\text{+ A1}{}_2\text{O}{}_3$), and for divalent versus $\text{TiO}{}_2\text{TiO}{}_2\text{+ A1}{}_2\text{O}{}_3\text{+ Cr}{}_2\text{O}{}_3$. For Cr-Al substitution the relationship is linear and is negative for Mg-rich spinel and positive for Fe-Ti rich spinel. In general a combination of aluminous-rich chromite and ulvöspinel in the Luna 16 samples, combined with the chromian-pleonaste in Apollo 14 define comparable major compositional trends to those observed in Luna 20. Ilmenite is present in trace amounts. It is exsolved from pleonaste and pyroxene, is present in subsolidusreduced ulvöspinel and has undergone reequilibration to produce oriented intergrowths of chromite + rutile. Primary ilmenite is among the most magnesian-rieh (6 wt.% MgO) yet found in the lunar samples. The high MgO, inferred high Cr₂O₃ concentrations and the iron content of rutile (2.5 wt.% FeO) suggest crystallization at high temperatures and pressures for some components of the Luna 20 soil.