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1.
We have determined Cr diffusion coefficients (D) in orthopyroxene parallel to the a-, b-, and c-axial directions as a function temperature at f(O2) corresponding to those of the wüstite-iron (WI) buffer. Diffusion is found to be significantly anisotropic with D(//c) > D(//b) > D(//a), conforming to an earlier theoretical prediction. Increase of f(O2) from WI buffer conditions to 4.5 log unit above the buffer at 950 and 1050 °C leads to decrease of D(Cr) by a factor of two to three, possibly suggesting significant contribution from an interstitial diffusion mechanism. We have used the diffusion data to calculate the closure temperatures (Tc) of the Mn-Cr decay system in orthopyroxene as a function of initial temperature (T0), grain size (a) and cooling rate for spherical and plane sheet geometries. We also present graphical relations that permit retrieval of cooling rates from knowledge of the resetting of Mn-Cr ages in orthopyroxene during cooling, T0 and a. Application of these relations to the Mn-Cr age data of the cumulate eucrite Serra de Magé yields a Tc of 830-980 °C, and cooling rates of 2-27 °C/Myr at Tc and ∼1-13 °C/Myr at 500 °C. It is shown that the cooling of Serra de Magé to the closure temperature of the Mn-Cr system took place at its original site in the parent body, and thus implies a thickness for the eucrite crust in the commonly accepted HED parent body, Vesta, of greater than 30 km. This thickness of the eucrite crust is compatible only with a model of relatively olivine-poor bulk mineralogy in which olivine constitutes 19.7% of the total asteroidal mass.  相似文献   

2.
The elucidation of thermal histories by geochronological and isotopic means is based fundamentally on solid-state diffusion and the concept of closure temperatures. Because diffusion is thermally activated, an analytical solution of the closure temperature (T c *) can only be obtained if the diffusion coefficient D of the diffusion process is measured at two or more different temperatures. If the diffusion coefficient is known at only one temperature, however, the true closure temperature (T c *) cannot be calculated analytically because there exist an infinite number of possible (apparent) closure temperatures (Tˉ c ) which can be generated by this single datum. By introducing further empirical constraints to limit the range of possible closure temperatures, however, mathematical analysis of a modified form of the closure temperature equation shows that it is possible to make both qualitative and quantitative estimates of T c * given knowledge of only one diffusion coefficient D M measured at one temperature T M . Qualitative constraints of the true closure temperature T c * are obtained from the shapes of curves on a graph of the apparent T c (Tˉ c ) vs. activation energy E, in which each curve is based on a single diffusion coefficient measurement D M at temperature T M . Using a realistic range of E, the concavity of the curve shows whether T M is less than, approximately equal to, or greater than T c *. Quantitative estimates are obtained by considering two dimensionless parameters [ln êRT^ c vs. T c */T M ] derived from these curves. When these parameters are plotted for known argon diffusion data and for a given diffusion size and cooling rate, it is found that the resultant curves are almost identical for all of the commonly dated K–Ar minerals – biotite, phlogopite, muscovite, hornblende and orthoclase – in spite of differences in their diffusion parameters. A common curve for Ar diffusion can be derived by least-squares fitting of all the Ar diffusion data and provides a way of predicting a “model” closure temperature T cm from a single diffusion coefficient D M at temperature T M . Preliminary diffusion data for a labradorite lead to a T cm of 507 ± 17 °C and a corresponding activation energy of about 65 kcal/mol, given a grain size of 200 μm and a cooling rate of 5 °C/Ma. Curves for He diffusion in silicates (augite, quartz and sanidine) also overlap to a significant degree, both among themselves and with the Ar model curve, suggesting that a single model curve may be a good representation of noble gas closure temperatures in silicates. An analogous model curve for a selection of 18O data can also be constructed, but this curve differs from the Ar model curve. A single model curve for cationic species does not appear to exist, however, suggesting that chemical bonding relationships between the ionic size/charge and crystal structure may influence the closure temperatures of diffusing cations. An indication of the degree of overlap among the various curves for Ar, He, 18O and cations is also obtained by considering the dimensionless parameter E/RT c *; for the noble gases and 18O, E/RT c * values for the respective minerals are very similar, whereas for cations, there is significant dispersion. Given these constraints, this may be a potential method of estimating closure temperatures for certain diffusing species when there are limited diffusion data. Received: 1 July 1999 / Accepted: 24 March 2000  相似文献   

3.
《Journal of Structural Geology》1999,21(8-9):1255-1265
Isotope diffusion in a mineral is strongly temperature dependent but is also a function of grain size. Deformation must, therefore, be an important consideration in the interpretation of isotopic data because it provides a means of modifying grain size and shape. We illustrate the range of different deformation mechanisms common in micas and use simple models to investigate the relationship between these and isotope diffusion. We consider three different thermal scenarios with deformation taking place during: (a) the prograde heating path, (b) at the closure temperature of the deforming mineral, and (c) at temperatures significantly below the closure temperature. We have modelled these simple systems using a finite difference algorithm that simulates argon diffusion profiles and bulk ages. This modelling illustrates that obtaining deformation ages is critically dependent on an understanding and recognition of the different deformation mechanisms that have affected the sample. In the cases where deformation causes a change in grain size, it is important to characterise both the temperature at which deformation takes place and the closure temperature of grains formed during the deformation. The development of grains with Tc greater than the deformation temperature may record a deformation age. Examples of this condition include: (i) neocrystallisation; (ii) grain size reduction occurring at temperatures below Tc (of the reduced grain size) where the deformation mechanism has reset the grains; and (iii) deformation-induced grain coarsening.  相似文献   

4.
Oxygen isotope fractionation between coexisting minerals in slowly cooled rocks conveys information about their cooling history. By using the fast grain boundary （FGB） model to simulate closed-system diffusive ex- change of oxygen isotopes between coexisting minerals, I show that the apparent equilibrium temperatures （Tae） by the mineral pair with the largest isotopic fractionation （PLIF） always lies between the closure temperatures （To） of those two minerals. Therefore, when the rate of oxygen diffusion and hence Tc for the PLIF chance to be comparable （such as in the case of quartz and magnetite）, Tae will serve as a good approximation of To regardless of variation in mineral proportions. The specialty of the PLIF in constraining Tac within their Tc range can be generalized to other stable isotope systems and element partitioning. By approximating Tc with Tac and inverting Dodson＇s equation, the cooling rate of plutonic or metamorphic rocks can be inferred.  相似文献   

5.
(U-Th)/He chronometry of zircon has a wide range of potential applications including thermochronometry, provided the temperature sensitivity (e.g., closure temperature) of the system be accurately constrained. We have examined the characteristics of He loss from zircon in a series of step-heating diffusion experiments, and compared zircon (U-Th)/He ages with other thermochronometric constraints from plutonic rocks. Diffusion experiments on zircons with varying ages and U-Th contents yield Arrhenius relationships which, after about 5% He release, indicate Ea = 163-173 kJ/mol (39-41 kcal/mol), and D0 = 0.09-1.5 cm2/s, with an average Ea of 169 ± 3.8 kJ/mol (40.4 ± 0.9 kcal/mol) and average D0 of 0.46+0.87−0.30 cm2/s. The experiments also suggest a correspondence between diffusion domain size and grain size. For effective grain radius of 60 μm and cooling rate of 10°C/myr, the diffusion data yield closure temperatures, Tc, of 171-196°C, with an average of 183°C. The early stages of step heating experiments show complications in the form of decreasing apparent diffusivity with successive heating steps, but these are essentially absent in later stages, after about 5-10% He release. These effects are independent of radiation dosage and are also unlikely to be due to intracrystalline He zonation. Regardless of the physical origin, this non-Arrhenius behavior is similar to predictions based on degassing of multiple diffusion domains, with only a small proportion (<2-4%) of gas residing in domains with a lower diffusivity than the bulk zircon crystal. Thus the features of zircon responsible for these non-Arrhenius trends in the early stages of diffusion experiments would have a negligible effect on the bulk thermal sensitivity and closure temperature of a zircon crystal.We have also measured single-grain zircon (U-Th)/He ages and obtained 40Ar/39Ar ages for several minerals, including K-feldspar, for a suite of slowly cooled samples with other thermochronologic constraints. Zircon He ages from most samples have 1 σ reproducibilities of about 1-5%, and agree well with K-feldspar 40Ar/39Ar multidomain cooling models for sample-specific closure temperatures (170-189°C). One sample has a relatively poor reproducibility of ∼24%, however, and a mean that falls to older ages than predicted by the K-feldspar model. Microimaging shows that trace element zonation of a variety of styles is most pronounced in this sample, which probably leads to poor reproducibility via inaccurate α-ejection corrections. We present preliminary results of a new method for characterizing U-Th zonation in dated grains by laser-ablation, which significantly improves zircon He age accuracy.In summary, the zircon (U-Th)/He thermochronometer has a closure temperature of 170-190°C for typical plutonic cooling rates and crystal sizes, it is not significantly affected by radiation damage except in relatively rare cases of high radiation dosage with long-term low-temperature histories, and most ages agree well with constraints provided by K-spar 40Ar/39Ar cooling models. In some cases, intracrystalline U-Th zonation can result in inaccurate ages, but depth-profiling characterization of zonation in dated grains can significantly improve accuracy and precision of single-grain ages.  相似文献   

6.
New Hornblende K-Ar and 39Ar-40Ar and mica Rb-Sr and K-Ar ages are used to place specific timemarks on a well-constrained pressure-temperature path for the late Alpine metamorphism in the Western Tauern Window. After identification of excess 40Ar, the closure behavior of Ar in hornblende is compared with that of Sr and Ar in phengite and biotite. Samples were collected in three locations, whose maximum temperatures were 570° C (Zemmgrund), 550° C (Pfitscher Joch), and 500–540° C (Landshuter Hütte).The average undisturbed age sequence found is: Phengite Rb-Sr (20 Ma)>hornblende K-Ar (18 Ma)>phengite K-Ar (15 Ma)>biotite Rb-Sr, K-Ar (13.3 Ma)>apatite FT (7 Ma). Except for the phengite Rb-Sr age, the significance of which is debatable, all ages are cooling ages. No compositional effects are seen for closure in biotite. Additionally, Rb-Sr phengite ages from shearzones possibly indicate continuous shearing from 20 to 15 Ma, with reservations regarding the validity of the initial Sr correction and possible variations of the closure temperatures. The obviously lower closure temperature (T c) for Ar in these hornblendes than for Sr in the unsheared phengites indicates that the T c sequence in the Western Tauern Window is different from those observed in other terrains. In spite of this discrepancy, valuable geological conclusions can be drawn if the application of closure temperatures is limited to this restricted area with similar T, P and : (1) All ages of samples located on equal metamorphic isotherms decrease from east to west by about 1 Ma which is the result of a westward tilting of the Tauern Window during uplift. (2) In a PT-path, the undisturbed cooling ages yield constantly decreasing uplift rates from 3.6 mm/a to 0.1 mm/a. (3) Use of recently published diffusion data for Ar in hornblende (T c=520° C) and biotite (T c=320° C) suggests an extrapolated phengite closure temperature for Sr at 550° C. This suggests that the prograde thermal metamorphism at this tectonic level of the Tauern Window lasted until some 20 Ma ago.  相似文献   

7.
To evaluate the potential of (U–Th)/He geochronometry and thermochronometry of zircon, we measured He diffusion characteristics in zircons from a range of quickly and slowly cooled samples, (U–Th)/He ages of zircons from the quickly cooled Fish Canyon Tuff, and age-paleodepth relationships for samples from 15 to 18 km thick crustal section of the Gold Butte block, Nevada. (U–Th)/He ages of zircons from the Fish Canyon Tuff are consistent with accepted ages for this tuff, indicating that the method can provide accurate ages for quickly cooled samples. Temperature-dependent He release from zircon is not consistent with thermally activated volume diffusion from a single domain. Instead, in most samples apparent He diffusivity decreases and activation energy (Ea) increases as cycled step-heating experiments proceed. This pattern may indicate a range of diffusion domains with distinct sizes and possibly other characteristics. Alternatively, it may be the result of ongoing annealing of radiation damage during the experiment. From these data, we tentatively suggest that the minimum Ea for He diffusion in zircon is about 44 kcal/mol, and the minimum closure temperature (Tc, for a cooling rate of 10 °C/myr) is about 190 °C. Age–paleodepth relationships from the Gold Butte block suggest that the base of the zircon He partial retention zone is at pre-exhumation depths of about 9.5–11 km. Together with constraints from other thermochronometers and a geothermal gradient derived from them in this location, the age–depth profile suggests a He Tc of about 200 °C for zircon, in reasonable agreement with our interpretation of the laboratory measurements. A major unresolved question is how and when radiation damage effects become significant for He loss from this mineral.  相似文献   

8.
We have determined the Nd3+ diffusion kinetics in natural enstatite crystals as a function of temperature, f(O2) and crystallographic direction at 1 bar pressure and applied these data to several terrestrial and planetary problems. The diffusion is found to be anisotropic with the diffusion parallel to the c-axial direction being significantly greater than that parallel to a- and b-axis. Also, D(//a) is likely to be somewhat greater than D(//b). Diffusion experiments parallel to the b-axial direction as a function of f(O2) do not show a significant dependence of D(Nd3+) on f(O2) within the range defined by the IW buffer and 1.5 log unit above the WM buffer. The observed diffusion anisotropy and weak f(O2) effect on D(Nd3+) may be understood by considering the crystal structure of enstatite and the likely diffusion pathways. Using the experimental data for D(Nd3+), we calculated the closure temperature of the Sm-Nd geochronological system in enstatite during cooling as a function of cooling rate, grain size and geometry, initial (peak) temperature and diffusion direction. We have also evaluated the approximate domain of validity of closure temperatures calculated on the basis of an infinite plane sheet model for finite plane sheets showing anisotropic diffusion. These results provide a quantitative framework for the interpretation of Sm-Nd mineral ages of orthopyroxene in planetary samples. We discuss the implications of our experimental data to the problems of melting and subsolidus cooling of mantle rocks, and the resetting of Sm-Nd mineral ages in mesosiderites. It is found that a cooling model proposed earlier [Ganguly J., Yang H., Ghose S., 1994. Thermal history of mesosiderites: Quantitative constraints from compositional zoning and Fe-Mg ordering in orthopyroxene. Geochim. Cosmochim. Acta 58, 2711-2723] could lead to the observed ∼90 Ma difference between the U-Pb age and Sm-Nd mineral age for mesosiderites, thus obviating the need for a model of resetting of the Sm-Nd mineral age by an “impulsive disturbance” [Prinzhoffer A, Papanastassiou D.A, Wasserburg G.J., 1992. Samarium-neodymium evolution of meteorites. Geochim. Cosmochim. Acta 56, 797-815].  相似文献   

9.
The role of internal deformation in resetting argon ages of micas has been investigated by measuring 40Ar/39Ar ratios of biotite and muscovite, before and after experimentally deforming them. Neither mica crushed cataclastically at room temperature on-line with a mass spectrometer showed any measurable change in 40Ar/39Ar age. Muscovite crystals either sheared along the K-interlayer and/or kinked at 400 °C and 100–200 MPa confining pressure, exhibit small (0.7–1.0%) reductions in age and marked increases in bulk diffusion coefficients, as determined from argon release during the initial stages of step-heating between 550 and 810 °C. We conclude that the relatively young ages of fine-grained mica populations in naturally deformed mylonites result primarily from grain size refinement and reductions in length scale for volume diffusion and/or by syntectonic neocrystallization. Internal deformation involving dislocation slip and kinking may contribute to some argon loss by pipe diffusion, but reductions in closure temperature associated with multipath diffusion are small.  相似文献   

10.
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   

11.
In the last decade the zircon (U-Th)/He (ZHe) thermochronometer has been applied to a variety of geologic problems. Although bulk diffusion coefficients for He in zircon are available from laboratory step-heating experiments, little is known about the diffusion mechanism(s) and their dependence on the crystallographic structure of zircon. Here, we investigate the diffusion of He in perfectly crystalline zircon using atomistic simulation methods that provide insights into the structural pathways of He migration in zircon. Empirical force fields and quantum-mechanical calculations reveal that the energy barriers for He diffusion are strongly dependent on structure. The most favorable pathway for He diffusion is the [0 0 1] direction through the open channels parallel to the c-axis (, activation energy for tracer diffusion of a He atom along [0 0 1]). In contrast, energy barriers are higher in other directions where narrower channels for He diffusion are identified, such as [1 0 0], [1 0 1], and [1 1 0] (ΔE∗ of 44.8, 101.7, and 421.3 kJ mol−1, respectively). Molecular dynamics simulations are in agreement with these results and provide additional insight in the diffusion mechanisms along different crystallographic directions, as well as the temperature dependence. Below the closure temperature of He in zircon [Tc ∼ 180 °C, Reiners P. W., Spell T. L., Nicolescu S., and Zanetti K. A. (2004) Zircon (U-Th)/He thermochronometry: He diffusion and comparisons with Ar-40/Ar-39 dating. Geochim. Cosmochim. Acta68, 1857-1887], diffusion is anisotropic as He moves preferentially along the [0 0 1] direction, and calculated tracer diffusivities along the two most favorable directions differ by approximately five orders of magnitude (D[001]/D[100] ∼ 105, at T = 25 °C). Above this temperature, He atoms start to hop between adjacent [0 0 1] channels, along [1 0 0] and [0 1 0] directions (perpendicular to the c-axis). The diffusion along [1 0 0] and [0 1 0] is thermally activated, such that at higher temperatures, He diffusion in zircon becomes nearly isotropic (D[001]/D[100] ∼ 10, at T = 580 °C). These results suggest that the anisotropic nature of He diffusion at temperatures near the closure temperature should be considered in future diffusivity experiments. Furthermore, care should be taken when making geologic interpretations (e.g., exhumation rates, timing of cooling, etc.) from this thermochronometer until the effects of anisotropic diffusion on bulk ages and closure temperature estimates are better quantified.  相似文献   

12.
Closure temperature in cooling geochronological and petrological systems   总被引：1，自引：0，他引：1  
Closure temperature (T c ) of a geochronological system may be defined as its temperature at the time corresponding to its apparent age. For thermally activated diffusion (D=D o e ?E/RT it is given by $$T_c = R/[E ln (A \tau D_0 /a^2 )]$$ (i) in which R is the gas constant, E the activation energy, τ the time constant with which the diffusion coefficient D diminishes, a is a characteristic diffusion size, and A a numerical constant depending on geometry and decay constant of parent. The time constant τ is related to cooling rate by $$\tau = R/(Ed T^{ - 1} /dt) = - RT^2 /(Ed T/dt).$$ (ii) Eq. (i) is exact only if T ?1 increases linearly with time, but in practice a good approximation is obtained by relating τ to the slope of the cooling curve at T c. If the decay of parent is very slow, compared with the cooling time constant, A is 55, 27, or 8.7 for volume diffusion from a sphere, cylinder or plane sheet respectively. Where the decay of parent is relatively fast, A takes lower values. Closure temperatures of 280–300° C are calculated for Rb-Sr dates on Alpine biotites from measured diffusion parameters, assuming a grain size of the order 0.5 mm. The temperature recorded by a “frozen” chemical system, in which a solid phase in contact with a large reservoir has cooled slowly from high temperatures, is formally identical with geochronological closure temperature.  相似文献   

13.
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14.
ABSTRACT There is no significant difference in the diffusion profiles across albite-adularia bicrystals that were simultaneously deformed at a strain rate of 10-6S-1 and those from hydrostatic experiments at the same conditions (1500 MPa and 1000°C for 156 h). This indicates that the bulk alkali diffusion rate, which is the sum of lattice diffusion (D, 1) and dislocation pipe diffusion (Dp), is not significantly enhanced by dislocations at these conditions, and that the maximum value for the ratio of Dp/D1 is about 105. This is equal to the value previously reported for‘oxygen’diffusion in albite. If this ratio is independent of temperature, the contribution of either static (pre-deformed) or moving (syn-deformed) dislocations to the bulk diffusion rate of alkalis is probably minor at all metamorphic conditions. For Al and Si diffusion the ratio of Dp/D1 may be larger if D1 is lower. Thus a significant contribution from dislocations to bulk diffusion cannot be ruled out, especially during simultaneous deformation.  相似文献   

15.
Singh  A. P.  Roy  Indrajit G.  Kumar  Santosh  Kayal  J. R. 《Natural Hazards》2013,77(1):33-49

Seismic source characteristics in the Kachchh rift basin and Saurashtra horst tectonic blocks in the stable continental region (SCR) of western peninsular India are studied using the earthquake catalog data for the period 2006–2011 recorded by a 52-station broadband seismic network known as Gujarat State Network (GSNet) running by Institute of Seismological Research (ISR), Gujarat. These data are mainly the aftershock sequences of three mainshocks, the 2001 Bhuj earthquake (M w 7.7) in the Kachchh rift basin, and the 2007 and 2011 Talala earthquakes (M w ≥ 5.0) in the Saurashtra horst. Two important seismological parameters, the frequency–magnitude relation (b-value) and the fractal correlation dimension (D c) of the hypocenters, are estimated. The b-value and the D c maps indicate a difference in seismic characteristics of these two tectonic regions. The average b-value in Kachchh region is 1.2 ± 0.05 and that in the Saurashtra region 0.7 ± 0.04. The average D c in Kachchh is 2.64 ± 0.01 and in Saurashtra 2.46 ± 0.01. The hypocenters in Kachchh rift basin cluster at a depth range 20–35 km and that in Saurashtra at 5–10 km. The b-value and D c cross sections image the seismogenic structures that shed new light on seismotectonics of these two tectonic regions. The mainshock sources at depth are identified as lower b-value or stressed zones at the fault end. Crustal heterogeneities are well reflected in the maps as well as in the cross sections. We also find a positive correlation between b- and D c-values in both the tectonic regions.

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16.
Forty-four biotite samples collected about a lithologic contact between pelite and amphibolite were analyzed for 40Ar/39Ar and demonstrate the importance of bulk Ar diffusivity and system geometry—factors not usually considered in the interpretation and collection of 40Ar/39Ar age data. The resulting 40Ar/39Ar apparent ages range from 11.30 ± 0.05 Ma to 17.90 ± 0.10 Ma. The ages (and excess argon contents) are spatially and lithologically correlated. The pelite samples all yield ages clustering around ∼12 Ma, the age expected for cooling through biotite closure (∼360°C) in this region of the Alps. Ages in the amphibolite biotites are older, showing a smooth trend between 15 Ma at the contact with the pelite to 18 Ma, 34 cm from the contact. This data shows that characterization of the Ar closure age for biotite in a given system should not rest on a single sample, as otherwise irresolvable differences in age between samples within the same outcrop can exist. A generalized mechanistic model for excess argon is presented. The presence (or absence) of excess Ar depends on an intrinsic system parameter, τT, the transmissive timescale, which is the characteristic time for 40Ar to escape through the local intergranular transporting medium (ITM) to some sink for argon. To prevent buildup of geochronologically significant excess 40Ar, τT must be very short relative to the true closure age of the mineral. A FORTRAN code including radiogenic Ar production, diffusive loss of Ar from biotite, and bulk Ar diffusion through the ITM has been developed. Application of numerical modeling suggests that the time-averaged effective bulk diffusivity, DeffAr, in the biotite-amphibolite rock during early retrograde cooling is 2.2 ± 1.0 × 10−8 m2/yr (assuming steady state conditions) - the first such measurement available. Numerical modeling also provides information about the transmissivity and geologic history specific to the field site, including a drop in DeffAr at 15.5 ± 1.0 Ma. The timing of this drop is related to coincident rheological changes and the onset of rapid exhumation of the nappe stack.  相似文献   

17.
Recent work [Shuster D. L., Flowers R. M. and Farley K. A. (2006) The influence of natural radiation damage on helium diffusion kinetics in apatite. Earth Planet. Sci. Lett.249(3-4), 148-161] revealing a correlation between radiogenic 4He concentration and He diffusivity in natural apatites suggests that helium migration is retarded by radiation-induced damage to the crystal structure. If so, the He diffusion kinetics of an apatite is an evolving function of time and the effective uranium concentration in a cooling sample, a fact which must be considered when interpreting apatite (U-Th)/He ages. Here we report the results of experiments designed to investigate and quantify this phenomenon by determining He diffusivities in apatites after systematically adding or removing radiation damage.Radiation damage was added to a suite of synthetic and natural apatites by exposure to between 1 and 100 h of neutron irradiation in a nuclear reactor. The samples were then irradiated with a 220 MeV proton beam and the resulting spallogenic 3He used as a diffusant in step-heating diffusion experiments. In every sample, irradiation increased the activation energy (Ea) and the frequency factor (Do/a2) of diffusion and yielded a higher He closure temperature (Tc) than the starting material. For example, 100 h in the reactor caused the He closure temperature to increase by as much as 36 °C. For a given neutron fluence the magnitude of increase in closure temperature scales negatively with the initial closure temperature. This is consistent with a logarithmic response in which the neutron damage is additive to the initial damage present. In detail, the irradiations introduce correlated increases in Ea and ln(Do/a2) that lie on the same array as found in natural apatites. This strongly suggests that neutron-induced damage mimics the damage produced by U and Th decay in natural apatites.To investigate the potential consequences of annealing of radiation damage, samples of Durango apatite were heated in vacuum to temperatures up to 550 °C for between 1 and 350 h. After this treatment the samples were step-heated using the remaining natural 4He as the diffusant. At temperatures above 290 °C a systematic change in Tc was observed, with values becoming lower with increasing temperature and time. For example, reduction of Tc from the starting value of 71 to ∼52 °C occurred in 1 h at 375 °C or 10 h at 330 °C. The observed variations in Tc are strongly correlated with the fission track length reduction predicted from the initial holding time and temperature. Furthermore, like the neutron irradiated apatites, these samples plot on the same Ea − ln(Do/a2) array as natural samples, suggesting that damage annealing is simply undoing the consequences of damage accumulation in terms of He diffusivity.Taken together these data provide unequivocal evidence that at these levels, radiation damage acts to retard He diffusion in apatite, and that thermal annealing reverses the process. The data provide support for the previously described radiation damage trapping kinetic model of Shuster et al. (2006) and can be used to define a model which fully accommodates damage production and annealing.  相似文献   

18.
The adiabatic single-crystal elastic moduli of a natural sample of monticellite (CaMgSiO4), with the olivine crystal structure, have been measured under ambient conditions using Brillouin spectroscopy. From the single-crystal moduli the aggregate bulk and shear moduli are calculated to be K s=106±1 and = 55.2±0.4 GPa, respectively. These results are consistent with a systematic decrease in bulk modulus with increasing molar volume among the olivine-structured silicates. The longitudinal moduli decrease in the order c 11>c 33>c22, indicating that the structure is stiffest along the a axis and most compliant along the b axis. This relationship among the longitudinal moduli holds for all silicate and germanate olivines, and is thus inferred to result from the topology of the olivine crystal structure. However, the moduli obtained in this study are at variance with previous conclusions concerning deviations from the Cauchy relations (e.g. c 12=c 44). For monticellite, off-diagonal shear moduli of the c 12-type are uniformly greater than pure shear moduli such as c 44. Similar behavior is found in pyroxenes such as diopside. The relative magnitudes of shear and off-diagonal moduli are not, therefore, a diagnostic chemical signature in minerals with complex crystal structures.Department of Applied Physics, Stanford University, Stanford CA, USA  相似文献   

19.
A synthetic clinopyroxene with composition LiFe3+Ge2O6, monoclinic s.g. P21/c, a = 9.8792(7), b = 8.8095(5), c = 5.3754(3) Å, β = 108.844(6)°, V = 442.75(16) Å3, has been studied by in situ low- and high-temperature single-crystal X-ray diffraction. The variation of lattice parameters and the intensity of the b-type reflections (h + k = 2n + 1, only present in the P-symmetry) with increasing temperature showed a displacive phase transition from space group P21/c to C2/c at a transition temperature T tr = 789 K, first order in character, with a sudden volume increase of 1.6% and a decrease of β by 1° at the transition. This spontaneous dilatation is reversible, shows a limited hysteresis of ±10°C, and corresponds to the vanishing of the b-type reflections, thus indicating a symmetry increase to space group C2/c. Below T tr an expansion is observed for all the cell parameters, while the β angle remained almost constant; at T > T tr the thermal volume expansion is due to dilatation of the structure in the $(\bar{1}\,0\,1) A synthetic clinopyroxene with composition LiFe3+Ge2O6, monoclinic s.g. P21/c, a = 9.8792(7), b = 8.8095(5), c = 5.3754(3) ?, β = 108.844(6)°, V = 442.75(16) ?3, has been studied by in situ low- and high-temperature single-crystal X-ray diffraction. The variation of lattice parameters and the intensity of the b-type reflections (h + k = 2n + 1, only present in the P-symmetry) with increasing temperature showed a displacive phase transition from space group P21/c to C2/c at a transition temperature T tr = 789 K, first order in character, with a sudden volume increase of 1.6% and a decrease of β by 1° at the transition. This spontaneous dilatation is reversible, shows a limited hysteresis of ±10°C, and corresponds to the vanishing of the b-type reflections, thus indicating a symmetry increase to space group C2/c. Below T tr an expansion is observed for all the cell parameters, while the β angle remained almost constant; at T > T tr the thermal volume expansion is due to dilatation of the structure in the ([`1] 0 1)(\bar{1}\,0\,1) plane, mostly along [0 1 0], and pure shear in the (0 1 0) plane due to the decrease of β. From comparison with silicate analogues, the germanate clinopyroxenes are more expansible, while the P21/c expands more than the C2/c phase. The evolution of Q 2 (calculated as the normalized intensity of b-type reflections) with T in the framework of the Landau theory has been done using a standard expression for a first order phase transition. We observe a jump of Q 02 = 0.538(2) at T tr, with T c of 481(7) K, b/a = −2,290 K, and c/a = 3,192 K, and thus far from being tri-critical point. A closely related composition (LiFe3+Si2O6) shows an equivalent phase transition at 228 K, which is very close to the tri-critical point and 561 K cooler. This result indicates that a change in the composition of tetrahedral sites can have dramatic effects on the P21/c ↔ C2/c displacive phase transition in clinopyroxenes. The major changes observed in the evolution of the crystal structure with T are observed in the M2 polyhedron, with a volume decrease by ca. 13.3%, compared to ca. 1.3% observed in the M1 polyhedron. The tetrahedra behave as rigid units with neither a significant change of volume at T > T tr (<1‰), nor a change of tilting of the basal plane. No change in coordination is observed at T > T tr in the M2 polyhedron, which remains sixfold coordinated although a strong deformation of this polyhedron is observed. This deformation is related to a strong change by 51.4° at T tr of the kinking angle (O3–O3–O3 angle) of the B-chain of tetrahedra, which switches from O-rotated to S-rotated [from 143.3(5)° to 194.7(6)°]. The A-chain is S-rotated at T < T tr [206.8(5)° at 703 K] and extends by 12° at the transition.  相似文献   

20.
Structural overprinting relationships indicate that two discrete terranes, Mt. Stafford and Weldon, occur in the Anmatjira Range, northern Arunta Inlier, central Australia. In the Mt. Stafford terrane, early recumbent structures associated with D1a,1b deformation are restricted to areas of granulite facies metamorphism and are overprinted by upright, km-scale folds F1c), which extend into areas of lower metamorphic grade. Structural relationships are simple in the low—grade rocks, but complex and variable in higher grade equivalents. The three deformation events in the Mt. Stafford terrane constitute the first tectonic cycle (D1-D2) deformation in the Weldon terrane comprises the second tectonic cycle. The earliest foliation (S2a) was largely obliterated by the dominant reclined to recumbent mylonitic foliation (S2b), produced during progressive non-coaxial deformation, with local sheath folds and W- to SW-directed thrusts. Locally, (D2d) tectonites have been rotated by N—S-trending, upright (F2c) folds, but the regional upright fold event (F2d), also evident in the adjacent Reynolds Range, rotated earlier surfaces into shallow-plunging, NW—SE-trending folds that dominate the regional outcrop pattern.The terranes can be separated on structural, metamorphic and isotopic criteria. A high-strain D2 mylonite zone, produced during W- to SW-directed thrusting, separates the Weldon and Mt. Stafford terranes. 1820 Ma megacrystic granites in the Mt. Stafford terrane intruded high-grade metamorphic rocks that had undergone D1a and D1b deformation, but in turn were deformed by S1c, which provides a minimum age limit for the first structural—metamorphic event. 1760 Ma charnockites in the Weldon terrane were emplaced post-D2a, and metamorphosed under granulite facies conditions during D2b, constraining the second tectonic cycle to this period.Each terrane is associated with low-P, high-T metamorphism, characterized by anticlockwise P—T—t paths, with the thermal peaks occurring before or very early in the tectonic cycle. These relations are not compatible with continental-style collision, nor with extensional tectonics as the deformation was compressional. The preferred model involves thickening of previously thinned lithosphere, at a stage significantly after (>50 Ma) the early extensional event. Compression was driven by external forces such as plate convergence, but deformation was largely confined to and around composite granitoid sheets in the mid-crust. The sheets comprise up to 80% of the terranes and induced low-P, high-T metamorphism, including migmatization, thereby markedly reducing the yield strength and accelerating deformation of the country rocks. Mid-crustal ductile shearing and reclined to recumbent folding resulted, followed by upright folding that extended beyond the thermal anomaly. Thus, thermal softening induced by heat-focusing is capable of generating discrete structural terranes characterized by subhorizontal ductile shear in the mid-crust, localized around large granitoid intrusions.  相似文献   

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