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1.
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   

2.
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   

3.
 Tracer diffusion coefficients of Mg in natural aluminosilicate garnets of composition Alm38Pyr50Gr10Sp2 and Alm73Pyr21Gr5Sp1 have been measured at 1 bar, 750-850° C and at 8.5 GPa, 1300° C by chemically depositing a salt layer enriched in 26Mg on the specially prepared surface of a garnet single crystal. Diffusion anneals at 1 atmosphere (101325 Pa) were carried out at a controlled f O 2 of ∼10−17.5 bars maintained by a flowing gas mix of CO-CO2. Annealing conditions were carefully chosen to avoid decomposition of garnet by redox reactions. High pressure anneals were carried out in a multianvil apparatus. Induced diffusion profiles (0.1–0.6 μm) were measured by an ion-microprobe with SIMS attachment. Diffusion coefficients at 1 atmosphere are in excellent agreement with extrapolation of data from high P-T experiments (Loomis et al. 1985; Chakraborty and Ganguly 1992) and also with the low temperature (750–900° C) dataset of Cygan and Lasaga (1985) if the diffusion coefficients are assumed to be proportional to f O 2 1/6. Such an f O 2 dependence, however, makes this dataset inconsistent with the recent dataset of Schwandt et al. (1995) on garnets of composition (Alm15Pyr72Gr13Sp0) unless a strong compositional dependence of Mg tracer diffusivity for Mg-rich garnets is invoked. The present experimental results show that such a compositional dependence is weak to non-existent for garnets with >38 mole percent almandine component. It is emphasized that the temperature dependence of diffusion coefficients at constant oxygen fugacities (activation energy ≈54 kcal/mol) are different from that along an oxygen fugacity buffer (activation energy ≈64.5 kcal/mol), as already pointed out by Chakraborty and Ganguly (1991). This distinction is of importance for modelling natural processes. The measurements at low temperatures either eliminate the need for, or greatly reduce the uncertainty of, extrapolation of laboratory data for modelling metamorphic processes. The high pressure results combined with those from Chakraborty and Ganguly (1992) and Loomis et al. (1985) indicate that pressure dependence of Mg tracer diffusivity in garnets is much stronger than that in forsterite (Chakraborty et al. 1994). This difference in pressure dependence of diffusivity may be caused by the difference in compressibility of the coordination polyhedra of Mg between olivines and garnets. Activation volumes of Mg tracer diffusion as high as 8 cm3/mol may be estimated using the present data in combination with earlier results. These data suggest that at a temperature of 1300° C, Mg tracer diffusion rates in garnets will decrease by an order of magnitude for every 100 km depth. The pressure effect will be stronger at lower temperatures. For calculations involving diffusion coefficients of garnets at high pressures (e.g. mantle xenoliths, eclogites) the pressure dependence of diffusivity must be taken into account. Received: 21 December 1994 / Accepted: 22 September 1995  相似文献   

4.
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   

5.
  The diffusivity of water has been investigated for a haplogranitic melt of anhydrous composition Qz28Ab38Or34 (in wt %) at temperatures of 800–1200°C and at pressures of 0.5–5.0 kbar using the diffusion couple technique. Water contents of the starting glass pairs varied between 0 and 9 wt %. Concentration-distance profiles for the different water species (molecular water and hydroxyl groups) were determined by near-infrared microspectroscopy. Because the water speciation of the melt is not quenchable (Nowak 1995; Nowak and Behrens 1995; Shen and Keppler 1995), the diffusivities of the individual species can not be evaluated directly from these profiles. Therefore, apparent chemical diffusion coefficients of water (D water) were determined from the total water profiles using a modified Boltzmann-Matano analysis. The diffusivity of water increases linearly with water content <3 wt % but exponentially at higher water contents. The activation energy decreases from 64 ± 10 kJ/mole for 0.5 wt % water to 46 ± 5 kJ/mole for 4 wt % water but remains constant at higher water contents. A small but systematic decrease of D water with pressure indicates an average activation volume of about 9 cm3/mole. The diffusivity (in cm2/s) can be calculated for given water content (in wt %), T (in K) and P (in kbar) by
in the ranges 1073 K ≤ T ≤ 1473 K; 0.5 kbar ≤ P≤ 5␣kbar; 0.5 wt % ≤ C water ≤ 6 wt %. The absence of alkali concentration gradients in the glasses after the experiments shows that interdiffusion of alkali and H+ or H3O+ gives no contribution to the transport of water in aluminosilicate melts. The H/D interdiffusion coefficients obtained at 800°C and 5 kbar using glass pieces with almost the same molar content of either water or deuterium oxide are almost identical to the chemical diffusivities of water. This indicates that protons are transported by the neutral component H2O under these conditions. Received: 26 March 1996 / Accepted: 23 August 1996  相似文献   

6.
 Cation tracer diffusion coefficients, DMe *, for Me=Fe, Mn, Co and Ti, were measured using radioactive isotopes in the spinel solid solution (Ti x Fe 1−x )3−δO4 as a function of the oxygen activity. Experiments were performed at different cationic compositions (x=0, 0.1, 0.2 and 0.3) at 1100, 1200, 1300 and 1400 °C. The oxygen activity dependence of all data for DMe * at constant temperature and cationic composition can be described by equations of the type DMe *=D∘ Me[V]. CV·a O2 2/3+DMe[I] ∘·a O2 −2/3·DMe[V] ∘ and DMe[I] ∘ are constants and CV is a factor of the order of unity which decreases with increasing δ. All log DMe * vs. loga O2 curves obtained for different values of x and for different temperatures go through a minimum due to a change in the type of point defects dominating the cation diffusion with oxygen activity. Cation vacancies prevail for the cation diffusion at high oxygen activities while cation interstitials become dominant at low oxygen activities. At constant values of x, DMe[V] ∘ decreases with increasing temperature while DMe[I] ∘ increases.  相似文献   

7.
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   

8.
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   

9.
 The partitioning of Fe and Mg between the M1 and M2 octahedral sites of olivine has been investigated by in situ time-of-flight neutron powder diffraction. The degree of M-cation order was determined from direct measurements of site occupancies in a synthetic sample of Fo50Fa50 heated to 1250 °C at the Fe-FeO oxygen buffer. Fe shows slight preference for M1 at temperatures below about 600 °C, progressively disordering on heating to this temperature. Above 630 °C, the temperature at which site preferences cross over (T cr), Fe preferentially occupies M2, becoming progressively more ordered into M2 on increasing temperature. The cation-ordering behaviour is discussed in relation to the temperature dependence of the M1 and M2 site geometries, and it is suggested that vibrational entropy, crystal field effects and changes in bond characteristics play a part in the cross-over of partitioning behaviour. The temperature dependence of site ordering is modelled using a Landau expansion of the free energy of ordering of the type ΔG = −hQ + gTQ +  (T − T c)Q 2 +  Q 4, with a/h = 0.00406 K−1, b/h = 2.3, T c = 572 K and g/h = 0.00106 K−1. These results suggest that the high-temperature ordering behaviour across the forsterite-fayalite join will have a bearing on the activity-composition relations of this important rock-forming mineral, and indicate that Fe-Mg olivine solid solutions become less ideal as temperature increases. Received: 12 August 1999 / Accepted: 25 April 2000  相似文献   

10.
Summary  Transmission M?ssbauer spectra of synthetic Ca-free P21/c Mg0.22Fe0.78SiO3 clinopyroxene were collected at temperatures in the range 4.2 to 745 K and in an external magnetic field of 60 kOe at 180 K. The magnetic order-disorder transition temperature was determined by M?ssbauer thermoscanning to be 21 ± 3 K. Above this temperature, all M?ssbauer spectra consist of a superposition of two doublets, respectively produced by Fe2+ ions at an almost regular octahedral M1 site and at a more distorted octahedral M2 site. The temperature variation of the Fe2+ center shifts were analyzed using the Debye model for the lattice vibrations. The characteristic M?ssbauer temperatures were found to be 356 K ± 35 K for M1 and 333 K ± 25 K for M2. From the external field (60 kOe) M?ssbauer spectrum recorded at 180 K, the principal component V zz of the electric field gradient (EFG) was determined to be positive for both sites but precise values for the magnitudes of the asymmetry parameters η of the EFG could not be determined. The temperature variations of the M1 and M2 quadrupole splittings ΔE Q(T ) are consistent with the higher distortion of the M2 octahedra. Using the crystal-field model to interpret ΔE Q(T ), the energy gaps δ1 and δ2 of the first excited electronic states within the 5D orbital term were estimated to be 410 ± 50 cm−1 and 730 ± 50 cm−1 for M1, and δ1 = 1050 ± 75 cm−1 for M2. Received May 29, 2000;/revised version accepted July 13, 2001  相似文献   

11.
 The equilibrium water content of cordierite has been measured for 31 samples synthesized at pressures of 1000 and 2000 bars and temperatures from 600 to 750° C using the cold-seal hydrothermal technique. Ten data points are presented for pure magnesian cordierite, 11 data points for intermediate iron/magnesium ratios from 0.25 to 0.65 and 10 data points for pure iron cordierite. By representing the contribution of H2O to the heat capacity of cordierite as steam at the same temperature and pressure, it is possible to calculate a standard enthalpy and entropy of reaction at 298.18° K and 1 bar for, (Mg,Fe)2Al4Si5O18+H2O ⇄ (Fe,Mg)2Al4Si5O18.H2O Combining the 31 new data points with 89 previously published experimental measurements gives: ΔH ° r =–37141±3520 J and ΔS °  r =–99.2±4 J/degree. This enthalpy of reaction is within experimental uncertainty of calorimetric data. The enthalpy and entropy of hydration derived separately for magnesian cordierite (–34400±3016 J, –96.5±3.4 J/degree) and iron cordierite (–39613±2475, –99.5±2.5 J/degree) cannot be distinguished within the present experimental uncertainty. The water content as a function of temperature, T(K), and water fugacity, f(bars), is given by n H2O=1/[1+1/(K ⋅ f H2O)] where the equilibrium constant for the hydration reaction as written above is, ln K=4466.4/T–11.906 with the standard state for H2O as the gas at 1 bar and T, and for cordierite components, the hydrous and anhydrous endmembers at P and T. Received: 2 August 1994/Accepted: 7 February 1996  相似文献   

12.
 The monoclinic titanite-like high-pressure form of calcium disilicate has been synthesized and quenched to ambient conditions to form the triclinic low-pressure phase containing silicon in four-, five- and sixfold coordination. The enthalpy of formation of the quench product has been measured by high-temperature oxide melt calorimetry. The value obtained from samples from a series of several synthesis experiments is ΔH f = (−26.32 ± 4.27) kJ mol−1 for the formation from the component oxides, or ΔH f  = (−2482.81 ± 4.59) kJ mol−1 for the formation from the elements. The result is identical within experimental error to available estimates, although the previously predicted energy difference between the monoclinic and triclinic phases could not be verified. Received: 16 February 2000 / Accepted: 14 July 2000  相似文献   

13.
We have experimentally determined the tracer diffusion coefficients (D*) of 44Ca and 26Mg in a natural diopside (~Di96) as function of crystallographic direction and temperature in the range of 950–1,150 °C at 1 bar and f(O2) corresponding to those of the WI buffer. The experimental data parallel to the a*, b, and c crystallographic directions show significant diffusion anisotropy in the a–c and b–c planes, with the fastest diffusion being parallel to the c axis. With the exception of logD*(26Mg) parallel to the a* axis, the experimental data conform to the empirical diffusion “compensation relation”, converging to logD ~ −19.3 m2/s and T ~ 1,155 °C. Our data do not show any change of diffusion mechanism within the temperature range of the experiments. Assuming that D* varies roughly linearly as a function of angle with respect to the c axis in the a–c plane, at least within a limited domain of ~20° from the c-axis, our data do not suggest any significant difference between D*(//c) and D*(⊥(001)), the latter being the diffusion data required to model compositional zoning in the (001) augite exsolution lamellae in natural clinopyroxenes. Since the thermodynamic mixing property of Ca and Mg is highly nonideal, calculation of chemical diffusion coefficient of Ca and Mg must take into account the effect of thermodynamic factor (TF) on diffusion coefficient. We calculate the dependence of the TF and the chemical interdiffusion coefficient, D(Ca–Mg), on composition in the diopside–clinoenstatite mixture, using the available data on mixing property in this binary system. Our D*(Ca) values parallel to the c axis are about 1–1.5 log units larger than those Dimanov et al. (1996). Incorporating the effect of TF, the D(Ca–Mg) values calculated from our data at 1,100–1,200 °C is ~0.6–0.7 log unit greater than the experimental quasibinary D((Ca–Mg + Fe)) data of Fujino et al. (1990) at 1 bar, and ~0.6 log unit smaller than that of Brady and McCallister (1983) at 25 kb, 1,150 °C, if our data are normalized to 25 kb using activation volume (~4 and ~6 cm3/mol for Mg and Ca diffusion, respectively) calculated from theoretical considerations.  相似文献   

14.
 Enthalpies of drop solution (ΔH drop-sol) of CaGeO3, Ca(Si0.1Ge0.9)O3, Ca(Si0.2Ge0.8)O3, Ca(Si0.3Ge0.7)O3 perovskite solid solutions and CaSiO3 wollastonite were measured by high-temperature calorimetry using molten 2PbO · B2O3 solvent at 974 K. The obtained values were extrapolated linearly to the CaSiO3 end member to give ΔH drop-sol of CaSiO3 perovskite of 0.2 ± 4.4 kJ mol−1. The difference in ΔH drop-sol between CaSiO3, wollastonite, and perovskite gives a transformation enthalpy (wo → pv) of 104.4 ± 4.4 kJ mol−1. The formation enthalpy of CaSiO3 perovskite was determined as 14.8 ± 4.4 kJ mol−1 from lime + quartz or −22.2 ± 4.5 kJ mol−1 from lime + stishovite. A comparison of lattice energies among A2+B4+O3 perovskites suggests that amorphization during decompression may be due to the destabilizing effect on CaSiO3 perovskite from a large nonelectrostatic energy (repulsion energy) at atmospheric pressure. By using the formation enthalpy for CaSiO3 perovskite, phase boundaries between β-Ca2SiO4 + CaSi2O5 and CaSiO3 perovskite were calculated thermodynamically utilizing two different reference points [where ΔG(P,T )=0] as the measured phase boundary. The calculations suggest that the phase equilibrium boundary occurs between 11.5 and 12.5 GPa around 1500 K. Its slope is still not well constrained. Received: 20 September 2000 / Accepted: 17 January 2001  相似文献   

15.
 Calorimetric and P–V–T data for the high-pressure phase Mg5Al5Si6O21(OH)7 (Mg-sursassite) have been obtained. The enthalpy of drop solution of three different samples was measured by high-temperature oxide melt calorimetry in two laboratories (UC Davis, California, and Ruhr University Bochum, Germany) using lead borate (2PbO·B2O3) at T=700 ∘C as solvent. The resulting values were used to calculate the enthalpy of formation from different thermodynamic datasets; they range from −221.1 to −259.4 kJ mol−1 (formation from the oxides) respectively −13892.2 to −13927.9 kJ mol−1 (formation from the elements). The heat capacity of Mg5Al5Si6O21(OH)7 has been measured from T=50 ∘C to T=500 ∘C by differential scanning calorimetry in step-scanning mode. A Berman and Brown (1985)-type four-term equation represents the heat capacity over the entire temperature range to within the experimental uncertainty: C P (Mg-sursassite) =(1571.104 −10560.89×T −0.5−26217890.0 ×T −2+1798861000.0×T −3) J K−1 mol−1 (T in K). The P V T behaviour of Mg-sursassite has been determined under high pressures and high temperatures up to 8 GPa and 800 ∘C using a MAX 80 cubic anvil high-pressure apparatus. The samples were mixed with Vaseline to ensure hydrostatic pressure-transmitting conditions, NaCl served as an internal standard for pressure calibration. By fitting a Birch-Murnaghan EOS to the data, the bulk modulus was determined as 116.0±1.3 GPa, (K ′=4), V T,0 =446.49 3 exp[∫(0.33±0.05) × 10−4 + (0.65±0.85)×10−8 T dT], (K T/T) P  = −0.011± 0.004 GPa K−1. The thermodynamic data obtained for Mg-sursassite are consistent with phase equilibrium data reported recently (Fockenberg 1998); the best agreement was obtained with Δf H 0 298 (Mg-sursassite) = −13901.33 kJ mol−1, and S 0 298 (Mg-sursassite) = 614.61 J K−1 mol−1. Received: 21 September 2000 / Accepted: 26 February 2001  相似文献   

16.
Self-diffusion of Si under anhydrous conditions at 1 atm has been measured in natural zircon. The source of diffusant for experiments was a mixture of ZrO2 and 30Si-enriched SiO2 in 1:1 molar proportions; experiments were run in crimped Pt capsules in 1-atm furnaces. 30Si profiles were measured with both Rutherford backscattering spectrometry (RBS) and nuclear reaction analysis with the resonant nuclear reaction 30Si(p,γ)31P. For Si diffusion normal to c over the temperature range 1,350–1,550°C, we obtain an Arrhenius relation D = 5.8 exp(−702 ± 54 kJ mol−1/RT) m2 s−1 for the NRA measurements, which agrees within uncertainty with an Arrhenius relation determined from the RBS measurements [62 exp(−738 ± 61 kJ mol−1/RT) m2 s−1]. Diffusion of Si parallel to c appears slightly faster, but agrees within experimental uncertainty at most temperatures with diffusivities for Si normal to c. Diffusion of Si in zircon is similar to that of Ti, but about an order of magnitude faster than diffusion of Hf and two orders of magnitude faster than diffusion of U and Th. Si diffusion is, however, many orders of magnitude slower than oxygen diffusion under both dry and hydrothermal conditions, with the difference increasing with decreasing temperature because of the larger activation energy for Si diffusion. If we consider Hf as a proxy for Zr, given its similar charge and size, we can rank the diffusivities of the major constituents in zircon as follows: D Zr < D Si << D O, dry < D O, ‘wet’.  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.
The crystal structures of 212 experimentally synthesized, igneous clinopyroxenes were modeled from electronprobe chemical data. The coexisting melts span a wide range of petrologically relevant, dry and hydrous compositions, characterized by variable enrichment in silica and alkalis. Experimental conditions pertain to Earth's crust and uppermost mantle (P = 0–24 kbar; garnet absent) and a variety of f O2 values (from CCO-buffered to air-buffered) and mineral assemblages (Cpx ± Opx ± Pig ± Ol ± Plag ± Spl ± Mt ± Amp ± Ilm). Unit-cell volume (Vcell) versus M1-polyhedron volume (VM1) relations were investigated over a range of pressures and temperatures using data derived from structure modeling and corrected for thermal expansivity and compressibility. The relationships between pressure and clinopyroxene structural parameters were found to be dependent on the nature of the coexisting melt. To reduce compositional effects, only clinopyroxenes belonging to mildly alkaline (MA) and tholeiitic (TH) series were considered. Pressure was modeled as a linear function of Vcell, VM1, and Mg/(Mg + Fe2+)Cpx ratio. A calibration based on the whole data set (MA + TH) reproduced the experimental pressures within 1.4 kbar at the 1-σ level. The maximum residuals were 3.5 kbar and 3.9 kbar for MA- and TH-clinopyroxenes, respectively. Better statistics were obtained by considering MA- and TH-clinopyroxenes separately. A calibration based on the 69 MA-clinopyroxenes reproduced the experimental pressures within 1.1 kbar (1σ) and with a maximum residual of 2.7 kbar. A calibration based on the 143 TH-clinopyroxenes reproduced the experimental pressures within 1.0 kbar (1σ) and with a maximum residual of 3.4 kbar. When these geobarometers are applied to natural samples for which P is unknown, the correction for compressibility is necessarily made through a trial-and-error procedure. This expedient propagates an additional error that increases the above uncertainties and residuals by a factor of about 2. Applications to natural, igneous rocks for which the pressures of crystallization could be constrained based on experimental, petrological or geological evidence yielded pressure estimates that reproduced the expected values to within ca. 2 kbar. Compared to the MA-formulation, the TH-formulation appears to be less robust to variations in magma composition. When applied to high-pressure (>10 kbar) clinopyroxenes synthesized from very low Na (Na2O < 1.5%) melts, the latter geobarometer can underestimate P by as much as 6 kbar. Calculation of P through the present geobarometers requires clinopyroxene major-element composition and an independent, accurate estimate of crystallization T. Underestimating T by 20 °C propagates into a 1-kbar increase in calculated P. The proposed geobarometers are incorporated in the CpxBar software program, which is designed to retrieve the pressure of crystallization from a clinopyroxene chemical analysis. Received: 11 June 1998 / Accepted: 12 November 1998  相似文献   

19.
The excess vibrational entropy (ΔS vibex) of several silicate solid solutions are found to be linearly correlated with the differences in end-member volumes (ΔV i ) and end-member bulk moduli (Δκ i ). If a substitution produces both, larger and elastically stiffer polyhedra, then the substituted ion will find itself in a strong enlarged structure. The frequency of its vibration is decreased because of the increase in bond lengths. Lowering of frequencies produces larger heat capacities, which give rise to positive excess vibrational entropies. If a substitution produces larger but elastically softer polyhedra, then increase and decrease of mean bond lengths may be similar in magnitude and their effect on the vibrational entropy tends to be compensated. The empirical relationship between ΔS vibex, ΔV i and Δκ i , as described by ΔS vibex = (ΔV i  + mΔκ i )f, was calibrated on six silicate solid solutions (analbite–sanidine, pyrope–grossular, forsterite–fayalite, analbite–anorthite, anorthite–sanidine, CaTs–diopside) yielding m = 0.0246 and f = 2.926. It allows the prediction of ΔS vibex behaviour of a solid solution based on its volume and bulk moduli end-member data.  相似文献   

20.
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   

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