Dissolution kinetics of diopside as a function of solution saturation state: Macroscopic measurements and implications for modeling of geological storage of CO₂     

Damien Daval  Roland Hellmann  Delphine Tisserand  François Guyot 《Geochimica et cosmochimica acta》2010,74(9):2615-5525

Measurements of the dissolution rate of diopside (r) were carried out as a function of the Gibbs free energy of the dissolution reaction (ΔG_r) in a continuously stirred flow-through reactor at 90 °C and pH_90 °C = 5.05. The overall relation between r and ΔG_r was determined over a free energy range of −130.9 < ΔG_r < −47.0 kJ mo1⁻¹. The data define a highly non-linear, sigmoidal relation between r and ΔG_r. At far-from-equilibrium conditions (ΔG_r ? −76.2 kJ mo1⁻¹), a rate plateau is observed. In this free energy range, the rates of dissolution are constant, independent of [Ca], [Mg] and [Si] concentrations, and independent of ΔG_r. A sharp decrease of the dissolution rate (∼1 order of magnitude) occurs in the transition ΔG_r region defined by −76.2 < ΔG_r ? −61.5 kJ mo1⁻¹. Dissolution closer to equilibrium (ΔG_r > −61.5 kJ mo1⁻¹) is characterised by a much weaker inverse dependence of the rates on ΔG_r. Modeling the experimental r-ΔG_r data with a simple classical transition state theory (TST) law as implemented in most available geochemical codes is found inappropriate. An evaluation of the consequences of the use of geochemical codes where the r-ΔG_r relation is based on basic TST was carried out and applied to carbonation reactions of diopside, which, among other reactions with Ca- and Mg-bearing minerals, are considered as a promising process for the solid state sequestration of CO₂ over long time spans. In order to take into account the actual experimental r-ΔG_r relation in the geochemical code that we used, a new module has been developed. It reveals a dramatic overestimation of the carbonation rate when using a TST-based geochemical code. This points out that simulations of water-rock-CO₂ interactions performed with classical geochemical codes should be evaluated with great caution.  相似文献   

Dissociation constants of calcite and CaHC0₃⁺ from 0 to 50°C     

Roger L Jacobson  Donald Langmuir 《Geochimica et cosmochimica acta》1974,38(2):301-318

From conductance measurements, the negative logarithm of the dissociation constant of the CaHCO₃₊ ion pair, pK(CaHCO₃⁺), is 0.7, 1.0 and 1.35 within ±0.05 units at 0, 25 and 60°C, respectively. A revaluation of published and unpublished data yields pK(CaCO₃⁰) ≈ 3.2 at 25°C. Use of these pK's to compute the dissociation constant of calcite (Kc) from published calcite solubility measurements in pure water gives pKc values which increase markedly with ionic strength. However, if the ion pairs are ignored, computed pKc values are nearly constant with ionic strength. All reasonable attempts to eliminate the trend in pKc by adjusting ion activity coefficients, and/or values of K(CaCO₃⁰) failed, so the dilemma remains. Kc values computed from the most reliable published calcite solubility data are in good agreement with such values based on solubility data measured in this study at 5, 15, 35 and 50°C. Study results ignoring ion pairs are accurately represented by the equation log Kc = 13.870 — (3059/T) ?0.04035T, and correspond to ?8.35, ?8.42, and ?8.635 at 0, 25 and 50°C, respectively. The logarithmic expression leads to ΔH_r^o = ?2420 ± 300 cal/mol, ΔCp = ?110 ± 2 cal/deg mol, and ΔS_r^o = ?46.6 ± 1.0 cal/deg mol for the calcite dissociation reaction at 25°C. The dependence of Kc on temperature when CaCO₃⁰ and CaHCO₃⁺ are assumed, is described by log Kc = 13.543 ? (3000/T) ? 0.0401T which yields ?8.39, ?8.47, and -8.70 at 0, 25 and 50°C. This gives ΔH_r^o = ?2585 ± 300 cal/mol, ΔCp = ?109 ± 2 cal/deg mol, and ΔS_r⁰ = ?47.4 ± 1.0 cal/deg mol at 25°C.  相似文献   

Effect of solution saturation state and temperature on diopside dissolution     

Suvasis Dixit  Susan A Carroll 《Geochemical transactions》2007,8(1):1-14

Steady-state dissolution rates of diopside are measured as a function of solution saturation state using a titanium flow-through reactor at pH 7.5 and temperature ranging from 125 to 175°C. Diopside dissolved stoichiometrically under all experimental conditions and rates were not dependent on sample history. At each temperature, rates continuously decreased by two orders of magnitude as equilibrium was approached and did not exhibit a dissolution plateau of constant rates at high degrees of undersaturation. The variation of diopside dissolution rates with solution saturation can be described equally well with a ion exchange model based on transition state theory or pit nucleation model based on crystal growth/dissolution theory from 125 to 175°C. At 175°C, both models over predict dissolution rates by two orders of magnitude indicating that a secondary phase precipitated in the experiments. The ion exchange model assumes the formation of a Si-rich, Mg-deficient precursor complex. Lack of dependence of rates on steady-state aqueous calcium concentration supports the formation of such a complex, which is formed by exchange of protons for magnesium ions at the surface. Fit to the experimental data yields where the Mg-H exchange coefficient, n = 1.39, the apparent activation energy, E _a = 332 kJ mol^-1, and the apparent rate constant, k = 10^41.2 mol diopside cm^-2 s^-1. Fits to the data with the pit nucleation model suggest that diopside dissolution proceeds through retreat of steps developed by nucleation of pits created homogeneously at the mineral surface or at defect sites, where homogeneous nucleation occurs at lower degrees of saturation than defect-assisted nucleation. Rate expressions for each mechanism (i) were fit to where the step edge energy (α) for homogeneously nucleated pits were higher (275 to 65 mJ m^-2) than the pits nucleated at defects (39 to 65 mJ m^-2) and the activation energy associated with the temperature dependence of site density and the kinetic coefficient for homogeneously nucleated pits (E_{b-homogeneous} = 2.59 × 10^-16 mJ K^-1) were lower than the pits nucleated at defects (E_{b-defect assisted} = 8.44 × 10^-16 mJ K^-1).  相似文献   

Luminescence excitation spectra of Mn2+ in synthetic forsterite     

G. R. Green  G. Walker 《Physics and Chemistry of Minerals》1985,12(5):271-278

Detailed ligand-field spectra of Mn²⁺ in both microcrystalline and single-crystal synthetic forsterite are obtained using the technique of luminescence excitation spectroscopy. It is shown that Mn²⁺ has an almost exclusive preference for one particular cation site which is most probably the M2 site. Low temperature measurements reveal a no-phonon (purely electronic) transition at 16,260 cm^?1 (615 nm) which is the energy of the lowest split component of the ⁴ T ₁(G) state above the ground state. Phonon replicas of this transition are evident showing that a particular phonon mode (180 cm^?1) is dominantly involved. An analysis of the polarized spectra of Mn²⁺ in single-crystal forsterite shows the choice of C _2v (C ₂, σ _d ) pseudosymmetry for the M2 site yields the best agreement with the polarization dependence of the transitions between the ligand-field states of the Mn²⁺ ion in this site.  相似文献   

Computation of surface energies in an electrostatic point charge model: I. Theory     

C. F. Woensdregt 《Physics and Chemistry of Minerals》1992,19(1):52-58

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and Ψ(x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy (γ ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy γ is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.  相似文献   

Origin of low-Ca pyroxene in amoeboid olivine aggregates: Evidence from oxygen isotopic compositions     

Alexander N. Krot  Timothy J. Fagan  Kazuhide Nagashima  Hisayoshi Yurimoto 《Geochimica et cosmochimica acta》2005,69(7):1873-1881

Amoeboid olivine aggregates (AOAs) in primitive carbonaceous chondrites consist of forsterite (Fa_<2), Fe,Ni-metal, spinel, Al-diopside, anorthite, and rare gehlenitic melilite (Åk_<15). ∼10% of AOAs contain low-Ca pyroxene (Fs_1-3Wo_1-5) that is in corrosion relationship with forsterite and is found in three major textural occurrences: (i) thin (<15 μm) discontinuous layers around forsterite grains or along forsterite grain boundaries in AOA peripheries; (ii) 5-10-μm-thick haloes and subhedral grains around Fe,Ni-metal nodules in AOA peripheries, and (iii) shells of variable thickness (up to 70 μm), commonly with abundant tiny (3-5 μm) inclusions of Fe,Ni-metal grains, around AOAs. AOAs with the low-Ca pyroxene shells are compact and contain euhedral grains of Al-diopside surrounded by anorthite, suggesting small (10%-20%) degree of melting. AOAs with other textural occurrences of low-Ca pyroxene are rather porous. Forsterite grains in AOAs with low-Ca pyroxene have generally ¹⁶O-rich isotopic compositions (Δ¹⁷O < −20‰). Low-Ca pyroxenes of the textural occurrences (i) and (ii) are ¹⁶O-enriched (Δ¹⁷O < −20‰), whereas those of (iii) are ¹⁶O-depleted (Δ¹⁷O = −6‰ to −4‰). One of the extensively melted (>50%) objects is texturally and mineralogically intermediate between AOAs and Al-rich chondrules. It consists of euhedral forsterite grains, pigeonite, augite, anorthitic mesostasis, abundant anhedral spinel grains, and minor Fe,Ni-metal; it is surrounded by a coarse-grained igneous rim largely composed of low-Ca pyroxene with abundant Fe,Ni-metal-sulfide nodules. The mineralogical observations suggest that only spinel grains in this igneous object were not melted. The spinel is ¹⁶O-rich (Δ¹⁷O ∼ −22‰), whereas the neighboring plagioclase mesostasis is ¹⁶O-depleted (Δ¹⁷O ∼ −11‰).We conclude that AOAs are aggregates of solar nebular condensates (forsterite, Fe,Ni-metal, and CAIs composed of Al-diopside, anorthite, spinel, and ±melilite) formed in an ¹⁶O-rich gaseous reservoir, probably CAI-forming region(s). Solid or incipiently melted forsterite in some AOAs reacted with gaseous SiO in the same nebular region to form low-Ca pyroxene. Some other AOAs appear to have accreted ¹⁶O-poor pyroxene-normative dust and experienced varying degrees of melting, most likely in chondrule-forming region(s). The most extensively melted AOAs experienced oxygen isotope exchange with ¹⁶O-poor nebular gas and may have been transformed into chondrules. The original ¹⁶O-rich signature of the precursor materials of such chondrules is preserved only in incompletely melted grains.  相似文献   

Complex formation of Cm(III) with formate studied by time-resolved laser fluorescence spectroscopy     

《Applied Geochemistry》2015

Pore waters of natural clays, which are investigated as potential host rock formations for high-level nuclear waste, are known to contain large amounts of low-molecular weight organic compounds. These small organic ligands might impact the aqueous geochemistry of the stored radionuclides and, thus, their migration behavior. In the present work, the complexation of Cm(III) with formate in aqueous NaCl solution is investigated by time-resolved laser fluorescence spectroscopy (TRLFS) as a function of the ionic strength (0.5–3.0 mol/kg), the ligand concentration (0–0.2 mol/kg) and the temperature (20–90 °C). The Cm(III) speciation is determined by deconvolution of the emission spectra. The obtained distribution of Cm(III) species is used to calculate the conditional stability constants (log K′(T)) at a given temperature and ionic strength which are extrapolated to zero ionic strength by using the specific ion interaction theory (SIT). Thus, the thermodynamic log K⁰_n(T) values for the formation of [Cm(Form)_n]⁽³⁻ⁿ⁾⁺ (n = 1, 2) and the ion interaction coefficients (ε(i,k)) for [Cm(Form)_n]⁽³⁻ⁿ⁾⁺ (n = 1, 2) with Cl⁻ are obtained. The log K⁰₁(T) (2.11 (20 °C)–2.49 (90 °C)) and log K⁰₂(T) values (1.17 (30 °C–2.01 (90 °C)) increase continuously with increasing temperature. The log K⁰_n(T) values are used to derive the standard reaction enthalpies and entropies (Δ_rH⁰_m, Δ_rS⁰_m) of the respective complexation reactions according to the Van’t Hoff equation. In all cases, positive Δ_rH⁰_m and Δ_rS⁰_m values are obtained. Thus, both complexation steps are endothermic and entropy-driven.  相似文献   

K-H₃OFe₃(SO₄)₂(OH)₆铁矾的XRD研究     

许涛  邹来昌  阮仁满  廖占丕  苏秀珠  苏妤芸  黄丽娟 《岩石矿物学杂志》2013,32(6):995-1000

根据X射线衍射(XRD)分析发现: A Fe₃(SO₄)₂(OH)₆(A=K⁺、H₃O⁺)系列铁钒的XRD数据十分相近,难以用XRD区别,需通过能谱(EDS)辅助分析,才能区分此类铁矾。另外,此类铁矾的003和107面网间距d随K⁺含量增大而增大,且呈一元三次方程的关系;而033和220面网间距d随K⁺含量增大而减小,呈一元二次方程的关系。对该现象从铁矾晶体结构方面进行解释:K⁺、H₃O⁺离子位于较大空隙中,且沿着Z轴方向排列,当K⁺、H₃O⁺离子之间相互替换时,会导致该铁矾晶体结构在Z轴方向有较明显的变化。  相似文献   

Static stress drop inferred from near-fault parameters for the 1999 Chi–Chi earthquake in Taiwan     

《Journal of Asian Earth Sciences》2013

In 2001, a special issue of the Bulletin of the Seismological Society of America (BSSA) featured seismological research for the 1999 Chi–Chi Taiwan earthquake. This study uses source parameters suggested by the first author in this special issue to estimate static stress drop associated with the Chi–Chi earthquake. The waveform simulation method was used to carefully examine these source parameters. The simulation results indicate that source parameters, inferred from near-fault observations, are well determined. According to the rupture area and slip, the static stress drops (Δσ_s) obtained were distributed between a small value of 47 bars near the epicentral region and a much larger value (>200 bars) to the north. Similar trends in dynamic stress drop (Δσ_d) were also recognized by the first author in his paper published in 2001 BSSA special issue. Comparing the Δσ_s with Δσ_d, satisfies the relation Δσ_s/Δσ_d ≈ 1. This relation suggests that fault motion is mostly spent releasing seismic wave energy during the rupture process of the Chi–Chi earthquake. The consistency between static and dynamic stress drops thus provides a measure of energy-moment (E_s/M₀) ratios, which range from 9.0 × 10⁻⁵ to 6.5 × 10⁻⁴. The average E_s/M₀ ratio estimated for the northern portions of the fault is 3.4 × 10⁻⁴, which is about 3 times that of the south. Such a high E_s/M₀ ratio can be interpreted as having low strength in the rupture for the northern portions of the fault, where the fault would release less energy per unit rupture surface to create the new rupture.  相似文献   

Olivine/melt transition metal partitioning, melt composition, and melt structure—Melt polymerization and Q-speciation in alkaline earth silicate systems     

Bjorn O. Mysen 《Geochimica et cosmochimica acta》2008,72(19):4796-4812

The two most abundant network-modifying cations in magmatic liquids are Ca²⁺ and Mg²⁺. To evaluate the influence of melt structure on exchange of Ca²⁺ and Mg²⁺ with other geochemically important divalent cations (m-cations) between coexisting minerals and melts, high-temperature (1470-1650 °C), ambient-pressure (0.1 MPa) forsterite/melt partitioning experiments were carried out in the system Mg₂SiO₄-CaMgSi₂O₆-SiO₂ with ?1 wt% m-cations (Mn²⁺, Co²⁺, and Ni²⁺) substituting for Ca²⁺ and Mg²⁺. The bulk melt NBO/Si-range (NBO/Si: nonbridging oxygen per silicon) of melt in equilibrium with forsterite was between 1.89 and 2.74. In this NBO/Si-range, the NBO/Si(Ca) (fraction of nonbridging oxygens, NBO, that form bonds with Ca²⁺, Ca²⁺-NBO) is linearly related to NBO/Si, whereas fraction of Mg²⁺-NBO bonds is essentially independent of NBO/Si. For individual m-cations, rate of change of K_D(m−Mg) with NBO/Si(Ca) for the exchange equilibrium, m^melt + Mg^olivine ? m^olivine + Mg^melt, is linear. K_D(m−Mg) decreases as an exponential function of increasing ionic potential, Z/r² (Z: formal electrical charge, r: ionic radius—here calculated with oxygen in sixfold coordination around the divalent cations) of the m-cation. The enthalpy change of the exchange equilibrium, ΔH, decreases linearly with increasing Z/r² [ΔH = 261(9)-81(3)·Z/r² (Å⁻²)]. From existing information on (Ca,Mg)O-SiO₂ melt structure at ambient pressure, these relationships are understood by considering the exchange of divalent cations that form bonds with nonbridging oxygen in individual Qⁿ-species in the melts. The negative ∂K_D(m−Mg)/∂(Z/r²) and ∂(ΔH)/∂(Z/r²) is because increasing Z/r² is because the cations forming bonds with nonbridging oxygen in increasingly depolymerized Qⁿ-species where steric hindrance is decreasingly important. In other words, principles of ionic size/site mismatch commonly observed for trace and minor elements in crystals, also govern their solubility behavior in silicate melts.  相似文献   

The dependence of albite feldspar dissolution kinetics on fluid saturation state at acid and basic pH: Progress towards a universal relation     

Roland Hellmann  Damien Daval  Delphine Tisserand 《Comptes Rendus Geoscience》2010,342(7-8):676-684

Here we report on two separate ongoing, multi-year investigations on the dependence of the dissolution rate (R) of albite feldspar on fluid saturation state, as defined by the Gibbs free energy of reaction (ΔG_r) for dissolution. The investigations are based on dissolution at pH 9.2, 150 °C and pH 3.3, 100 °C. Both studies reveal that the R–ΔG_r relation is highly non-linear and sigmoidal. The kinetic data from the first study, being the most complete, can be fitted with a sigmoidal rate curve that is composed of two separate, parallel rate laws that represent distinct mechanisms of dissolution. The switch between one dominant mechanism and the other may be controlled by a critical free energy. The fact that in both studies the same type of sigmoidal R–ΔG_r relation exists for dissolution at different pH and temperature condition suggests that this behavior may be universal for albite and other feldspars. Moreover, the experimental data contradict the commonly used R–ΔG_r relation that is loosely based on transition state theory (TST). This has important implications with respect to the accuracy of geochemical codes that model water–rock interactions at near-equilibrium conditions.  相似文献   

Exploring sustainability of aquifers based on predictive modeling of sorption characteristics of arsenic enriched Holocene sediments in Bangladesh     

M. Tauhid-Ur-Rahman  Akira ManoKeiko Udo  Yoshinobu Ishibashi 《Applied Geochemistry》2011,26(4):636-647

The importance of accessing safe aquifers in areas with high As is being increasingly recognized. The present study aims to investigate the sorption and mobility of As at the sediment-groundwater interface to identify a likely safe aquifer in the Holocene deposit in southwestern Bangladesh. The upper, shallow aquifer at around 18 m depth, which is composed mainly of very fine, grey, reduced sand and contains 24.3 μg/g As, was found to produce highly enriched groundwater (190 μg/L As). In contrast, deeper sediments are composed of partly oxidized, brownish, medium sand with natural adsorbents like Fe- and Al-oxides; they contain 0.76 μg/g As and impart low As concentrations to the water (4 μg/L). These observations were supported by spectroscopic studies with SEM, TEM, XRD and XRF, and by adsorption, leaching, column tests and sequential extraction. A relatively high in-situ dissolution rate (R_r) of 1.42 × 10⁻¹⁶ mol/m²/s was derived for the shallower aquifer from the inverse mass-balance model. The high R_r may enhance As release processes in the upper sediment. The field-based reaction rate (K_r) was extrapolated to be roughly 1.23 × 10⁻¹³ s⁻¹ and 6.24 × 10⁻¹⁴ s⁻¹ for the shallower and deeper aquifer, respectively, from the laboratory-obtained adsorption/desorption data. This implies that As is more reactive in the shallower aquifer. The partition coefficient for the distribution of As at the sediment-water interface (K_d-As) was found to range from 5 to 235 L/kg based on in-situ, batch adsorption, and flow-through column techniques. Additionally, a parametric equation for K_d-As (R² = 0.67) was obtained from the groundwater pH and the logarithm of the leachable Fe and Al concentrations in sediment. A one-dimensional finite-difference numerical model incorporating K_d and K_r showed that the shallow, leached As can be immobilized and prevented from reaching the deeper aquifer (∼150 m) after 100 year by a natural filter of oxidizing sand and adsorbent minerals like Fe and Al oxides; in this scenario, 99% of the As in groundwater is reduced. The deeper aquifer appears to be an adequate source of sustainable, safe water.  相似文献   

First-principles investigation of the concentration effect on equilibrium fractionation of Ca isotopes in forsterite     

Song  Yahui  Li  Yonghui  Wang  Wenzhong  Wu  Zhongqing 《中国地球化学学报》2019,38(4):497-507

Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation (10³lnα). Based on the density functional theory, we investigated how the average Ca–O bond length and the reduced partition function ratios (10³lnβ) and 10³lnα of ⁴⁴Ca/⁴⁰Ca in forsterite (Fo) are affected by its Ca concentration. Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 Å with the Ca/(Ca + Mg) varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64. However, outside this narrow range, i.e., Ca/(Ca + Mg) is lower than 1/64 or higher than 1/8, Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant. Because the 10³lnβ is negatively correlated with Ca–O bond length, the 10³lnβ significantly increases with decreasing Ca/(Ca + Mg) when 1/64 < Ca/(Ca + Mg) < 2/16. As a consequence, the 10³lnα between forsterite and other minerals also strongly depend on the Ca content in forsterite. Combining previous studies with our results, the heavier Ca isotopes enrichment sequence in minerals is: forsterite > orthopyroxene > clinopyroxene > calcite ≈ diopside > dolomite > aragonite. Olivine and pyroxenes are enriched in heavier Ca isotope compared to carbonates. The 10³lnα between forsterite with a Ca/(Ca + Mg) of 1/64 and clinopyroxene (Ca/Mg = 1/1, i.e., diopside) is up to ~ 0.64‰ at 1200 K. The large 10³lnα_Fo-diopside relative to the current analytical precision for Ca isotope measurements suggests that the dependence of 10³lnα_Fo-diopside on temperature can be used as a thermometer, similar to the one based on the 10³lnα of ⁴⁴Ca/⁴⁰Ca between orthopyroxene and diopside. These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.

  相似文献   

Strontium and samarium diffusion in diopside   总被引：1，自引：0，他引：1  

Mark Sneeringer  Stanley R. Hart  Nobumichi Shimizu 《Geochimica et cosmochimica acta》1984,48(8):1589-1608

The volume chemical diffusion of trace amounts of Sr in diopside has been measured as a function of temperature (1100–1300°C), pressure (1 bar–20 kbar), crystallographic direction, and composition. Three experimental/analytical techniques were employed: radiotracer and sectioning; stable tracer and ion microprobe; and Rutherford back-scattering spectroscopy. Comparison of the three yielded excellent agreement. Both natural and synthetic single crystal samples were used with results in the natural diopside giving diffusivities approximately two orders of magnitude greater than those in the man-made crystals. Samarium diffusion in the synthetic crystals was also examined with the ion probe technique with results similar to Sr.Arrhenius relations for diffusion (D = D₀exp[?ΔH_a/RT]) were calculated for different pressures and analytical techniques, and activation volumes (gDV_a) were derived from the equation D = D' exp[?PΔV_a/ RT]. Values of ΔV_a were negative for Sr diffusion. An empirical relation describing the temperature and pressure dependence of D for Sr in the c direction of the synthetic samples is: D(P, T) = 1200 (cm²/sec) exp[?122 (Kcal/mol)/RT (°K)]exp[?P (bar)/(2.94T ? 4640)R]. The expression for D_Sr in the natural samples (c direction) at one atmosphere is: D(0, T) = 54 (cm²/sec) exp[?97 (Kcal/mol)/RT (°K)]. A single compensation trend for all the data was evident for all values of D₀ and ΔH_a in the synthetic crystals.A number of models of geologic processes were investigated in light of the present data. Closure temperatures (T_c) were calculated for examples of mineral-mineral age-dating and trace element geothermometry. High values of T_c indicate that pyroxenes record emplacement events and are generally not disturbed unless a fluid enters the system. Isotopic equilibration times were examined for lower crustal xenoliths and the mantle source region for MORB using the formula of Hofmann and Hart (1978). Equilibration was shown to be too fast for production of isotopic anomalies in MORB via disequilibrium melting. Also. reasonable residence times at lower crustal temperatures were shown to produce the mineralogical-scale isotopic homogeneity observed in a crustal xenolith from Kilbourne Hole, New Mexico.  相似文献   

Dissolution kinetics as a function of the Gibbs free energy of reaction: An experimental study based on albite feldspar   总被引：1，自引：0，他引：1  

Roland Hellmann  Delphine Tisserand 《Geochimica et cosmochimica acta》2006,70(2):364-383

Here we report on an experimental investigation of the relation between the dissolution rate of albite feldspar and the Gibbs free energy of reaction, ΔG_r. The experiments were carried out in a continuously stirred flow-through reactor at 150 °C and pH_(150 °C) 9.2. The dissolution rates R are based on steady-state Si and Al concentrations and sample mass loss. The overall relation between ΔG_r and R was determined over a free energy range of −150 < ΔG_r < −15.6 kJ mol⁻¹. The data define a continuous and highly non-linear, sigmoidal relation between R and ΔG_r that is characterized by three distinct free energy regions. The region furthest from equilibrium, delimited by −150 < ΔG_r < −70 kJ mol⁻¹, represents an extensive dissolution rate plateau with an average rate . In this free energy range the rates of dissolution are constant and independent of ΔG_r, as well as [Si] and [Al]. The free energy range delimited by −70 ? ΔG_r ? −25 kJ mol⁻¹, referred to as the ‘transition equilibrium’ region, is characterized by a sharp decrease in dissolution rates with increasing ΔG_r, indicating a very strong inverse dependence of the rates on free energy. Dissolution nearest equilibrium, defined by ΔG_r > −25 kJ mol⁻¹, represents the ‘near equilibrium’ region where the rates decrease as chemical equilibrium is approached, but with a much weaker dependence on ΔG_r. The lowest rate measured in this study, R = 6.2 × 10⁻¹¹ mol m⁻² s⁻¹ at ΔG_r = −16.3 kJ mol⁻¹, is more than two orders of magnitude slower than the plateau rate. The data have been fitted to a rate equation (adapted from Burch et al. [Burch, T. E., Nagy, K. L., Lasaga, A. C., 1993. Free energy dependence of albite dissolution kinetics at 80 °C and pH 8.8. Chem. Geol.105, 137-162]) that represents the sum of two parallel reactions