Diffusion kinetics of Fe and Mg in aluminous spinel: experimental determination and applications

The diffusion coefficients of Fe²⁺ and Mg in aluminous spinel at ∼20 kb, 950 to 1325°C, and at 30 kb, 1125°C have been determined via diffusion couple experiments and numerical modeling of the induced diffusion profiles. The oxygen fugacity, fO₂, was constrained by graphite encapsulating materials. The retrieved self-diffusion coefficients of Fe²⁺ and Mg at ∼20 kb, 950 to 1325°C, fit well the Arrhenian relation, D = D₀exp(−Q/RT), where Q is the activation energy, with D₀(Fe) = 1.8 (±2.8) × 10⁻⁵, D₀(Mg) = 1.9 (±1.4) × 10⁻⁵ cm²/s, Q(Fe) = 198 ± 19, and Q(Mg) = 202 ± 8 kJ/mol. Comparison with the data at 30 kb suggests an activation volume of ∼5 cm³/mol. From analysis of compositional zoning in natural olivine-spinel assemblages in ultramafic rocks, previous reports concluded that D(Fe-Mg) in spinel with Cr/(Cr + Al) ≤0.5 is ∼10 times that in olivine. The diffusion data in spinel and olivine have been applied to the problems of preservation of Mg isotopic inhomogeneity in spinel within the plagioclase-olivine inclusions in Allende meteorite and cooling rates of terrestrial ultramafic rocks.     

Energetics of multicomponent diffusion in molten CaO-Al2O3-SiO2

The energetics of multicomponent diffusion in molten CaO-Al₂O₃-SiO₂ (CAS) were examined experimentally at 1440 to 1650°C and 0.5 to 2 GPa. Two melt compositions were investigated: a haplodacitic melt (25 wt.% CaO, 15% Al₂O₃, and 60% SiO₂) and a haplobasaltic melt (35% CaO, 20% Al₂O₃, and 45% SiO₂). Diffusion matrices were measured in a mass-fixed frame of reference with simple oxides as end-member components and Al₂O₃ as a dependent variable. Chemical diffusion in molten CAS shows clear evidence of diffusive coupling among the components. The diffusive flux of SiO₂ is significantly enhanced whenever there is a large CaO gradient that is oriented in a direction opposite to the SiO₂ gradient. This coupling effect is more pronounced in the haplodacitic melt and is likely to be significant in natural magmas of rhyolitic to andesitic compositions. The relative magnitude of coupled chemical diffusion is not very sensitive to changes in temperature and pressure.To a good approximation, the measured diffusion matrices follow well-defined Arrhenius relationships with pressure and reciprocal temperature. Typically, a change in temperature of 100°C results in a relative change in the elements of diffusion matrix of 50 to 100%, whereas a change in pressure of 1 GPa introduces a relative change in elements of diffusion matrix of 4 to 6% for the haplobasalt, and less than 5% for the haplodacite. At a pressure of 1 GPa, the ratios between the major and minor eigenvalues of the diffusion matrix λ₁/λ₂ are not very sensitive to temperature variations, with an average of 5.5 ± 0.2 for the haplobasalt and 3.7 ± 0.6 for the haplodacite. The activation energies for the major and minor eigenvalues of the diffusion matrix are 215 ± 12 and 240 ± 21 kJ mol⁻¹, respectively, for the haplodacite and 192 ± 8 and 217 ± 14 kJ mol⁻¹ for the haplobasalt. These values are comparable to the activation energies for self-diffusion of calcium and silicon at the same melt compositions and pressure. At a fixed temperature of 1500°C, the ratios λ₁/λ₂ increase with the increase of pressure, with λ₁/λ₂ varying from 2.5 to 4.1 (0.5 to 1.3 GPa) for the haplodacite and 4 to 6.5 (0.5 to 2.0 GPa) for the haplobasalt. The activation volumes for the major and minor eigenvalues of the diffusion matrix are 0.31 ± 0.44 and 2.3 ± 0.8 cm³ mol⁻¹, respectively, for the haplodacite and −1.48 ± 0.18 and −0.42 ± 0.24 cm³ mol⁻¹ for the haplobasalt. These values are quite different from the activation volumes for self-diffusion of calcium and silicon at the same melt compositions and temperature. These differences in activation volumes between the two melts likely result from a difference in the structure and thermodynamic properties of the melt between the two compositions (e.g., partial molar volume).Applications of the measured diffusion matrices to quartz crystal dissolution in molten CAS reveal that the activation energy and activation volume for quartz dissolution are almost identical to the activation energy and activation volume for diffusion of the minor or slower eigencomponent of the diffusion matrix. This suggests that the diffusion rate of slow eigencomponent is the rate-limiting factor in isothermal crystal dissolution, a conclusion that is likely to be valid for crystal growth and dissolution in natural magmas when diffusion in liquid is the rate-limiting factor.     

Tracer diffusion of Mg, Ca, Sr, and Ba in Na-aluminosilicate melts

We employed the thin source technique to investigate tracer diffusion of Mg, Ca, Sr, and Ba in glasses and supercooled melts of albite (NaAlSi₃O₈) and jadeite (NaAlSi₂O₆) compositions. The experiments were conducted at 1 bar and at temperatures between 645 and 1025°C. Typical run durations ranged between 30 min and 35 days. The analysis of the diffusion profiles was performed with the electron microprobe. Diffusivities of Ca, Sr, and Ba were found to be independent of either duration t of the experiment or tracer concentration M, initially introduced into the sample. Mg exhibits a diffusivity depending on run time and concentration and tracer diffusivity is derived by extrapolation to M/√t = 0. Temperature dependence of the diffusivity D can be represented by an Arrhenius equation D = D_o exp(−E_a/RT), yielding the following least-squares fit parameters (with D in m²/s and E_a in kJ/mol): D_Mg = 1.8 · 10⁻⁵ exp(−234 ± 20/RT), D_Ca = 3.5 · 10⁻⁶ exp(−159 ± 6/RT), D_Sr = 3.6 · 10⁻⁶ exp(−160 ± 6/RT), and D_Ba = 6.0 · 10⁻⁶ exp(−188 ± 12/RT) for albite; and D_Mg = 8.3 · 10⁻⁶ exp(−207 ± 18/RT), D_Ca = 3.8 · 10⁻⁶ exp(−153 ± 4/RT), D_Sr = 2.3 · 10⁻⁶ exp(−150 ± 4/RT), and D_Ba = 3.7 · 10⁻⁵ exp(−198 ± 4/RT) for jadeite composition. Ca and Sr diffusivities agree within error in both compositions and exhibit the fastest diffusivities, whereas Mg reveals the lowest diffusivity. The relationship between activation energy and radius shows a minimum at Ca and Sr for albite and jadeite compositions extending the relationship already observed elsewhere for alkalies. With increasing substitution of Si by (Na + Al), diffusivities increase, whereas activation energies decrease. Furthermore, a simple model modified from that of Anderson and Stuart (Anderson O. L. and Stuart D. A., “Calculation of activation energy of ionic conductivity in silica glasses by classical methods,” J. Am. Ceram. Soc.37, 573-580, 1954) is discussed for calculating the activation energies.     

Hydration-dehydration behavior and thermodynamics of chabazite

Equilibrium in the chabazite-H₂O system was investigated by isothermal thermogravimetric analysis over a large range of temperatures (from 23 to 315°C) and H₂O-vapor pressures (from 0.03 to 28 mbar). Thermodynamic analysis of the phase-equilibrium data revealed the existence of three energetically distinct types of H₂O, referred to as S-1, S-2, and S-3. At 23°C and 26 mbar of H₂O-vapor pressure, chabazite has maximum H₂O occupancies of 8.2, 11.1, and 3.1 wt.% for S-1, S-2, and S-3, respectively. During dehydration, S-1 H₂O is lost first, followed by S-2 H₂O and then S-3 H₂O, with significant overlap for S-1 and S-2 as well as S-2 and S-3. The thermodynamics of chabazite-H₂O were modeled using three independent equilibrium formulations for S-1, S-2, and S-3. These formulations yielded standard-state molar Gibbs free energy of hydration of −21.8 ± 0.6, −52.1 ± 1.8, and −111.7 ± 6.7 kJ/mol for S-1, S-2, and S-3. Standard-state molar enthalpies of hydration for each type of H₂O are −65.6 ± 0.5, −100.1 ± 1.6, and −156.9 ± 6.2 kJ/mol, respectively. Integral molar values for the Gibbs free energy of hydration for each type of H₂O are −19.0 ± 0.7, −40.1 ± 2.1, and −76.9 ± 9.6 kJ/mol, respectively. Integral molar values for the enthalpy of hydration for each type of H₂O are −62.8 ± 0.6, −88.1 ± 1.9, and −122.2 ± 9.3 kJ/mol, respectively. Integration of the predicted total partial molar enthalpy of hydration for all three types of H₂O over the full H₂O content of chabazite gave an integral molar enthalpy of −39.65 ± 9.3 kJ/mol relative to liquid water. The thermodynamic data obtained for the hydration of natural chabazite were used to predict the hydration state of chemically similar chabazites under various temperatures and P_H2O, ranging from 25 to 400°C and from 10⁻⁵ to 10⁴ bars.     

Diffusion of lead in plagioclase and K-feldspar: an investigation using Rutherford Backscattering and Resonant Nuclear Reaction Analysis

Chemical diffusion of Pb has been measured in K-feldspar (Or₉₃) and plagioclase of 4 compositions ranging from An₂₃ to An₉₃ under anhydrous, 0.101 MPa conditions. The source of diffusant for the experiments was a mixture of PbS powder and ground feldspar of the same composition as the sample. Rutherford Backscattering (RBS) was used to measure Pb diffusion profiles. Over the temperature range 700–1050°C, the following Arrhenius relations were obtained (diffusivities in m²s^-1):Oligoclase (An₂₃): Diffusion normal to (001): log D = ( – 6.84 ± 0.59) – [(261 ± 13 kJ mol ^–1)/2.303RT]Diffusion normal to (010): log D = ( – 3.40 ± 0.50) – [(335 ± 11 kJ mol ^–1)/2.303RT]Andesine (An₄₃): Diffusion normal to (001): log D = ( – 6.73 ± 0.54) – [(266 ± 12 kJ mol ^–1)/2.303RT] Diffusion normal to (010) appears to be only slightly slower than diffusion normal to (001) in andesine.Labradorite (An₆₇): Diffusion normal to (001): log D = ( – 7.16 ± 0.61) – [(267 ± 13 kJ mol ^–1)/2.303RT] Diffusion normal to (010) is slower by 0.7 log units on average.Anorthite Diffusion normal to (010): log D = ( – 5.43 ± 0.48) – [(327 ± 11 kJ mol ^–1)/2.303RT]K-feldspar (Or₉₃): Diffusion normal to (001): log D = ( – 4.74 ± 0.52) – [(309 ± 16 kJ mol ^–1)/2.303RT] Diffusion normal to (010): log D = ( – 5.99 ± 0.51) – [(302 ± 11 kJ mol ^–1)/2.303RT]In calcic plagioclase, Pb uptake is correlated with a reduction of Ca, indicating the involvement of PbCa exchange in chemical diffusion. Decreases of Na and K concentrations in sodic plagioclase and K-feldspar, respectively, are correlated with Pb uptake and increase in Al concentration (measured by resonant nuclear reaction analysis), suggesting a coupled process for Pb exchange in these feldspars. These results have important implications for common Pb corrections and Pb isotope systematics. Pb diffusion in apatite is faster than in the investigated feldspar compositions, and Pb diffusion rates in titanite are comparable to both K-feldspar and labradorite. Given these diffusion data and typical effective diffusion radii for feldspars and accessory minerals, we may conclude that feldspars used in common Pb corrections are in general less inclined to experience diffusion-controlled Pb isotope exchange than minerals used in U-Pb dating that require a common Pb correction.     

Calorimetric measurements of fusion enthalpies for Ni2SiO4 and Co2SiO4 olivines and application to olivine-liquid partitioning

Calorimetric measurements of fusion enthalpies for Ni₂SiO₄ and Co₂SiO₄ olivines were carried out using a high-temperature calorimeter, and Ni and Co partitioning between olivine and silicate liquid was analyzed using the measured heats of fusion. The fusion enthalpy of Co₂SiO₄ olivine measured by transposed-temperature drop calorimetry was 103 ± 15 kJ/mol at melting point (1688 K). The fusion enthalpy of Ni₂SiO₄ olivine was calculated based on the enthalpies of liquids in the system An₅₀Di₅₀-Ni₂SiO₄ measured by transposed-temperature drop calorimetry at 1773 K, and was 221 ± 26 kJ/mol at its metastable melting point (1923 K). The fusion enthalpy of Ni₂SiO₄ is the largest among those of olivine group, this is caused by the large crystal field stabilization energy of six-coordinated Ni²⁺ in olivine. The larger fusion enthalpy of Ni₂SiO₄ can account for the large and variable partition coefficient of Ni between olivine and silicate liquid. Based on the comparison between partition coefficients calculated from thermodynamic data and those observed in partition experiments, it is considered that the magnitude of partition coefficients is primarily dependent on the heats of fusion of the components. Furthermore, the activity coefficients for Ni-, Co- and Mn-bearing components in magmatic liquid are nearly of the same magnitude.     

Oxygen diffusion in three silicate melts along the join diopside-anorthite

The self-diffusion of oxygen has been measured for three silicate melts along the join diopsideanorthite. The experiments were done by isotope exchange between an “infinite” reservoir of oxygen gas and spheres of melt. The oxygen self-diffusion coefficients for the three melts are given as: C-1(diopside): D = 1.64 × 10¹ exp(?(63.2 ± 20)(kcal/mole)/RT) cm²/sec C-2(Di₅₈An₄₂): D = 1.35 × 10^?1 exp(?(46.8 ± 9)(kcal/mole)/RT) cm²/sec C-3(Di₄₀An₆₀): D = 1.29 × 10^?2 exp(?(44.2 ± 6)(kcal/mole)/RT) cm²/secThe self-diffusion coefficients do not agree with the Eyring equation unless mean ionic jump distances (λ) considerably larger than the diameter of oxygen anion are assumed. However, the sense of variation of the actual diffusivities is as the Eyring equation predicts.Consideration of the results of this study and the bulk of previous work shows that oxygen appears to conform to the compensation law for cationic diffusion in silicate melts and glasses. The range of oxygen diffusivities was also found to encompass the field of divalent cation diffusivities in silicate melts.Those results imply that the diffusion of oxygen in silicate melts may involve a contribution from a cation-like diffusion mechanism (discrete O^2? anions) as well as contributions from the diffusion of larger structural units.     

Activation volumes for oxygen exchange between the GaO4Al12(OH)24(H2O)127+(aq) (GaAl12) polyoxocation and aqueous solution from variable pressure O NMR spectroscopy

Activation volumes for exchange of oxygen between bulk aqueous solution and sites in the GaO₄Al₁₂(OH)₂₄(H₂O)₁₂⁷⁺(aq) (GaAl₁₂) complex were measured by variable-pressure ¹⁷O NMR techniques. Near 322 K, rates of exchange for the less labile set of bridging hydroxyls in the GaAl₁₂ decrease by a factor of about two with increasing pressure from 0.1 to 350 MPa. These data indicate a substantially positive activation volume of ΔV^‡ = +7 ± 1 cm³/mol, which is the first activation volume measured for a bridging hydroxyl in a polynuclear complex. This result suggests significant bond-lengthening in the activation step. Electrostriction effects should be small because exchange occurs via a pH-independent path under the experimental conditions. The second, more labile set of bridging hydroxyls exchange too rapidly for the variable-pressure techniques employed here. The exchange of bound-water molecules on the GaAl₁₂ was observed at P = 350 MPa using the ¹⁷O-NMR line-broadening technique. Comparison with previous measurements at 0.1 MPa indicates decreasing line width from 0.1 to 350 MPa for temperatures at which exchange dominates, yielding an activation volume of ΔV^‡ = +3(± 1) cm³/mol. This activation volume is smaller than the value for the Al(H₂O)₆³⁺ complex, suggesting that water exchange on the larger GaAl₁₂ complex has less dissociative character although the average charge density is lower.     

Effects of seawater carbonate ion concentration and temperature on shell U, Mg, and Sr in cultured planktonic foraminifera

We investigate the sensitivity of U/Ca, Mg/Ca, and Sr/Ca to changes in seawater [CO₃²⁻] and temperature in calcite produced by the two planktonic foraminifera species, Orbulina universa and Globigerina bulloides, in laboratory culture experiments. Our results demonstrate that at constant temperature, U/Ca in O. universa decreases by 25 ± 7% per 100 μmol [CO₃²⁻] kg⁻¹, as seawater [CO₃²⁻] increases from 110 to 470 μmol kg⁻¹. Results from G. bulloides suggest a similar relationship, but U/Ca is consistently offset by ∼+40% at the same environmental [CO₃²⁻]. In O. universa, U/Ca is insensitive to temperature between 15°C and 25°C. Applying the O. universa relationship to three U/Ca records from a related species, Globigerinoides sacculifer, we estimate that Caribbean and tropical Atlantic [CO₃²⁻] was 110 ± 70 μmol kg⁻¹ and 80 ± 40 μmol kg⁻¹ higher, respectively, during the last glacial period relative to the Holocene. This result is consistent with estimates of the glacial-interglacial change in surface water [CO₃²⁻] based on both modeling and on boron isotope pH estimates. In settings where the addition of U by diagenetic processes is not a factor, down-core records of foraminiferal U/Ca have potential to provide information about changes in the ocean’s carbonate concentration.Below ambient pH (pH < 8.2), Mg/Ca decreased by 7 ± 5% (O. universa) to 16 ± 6% (G. bulloides) per 0.1 unit increase in pH. Above ambient pH, the change in Mg/Ca was not significant for either species. This result suggests that Mg/Ca-based paleotemperature estimates for the Quaternary, during which surface-ocean pH has been at or above modern levels, have not been biased by variations in surface-water pH. Sr/Ca increased linearly by 1.6 ± 0.4% per 0.1 unit increase in pH. Shell Mg/Ca increased exponentially with temperature in O. universa, where Mg/Ca = 0.85 exp (0.096*T), whereas the change in Sr/Ca with temperature was within the reproducibility of replicate measurements.     

熔融SiO2中原子自扩散性质的分子动力学模拟

研究地幔熔体中元素的扩散性质有着重要的意义,因其影响着元素的交换和分馏过程。SiO2 作为地幔组成的重要组
分之一,其物理化学行为对于地幔动力学过程有着重要的意义。本文研究了SiO2 熔体中元素的扩散机制和自扩散系数与
压力的关系,采用Morse stretch 势场对含有4500 个原子的熔融SiO2 体系进行了分子动力学模拟,计算了硅氧自扩散系数在
3000 K 温度下随压力的变化。模拟结果显示,在0.0001~40 GPa的压力区间,硅氧元素的自扩散系数均先上升后下降,在
17.5 GPa 时达到最大值,O 原子的扩散速率略高于Si 原子。硅氧元素的扩散方式为缺陷控制运移机制,其中硅原子的五配位
结构的形成是关键,为导致扩散系数随压力增大而上升的主要原因,扩散系数的最大值意味着SiO2 熔体中5 配位硅形成机
制的改变。本文也计算了单位［SiO2］的平均体积和压力的关系,结果与实验很吻合。     

Phase relations on the diopside-jadeite-hedenbergite join up to 24 GPa and stability of Na-bearing majoritic garnet

Phase relations on the diopside (Di)-hedenbergite (Hd)-jadeite (Jd) system modeling mineral associations of natural eclogites were studied for the compositions (mol %) Di₇₀Jd₃₀, Di₅₀Jd₅₀, Di₃₀Jd₇₀, Di₂₀Hd₈₀, and Di₄₀Hd₁₀Jd₅₀ using a toroidal anvil-with-hole (7 GPa) and a Kawai-type 6-8 multianvil apparatus (12-24 GPa). We established that Di, Hd, and Jd form complete series of solid solutions at 7 GPa, and melting temperatures of pure Di (1980 °C) and Jd (1870 °C) for that pressure were estimated experimentally. The melting temperature for the Di₅₀Jd₅₀ composition at 15.5 GPa is 2270 °C. The appearance of garnet is clearly dependent on initial clinopyroxene composition: at 1600 °C the first garnet crystals are observed at 13.5 GPa in the jadeite-rich part of the system (Di₃₀Jd₇₀), whereas diopside-rich starting material (Di₇₀Jd₃₀) produces garnet only above 17 GPa. The proportion of garnet increases rapidly above 18 GPa as pyroxene dissolves in the garnet structure and pyroxene-free garnetites are produced from diopside-rich starting materials. In all experiments, garnet coexists with stishovite (St). At a pressure above 18 GPa, pyroxene is completely replaced by an assemblage of majorite (Maj) + St + CaSiO₃-perovskite (Ca-Pv) in Ca-rich systems, whereas Maj is associated with almost pure Jd up to a pressure of 21.5 GPa. Above ∼22 GPa, Maj, and St are associated with NaAlSiO₄ with calcium ferrite structure (Cf). We established that an Hd component also spreads the range of pyroxene stability up to 20 GPa. In the Di₇₀Jd₃₀ system at 24 GPa an assemblage of Maj + Ca-Pv + MgSiO₃ with ilmenite structure (Mg-Il) was obtained. The experimentally established correlation between Na, Si, and Al contents in Maj and pressure in Grt(Maj)-pyroxene assemblages, may be the basis for a “majorite” geobarometer. The results of our experiments are applicable to the upper mantle and the transition zone of the Earth (400-670 km), and demonstrate a wide range of transformations from eclogite to perovskite-bearing garnetite. In addition, the mineral associations obtained from the experiments allowed us to simulate parageneses of inclusions in diamonds formed under the conditions of the transition zone and the lower mantle.     

Studies of equilibrium, structure, and dynamics in the aqueous Al(iii)-oxalate-fluoride system by potentiometry, C and F NMR spectroscopy

The AlOx_1-3 (Ox = oxalate) species were identified in 0.6 M aqueous NaCl by ¹³C nuclear magnetic resonance (NMR). Rate constants and activation parameters for intramolecular cis/trans isomerization of the Werner-type AlOx₂⁻ complex (k(298 K) = 5 s⁻¹, ΔH^# = 67 ± 5 kJ mol⁻¹, ΔS^# = −6 ± 6 J mol⁻¹ K⁻¹, the rate determining step could be the breaking of the Al-O(C=O) bond) and a very slow intermolecular ligand exchange reaction of AlOx₃³⁻ complex and the free ligand (k₃₀(298 K) = 6.6 · 10⁻⁵ s⁻¹, ΔH^# = 164 ± 17 kJ mol⁻¹, ΔS^# = 225 ± 51 J mol⁻¹ K⁻¹, D/I_d mechanism) were determined by dynamic 1D and 2D ¹³C NMR measurements. Mixed complexes, AlFOx, AlFOx₂^2-, AlF₂Ox⁻, and AlF₂Ox₂^3-, with overall stability (logβ) of 11.53 ± 0.03, 15.67 ± 0.03, 15.74 ± 0.02, and 19.10 ± 0.04 were measured by potentiometry using pH- and fluoride-selective electrodes and confirmed by ¹³C and¹⁹F NMR. The role of these complexes in gibbsite dissolution was modeled. The mixed Al(III)-Ox^2--F⁻ complexes have to be considered as the chemical speciation of Al(III) in natural waters is discussed.     

Ar and K partitioning between clinopyroxene and silicate melt to 8 GPa

The relative incompatibility of Ar and K are fundamental parameters in understanding the degassing history of the mantle. Clinopyroxene is the main host for K in most of the upper mantle, playing an important role in controlling the K/Ar ratio of residual mantle and the subsequent time-integrated evolution of ⁴⁰Ar/³⁶Ar ratios. Clinopyroxene also contributes to the bulk Ar partition coefficient that controls the Ar degassing rate during mantle melting. The partitioning of Ar and K between clinopyroxene and quenched silicate melt has been experimentally determined from 1 to 8 GPa for the bulk compositions Ab₈₀Di₂₀ (80 mol% albite-20 mol% diopside) and Ab₂₀Di₈₀ with an ultraviolet laser ablation microprobe (UVLAMP) technique for Ar analysis and the ion microprobe for K. Data for Kr (UVLAMP) and Rb (ion probe) have also been determined to evaluate the role of crystal lattice sites in controlling partitioning. By excluding crystal analyses that show evidence of glass contamination, we find relatively constant Ar partition coefficients (D_Ar) of 2.6 × 10⁻⁴ to 3.9 × 10⁻⁴ for the Ab₈₀Di₂₀ system at pressures from 2 to 8 GPa. In the Ab₂₀Di₈₀ system, D_Ar shows similar low values of 7.0 × 10⁻⁵ and 3.0 × 10⁻⁴ at 1 to 3 GPa. All these values are several orders of magnitude lower than previous measurements on separated crystal-glass pairs.D_K is 10 to 50 times greater than D_Rb for all experiments, and both elements follow parallel trends with increasing pressure, although these trends are significantly different in each system studied. The D_K values for clinopyroxene are at least an order of magnitude greater than D_Ar under all conditions investigated here, but D_Ar appears to show more consistent behavior between the two systems than K or Rb. The partitioning behavior of K and Rb can be explained in terms of combined pressure, temperature, and crystal chemistry effects that result in changes for the size of the clinopyroxene M2 site. In the Ab₂₀Di₈₀ system, where clinopyroxene is diopside rich at all pressures, D_K and D_Rb increase with pressure (and temperature) in an analogous fashion to the well-documented behavior of Na. For the Ab₈₀Di₂₀ system, the jadeite content of the clinopyroxene increases from 22 to 75 mol% with pressure resulting in a contraction of the M2 site. This has the effect of discriminating against the large K⁺ and Rb⁺ ions, thereby countering the effect of increasing pressure. As a consequence D_K and D_Rb do not increase with pressure in this system.In contrast to the alkalis (Na, K, and Rb), D_Kr values are similar to D_Ar despite a large difference in atomic radius. This lack of discrimination (and the constant D_Ar over a range of crystal compositions) is also consistent with incorporation of these heavier noble gases at crystal lattice sites and a predicted consequence of their neutrality or “zero charge.” Combined with published D_Ar values for olivine, our results confirm that magma generation is an efficient mechanism for the removal of Ar from the uppermost 200 km of the mantle, and that K/Ar ratios in the residuum are controlled by the amount of clinopyroxene. Generally, Ar is more compatible than K during mantle melting because D_Ar for olivine is similar to D_K for clinopyroxene. As a result, residual mantle that has experienced variable amounts of melt extraction may show considerable variability in time-integrated ³⁶Ar/⁴⁰Ar.     

Diffusion and viscosity of Mg2SiO4 liquid at high pressure from first-principles simulations

We investigate two key transport properties, self-diffusion and viscosity, of Mg₂SiO₄ liquid as a function of temperature and pressure using density functional theory-based molecular dynamics method. Liquid dynamics in a 224-atom supercell was captured in equilibrium simulations of relatively long durations (50-300 ps) to obtain an acceptable convergence. Our results show that Mg and Si are, respectively, the most and least mobile species at most conditions studied and all diffusivities become similar at high pressure. With increasing temperature from 2200 to 6000 K at ambient pressure, the self-diffusivities increase by factors of 25 (Mg), 80 (Si) and 65 (O), and the viscosity decreases by a factor of 30. The predicted temperature variations of all transport coefficients closely follow the Arrhenian law. However, their pressure variations show a significant non-Arrhenian behavior and also are sensitive to temperature. At 3000 K, the diffusivity (viscosity) decreases (increases) by more than one order of magnitude between 0 and 50 GPa with their activation volumes increasing on compression. Over the entire mantle pressure range, the variations at 4000 K are of two orders of magnitude with nearly constant activation volumes whereas the variations at 6000 K are within one order of magnitude with decreasing activation volumes. The predicted complex dynamical behavior of Mg₂SiO₄ liquid can be associated with the structural changes occurring on compression. We also estimate the diffusivity and viscosity profiles along a magma ocean isentrope, which suggest that the melt transport properties vary modestly over the relevant magma ocean depth ranges.     

Flow of river water into a Karstic limestone aquifer. 1. Tracing the young fraction in groundwater mixtures in the Upper Floridan Aquifer near Valdosta, Georgia

The quality of water in the Upper Floridan aquifer near Valdosta, Georgia is affected locally by discharge of Withlacoochee River water through sinkholes in the river bed. Data on transient tracers and other dissolved substances, including Cl⁻, ³H, tritiogenic helium-3 (³He), chlorofluorocarbons (CFC-11, CFC-12, CFC-113), organic C (DOC), O₂ (DO), H₂S, CH₄, δ¹⁸O, δD, and ¹⁴C were investigated as tracers of Withlacoochee River water in the Upper Floridan aquifer. The concentrations of all tracers were affected by dilution and mixing. Dissolved Cl⁻, δ¹⁸O, δD, CFC-12, and the quantity (³H+³He) are stable in water from the Upper Floridan aquifer, whereas DOC, DO, H₂S, CH₄, ¹⁴C, CFC-11, and CFC-113 are affected by microbial degradation and other geochemical processes occurring within the aquifer. Groundwater mixing fractions were determined by using dissolved Cl⁻ and δ¹⁸O data, recognizing 3 end-member water types in the groundwater mixtures: (1) Withlacoochee River water (δ¹⁸O=−2.5±0.3‰, Cl⁻=12.2±2 mg/l), (2) regional infiltration water (δ¹⁸O=−4.2±0.1‰, Cl⁻=2.3±0.1 mg/l), and (3) regional paleowater resident in the Upper Floridan aquifer (δ¹⁸O=−3.4±0.1‰, Cl⁻=2.6±0.1 mg/l) (uncertainties are ±1σ). Error simulation procedures were used to define uncertainties in mixing fractions. Fractions of river water in groundwater range from 0 to 72% and average 10%. The influence of river-water discharge on the quality of water in the Upper Floridan aquifer was traced from the sinkhole area on the Withlacoochee River 25 km SE in the direction of regional groundwater flow. Infiltration of water is most significant to the N and NW of Valdosta, but becomes negligible to the S and SE in the direction of general thickening of post-Eocene confining beds overlying the Upper Floridan aquifer.     

Isopiestic measurement of the osmotic and activity coefficients for the NaOH-NaAl(OH)4-H2O system at 313.2 K

By using a specially designed and constructed isopiestic apparatus, we measured the osmotic coefficients at 313.2 K for the NaOH-NaAl(OH)₄-H₂O system with the total alkali molality, m_NaOHT (m_NaOH + m_NaAl[OH]4), from 0.05 mol/kg H₂O to 12 mol/kg H₂O and α_K (m_NaOHT/m_NaAl(OH)4) from 1.64 to 5.53. The mean standard deviation of the measurements is 0.0038. Several sets of the Pitzer model parameters for NaOH-NaAl(OH)₄-H₂O system were then obtained by regressing the measured osmotic coefficients with the Pitzer model and the Pitzer model parameters for NaOH(aq). One set of the results is as follows: β⁽⁰⁾_NaOH: 0.08669, β⁽¹⁾_NaOH: 0.31446, β⁽²⁾_NaOH: −0.00007367, C^Φ_NaOH: 0.003180, β⁽⁰⁾_NaAl(OH)4: 0.03507, β⁽¹⁾_NaAl(OH)4: 0.02401, C^Φ_NaAl(OH)4: −0.001066, θ_{OH⁻Al(OH)4⁻}: 0.08177, Ψ_Na⁺OH⁻_Al(OH)4⁻: −0.01162. The mean standard difference between the calculated and the measured osmotic coefficients is 0.0088. With the obtained Pitzer model parameters, we calculated the values of K = (γ_{NaAl(OH)4,cal²} · m_{Al(OH)4⁻,exp})/(γ_NaOH,cal² · m_OH⁻,exp) for the gibbsite solubility. The results show that the obtained Pitzer model parameters are reliable, and the relative error of the calculated activity coefficients should be < 2.1%. We also compared the calculated gibbsite solubility data among several activity coefficients models over a range of m_NaOHT at various temperatures. The comparison indicates that our activity coefficients model may be approximately applied in the ranges of temperature from 298.2 to 323.2 K and m_NaOHT from 0 to 8 mol/kg H₂O. We also calculated the stoichiometric activity coefficients of NaOH and NaAl(OH)₄ and the activity of H₂O for the NaOH-NaAl(OH)₄-H₂O system, and these calculations establish their variations with m_NaOHT and α_K. These variations imply that the strengths of the repulsive interactions among various anions are in the following sequence: Al(OH)₄⁻-Al(OH)₄⁻ < Al(OH)₄⁻-OH⁻ < OH⁻-OH⁻, and the attractive interaction between Al(OH)₄⁻ and H₂O is weaker than that between OH⁻ and H₂O.     

Experimental determination of the diffusion coefficient for calcium in olivine between 900°C and 1500°C

Experiments have been carried out to determine the temperature, oxygen fugacity (fO₂) and compositional dependence of the tracer diffusion coefficient (D) of calcium in olivine. These data constrain the diffusion coefficient over the temperature range 900 to 1500°C for the three principal crystallographic axes. Well constrained linear relationships between the reciprocal of the absolute temperature and log(D) exist at any given oxygen fugacity. There is a strong dependence of the diffusion coefficient on oxygen fugacity with D ∝ fO₂^(1/3). This makes a knowledge of the T-fO₂ path followed by geological samples a prerequisite for modelling Ca diffusion in olivine. The best fitting preexponential factor (Do) and activation energy (E) to the Arrhenius equation log (D) = log [Do exp(−E/RT)] + 0.31Δ log fO₂ for Ca diffusion in olivine at a given oxygen fugacity (fO₂*) are given by:diffusion along [100]: log [Do (m²/s)] = −10.78 ± 0.43; E = 193 ± 11 kJ/moldiffusion along [010]: log [Do (m²/s)] = −10.46 ± 0.37; E = 201 ± 10 kJ/moldiffusion along [001]: log [Do (m²/s)] = −10.02 ± 0.29; E = 207 ± 8 kJ/molwhere Δ log fO₂ = log[fO₂*] − log[10⁻¹²] with fO₂* in units of bars. There is no measurable compositional dependence of the diffusion coefficient between Fo₈₃ and Fo₉₂. Diffusion in Fo₁₀₀ has a much higher activation energy than in Fe-bearing olivine and has a weaker fO₂ dependence.     

Energetics of anhydrite, barite, celestine, and anglesite: a high-temperature and differential scanning calorimetry study

The thermochemistry of anhydrous sulfates (anglesite, anhydrite, arcanite, barite, celestine) was investigated by high-temperature oxide melt calorimetry and differential scanning calorimetry. Complete retention and uniform speciation of sulfur in the solvent was documented by (a) chemical analyses of the solvent (3Na₂O · 4MoO₃) with dissolved sulfates, (b) Fourier transform infrared spectroscopy confirming the absence of sulfur species in the gases above the solvent, and (c) consistency of experimental determination of the enthalpy of drop solution of SO₃ in the solvent. Thus, the principal conclusion of this study is that high-temperature oxide melt calorimetry with 3Na₂O · 4MoO₃ solvent is a valid technique for measurement of enthalpies of formation of anhydrous sulfates. Enthalpies of formation (in kJ/mol) from the elements (ΔH_f^o) were determined for synthetic anhydrite (CaSO₄) (−1433.8 ± 3.2), celestine (SrSO₄) (−1452.1 ± 3.3), anglesite (PbSO₄) (−909.9 ± 3.4), and two natural barite (BaSO₄) samples (−1464.2 ± 3.7, −1464.9 ± 3.7). The heat capacity of anhydrite, barite, and celestine was measured between 245 and 1100 K, with low- and high-temperature Netzsch (DSC-404) differential scanning calorimeters. The results for each sample were fitted to a Haas-Fisher polynomial of the form C_p(245 K < T < 1100 K) = a + bT + cT⁻² + dT^−0.5 + eT². The coefficients of the equation are as follows: for anhydrite a = 409.7, b = −1.764 × 10⁻¹, c = 2.672 × 10⁶, d = −5.130 × 10³, e = 8.460 × 10⁻⁵; for barite, a = 230.5, b = −0.7395 × 10⁻¹, c = −1.170 × 10⁶, d = −1.587 × 10³, e = 4.784 × 10⁻⁵; and for celestine, a = 82.1, b = 0.8831 × 10⁻¹, c = −1.213 × 10⁶, d = 0.1890 × 10³, e = −1.449 × 10⁻⁵. The 95% confidence interval of the measured C_p varies from 1 to 2% of the measured value at low temperature up to 2 to 5% at high temperature. The measured thermochemical data improve or augment the thermodynamic database for anhydrous sulfates and highlight the remaining discrepancies.     

Experimental study of the stability of aluminate-borate complexes in hydrothermal solutions

Formation of aqueous aluminate-borate complexes was characterized at 25°C using ²⁷Al NMR spectroscopy, and at 50-200°C via measurements of gibbsite and boehmite solubility in the presence of boric acid. ²⁷Al spectra performed at pH = 9 in Al-B solution with m(B) = 0.02 show the presence of two peaks at 80.5 and 74.5 ppm which correspond to Al(OH)₄⁻ and a single Al-substituted Q¹_Al dimer, Al(OH)₃OB(OH)₂⁻, respectively. In 0.08 m and 0.2 m borate solution, a third peak appears at 68.5 ppm which can be assigned to the Q²_Al trimer Al(OH)₂O₂(B(OH)₂)₂⁻. These chemical shifts are close to those measured for Al(OH)₃OSi(OH)₃⁻ and Al(OH)₂O₂(Si(OH)₃)₂⁻ (74 and 69.5 ppm, respectively; Pokrovski et al., Min. Mag.62a (1998), 1194) which demonstrates the similar structure of Al-B and Al-Si complexes formed in alkaline solutions. Gibbsite and boehmite solubility were measured in weakly basic solutions as a function of boric acid concentration at 50°C and 78 to 200°C, respectively. Equilibrium was reached within several days at m(B) = 0.01-0.1, but more slowly at higher boron concentrations, and at 50°C and m(B) = 0.2, Al concentration increased continuously during at least 3 months as a result of the sluggish formation of Al-polyborates. The equilibrium constant of the reaction Al(OH)₄⁻ + B(OH)₃⁰_(aq) = Al(OH)₃OB(OH)₂⁻ + H₂O decreases very slowly with increasing temperature to 200°C. The log K values are 1.58 ± 0.10, 1.46 ± 0.10, 1.52 ± 0.15, and 1.25 ± 0.15 at 50, 78, 150 and 200°C, respectively, which result in the following values of the standard thermodynamic properties for this reaction: Δ_rG⁰ = −9.22 ± 3.25 kJ/mol, Δ_rH⁰ = −4.6 ± 2.5 kJ/mol, Δ_rS⁰ = 15.5 ± 6.9 J/mol K. The thermodynamic data generated in this study indicate that Al-B complexes can dominate aqueous aluminum speciation in solutions containing ≥0.7 g/L of boron at temperature to at least 400°C.