Constraining cooling histories: rutile and titanite chronology and diffusion modelling in NW Bhutan

U–Pb analyses of rutile and titanite commonly yield ages that constrain the timing of cooling rather than the timing of their crystallization. Rutile which grew at or close to peak temperature conditions in a mafic granulite, intermediate granulite and mafic amphibolite within juxtaposed litho/tectonostratigraphic units in the Greater Himalayan Sequence (GHS) of NW Bhutan yield LA–MC–ICP–MS U–Pb lower intercept cooling ages of 10.1 ± 0.4, 10.8 ± 0.1 and 10.0 ± 0.3 Ma, respectively. Numerical finite‐difference diffusion models constrained by previously published temperature–time and Pb diffusion data suggest that these ages are best explained by rapid cooling from peak temperature conditions of ～800 °C at 14 Ma in the granulite‐bearing unit and ～650 °C at 12 Ma in the amphibolite‐bearing unit. The good fit between the model and analysed ages confirms the relatively high retention of Pb in rutile suggested by the experimental data. Titanite that grew during an exhumation‐related amphibolite facies overprint on an eclogite facies mineral assemblage from the neighbouring Jomolhari Massif yields a U–Pb lower intercept cooling age of 14.6 ± 1.2 Ma. Diffusion modelling suggests that this age is too old to be consistent with the temperature–time paths inferred for the rutile‐bearing samples. Instead, the titanite age suggests cooling from ～650 °C at an earlier time of 17–15 Ma, implying that the high‐grade rocks in the Jomolhari Massif experienced a different cooling history from the rest of the GHS in NW Bhutan. Together these data show that high‐grade rocks from three apparently different structural levels of the GHS in NW Bhutan experienced rapid cooling at >40 °C Ma^?1 at varying times. The highest grade granulite facies rocks were exhumed from deeper structural levels that are not exposed, not preserved, or not yet recognized west of eastern Nepal. A progressive along‐strike change in tectonic regime, metamorphic history and/or exhumation mechanism across the orogen is implied by these thermochronologic data.     

Effects of diffusional modification of garnet growth zoning on P-T path calculations

The effect of intragranular diffusion on chemical zoning in garnet and on P-T paths calculated from that zoning was evaluated using a numerical model of multicomponent diffusion in combination with simulations of garnet growth. Syn-and post-growth diffusion of Mg–Fe–Mn–Ca species in garnet was calculated for a model pelitic assemblage over a range of temperatures from 485 to 635°C. Compositions from zoned garnet, as modified by diffusion, hypothetical inclusions of plagioclase within garnet and matrix phases were used to reconstruct pressure-temperature (P-T) paths from isobaric and polybaric model histories. P-T path calculations, based on numerical simulations conducted over an input isobaric heating path that reached peak temperatures between 585 and 635°C, show that relaxation of garnet compositional gradients by diffusion can induce modest to appreciable curvature in the inferred paths. Retrieved paths also indicated somewhat smaller overall temperature changes relative to the actual temperature difference of the input path. The magnitude of these distortions is shown to depend upon the heating and cooling rate and garnet crystal size as well as the actual peak temperature condition. The effect of diffusion on path trajectories in simulations with thermal histories that also included cooling were comparable to heating-only models that reached peak temperatures approximately 15–30°C higher. Compositions of garnets with radii less than 1 mm, that reached actual peak temperatures of 605°C along temperature-time histories characteristic of regional metamorphism, experienced sufficient diffusional relaxation to introduce errors of hundreds of bars to in excess of one kilobar in path trajectories. Path distortions were significant at heating/cooling rates less than 10°C/Ma, but rapidly diminished for rates faster than this. In polybaric simulations diffusion effects were least noticeable when the actual pressure-temperature conditions changed in a clockwise sense (i.e., convex to higher P and higher T), but apprecciable modification was seen in path models that underwent counterclockwise changes in P and T. Reequilibration of garnet rim compositions occurred during cooling on all paths, and temperature maxima obtained from garnet-biotite geothermometry underestimated actual peak conditions by 40 to 70°C. Calculations suggest that P-T path trajectories calculated from garnets of at least 1 mm size, and that experienced actual thermal maxima below 585°C, are not likely to be distorted by diffusional effects during regional metamorphism. However, P-T path reconstructions based on garnet zonation with smaller grains or higher temperatures may lead to misinterpretation of crystallization history. The partitioning record of peak metamorphic temperatures may be destroyed by diffusional reequilibration of garnet rim compositions during cooling, seriously complicating the task of quantitatively estimating diffusion effects on path calculations.     

Fast exhumation of the ultrahigh-pressure Alpe Arami garnet peridotite (Central Alps, Switzerland): constraints from geospeedometry and thermal modelling

Previous studies suggest that the metamorphic evolution of the ultrahigh‐pressure garnet peridotite from Alpe Arami was characterized by rapid subduction to a depth of c. 180 km with partial chemical equilibration at c. 5.9 Gpa/1180 °C and an initial stage of near‐isothermal decompression followed by enhanced cooling. In this study, average cooling rates were constrained by diffusion modelling on retrograde Fe–Mg zonation profiles across garnet porphyroclasts. Considering the effects of temperature, pressure and garnet bulk composition on the Fe–Mg interdiffusion coefficient, cooling rates of 380–1600 °C Myr^?1 for the interval from 1180 to 800 °C were obtained. Similar or even higher average cooling rates resulted from thermal modelling, whereby the characteristics of the calculated temperature‐time path depend on the shape and size of the hot peridotite body and the boundary conditions of the cooling process. The very high cooling rates obtained from both geospeedometry and thermal modelling imply extremely fast exhumation rates of c. 15 mm yr^?1 or more. These results agree with the range of exhumation rates (16–50 mm yr^?1) deduced from geochronological results. It is suggested that the Alpe Arami peridotite passively returned towards the surface as part of a buoyant sliver, caused as a consequence of slab breakoff.     

On the interpretation of peak metamorphic temperatures in light of garnet diffusion during cooling

Abstract Finite difference models of Fe-Mg diffusion in garnet undergoing cooling from metamorphic peak conditions are used to infer the significance of temperatures calculated using garnet-biotite Fe-Mg exchange thermometry. For rocks cooled from high grades where the garnet was initially homogeneous, the calculated temperature (T_calc) using garnet core and matrix biotite depends on the size of the garnet, the ratio of garnet to biotite in the rock (V_garnet/V_biotite) and the cooling rate. For garnets with radii of 1 mm and V_garnet/V_biotite<1, T_calc is 633, 700 and 777°C for cooling rates of 1, 10 and 100°C/Ma. For V_garnet/V_biotite= 1 and 4 and a cooling rate of 10° C/Ma, T_calc is approximately 660 and 610° C, respectively. Smaller and larger garnets have lower and higher T_calc, respectively. These results suggest that peak metamorphic temperatures may be reliably attained from rocks crystallized at conditions below T_calc of the garnet core, provided that V_garnet/V_biotite is sufficiently small (<0.1) and that the composition of the biotite at the metamorphic peak has not been altered during cooling. Numerical experiments on amphibolite facies garnets with nominal peak temperatures of 550–600° C generate a ‘well’in Fe/(Fe + Mg) near the rim during cooling. Maximum calculated temperatures for the assemblage garnet + chlorite + biotite + muscovite + plagioclase + quartz using the Fe/(Fe + Mg) at the bottom of the ‘well’with matrix biotite range from 23–43° C to 5–12° C below the peak metamorphic temperature for cooling rates of 1 and 100° C/Ma, respectively. Maximum calculated temperatures for the assemblage garnet + staurolite + biotite + muscovite + plagioclase + quartz are approximately 70° C below the peak metamorphic temperature and are not strongly dependent on cooling rate. The results of this study indicate that it may be very difficult to calculate peak metamorphic temperatures using garnet-biotite Fe-Mg exchange thermometry on amphibolite facies rocks (T_max > 550° C) because the rim composition of the garnet, which is required to calculate the peak temperature, is that most easily destroyed by diffusion.     

Cretaceous evolution of a metamorphic core complex,the Veporic unit,Western Carpathians (Slovakia): P–T conditions and in situ40Ar/39Ar UV laser probe dating of metapelites

Alpine metamorphism, related to the development of a metamorphic core complex during Cretaceous orogenic events, has been recognized in the Veporic unit, Western Carpathians (Slovakia). Three metamorphic zones have been distinguished in the metapelites: 1, chloritoid + chlorite + garnet; 2, garnet + staurolite + chlorite; 3, staurolite + biotite + kyanite. The isograds separating the metamorphic zones have been modelled by discontinuous reactions in the system K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O (KFMASH). The isograds are roughly parallel to the north‐east‐dipping foliation related to extensional updoming along low‐angle normal faults. Thermobarometric data document increasing P–T conditions from c. 500 °C and 7–8 kbar to c. 620 °C and 9–10 kbar, reflecting a coherent metamorphic field gradient from greenschist to middle amphibolite facies. ⁴⁰Ar/³⁹Ar data obtained by high spatial resolution in situ ultraviolet (UV) laser ablation of white micas from the rock slabs constrain the timing of cooling and exhumation in the Late Cretaceous. Mean dates are between 77 and 72 Ma; however, individual white mica grains record a range of apparent ⁴⁰Ar/³⁹Ar ages indicating that cooling below the blocking temperature for argon diffusion was not instantaneous. The reconstructed metamorphic P–T–t path is ‘clockwise’, reflecting post‐burial decompression and cooling during a single Alpine orogenic cycle. The presented data suggest that the Veporic unit evolved as a metamorphic core complex during the Cretaceous growth of the Western Carpathian orogenic wedge. Metamorphism was related to collisional crustal shortening and stacking, following closure of the Meliata Ocean. Exhumation was accomplished by synorogenic (orogen‐parallel) extension and unroofing in an overall compressive regime.     

Garnet-biotite diffusion mechanisms in complex high-grade orogenic belts: Understanding and constraining petrological cooling rates in granulites from Ribeira Fold Belt (SE Brazil)

Cooling rates based on the retrograde diffusion of Fe²⁺ and Mg between garnet and biotite inclusions commonly show two contrasting scenarios: a) narrow closure temperature range with apparent absence of retrograde diffusion; or b) high result dispersion due to compositional variations in garnet and biotite. Cooling rates from migmatites, felsic and mafic granulites from Ribeira Fold Belt (SE Brazil) also show these two scenarios. Although the former can be explained by very fast cooling, the latter is often the result of open-system behaviour caused by deformation. Retrogressive cooling during the exhumation of granulite-facies rocks is often processed by thrusting and shearing which may cause plastic deformation, fractures and cracks in the garnet megablasts, allowing chemical diffusion outside the garnet megablast – biotite inclusion system.However, a careful use of garnets and biotites with large Fe/Mg variation and software that reduces result dispersion provides a good correlation between closure temperatures and the size of biotite inclusions which are mostly due to diffusion and compositional readjustment to thermal evolution during retrogression.Results show that felsic and mafic granulites have low cooling rates (1–2 °C/Ma) at higher temperatures and high cooling rates (∼100 °C/Ma) at lower temperatures, suggesting a two-step cooling/exhumation process, whereas migmatites show a small decrease in cooling rates during cooling (from 2.0 to 0.5 °C/Ma). These results agree with previously obtained thermochronological data, which indicates that this method is a valid tool to obtain meaningful petrological cooling rates in complex high-grade orogenic belts, such as the Ribeira Fold Belt.     

Highly retentive core domains in K-feldspar and their implications for 40Ar/39Ar thermochronology illustrated by determining the cooling curve for the Capoas Granite,Palawan, The Philippines

K-feldspar from the late Miocene Capoas Granite on Palawan in The Philippines appears to contain highly retentive diffusion domains that are closed to argon diffusion at near-solidus temperatures during cooling of this ～7 km-diameter pluton. This is an important result, for K-feldspar is commonly considered not retentive in terms of its ability to retain argon. Closure temperatures for argon diffusion in K-feldspars are routinely claimed to be in the range ～150–400°C but the release of ³⁹Ar from irradiated K-feldspar during furnace step-heating experiments in vacuo yields Arrhenius data that imply the existence of highly retentive core domains, with inferred closure temperatures that can exceed ～500–700°C. These high closure temperatures from the Capoas Granite K-feldspar are consistent with the coincidence of ⁴⁰Ar/³⁹Ar ages with U–Pb zircon ages at ca 13.5 ± 0.2 Ma. The cooling rate then accelerated, but the rate of change had considerably slowed by ca 12 Ma. Low-temperature (U–Th)/He thermochronology shows that the cooling rate once again accelerated at ca 11 Ma, perhaps owing to renewed tectonic activity.     

Zircon (U-Th)/He thermochronometry: He diffusion and comparisons with Ar/Ar dating

(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 E_a = 163-173 kJ/mol (39-41 kcal/mol), and D₀ = 0.09-1.5 cm²/s, with an average E_a 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, T_c, 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.     

Effect of pressure on closure temperature of a trace element in cooling petrological systems

Closure temperature is important to many diffusion-related problems involving cooling. The classic model of Dodson and its modifications for cooling petrological systems are formulated at constant pressure. Many petrologic processes involve changes in both temperature and pressure. The effect of changing pressure on diffusional loss in cooling petrological systems has not been considered in Dodson’s model. During upwelling, the decompression rate is related to the cooling rate through the slope of the upwelling path. Simple analytical expressions for the average or mean closure temperature and closure pressure in cooling-upwelling mono-mineralic and bi-mineralic systems are obtained by noting that both temperature and pressure decrease as a function of time along the upwelling path. These pressure-adjusted equations are nearly identical to closure temperature equations for isobaric cases if one replaces the activation energy and pre-exponential factor for diffusion in the isobaric formulations by the path-dependent activation energy and pre-exponential factor. The latter also depend on the slope of the upwelling path. The competing effects between pressure and temperature on diffusion during upwelling result in reductions in the effective activation enthalpy for diffusion and exchange enthalpy for partitioning, which in turn leads to systematic deviations in closure temperatures from cases of constant pressure. For systems with large activation volume for diffusion, it may be possible to deduce upwelling path and upwelling rate from closure temperatures and closure pressures of selected elements. Examples of closure temperature and closure pressure for REE diffusion in garnet and clinopyroxene and in garnet–clinopyroxene aggregates are presented and discussed in the context of the minor’s rule and the REE-in-garnet–clinopyroxene thermobarometer. Closure temperatures for middle-to-heavy REE in garnet–clinopyroxene aggregates are controlled primarily by diffusion in clinopyroxene unless the modal abundance of garnet is very small or the effective grain size of clinopyroxene is considerably smaller than that of garnet.     

Comparison between grain size and multi-mineral Ar/Ar thermochronology

In the case of volume diffusion, the closure temperature of a mineral is function of, among other factors, the characteristic diffusion dimension, which can be approximated by the grain size of the mineral analysed for grains smaller than or similar in size to the diffusion domains. The theoretical possibility of single mineral grain size thermochronology had been demonstrated empirically in earlier studies, mostly using biotite. In order to examine the potential of this method, it was tested alongside the widely used multi-mineral ⁴⁰Ar/³⁹Ar thermochronology. The sample comes from the granitic McLean pluton, in the south section of the Grenville orogeny. Seven grain size separates of biotite (ranging between 90 and 1000 μm), eight size fractions of amphibole (between 63 and 1000 μm), and three size fractions of K-feldspar (250-600 μm) were extracted and dated by the laser step-heating ⁴⁰Ar/³⁹Ar method. The total gas ages obtained behave as theoretically predicted, with increasing ages for increasing grain sizes, including for K-feldspar, but with the exception of the smallest and the largest grains for biotite and amphibole. The calculated cooling rates are ca. 0.7 °C/Ma for K-feldspar, ca. 2.5 °C/Ma for biotite, and ca. 11 °C/Ma for amphibole, corresponding very well to a monotonic cooling of the McLean pluton. A quick initial thermal re-equilibration with the cooler host-rocks is followed by a much slower cooling on a thermal path parallel to that of the Frontenac Terrain situated immediately to the southeast. The validity of the single mineral grain size thermochronology is demonstrated by comparison with the thermal evolution of the adjacent units and with the cooling history derived from a multi-mineral thermochronology, suggesting that it can be routinely used. The application of this method can be hampered by insufficiently low analytical uncertainties.     

Influence of dissolution/reprecipitation reactions on metamorphic greenschist to amphibolite facies mica 40Ar/39Ar ages in the Longmen Shan (eastern Tibet)

Linking ages to metamorphic stages in rocks that have experienced low‐ to medium‐grade metamorphism can be particularly tricky due to the rarity of index minerals and the preservation of mineral or compositional relicts. The timing of metamorphism and the Mesozoic exhumation of the metasedimentary units and crystalline basement that form the internal part of the Longmen Shan (eastern Tibet, Sichuan, China), are, for these reasons, still largely unconstrained, but crucial for understanding the regional tectonic evolution of eastern Tibet. In situ core‐rim ⁴⁰Ar/³⁹Ar biotite and U–Th/Pb allanite data show that amphibolite facies conditions (~10–11 kbar, 530°C to 6–7 kbar, 580°C) were reached at 210–180 Ma and that biotite records crystallization, rather than cooling, ages. These conditions are mainly recorded in the metasedimentary cover. The ⁴⁰Ar/³⁹Ar ages obtained from matrix muscovite that partially re‐equilibrated during the post peak‐P metamorphic history comprise a mixture of ages between that of early prograde muscovite relicts and the timing of late muscovite recrystallization at c. 140–120 Ma. This event marks a previously poorly documented greenschist facies metamorphic overprint. This latest stage is also recorded in the crystalline basement, and defines the timing of the greenschist overprint (7 ± 1 kbar, 370 ± 35°C). Numerical models of Ar diffusion show that the difference between ⁴⁰Ar/³⁹Ar biotite and muscovite ages cannot be explained by a slow and protracted cooling in an open system. The model and petrological results rather suggest that biotite and muscovite experienced different Ar retention and resetting histories. The Ar record in mica of the studied low‐ to medium‐grade rocks seems to be mainly controlled by dissolution–reprecipitation processes rather than by diffusive loss, and by different microstructural positions in the sample. Together, our data show that the metasedimentary cover was thickened and cooled independently from the basement prior to c. 140 Ma (with a relatively fast cooling at 4.5 ± 0.5°C/Ma between 185 and 140 Ma). Since the Lower Cretaceous, the metasedimentary cover and the crystalline basement experienced a coherent history during which both were partially exhumed. The Mesozoic history of the Eastern border of the Tibetan plateau is therefore complex and polyphase, and the basement was actively involved at least since the Early Cretaceous, changing our perspective on the contribution of the Cenozoic geology.     

Modelling white mica pressure‐temperature‐time (P‐T‐t) paths using thermobarometric and 40Ar/39Ar thermochronologic data

White micas are major rock forming minerals in igneous and metamorphic rocks, and their chemical and isotopic variations can be used to determine pressure, temperature and time (P‐T‐t) histories. We apply ⁴⁰Ar/³⁹Ar multi‐diffusion domain modelling to white micas from blueschists blocks in serpentinite matrix mélange from the exhumed Baja California subduction complex. Thermal history models yielded T‐t paths suggesting that ⁴⁰Ar* resides within multiple diffusion domains with varying ⁴⁰Ar* retentivity. Modelled white mica thermal histories and thermobarometric data were used to forward model continuous P‐T‐t paths. P‐T‐t paths are consistent with previous studies and are interpreted to constrain blueschist block exhumation paths within the Baja accretionary wedge. Our P‐T‐t models use temperature controlled ⁴⁰Ar/³⁹Ar step heat data in which argon loss by volume diffusion can be demonstrated, and for which the white mica petrogenesis is known.     

Diffusion of 40Ar in hornblende

Measured radiogenic ⁴⁰Ar loss from two compositionally contrasting hornblendes following isothermal-hydrothermal treatment have provided model diffusion coefficients in the temperature range of 750° C to 900° C. Eight experiments using a hornblende (77–600) with a Mg/(Mg +Fe) ratio of 0.72 yield a linear array on an Arrhenius plot with a slope corresponding to an activation energy of 66.1 kcal-mol^–1 and a frequency factor of 0.061 cm²-sec^–1, assuming spherical geometry for the mineral aggregate. Five experiments undertaken on a hornblende (M Mhb-1) with a Mg/(Mg+Fe) ratio of 0.36 show similar behavior to the Mgrich sample, suggesting that the diffusivity of Ar in hornblendes is not sensitive to the Mg/Fe ratio.These data are consistent with kinetic information obtained from a geological experiment using the thermal effect of a granitoid intrusion. Together these data yield an activation energy of 64.1±1.7 kcal-mol^–1 and a frequency factor of 0.024± _0.011 ^0.053 cm²-sec^–1. For a hornblende with an effective diffusion radius of 80 m, these diffusion parameters predict closure temperatures between 578° C and 490° C for cooling rates in the range 500 to 5° C-Ma^–1.     

Relationship between plagioclase crystallization and cooling rate in basaltic melts

Rock textures commonly preserve a record of the near-surface crystallization history of volcanic rocks. Under conditions of simple cooling without convection or mixing, textures will reflect sample cooling rate, the temperature at which crystallization was initiated, and the distribution of mineral phase precipitation across the crystallization interval. Compilation of plagioclase size and number density data on natural (dike, sill and lava lake) and experimental samples suggests that (1) growth and nucleation rates of plagioclase in natural basaltic samples are a predictable function of cooling rate, and (2) the observed crystallization rate dependence on cooling rate is similar to that observed in experiments initiated at subliquidus temperatures. Comparison of natural and experimental samples thus suggests that most basalts crystallize under conditions of heterogeneous nucleation, with the number density of preexisting nucleii partially controlling textural responses to cooling rate changes. Time scales of crystallization and cooling in magmatic systems are intimately linked through a balance between heat removal from the system and heat evolved through crystallization. Evaluation of textural data in the context of recent numerical models of crystallization in simple (one- and two-component systems) provides new insight into regularities in the crystallization behavior of basaltic magmas. For example, the rate of change in crystal size (and number density, as dictated by mass balance) has been used as a measure of the relative importance of time scales of crystallization and cooling in numerical models of crystallizing systems. In natural samples, plagioclase size scales with the length scale of cooling such that a logarithmic plot of grain size as a function of normalized distance across the dike has a slope that appears approximately independent of dike width (solidification time). Comparison with available textural data for other phenocryst phases suggests that the same may be true for pyroxene and magnetite crystallization, with each phase having a characteristic slope probably controlled by the thermodynamic properties of the crystallizing phase. Measured crystal size distributions are unimodal and show maximum frequencies in the smaller size classes; distributions broaden and the grain size at peak frequency increases with increasing crystallization times (decreasing cooling rates). In contrast, partially crystallized Makaopuhi lava lake samples have crystal size distributions that decrease exponentially with increasing crystal size. Measured size distributions in dikes can be explained by late stage modification of Makaopuhi-type distributions through loss of small crystals, possibly the consequence of growth without nucleation. Finally, this compilation of the textural response of basaltic magmas to changes in cooling rate suggests that empirical calibrations of crystallization rate dependence on cooling rate from natural samples provide a reasonable model for plagioclase crystallization in near-surface basaltic systems. Predicted growth rates will be slow and relatively constant (10^-10–10^-11 cm/s) for crystallization times expected in most shallow volcanic systems (<1000 years).     

Cation ordering of orthopyroxenes from the Skaergaard Intrusion: implications for the subsolidus cooling rates and permeabilities

 We have determined the quenched cation ordering states of five orthopyroxene crystals collected from the marginal border group and the lower zone a and b of the Skaergaard intrusion, and modeled these data to retrieve their closure temperatures (T _c) of Fe–Mg ordering and cooling rates. According to existing thermal models for the Skaergaard pluton, conductive cooling dominated the high and low temperature regimes, which were separated by an intermediate temperature regime in which the cooling was controlled primarily by convective fluid circulation. The cooling rates retrieved from the quenched cation ordering states of the orthopyroxene crystals strictly apply to temperatures around the closure temperatures of the ordering states, ∼340–400^° C, which fall at the transition from convective to the lower temperature conductive cooling. The cooling rates obtained from the cation ordering states of orthopyroxene vary from ∼1 to 270 K/ka. These results agree well with a thermal model calculated using an assumed average permeability of 10^-12 cm² for the pluton, but not completely with a model calculated on the basis of an average permeability of 10^-13 cm², although both values produced shifts of δ¹⁸O that are comparable to those observed in the pluton. Received: 27 February 1995/Accepted: 20 July 1995     

Rapid cooling and exhumation of eclogitic rocks from the Great Caucasus, Russia

Diffusion modelling of growth-zoned garnet is used in combination with standard geothermometric and geobarometric techniques to estimate cooling and denudation rates from the mafic eclogites of the Red Cliff area, Great Caucasus, Russia. Euhedral garnet porphyroblasts exhibit different degrees of prograde growth zoning depending on the size of the grain (100 μm to several mm in diameter). Zoning patterns are mainly expressed in terms of Fe–Mg exchange, with 100*Mg/(Mg+Fe) increasing from 18–20 to 33–37 from core to rim. Geothermobarometry yields conditions of 680±40 °C and a minimum of 1.6±0.2 GPa and of 660±40 °C and 0.8±0.2 GPa for the high-pressure and retrograde stages of equilibration, respectively. A temperature of 600±40 °C has been recorded for the late-stage metamorphic overprint in the mica schists surrounding the eclogites. Relaxation of garnet zoning profiles was modelled for three different hypothetical P–T –t trajectories, all with an initial temperature of 680 °C and a pressure change of 0.8 GPa. The first two trajectories involve decompression associated with regular cooling down to 660 °C (near isothermal) and 600 °C. The third path is a two-step trajectory comprising near-isobaric cooling down to 600 °C followed by isothermal decompression to 0.8 GPa. These P–T trajectories cover as wide a range of pressure and temperature changes endured by the rocks as possible, thus representing extreme cases for calculating cooling and exhumation rates. Calculations indicate that the zoning pattern of the smallest garnet (i.e. garnet for which the zoning is most easily eliminated during post-growth processes) along the different paths can be preserved for the following average exhumation and cooling rates: path 1, 143 mm a^?1 and 102 °C Ma^?1; path 2, 60 mm a^?1 and 171 °C Ma^?1; path 3, 11–30 mm a^?1 and 200–400 °C Ma^?1. These results are discussed in light of theoretical P–T–t paths extracted from thermal models of regions of thickened crust, and from analogue models of accretionary wedge and continental lithosphere subduction.     

Phase equilibria modelling and zircon age dating of pelitic granulites in Zhaojiayao,from the Jining Group of the Khondalite Belt,North China Craton

The Jining Group occurs as the eastern segment of the Khondalite Belt, North China Craton and is dominated by a series of granulite facies rocks involving ‘normal’ pelitic granulites recording peak temperatures of ~850 °C and ultrahigh‐temperature (UHT) pelitic granulites recording peak temperatures of 950–1100 °C. The P–T paths and ages of these two types of granulites are controversial. Three pelitic granulite samples in the Jining Group comprising two sillimanite–garnet gneiss samples (J1208 and J1210) and one spinel–garnet gneiss sample (J1303) were collected from Zhaojiayao, where ‘normal’ pelitic granulites occur, for determination of their metamorphic evolution and ages. Samples J1208 and J1210 are interpreted to record cooling paths from the T_max stages with P–T conditions respectively of ~870–890 °C/7–8 kbar and >840 °C/>7.5 kbar constrained from the stability fields of the observed mineral assemblages and the isopleths of plagioclase, garnet and biotite compositions in pseudosections. Sample J1303 is interpreted to record pre‐T_max decompression from the kyanite‐stability fields to the T_max stage of 950–1020 °C/8–9 kbar and a post‐T_max cooling path revealed mainly from the stability field of the observed mineral assemblage, the plagioclase zoning and the biotite composition isopleth in pseudosections. The post‐T_max cooling stage can be divided into suprasolidus and subsolidus stages. The suprasolidus cooling may not result in an equilibrium state at the solidus in a rock. Therefore, different minerals may record different P–T conditions along the cooling path; the inferred maximum temperature is commonly higher than the solidus as well as different solidi being recorded for different samples from the same outcrop but experiencing different degrees of melt loss. Plagioclase compositions, especially its zoning in plagioclase‐rich granulites, are predicted to be useful for recording the higher temperature conditions of a granulite's thermal history. The three samples studied seem to record the temperature range covering those of the ‘normal’ and UHT pelitic granulites in the Jining Group, suggesting that UHT conditions may be reached in ‘normal’ granulites without diagnostic UHT indicators. LA‐ICP‐MS zircon U–Pb data provide a continuous trend of concordant ²⁰⁷Pb/²⁰⁶Pb ages from 1.89 to 1.79 Ga for sample J1210, and from 1.94 to 1.80 Ga for sample J1303. These continuous and long age spectrums are interpreted to represent a slow cooling and exhumation process corresponding to the post‐T_max cooling P–T paths recorded by the pelitic granulites, which may have followed the exhumation of deeply buried rocks in a thickened crust region resulted from a collision event at c. 1.95 Ga as suggested by the pre‐T_max decompression P–T path.     

Interpreting zirconium‐in‐rutile thermometric results

At first sight, experimental results and observations on rocks suggest that the Zr content in rutile, where equilibrated with quartz and zircon, should be a useful thermometer for metamorphic rocks. However, diffusion data for Zr in rutile imply that thermometry should not, for plausible rates of cooling, give the high temperatures commonly observed in high‐grade metamorphic rocks. It is suggested here that such observations can be accounted for by high‐T diffusive closure of Si in rutile, causing the interior of rutile grains to become insensitive to the thermometer equilibrium well above the temperature of Zr diffusive closure. Paired with comparatively slow grain boundary diffusion and problematic zircon nucleation, this allows for cases of Zr retention in rutile through temperatures where Zr is still diffusively mobile within rutile grains. Other observations that may be accounted for in this context are large inter‐grain ranges of rutile Zr contents uncorrelated with rutile grain size, and flat Zr profiles across individual rutile grains, counter to what would be expected from diffusive closure. A consequence is that it is unlikely that Zr‐in‐rutile thermometry will be useful for estimating rock cooling rates.     

Diffusion compensation in natural silicates

The temperature dependence of diffusion is usually found to follow the Arrhenius law: D = D₀e^?E/RT Winchell (1969) showed that there is commonly an inter-dependence between D₀ and E (for diffusion in silicate glasses), such that diffusion of different species show a positive correlation on a log D₀ vs E plot. A similar effect was noted by Hofmann (1980) for cation diffusion in basalt. This implies that diffusion rates of different species tend to converge at a particular temperature; this effect is known as the ‘compensation effect’. I will show that this effect is also present for diffusion in feldspars and olivines. The equations for the compensation lines (with E given in kcal/mol) are: basalt—E = 50 + 7.5 log D₀ feldspar—E = 50.7 + 3.4 log D₀ olivine—E = 78.0 + 7.5 log D₀ The convergence, or crossover, temperatures for diffusion in various materials are: obsidian—3400°C basalt—1370°C olivine—1360°C feldspar—460°C Compensation plots are useful for evaluating and comparing experimental diffusion data (though of limited usefulness in a predictive sense) and for understanding ‘closure temperatures’ for diffusion in petrogenetic processes (since closure temperature, the temperature at which natural diffusion processes are frozen in, is dependent on E, log d₀, and cooling rate). I show that most diffusing species in feldspar have a closure-temperature close to the crossover or convergence temperature, implying that all species in feldspars can be expected to ‘freeze-in’ simultaneously at temperatures in the range 400–600°C (for cooling rates in the range 10¹–10⁵°C/myr). Closure temperatures of various species in olivine, on the other hand, span a much larger range (800°C) for a similar range in cooling rates, implying that different elements in olivine will record different time-temperature stages in petrogenetic processes.     

Intragrain oxygen isotope zoning in titanite by SIMS: Cooling rates and fluid infiltration along the Carthage‐Colton Mylonite Zone,Adirondack Mountains,NY, USA

Oxygen isotopes are an attractive target for zoning studies because of the ubiquity of oxygen‐bearing minerals and the dependence of mineral ¹⁸O/¹⁶O ratios on temperature and fluid composition. In this study, subtle intragrain oxygen isotope zoning in titanite is resolved at the 10‐μm scale by secondary ion mass spectrometry. The patterns of δ¹⁸O zoning differ depending on microstructural context of individual grains and reflect multiple processes, including diffusive oxygen exchange, partial recrystallization, grain‐size reduction, and grain growth. Using the chronological framework provided by structural relations, these processes can be related to specific events during the Grenville orogeny. Titanite was sampled from two outcrops within the Carthage‐Colton Mylonite Zone (CCMZ), a long‐lived shear zone that ultimately accommodated exhumation of the Adirondack Highlands from beneath the Adirondack Lowlands during the Ottawan phase (1090–1020 Ma) of the Grenville orogeny. Titanite is hosted in the Diana metasyenite complex, which preserves three sequentially developed fabrics: an early NW‐dipping protomylonitic fabric (S₁) is crosscut by near‐vertical ultramylonitic shear zones (S₂), which are locally reoriented by a NNW‐dipping mylonitic fabric (S₃). Texturally early titanite (pre‐S₂) shows diffusion‐dominated δ¹⁸O zoning that records cooling from peak Ottawan, granulite‐facies conditions. Numerical diffusion models in the program Fast Grain Boundary yield good fits to observed δ¹⁸O profiles for cooling rates of 50 ± 20 °C Ma^?1, which are considerably faster than the 1–5 °C Ma^?1 cooling rates previously inferred for the Adirondack Highlands from regional thermochronology. High cooling rates are consistent with an episode of rapid shearing and exhumation along the CCMZ during gravitational collapse of the Ottawan orogen at c. 1050 Ma. Texturally later titanite (syn‐S₂) has higher overall δ¹⁸O and shows a transition from diffusion‐dominated to recrystallization‐dominated δ¹⁸O zoning, indicating infiltration of elevated‐δ¹⁸O fluids along S₂ shear zones and continued shearing below the blocking temperature for oxygen (~≤500 °C for grain sizes at the study site). The texturally latest titanite (post‐S₃) has growth‐dominated δ¹⁸O zoning, consistent with porphyroblastic grain growth following cessation of shearing along the Harrisville segment of the CCMZ.