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1.
Diffusion of tetravalent cations in zircon   总被引：18，自引：1，他引：18  
Diffusion rates for the three tetravalent cations U, Th and Hf have been measured in synthetic zircon. Diffusant sources included oxide powders and ground pre-synthesized silicates. Rutherford backscattering spectrometry (RBS) was used to measure depth profiles. Over the temperature range 1400–1650 °C, the following Arrhenius relations were obtained (diffusion coefficients in m2sec−1): log D Th = (1.936 ± 0.9820) + (− 792 ± 34 kJ mol−1 /2.303 RT) log D U = (0.212 ± 2.440) + (− 726 ± 83 kJ mol−1 /2.303 RT) log D Hf = (3.206 ± 1.592) + (− 812 ± 54 kJ mol−1 /2.303 RT) The data show a systematic increase in diffusivity with decreasing ionic radius (i.e., faster diffusion rates for Hf than for U or Th), a trend also observed in our earlier study of rare earth diffusion in zircon. Diffusive fractionation may be a factor in the Lu-Hf system given the much slower diffusion rates of tetravalent cations when compared with the trivalent rare earths. The very slow diffusion rates measured for these tetravalent cations suggest that they are essentially immobile under most geologic conditions, permitting the preservation of fine-scale chemical zoning and isotopic signatures of inherited cores. Received: 12 July 1996 / Accepted: 2 December 1996  相似文献   

2.
Zr diffusion in titanite   总被引：2，自引：0，他引：2  
Chemical diffusion of Zr under anhydrous, pO2-buffered conditions has been measured in natural titanite. The source of diffusant was either zircon powder or a ZrO2–Al2O3–titanite mixture. Experiments were run in sealed silica glass capsules with solid buffers (to buffer at NNO or QFM). Rutherford Backscattering Spectrometry (RBS) was used to measure diffusion profiles. The following Arrhenius parameters were obtained for Zr diffusion parallel to c over the temperature range 753–1,100°C under NNO-buffered conditions: D Zr = 5.33 × 10−7 exp(−325 ± 30 kJ mol−1/RT) m2 s−1 Diffusivities are similar for experiments buffered at QFM. These data suggest that titanite should be moderately retentive of Zr chemical signatures, with diffusivities slower than those for O and Pb in titanite, but faster than those for Sr and the REE. When applied in evaluation of the relative robustness of the recently developed Zr-in-titanite geothermometer (Hayden and Watson, Abstract, 16th V.M. Goldschmidt Conference 2006), these findings suggest that Zr concentrations in titanite will be less likely to be affected by later thermal disturbance than the geothermometer based on Zr concentrations in rutile (Zack et al. in Contrib Mineral Petrol 148:471–488, 2004; Watson et al. in Contrib Mineral. Petrol, 2006), but much less resistant to diffusional alteration subsequent to crystallization than the Ti-in-Zircon geothermometer (Watson and Harrison in Science 308:841–844, 2005).  相似文献   

3.
Diffusion of four rare-earth elements and gallium has been measured in yttrium aluminum garnet (YAG). Sources of diffusant were mixtures of alumina and rare-earth element oxides for REE diffusion, and mixtures of gallium and yttrium oxides for Ga diffusion. Diffusion profiles were measured with Rutherford backscattering spectrometry (RBS). For the rare-earth elements investigated, the following Arrhenius relations were obtained: DLa=6.87×10–1 exp (–582±21 kJ mol–1 /RT) m2s–1 DNd=1.63×10–1 exp (–567±15 kJ mol–1 /RT) m2s–1 DDy=2.70×100 exp (–603±35 kJ mol–1 /RT) m2s–1 DYb=1.50×10–2 exp (–540±26 kJ mol–1 /RT) m2s–1 Diffusion rates for the rare earths are quite similar, in contrast with trends noted for zircon. It is likely that these differences are a consequence of the relative ionic radii of the REE and the cations for which they substitute in the mineral lattice. For gallium, the following Arrhenius relation was determined: DGa=9.96×10–6 exp (–404±19 kJ mol–1 /RT) m2s–1 Gallium diffuses faster than the REE in YAG and has a smaller activation energy for diffusion. These data mirror relative trends in diffusion rates for YIG, in which trivalent cations occupying tetrahedral and octahedral sites (i.e., Al, Ga, Fe) diffuse faster than trivalent cations occupying dodecahedral sites (i.e., Y and the REE), and suggest that the rate-limiting process in the diffusion-controlled regime of solid-state creep of YAG is the diffusion of yttrium. Received: 10 November 1997 / Revised; accepted: 13 March 1998  相似文献   

4.
 Diffusion rates for sulfur in rhyolite melt have been measured at temperatures of 800–1100° C, water contents of 0–7.3 wt%, and oxygen fugacities from the quartz-fayalite-magnetite buffer to air. Experiments involved dissolution of anhydrite or pyrrhotite into rhyolite melt over time scales of hours to days. Electron microprobe analysis was used to measure sulfur concentration profiles in the quenched glasses. Regression of the diffusion data in dry rhyolite melt gives Dsulfur=0.05·exp{−221±80RT}, which is one to two orders of magnitude slower than diffusion of other common magmatic volatiles such as H2O, CO2 and Cl-. Diffusion of sulfur in melt with 7 wt% dissolved water is 1.5 to 2 orders of magnitude faster than diffusion in the anhydrous melt, depending on temperature. Sulfur is known to dissolve in silicate melts as at least two different species, S2− and S6+, the proportions of which vary with oxygen fugacity; despite this, oxygen fugacity does not appear to affect sulfur diffusivity except under extremely oxidizing conditions. This result suggests that diffusion of sulfur is controlled by one species over a large range in oxygen fugacity. The most likely candidate for the diffusing species is the sulfide ion, S2−. Re-equilibration between S2− and S6+ in oxidized melts must generally be slow compared to S2− diffusion in order to explain the observed results. In a silicic melt undergoing degassing, sulfur will tend to be fractionated from other volatile species which diffuse more rapidly. This is consistent with analyses of tephra from the 1991 eruption of Mount Pinatubo, Philippines, and from other high-silica volcanic eruptions. Received: 26 April 1995 / Accepted: 1 November 1995  相似文献   

5.
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.  相似文献   

6.
Pb diffusion in rutile   总被引：16，自引：0，他引：16  
Diffusion of Pb was measured in natural and synthetic rutile under dry, 1 atmosphere conditions, using mixtures of Pb titanate or Pb sulfide and TiO2 as the sources of diffusant. Pb depth profiles were then measured with Rutherford Backscattering Spectrometry (RBS). Over the temperature range 700–1100 °C, the following Arrhenius relation was obtained for the synthetic rutile: D=3.9 × 10−10exp(−250 ± 12 kJ mol−1/RT) m2s−1. Results for diffusion in natural and synthetic rutile were quite similar, despite significant differences in trace element compositions. Mean closure temperatures calculated from the diffusion parameters are around 600 °C for rutile grains of ∼100 μm size. This is about 100 °C higher than rutile closure temperature determinations from past field-based studies, suggesting that rutile is more resistant to Pb loss through volume diffusion than previously thought. Received: 28 June 1999 / Accepted: 29 December 1999  相似文献   

7.
Li diffusion in zircon   总被引：2，自引：2，他引：0  
Diffusion of Li under anhydrous conditions at 1 atm and under fluid-present elevated pressure (1.0–1.2 GPa) conditions has been measured in natural zircon. The source of diffusant for 1-atm experiments was ground natural spodumene, which was sealed under vacuum in silica glass capsules with polished slabs of zircon. An experiment using a Dy-bearing source was also conducted to evaluate possible rate-limiting effects on Li diffusion of slow-diffusing REE+3 that might provide charge balance. Diffusion experiments performed in the presence of H2O–CO2 fluid were run in a piston–cylinder apparatus, using a source consisting of a powdered mixture of spodumene, quartz and zircon with oxalic acid added to produce H2O–CO2 fluid. Nuclear reaction analysis (NRA) with the resonant nuclear reaction 7Li(p,γ)8Be was used to measure diffusion profiles for the experiments. The following Arrhenius parameters were obtained for Li diffusion normal to the c-axis over the temperature range 703–1.151°C at 1 atm for experiments run with the spodumene source:
D\textLi = 7.17 ×10 - 7 exp( - 275 ±11 \textkJmol - 1 /\textRT)\textm2 \texts - 1. D_{\text{Li}} = 7.17 \times 10^{ - 7} { \exp }( - 275 \pm 11\,{\text{kJmol}}^{ - 1} /{\text{RT}}){\text{m}}^{2} {\text{s}}^{ - 1}.  相似文献   

8.
Chemical diffusion coefficients for oxygen in melts of Columbia River basalt (Ice Harbor Dam flow) and Mt. Hood andesite have been determined at 1 atm. The diffusion model is that of sorption or desorption of oxygen into a sphere of uniform initial concentration from a constant and semi-infinite atmosphere. The experimental design utilizes a thermogravimetric balance to monitor the rate of weight change arising from the response of the sample redox state to an imposed fO2. Oxygen diffusion coefficients are approximately an order-ofmagnitude greater for basaltic melt than for andesitic melt. At 1260° C, the oxygen diffusion coefficients are: D=1.65×10–6cm2/s and D=1.43×10–7cm2/s for the basalt and andesite melts, respectively. The high oxygen diffusivity in basaltic melt correlates with a high ratio of nonbridging oxygen/tetrahedrally coordinated cations, low melt viscosity, and high contents of network-modifying cations. The dependence of the oxygen diffusion coefficient on temperature is: D=36.4exp(–51,600±3200/RT)cm2/s for the basalt and D=52.5exp(–60,060±4900/RT)cm2/s for the andesite (R in cal/deg-mol; T in Kelvin). Diffusion coefficients are independent of the direction of oxygen diffusion (equilibrium can be approached from extremely oxidizing or reducing conditions) and thus, melt redox state. Characteristic diffusion distances for oxygen at 1260° C vary from 10-2 to 102 m over the time interval of 1 to 106 years. A compensation diagram shows two distinct trends for oxygen chemical diffusion and oxygen tracer diffusion. These different linear relationships are interpreted as supporting distinct oxygen transport mechanisms. Because oxygen chemical diffusivities are generally greater than tracer diffusivities and their Arrhenius activation energies are less, transport mechanisms involving either molecular oxygen or vacancy diffusion are favored.  相似文献   

9.
Magnesium self-diffusion coefficients were determined experimentally for diffusion parallel to each of the three crystallographic directions in natural orthoenstatite (En88Fs12). Experiments were conducted at 1 atm in CO-CO2 gas mixing furnaces, which provided oxygen fugacities equivalent to the iron-wüstite buffer. Diffusion of 25Mg was induced in polished samples of oriented orthoenstatite using a film of isotopically enriched 25MgO as the source material. Very short (<0.15 μm) diffusional penetration profiles were measured by ion microprobe depth profiling. The diffusion coefficients determined for four temperatures (900, 850, 800, 750 °C) provide the activation energies, E a , and frequency factors, D o, where D = D o exp (−E a /RT) for Mg self-diffusion parallel to each crystallographic direction: a-axis, E a  = 360 ± 52 kJ/mole and D o = 1.10 × 10−4 m2/s; b-axis, E a  = 339 ± 77 kJ/mole and D o = 6.93 × 10−6 m2/s and c-axis, E a  = 265 ± 66 kJ/mole and D o = 4.34 × 10−9 m2/s. In this temperature range, any possible anisotropy of cation diffusion is very small, however the activation energy for diffusion parallel to the c-axis (001) is the lowest and the activation energies for diffusion parallel to the a-axis (100) and b-axis (010) are higher. Application of these diffusion results to the silicate phases of the Lowicz mesosiderite meteorite provides cooling rates for the silicate portion of the meteorite (4–11 °C/100 years) that are similar, although slower, to previous estimates. These silicate cooling rates are still several orders of magnitude faster than the cooling rates (0.1 °C/106 years) for the metal portions. Received: 22 January 1997 / Accepted: 2 October 1997  相似文献   

10.
Diffusion of helium has been characterized in natural zircon and apatite. Polished slabs of zircon and apatite, oriented either normal or parallel to c were implanted with 100 keV 3He at a dose of 5 × 1015 3 He/cm2. Diffusion experiments on implanted zircon and apatite were run in Pt capsules in 1-atm furnaces. 3He distributions following experiments were measured with Nuclear Reaction Analysis using the reaction 3He(d,p)4He. For diffusion in zircon we obtain the following Arrhenius relations:
Although activation energies for diffusion normal and parallel to c are comparable, there is marked diffusional anisotropy, with diffusion parallel to c nearly 2 orders of magnitude faster than transport normal to c. These diffusivities bracket the range of values determined for He diffusion in zircon in bulk-release experiments, although the role of anisotropy could not be directly evaluated in those measurements.In apatite, the following Arrhenius relation was obtained over the temperature range of 148–449 °C for diffusion normal to c:
In contrast to zircon, apatite shows little evidence of anisotropy. He diffusivities obtained in this study fall about an order of magnitude lower than diffusivities measured through bulk release of He through step-heating, and within an order of magnitude of determinations where ion implantation was used to introduce helium and He distributions measured with elastic recoil detection.Since the diffusion of He in zircon exhibits such pronounced anisotropy, helium diffusional loss and closure cannot be modeled with simple spherical geometries and the assumption of isotropic diffusion. A finite-element code (CYLMOD) has recently been created to simulate diffusion in cylindrical geometry with differing radial and axial diffusion coefficients. We present some applications of the code in evaluating helium lost from zircon grains as a function of grain size and length to diameter ratios, and consider the effects of “shape anisotropy”, where diffusion is isotropic (as in the case of apatite) but shapes of crystal grains or fragments may depart significantly from spherical geometry.  相似文献   

11.
We have carried out a combined theoretical and experimental study of multicomponent diffusion in garnets to address some unresolved issues and to better constrain the diffusion behavior of Fe and Mg in almandine–pyrope-rich garnets. We have (1) improved the convolution correction of concentration profiles measured using electron microprobes, (2) studied the effect of thermodynamic non-ideality on diffusion and (3) explored the use of a mathematical error minimization routine (the Nelder-Mead downhill simplex method) compared to the visual fitting of concentration profiles used in earlier studies. We conclude that incorporation of thermodynamic non-ideality alters the shapes of calculated profiles, resulting in better fits to measured shapes, but retrieved diffusion coefficients do not differ from those retrieved using ideal models by more than a factor of 1.2 for most natural garnet compositions. Diffusion coefficients retrieved using the two kinds of models differ only significantly for some unusual Mg–Mn–Ca-rich garnets. We found that when one of the diffusion coefficients becomes much faster or slower than the rest, or when the diffusion couple has a composition that is dominated by one component (>75 %), then profile shapes become insensitive to one or more tracer diffusion coefficients. Visual fitting and numerical fitting using the Nelder-Mead algorithm give identical results for idealized profile shapes, but for data with strong analytical noise or asymmetric profile shapes, visual fitting returns values closer to the known inputs. Finally, we have carried out four additional diffusion couple experiments (25–35 kbar, 1,260–1,400 °C) in a piston-cylinder apparatus using natural pyrope- and almandine-rich garnets. We have combined our results with a reanalysis of the profiles from Ganguly et al. (1998) using the tools developed in this work to obtain the following Arrhenius parameters in D = D 0 exp{–[Q 1bar + (P–1)ΔV +]/RT} for D Mg* and D Fe*: Mg: Q 1bar = 228.3 ± 20.3 kJ/mol, D 0 = 2.72 (±4.52) × 10−10 m2/s, Fe: Q 1bar = 226.9 ± 18.6 kJ/mol, D 0 = 1.64 (±2.54) × 10−10 m2/s. ΔV + values were assumed to be the same as those obtained by Chakraborty and Ganguly (1992).  相似文献   

12.
Diffusion profiles in minerals are increasingly used to determine the duration of geological events. For this purpose, the distinction between growth and diffusion zoning is critical; it requires the understanding of complex features associated with multicomponent diffusion. Seed-overgrowth interdiffusion experiments carried out in the range 1,050–1,250°C at 1.3 GPa have been designed to quantify and better understand Fe–Mg–Ca interdiffusion in garnet. Some of the diffusion profiles measured by analytical transmission electron microscope show characteristic features of multicomponent diffusion such as uphill diffusion, chemical solitary waves, zero-flux planes and complex diffusion paths. We implemented three different methods to calculate the interdiffusion coefficients of the D matrix from the experimental penetration curves and determined that with Ca as the dependent component, the crossed coefficients of the D matrix are negative. Experiments and numerical simulations indicate that: (1) uphill diffusion in garnet can be observed indifferently on the three components Fe, Mg and Ca, (2) it takes the form of complementary depletion/repletion waves and (3) chemical waves occur preferentially on initially flat concentration profiles. Derived D matrices are used to simulate the fate of chemical waves in time, in finite crystals. These examples show that the flow of atoms in multicomponent systems is not necessarily unidirectional for all components; it can change both in space along the diffusion profile and in time. Moving zero-flux planes in finite crystals are transitory features that allow flux reversals of atoms in the diffusion zone. Interdiffusion coefficients of the D matrices are also analyzed in terms of eigenvalues and eigenvectors. This analysis and the experimental results show that depending on the composition of the diffusion couple, (1) the shape of chemical waves and diffusion paths changes; (2) the width of the diffusion zone for each component may or may not be identical; and (3) the width of diffusion calculated at a given D and duration may greatly vary. D matrices were retrieved from thirteen sets of diffusion profiles. Data were cast in Arrhenius relations. Linear regressions of the data yield activation energies equal to 368, 148, 394, 152 kJ mol−1 at 1 bar and frequency factors Do equal to 2.37 × 10−6, −4.46 × 10−16, −1.31 × 10−5, 9.85 × 10−15 m2 s−1 for [(D)\tilde]FeFeCa \tilde{D}_{FeFe}^{Ca} , [(D)\tilde]FeMgCa \tilde{D}_{FeMg}^{Ca} , [(D)\tilde]MgFeCa \tilde{D}_{MgFe}^{Ca} , [(D)\tilde]MgMgCa \tilde{D}_{MgMg}^{Ca} , respectively. These values can be used to calculate interdiffusion coefficients in Fe–Mg–Ca garnets and determine the duration of geological events in high temperature metamorphic or magmatic garnets.  相似文献   

13.
Diffusion coefficients for Sm, Sr, and Pb in fluorapatite at 900°–1250°C were obtained by measuring experimentally-induced diffusional uptake profiles of these elements in the margins of gem-quality apatite crystals. The crystals were immersed in synthetic melts enriched in the trace elements of interest and presaturated in apatite, and the resulting diffusion gradients were characterized by electron microprobe analysis. Except in the case of Pb, the diffusivities define good Arrhenius lines for the respective elements: DSm = 2.3 × 10?6exp(?52,200/RT) DSr = 412 exp(?100,000/RT). (Diffusion perpendicular to and parallel to c is measurably different in the case of Sr; the Arrhenius equation given above is an average for the two directions). Results on Pb were erratic, probably because extremely Pb-rich melts were used for some of the experiments. Data believed to be reliable define the following Arrhenius line: DPb = 0.035 exp(?70,000/RT). Constraints based on closure of natural apatites with respect to Pb suggest that the experimental data can be extrapolated, with sizeable uncertainty, to temperatures as low as 550°C.When applied to the question of isotopic and trace-element equilibration of residual or entrained apatites with crustal melts, the measured diffusivities indicate that 0.05-cm crystals will rarely preserve the original Pb-isotope characteristics of the source; the same is not true, however, of Sr (and, under some conditions, the REE), which may be unaffected at crystal cores during typical melting events.  相似文献   

14.
Diffusion coefficients of Cr and Al in chromite spinel have been determined at pressures ranging from 3 to 7 GPa and temperatures ranging from 1,400 to 1,700°C by using the diffusion couple of natural single crystals of MgAl2O4 spinel and chromite. The interdiffusion coefficient of Cr–Al as a function of Cr# (=Cr/(Cr + Al)) was determined as D Cr–Al = D 0 exp {−(Q′ + PV*)/RT}, where D 0 = exp{(10.3 ± 0.08) × Cr#0.54±0.02} + (1170 ± 31.2) cm2/s, Q′ = 520 ± 81 kJ/mol at 3 GPa, and V* = 1.36 ± 0.25 cm3/mol at 1,600°C, which is applicable up to Cr# = 0.8. The estimation of the self-diffusion coefficients of Cr and Al from Cr–Al interdiffusion shows that the diffusivity of Cr is more than one order of magnitude smaller than that of Al. These results are in agreement with patterns of multipolar Cr–Al zoning observed in natural chromite spinel samples deformed by diffusion creep.  相似文献   

15.
Chemical diffusivity measurements have been made on anhydrous metaluminous diffusion couples of dacite and rhyolite at 1 atm, 1200°–1400° C, and 10 kbar, 1300°–1600° C, and on anhydrous peraluminous and peralkaline dacite-rhyolite diffusion couples at 10 kbar, 1300°–1600° C. Chemical diffusivities for Si, Al, Fe, Mg, and Ca were measured in all experiments on the metaluminous diffusion couples using Boltzmann-Matano analysis, and Si diffusivities were measured on the other diffusion couples. Two 10 kbar metaluminous experiments were analyzed with the X-ray microprobe and diffusivities of Sr, Y, Zr and Nb were measured. Si diffusivity displays a weak negative correlation with SiO2 content over the range of 65%–75% SiO2. At a given SiO2 content chemical diffusivities of all non-alkali elements are usually within less than an order of magnitude of Si chemical diffusivity and are controlled by partitioning along the diffusion profile so as to maintain local equilibrium at each point along the profile. Alkali chemical diffusivities were not measured but can be estimated from the experiments to be orders of magnitude higher than non-alkali chemical diffusivities. Data were fit to Arrhenius equations for diffusivities measured at 65, 70 and 75% SiO2. At 1 atm the Arrhenius equation for non-alkalies at 70% SiO2 in the metaluminous system is:
  相似文献   

16.
This study examines the systematics and rate of alkali transport in haplogranite diffusion couples in which a chemical potential gradient in Al is established between near water-saturated metaluminous and peraluminous liquids that differ only in their initial content of normative corundum. At 800°C, measurable chemical diffusion of alkalis occurs throughout the entire length (∼1 cm) of the diffusion couples in 2–6 h, indicating long range diffusive communication through melt. Alkali transport results in homogenization of initially different Na/Al and ASI [=mol. Al2O3/(CaO + Na2O + K2O)] throughout the couples within ∼24 h, whereas initially homogenous K* evolves to become uniformly different between metaluminous and peraluminous ends. Calculated effective binary diffusion coefficients for alkalis in experiments that do not significantly violate the requirement of a semi-infinite chemical reservoir (0- to 2-h duration at 800°C) are similar to those observed in previous studies: in the range of (1–8) × 10−12 m2/s. Such a magnitude of diffusivity, however, is inadequate to account for the observed changes of alkali concentrations and molecular ratios throughout the couples in 2- to 6-h experiments. The latter changes are consistent with diffusivities estimated via the x 2 = Dt approximation, which yields effective values around 10−9 m2/s. These observations suggest that Fick’s law alone does not adequately describe the diffusive transport of alkalis in granitic liquids. In addition to simple ionic diffusion associated with local gradients in concentration or chemical potential of the diffusing component described by Fick’s second law (local diffusion), alkali transport through melt involves system-wide diffusion (field diffusion) driven by chemical potential gradients that also include components with which the alkalis couple or complex (e.g., Al). Field diffusion involves the coordinated migration of essentially all alkali cations, resembling a positive ionic current that drives the system to a metastable state having a minimum energy configuration with respect to alkali distribution. The net result is effective transport rates perhaps three orders of magnitude faster than simple local alkali diffusion, and at least seven to eight orders of magnitude faster than the diffusive equilibration of Al and Si.  相似文献   

17.
 Calcium self-diffusion rates in natural calcite single crystals were experimentally determined at 700 to 900° C and 0.1 MPa in a stream of CO2. Diffusion coefficients (D) were determined from 42Ca concentration profiles measured with an ion microprobe. The Arrhenius parameters yield an activation energy (Q)=382±37 kJ/mol and pre-exponential factor (D0)=0.13 m2/s, and there is no measurable anisotropy. Calcium grain boundary diffusion rates were experimentally determined in natural (Solnhofen) limestone and hot-pressed calcite aggregates at 650° to 850° C and 0.1 to 100 MPa pressure. The Solnhofen limestone was first pre-annealed for 24 h at 700° C and 100 MPa confining pressure under anhydrous conditions to produce an equilibrium microstructure for the diffusion experiments. Values for the product of the grain boundary diffusion coefficient (D′) and the effective grain boundary diffusion width (δ) were determined from 42Ca concentration profiles measured with an ion microprobe. The results show that there is no measurable difference between D′δ values obtained for pre-annealed Solnhofen samples at 0.1 and 100 MPa or between hot-pressed calcite aggregates and pre-annealed Solnhofen samples. The temperature dependence for calcium grain boundary diffusion in Solnhofen samples annealed at 0.1 MPa is described by the Arrhenius parameters D′ 0δ=1.5×10−9 m3/s and Q=267±47 kJ/mol. Comparison of the results of this study with previously published data show that calcium is the slowest volume diffusing species in calcite. The calcium diffusivities measured in this study place constraints on several geological processes that involve diffusive mass transfer including diffusion-accommodated mechanisms in the deformation of calcite rocks. Received: 19 December 1994/Accepted: 30 June 1995  相似文献   

18.
We have determined Fe–Mg diffusion coefficients in olivines from different sources (Nanga Parbat, Pakistan and San Carlos, Arizona, USA) at atmospheric pressure as a function of composition, oxygen fugacity (10−5–10−12 Pa) and temperature (700–1200°C) using thin films produced by pulsed laser deposition and RBS to analyze the concentration profiles. We have characterized the nano-scale structure and composition of the thin films annealed at various conditions and shown that the nature of the film (e.g. crystallinity, wetting behavior) depends strongly on the annealing conditions. If these variations are not taken into account in the form of boundary conditions for modeling the diffusion profiles, artifacts would result in the diffusion data. The diffusion coefficients obtained from 75 experiments reveal that (i) between fO2 of 10−5 and 10−10 Pa, diffusion along all three principal crystallographic directions in olivine, [100], [010] and [001], are described by a constant activation energy of ∼200 kJ/mol, precluding any temperature dependence of diffusion anisotropy and change of mechanism of diffusion at temperatures between 950 and 1200°C, (ii) diffusion coefficients increase with oxygen fugacity at fO2 > 10−10 Pa, with an fO2 exponent that lies between 1/4 and 1/7, and (iii) at fO2 below 10−10 Pa, and consequently at temperatures below ∼900°C, diffusion becomes weakly dependent/independent of fO2, indicating a change of diffusion mechanism. Activation energy of diffusion at these conditions is slightly higher, ∼220 kJ/mol. The data, including the change of mechanism, are analyzed in terms of point defect chemistry in Part II of this work to derive an equation that allows calculation of diffusivities in olivine over its entire field of stability. Availability of directly measured data at temperatures down to 700°C imply that for the first time diffusion coefficients can be interpolated, rather than extrapolated, for modeling most natural systems.  相似文献   

19.
Diffusion couples made from homogeneous gem quality natural pyrope and almandine garnets were annealed within graphite capsules under anhydrous conditions at 22–40 kbar, 1057–1400 °C in a piston-cylinder apparatus. The concentration profiles that developed in each couple were modeled to retrieve the self diffusion coefficients [D(I)] of the divalent cations Fe, Mg, Mn and Ca. Because of their usually low concentrations and lack of sufficient compositional change across the interface of the diffusion couples, only a few reliable data can be obtained for D(Ca) and D(Mn) from these experiments. However, nine sets of D(Fe) and D(Mg) data were retrieved in the above P-T range, and cast in the form of Arrhenian relation, D=D 0exp{−[Q(1 bar)+PΔV +]/RT}. The values of the activation energy (Q) and activation volume (ΔV +) depend on whether f O2 is constrained by graphite in the system C-O or held constant. For the first case, we have for Fe:Q(1 bar)=65,532±10,111 cal/mol, D 0=3.50 (±2.30)×10−5 cm2/s, ΔV +=5.6(±2.9) cm3/mol, and for Mg:Q(1 bar)=60,760±8,257 cal/mol, D 0=4.66 (±2.48)×10−5 cm2/s, ΔV +=5.3(±3.0) cm3/mol. Here the ΔV + values have been taken from Chakraborty and Ganguly (1992). For the condition of constant f O2, the Q values are ∼9 kcal lower and ΔV + values are ∼4.9 cm3/mol larger than the above values. Lower temperature extrapolation of the Arrhenian relation for D(Mg) is in good agreement with the Mg tracer diffusion data (D * Mg) of Chakraborty and Rubie (1996) and Cygan and Lasaga (1985) at 1 bar, 750–900 °C, when all data are normalized to the same pressure and to f O2 defined by graphite in the system C-O. The D * Mg data of Schwandt et al. (1995), on the other hand, are lower by more than an order of magnitude than the low temperature extrapolation of the present data, when all data are normalized to the same pressure and to f O2 defined by the graphite buffer. Comparison of the D(Fe), D(Mg) and D(Mn) data in the pyrope-almandine diffusion couple with those in the spessartine-almandine diffusion couple of Chakraborty and Ganguly (1992) shows that the self diffusion of Fe and Mn are significantly enhanced with the increase in Mn/Mg ratio; the enhancement effect on D(Mg) is, however, relatively small. Proper application of the self diffusion data to calculate interdiffusion coefficient or D matrix elements for the purpose of modeling of diffusion processes in natural garnets must take into account these compositional effects on D(I) along with the effects of thermodynamic nonideality, f O2, and pressure. Received: 8 May 1997 / Accepted: 2 October 1997  相似文献   

20.
Oxygen exchange experiments have been performed between single crystals of sanidine feldspar and oxygen gas enriched in 18O, at temperatures in the range 869–1053 °C, total pressure 1 atmosphere, for times up to 28 days. Oxygen isotope diffusion profiles in a direction perpendicular to (001) were determined with an ion microprobe. The experimental data obey a single Arrhenius relationship of the form D = 8.4 × 10−11 exp. (−245 ± 15 kJ mol−1/RT) m2s−1. The results indicate that oxygen diffusion in anhydrous sanidine feldspar is marginally slower than oxygen diffusion in anhydrous anorthite. Comparison with published atomistic simulation studies suggests that oxygen transport in feldspar is by an interstitial mechanism. Received: 17 October 1997 / Accepted: 6 July 1998  相似文献   

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