Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model

Helium diffusion from apatite is a sensitive function of the volume fraction of radiation damage to the crystal, a quantity that varies over the lifetime of the apatite. Using recently published laboratory data we develop and investigate a new kinetic model, the radiation damage accumulation and annealing model (RDAAM), that adopts the effective fission-track density as a proxy for accumulated radiation damage. This proxy incorporates creation of crystal damage proportional to α-production from U and Th decay, and the elimination of that damage governed by the kinetics of fission-track annealing. The RDAAM is a version of the helium trapping model (HeTM; 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, 148-161), calibrated by helium diffusion data in natural and partially annealed apatites. The chief limitation of the HeTM, now addressed by RDAAM, is its use of He concentration as the radiation damage proxy for circumstances in which radiation damage and He are not accumulated and lost proportionately from the crystal.By incorporating the RDAAM into the HeFTy computer program, we explore its implications for apatite (U-Th)/He thermochronometry. We show how (U-Th)/He dates predicted from the model are sensitive to both effective U concentration (eU) and details of the temperature history. The RDAAM predicts an effective He closure temperature of 62 °C for a 28 ppm eU apatite of 60 μm radius that experienced a 10 °C/Ma monotonic cooling rate; this is 8 °C lower than the 70 °C effective closure temperature predicted using commonly assumed Durango diffusion kinetics. Use of the RDAAM is most important for accurate interpretation of (U-Th)/He data for apatite suites that experienced moderate to slow monotonic cooling (1-0.1 °C/Ma), prolonged residence in the helium partial retention zone, or a duration at temperatures appropriate for radiation damage accumulation followed by reheating and partial helium loss. Under common circumstances the RDAAM predicts (U-Th)/He dates that are older, sometimes much older, than corresponding fission-track dates. Nonlinear positive correlations between apatite (U-Th)/He date and eU in apatites subjected to the same temperature history are a diagnostic signature of the RDAAM for many but not all thermal histories.Observed date-eU correlations in four different localities can be explained with the RDAAM using geologically reasonable thermal histories consistent with independent fission-track datasets. The existence of date-eU correlations not only supports a radiation damage based kinetic model, but can significantly limit the range of acceptable time-temperature paths that account for the data. In contrast, these datasets are inexplicable using the Durango diffusion model. The RDAAM helps reconcile enigmatic data in which apatite (U-Th)/He dates are older than expected using the Durango model when compared with thermal histories based on apatite fission-track data or other geological constraints. It also has the potential to explain at least some cases in which (U-Th)/He dates are actually older than the corresponding fission-track dates.     

He diffusion systematics in minerals: Evidence from synthetic monazite and zircon structure phosphates

Helium diffusivity was measured in synthetic rare-earth-element orthophosphates with systematically varying properties to evaluate potential controls on He transport in minerals. In the zircon structure phosphates (in this study, the phosphates of Tb, Dy, Ho, Er, Tm, Yb, and Lu as well as synthetic xenotime, YPO₄), He diffusion is strongly anisotropic. Transport apparently proceeds preferentially through channels aligned with the c-axis. The activation energy for diffusion is almost the same (122 ± 6 kJ/mol) in all members of this family, but there is a monotonic decrease in D_o with atomic number from TbPO₄ (∼10⁵ cm²/s) to LuPO₄ (∼10 cm²/s). The c-parallel channels become increasingly constricted in the same sequence, likely accounting for the systematically decreasing diffusivity. The He closure temperature (r = 1 cm, dT/dt = 10 °C/Myr) increases with atomic number from 44 °C for TbPO₄ to 88 °C for LuPO₄. Diffusion of radiogenic helium from natural zircon and xenotime is much slower than these synthetic analogs predict, suggesting that coupled substitution of REE and P for Zr and Si and/or radiation damage profoundly modify the energetics of interstitial He diffusion. In particular, α-recoil may play a key role by damaging the continuity and integrity of the channels.Monazite structure phosphates (here La, Ce, Pr, Nd, Sm, and Gd phosphate) are far more He retentive than those of the zircon structure. Activation energies increase smoothly with atomic number from LaPO₄ (183 kJ/mol) to NdPO₄ (224 kJ/mol) then decrease again to GdPO₄ (198 kJ/mol). D_o values mimic this pattern, spanning a range from ∼10⁻¹ cm²/s (GdPO₄) to 10⁴ cm²/s (NdPO₄). Nevertheless, He closure temperatures increase monotonically with atomic number, from 300 °C in LaPO₄ to 410 °C in GdPO₄. No evidence was obtained bearing on diffusion anisotropy, but the monazite structure lacks through-going channels so it is not expected. Diffusion parameters for radiogenic helium in natural monazite are similar to those obtained on the synthetic analogs.Ionic porosity is not the primary control on He diffusion in the orthophosphates. Within a given structure and with limited elemental substitution, ionic porosity and He closure temperature are negatively correlated, as predicted. However, differences between crystal structures are far more important than ion packing density: at comparable ionic porosity the monazite structure phosphates have He closure temperatures ∼300 °C higher than the xenotime structure phosphates. Modifications to the structures by radiation damage likely play a similarly significant role in controlling He diffusion.     

U and Th zonation in apatite observed by laser ablation ICPMS, and implications for the (U-Th)/He system

A laser-ablation inductively-coupled plasma mass spectrometry technique was developed to measure U, Th, and Ce zonation in polished sections of apatite for assessing the consequences of parent zonation for (U-Th)/He thermochronometry. The technique produces concentration maps with an averaging length-scale of ∼20 μm, comparable to the α-stopping distance, and a precision of ∼5% down to few ppm concentration levels. A model was developed to transform the measured concentration distribution into a simplified representation for use in spherical-geometry He production-diffusion models. To illustrate these methods, 30 sections of apatite from a single granite (GC863) were mapped. Every analyzed apatite from GC863 is zoned, with most grains having variable thickness rims and terminations that are enriched in U and Th by about a factor of three over the grain cores.Parent zonation has three independent effects on (U-Th)/He He ages: it influences the α ejection correction, the ⁴He concentration profile which governs diffusive loss, and, via radiation damage trap accumulation, spatial variability of diffusivity within the crystal. If the observed zonation is typical of the apatite population in GC863, use of the standard homogenous α ejection correction would cause He ages to be on average 3% too young, and with a large amount of grain-to-grain variability (9% too young in the most rim-enriched case to 6% too old in a core-enriched case). Independent of the ejection correction, the concentration profile modifies the effective closure temperature of the apatites by placing more (or less) ⁴He near the grain edge. The parent zonation in GC863 apatites causes closure temperatures to range from four degrees lower (rim-enriched case) to two degrees higher (core-enriched case) than applies in the homogenous case. Alpha ejection and concentration profile effects on He age are additive and of the same sense. In the case of typical grains in GC863 cooled between 1 and 10 °C/Ma, the two effects are roughly equal in magnitude. The effects of intracrystalline variations in radiation damage trap accumulation become apparent at slow cooling rates (1 °C/Ma). For example, in rim-enriched GC863 grains cooled at 1 °C/Ma, preferential accumulation of radiation damage traps near the grain rim almost compensates for the higher loss rate expected of ⁴He also located preferentially near the rim. Under some circumstances strong rim-enrichment may actually increase the effective closure temperature of an apatite. Zonation at the level observed in GC863 modifies the ⁴He/³He spectra substantially from that expected from a uniform distribution. Measured ⁴He/³He spectra are strikingly similar to predictions based on the mapped eU distributions of the very same crystals, supporting the overall validity of the analytical and interpretive approach presented here.The magnitude and style of U, Th zonation documented in GC863 is one possible source of frequently observed over-dispersion of apatite (U-Th)/He ages as well as anomalous ⁴He/³He spectra.     

Laser depth profiling studies of helium diffusion in Durango fluorapatite

Ultraviolet lasers coupled with sensitive mass spectrometers provide a useful way to measure laboratory-induced noble gas diffusion profiles in minerals, thus enabling the calculation of diffusion parameters. We illustrate this laser ablation depth profiling (LADP) technique for a previously well-studied mineral-isotopic system: ⁴He in Durango fluorapatite. LADP studies were conducted on oriented, polished slabs from a single crystal that were heated under vacuum to a variety of temperatures between 300 and 450 °C for variable times. The resolved ⁴He profiles exhibited error-function loss as predicted by previous bulk ⁴He diffusion studies. All of the slabs, regardless of crystallographic orientation, yielded modeled diffusivities that are statistically co-linear on an Arrhenius diagram, suggesting no diffusional anisotropy of ⁴He in this material. The data indicate an activation energy of 142.2 ± 5.0 (2σ) kJ/mol and diffusivity at infinite temperature - reported as ln(D₀) - of −4.71 ± 0.94 (2σ) m²/s. These values imply a bulk closure temperature for ⁴He in Durango fluorapatite of 74 °C for a 50 μm radius grain, infinite cylinder geometry, and a cooling rate of 10 °C/Myr.     

Low-temperature anisotropic diffusion of helium in zircon: Implications for zircon (U-Th)/He thermochronometry

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 [T_c ∼ 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.     

The effect of aqueous diffusion on the fractionation of chlorine and bromine stable isotopes

Diffusive isotopic fractionation factors are important in order to understand natural processes and have practical application in radioactive waste storage and carbon dioxide sequestration. We determined the isotope fractionation factors and the effective diffusion coefficients of chloride and bromide ions during aqueous diffusion in polyacrylamide gel. Diffusion was determined as functions of temperature, time and concentration. The effect of temperature is relatively large on the diffusion coefficient (D) but only small on isotope fractionation. For chlorine, the ratio, D_³⁵Cl/D_³⁷Cl varied from 1.00128 ± 0.00017 (1σ) at 2 °C to 1.00192 ± 0.00015 at 80 °C. For bromine, D_⁷⁹Br/D_⁸¹Br varied from 1.00098 ± 0.00009 at 2 °C to 1.0064 ± 0.00013 at 21 °C and 1.00078 ± 0.00018 (1σ) at 80 °C. There were no significant effects on the isotope fractionation due to concentration. The lack of sensitivity of the diffusive isotope fractionation to anything at the most common temperatures (0 to 30 °C) makes it particularly valuable for application to understanding processes in geological environments and an important natural tracer in order to understand fluid transport processes.     

The effect of long-term low-temperature exposure on apatite fission track stability: A natural annealing experiment in the deep ocean

Since studies on deep-sea cores were carried out in the early 1990s it has been known that ambient temperature may have a marked affect on apatite fission track annealing. Due to sluggish annealing kinetics, this effect cannot be quantified by laboratory annealing experiments. The unknown amount of low-temperature annealing remains one of the main uncertainties for extracting thermal histories from fission track data, particularly for samples which experienced slow cooling in shallow crustal levels. To further elucidate these uncertainties, we studied volcanogenic sediments from five deep-sea drill cores, that were exposed to maximum temperatures between ∼10° and 70 °C over geological time scales of ∼15-120 Ma. Mean track lengths (MTL) and etch pit diameters (Dpar) of all samples were measured, and the chemical composition of each grain analysed for age and track length measurements was determined by electron microprobe analysis. Thermal histories of the sampled sites were independently reconstructed, based on vitrinite reflectance measurements and/or 1D numerical modelling. These reconstructions were used to test the most widely used annealing models for their ability to predict low-temperature annealing. Our results show that long-term exposure to temperatures below the temperature range of the nominal apatite fission track partial annealing zone results in track shortening ranging between 4 and 11%. Both chlorine content and Dpar values explain the downhole annealing patterns equally well. Low chlorine apatite from one drill core revealed a systematic relation between Si-content and Dpar value. The question whether Si-substitution in apatite has direct and systematic effects on annealing properties however, cannot be addressed by our data. For samples, which remained at temperatures <30 °C, and which are low in chlorine, the Laslett et al. [Laslett G., Green P., Duddy I. and Gleadow A. (1987) Thermal annealing of fission tracks in apatite. Chem. Geol. 65, 1-13] annealing model predicts MTL up to 0.6 μm longer than those actually measured, whereas for apatites with intermediate to high chlorine content, which experienced temperatures >30 °C, the predictions of the Laslett et al. (1987) model agree with the measured MTL data within error levels. With few exceptions, predictions by the Ketcham et al. [Ketcham R., Donelick R. and Carlson W. (1999) Variability of apatite fission-track annealing kinetics. III: Extrapolation to geological time scales. Am. Mineral. 84/9, 1235-1255] annealing model are consistent with the measured data for samples which remained at temperatures below ∼30 °C. For samples which experienced maximum temperatures between ∼30 and 70 °C, and which are rich in chlorine, the Ketcham et al. (1999) model overestimates track annealing.     

Response of Precambrian zircon to the chemical abrasion (CA-TIMS) method and implications for improvement of age determinations

Electron backscatter imaging, Raman spectroscopy and U-Pb geochronology have been applied to Precambrian zircon grains that were annealed at 1000 and 1450 °C for various times, then leached with HF to constrain the conditions for healing radiation damage and attaining primary U-Pb zircon ages using the chemical abrasion (CA-TIMS) method. SEM images reveal a variety of textures for ZrO₂ overgrowths on 1450 °C annealed and leached zircon surfaces that depend on the degree of radiation damage and annealing history. Highly damaged zircon produces finer textures than zircon with less damage.Raman spectroscopy indicates that crystals with different levels of radiation damage are only partially restored by annealing at 1000 °C for 2-3 days. Longer annealing periods of 20 days are not noticeably more effective. Annealing at 1450 °C for 1 h results in partial breakdown of zircon but restores Raman peak widths and wave numbers to values characteristic of undamaged zircon after ZrO₂ overgrowths are removed by HF. Raman spectra are much less sensitive to polarization angle for annealed highly damaged grains than for weakly damaged zircon.U-Pb isotopic analyses of low to moderately damaged zircon (alpha fluence ranging up to 10¹⁹/g corresponding to an amorphization volume fraction of 80% or more) yield almost concordant data (0.3-0.5% discordance) after high-temperature annealing at 1450 °C followed by HF leaching at 195 °C. Analyses of cracked zircon annealed at 1450 °C and leached may remain discordant but those of uncracked grains are concordant. Most analyses show primary ²⁰⁷Pb/²⁰⁶Pb ages although cracked grains annealed at 1450 °C may produce discordant data with ²⁰⁷Pb/²⁰⁶Pb ages that are too young after leaching. The solubility of highly damaged, very disordered zircon (amorphization level of 99%) is only slightly reduced by annealing, and analyses of leach residues are strongly discordant although primary ²⁰⁷Pb/²⁰⁶Pb ages are obtained.Annealing of highly damaged zircon under any conditions apparently results in a mass of randomly oriented micro-crystals that pseudomorph the original grain. This could explain the fine-scale pattern observed on etched crystal surfaces, reduced anisotropy at the 5 μm scale of the Raman laser beam and high solubility in HF. It may be impossible to restore primary U-Pb isotopic ages in such cases but precise ages can still potentially be determined from ²⁰⁷Pb/²⁰⁶Pb ratios or by application of the air abrasion method.     

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.     

O and H diffusion in uraninite: Implications for fluid-uraninite interactions, nuclear waste disposal, and nuclear forensics

Diffusion coefficients for oxygen and hydrogen were determined from a series of natural uraninite-H₂O experiments between 50 and 700 °C. Under hydrous conditions there are two diffusion mechanisms: (1) an initial extremely fast-path diffusion mechanism that overprinted the oxygen isotopic composition of the entire crystals regardless of temperature and (2) a slower volume-diffusive mechanism dominated by defect clusters that displace or eject nearest neighbor oxygen atoms to form two interstitial sites and two partial vacancies, and by vacancy migration. Using the volume diffusion coefficients in the temperature range of 400-600 °C, diffusion coefficients for oxygen can be represented by D = 1.90e⁻⁵ exp (−123,382 J/RT) cm²/s and for temperatures between 100 and 300 °C the diffusion coefficients can be represented by D = 1.95e⁻¹⁰ exp (−62484 J/RT) cm²/s, where the activation energies for uraninite are 123.4 and 62.5 kJ/mol, respectively. Hydrogen diffusion in uraninite appears to be controlled by similar mechanisms as oxygen. Using the volume diffusion coefficients for temperatures between 50 and 700 °C, diffusion coefficients for hydrogen can be represented by D = 9.28e⁻⁶ exp (−156,528 J/RT) cm²/s for temperatures between 450 and 700 °C and D = 1.39e⁻¹⁴ exp (−34518 J/RT) cm²/s for temperatures between 50 and 400 °C, where the activation energies for uraninite are 156.5 and 34.5 kJ/mol, respectively.Results from these new experiments have implications for isotopic exchange during natural UO₂-water interactions. The exceptionally low δ¹⁸O values of natural uraninites (i.e. −32‰ to −19.5‰) from unconformity-type uranium deposits in Saskatchewan, in conjunction with theoretical and experimental uraninite-water and UO₃-water fractionation factors, suggest that primary uranium mineralization is not in oxygen isotopic equilibrium with coeval clay and silicate minerals. The low δ¹⁸O values have been interpreted as resulting from the low temperature overprinting of primary uranium mineralization in the presence of relatively modern meteoric fluids having δ¹⁸O values of ca. −18‰, despite petrographic and U-Pb isotope data that indicate limited alteration. Our data show that the anomalously low oxygen isotopic composition of the uraninite from the Athabasca Basin can be due to meteoric water overprinting under reducing conditions, and meteoric water or groundwater can significantly affect the oxygen isotopic composition of spent nuclear fuel in a geologic repository, with minimal change to the chemical composition or texture. Moreover, the rather fast oxygen and hydrogen diffusion coefficients for uraninite, especially at low temperatures, suggest that oxygen and hydrogen diffusion may impart characteristic isotopic signals that can be used to track the route of fissile material.     

Determining accurate temperature-time paths from U-Pb thermochronology: An example from the Kaapvaal craton, southern Africa

Thermochronology has revolutionized our understanding of the establishment and evolution of lithospheric thermal structure. However, many potential benefits provided by the application of diffusion theory to thermochronology have yet to be fully exploited. This study uses apatite (T_c = 450-550 °C) and titanite (T_c = 550-650 °C) U-Pb ID-TIMS thermochronology at the single- to sub-grain scale to separate the variable effects of volume diffusion of Pb from metamorphic (over)growth above and below the T_c of a mineral. Data are presented from two ca. 3227 Ma tonalite samples from north and south of the Barberton Greenstone Belt (BGB), southern Africa. Two distinct populations of apatite from a sample north of the BGB record fast cooling followed by metamorphic growth ∼10 Myr later. Both apatite and titanite dates from south of the BGB show a strong correlation with the grain size and record 100 Myr of post-emplacement cooling. Complex core-rim zoning observed in cathodoluminescence images of apatite is interpreted to reflect metamorphic overgrowth above the T_c. The age and topology of grain size versus date curves from titanite and apatite are used in combination with a finite-difference numerical model to show that slow, non-linear, cooling and not thermal resetting is responsible for the observed distribution. The thermal histories from either side of the BGB are very different and provide unique insight into the BGB’s tectonic evolution: a ∼70 Myr period of apparent stability after ca. 3.2 Ga terrane assembly was followed by fast exhumation south of the BGB that led to lower-crustal melting and intrusion of granitic batholiths ca. 3.14-3.10 Ga.     

Magnesium isotope fractionation in silicate melts by chemical and thermal diffusion

Two types of laboratory experiments were used to quantify magnesium isotopic fractionations associated with chemical and thermal (Soret) diffusion in silicate liquids. Chemical diffusion couples juxtaposing a molten natural basalt (SUNY MORB) and a molten natural rhyolite (Lake County Obsidian) were run in a piston cylinder apparatus and used to determine the isotopic fractionation of magnesium as it diffused from molten basalt to molten rhyolite. The thermal diffusion experiments were also run in a piston cylinder apparatus but with a sample made entirely of molten SUNY MORB displaced from the hotspot of the assembly furnace so that the sample would have a temperature difference of about 100-200 °C from one end to the other. The chemical diffusion experiments showed fractionations of ²⁶Mg/²⁴Mg by as much as 7‰, which resulted in an estimate for the mass dependence of the self-diffusion coefficients of the magnesium isotopes corresponding to D_26Mg/D_24Mg=(24/26)^β with β = 0.05. The thermal diffusion experiments showed that a temperature difference of about 100 °C resulted in the MgO, CaO, and FeO components of the basalt becoming slightly enriched by about 1 wt% in the colder end while SiO₂ was enriched by several wt% in the hotter end. The temperature gradient also fractionated the magnesium isotopes. A temperature difference of about 150 °C produced an 8‰ enrichment of ²⁶Mg/²⁴Mg at the colder end relative to the hotter end. The magnesium isotopic fractionation as a function of temperature in molten basalt corresponds to 3.6 × 10⁻²‰/°C/amu.     

α-Emitting mineral inclusions in apatite, their effect on (U-Th)/He ages, and how to reduce it

U-Th rich mineral inclusions in apatite are often held responsible for erroneously old (U-Th)/He ages, because they produce “parentless” He. Three aspects associated with this problem are discussed here. First, simple dimensional considerations indicate that for small mineral inclusions, the parentless helium problem might not be as serious as generally thought. For example, a mineral inclusion that is 10% the length, width and height of its host apatite needs to be a thousand times more concentrated in U and Th to produce an equal amount of He. Therefore, single isolated inclusions smaller than a few μm are unlikely to contribute significant helium. For larger or more abundant inclusions, the parentless helium problem can be solved by dissolution of the apatite and its inclusions in hot HF. Second, besides creating parentless helium, inclusions also complicate α-ejection corrections. Mathematical exploration of this latter problem for spherical geometries reveals that for randomly distributed inclusions, the probability distribution of single-grain ages is predicted to have a sharp mode at the mean age, with tails towards younger and older ages. Multiple-grain measurements will yield accurate and precise age estimates if 10 or more randomly distributed α-emitting mineral inclusions are present in a sample. Third, thermal modeling indicates that mineral inclusions have a non-trivial but minor (<5 °C) effect on the closure temperature. These predictions were tested on apatites from rapidly cooled migmatites of Naxos (Greece) which contain abundant U-rich zircon inclusions. Thirty-seven samples were subjected to two kinds of treatment. The “pooled” age (i.e., the synthetic multi-grain age computed from a number of single-grain analyses) of four inclusion-free samples (13 apatites), prepared in HNO₃ is 10.9 Ma, close to apatite and zircon fission-track ages from the same rock. (U-Th)/He ages of 14 inclusion-bearing samples dissolved in HNO₃ range between 9 and 45 Ma, with a pooled age of 22.6 Ma. The ages of 19 HF-treated samples range between 5 and 16 Ma, with 10 of 14 single-grain samples between 9 and 13 Ma and a pooled age of 10.9 Ma. These observations agree with the theoretical predictions and support the addition of HF-treated apatite (U-Th)/He dating to the thermochronological toolbox.     

Diffusion of Ar in muscovite

Hydrothermal treatment of closely sized muscovite aggregates in a piston-cylinder apparatus induced ⁴⁰Ar^∗ loss that is revealed in ⁴⁰Ar/³⁹Ar step heating spectra. Age spectra and Arrhenius data, however, differ from that expected from a single diffusion length scale. A numerical model of episodic loss assuming the presence of multiple diffusion domains yields excellent fits between synthetic and actual degassing spectra. We used this model to isolate ⁴⁰Ar^∗ loss from the grains that remained intact during hydrothermal treatment at 10 kbar permitting calculation of diffusion coefficients in the temperature range 730-600 °C. Diffusion data generated in this manner yield an activation energy (E) of 63 ± 7 kcal/mol and frequency factor (D_o) of 2.3  cm²/s. Experiments at 20 kbar yield diffusivities lower by about an order of magnitude and correspond to an activation volume of ∼14 cm³/mol. Together, these parameters predict substantially greater retentivity of Ar in muscovite than previously assumed and correspond to a closure temperature (T_c) of 425 °C for a 100 μm radius grain cooling at 10 °C/Ma at 10 kbar (T_c = 405 °C at 5 kbar. Age and log (r/r_o) spectra for the run products show strong correlations indicating that muscovites can retain Ar diffusion boundaries and mechanisms that define their natural retentivity during vacuum step heating. This may permit the application of high resolution, continuous ⁴⁰Ar/³⁹Ar thermochronology to low grade, regionally metamorphosed terranes.     

Experimental determination of the role of diffusion on Li isotope fractionation during basaltic glass weathering

In order to use lithium isotopes as tracers of silicate weathering, it is of primary importance to determine the processes responsible for Li isotope fractionation and to constrain the isotope fractionation factors caused by each process as a function of environmental parameters (e.g. temperature, pH). The aim of this study is to assess Li isotope fractionation during the dissolution of basalt and particularly during leaching of Li into solution by diffusion or ion exchange. To this end, we performed dissolution experiments on a Li-enriched synthetic basaltic glass at low ratios of mineral surface area/volume of solution (S/V), over short timescales, at various temperatures (50 and 90 °C) and pH (3, 7, and 10). Analyses of the Li isotope composition of the resulting solutions show that the leachates are enriched in ⁶Li (δ⁷Li = +4.9 to +10.5‰) compared to the fresh basaltic glass (δ⁷Li = +10.3 ± 0.4‰). The δ⁷Li value of the leachate is lower during the early stages of the leaching process, increasing to values close to the fresh basaltic glass as leaching progresses. These low δ⁷Li values can be explained in terms of diffusion-driven isotope fractionation. In order to quantify the fractionation caused by diffusion, we have developed a model that couples Li diffusion with dissolution of the glassy silicate network. This model calculates the ratio of the diffusion coefficients of both isotopes (a = D₇/D₆), as well as its dependence on temperature, pH, and S/V. a is mainly dependent on temperature, which can be explained by a small difference in activation energy (0.10 ± 0.02 kJ/mol) between ⁶Li⁺ and ⁷Li⁺. This temperature dependence reveals that Li isotope fractionation during diffusion is low at low temperatures (T < 20 °C), but can be significant at high temperatures. However, concerning hydrothermal fluids (T > 120 °C), the dissolution rate of basaltic glass is also high and masks the effects of diffusion. These results indicate that the high δ⁷Li values of river waters, in particular in basaltic catchments, and the fractionated values of hydrothermal fluids are mainly controlled by precipitation of secondary phases.     

Cr diffusion in orthopyroxene: Experimental determination, Mn-Cr thermochronology, and planetary applications

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 (T_c) 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 T_c of 830-980 °C, and cooling rates of 2-27 °C/Myr at T_c 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.     

Argon diffusion in plagioclase and implications for thermochronometry: A case study from the Bushveld Complex, South Africa

Plagioclase is not only the most abundant mineral in the Earth’s crust, but is present in almost all terrestrial tectonic settings and is widespread in most extraterrestrial material. Applying the K-Ar system to this common mineral would provide a powerful tool for quantifying thermal histories in a wide variety of settings. Nonetheless, plagioclase has rarely been used for thermochronometry, largely due to difficulties in simultaneously acquiring precise geochronologic data and quantifying argon diffusion kinetics from a mineral with low-K concentration. Here we describe an analytical technique that generates high-precision ⁴⁰Ar/³⁹Ar data and quantifies Ar diffusion kinetics of low-K minerals. We present results of five diffusion experiments conducted on single crystals of plagioclase from the Bushveld Complex, South Africa. The observed diffusion kinetics yield internally consistent thermochronological constraints, indicating that plagioclase is a reliable thermochronometer. Individual grains have activation energies of 155-178 kJ/mol and ln(D₀/a²) varies between 3.5 and 6.5. These diffusion parameters correspond to closure temperatures of 225-300 °C, for a 10 °C/Ma cooling rate. Age spectra generally conform to single-domain diffusive loss profiles, suggesting that grain-scale diffusion dominates argon transport in this fairly simple plagioclase. Conjointly examining several single-grain analyses enables us to distinguish episodic reheating from slow cooling and indicates that the Bushveld Complex cooled rapidly and monotonically from magmatic temperature to <300 °C over 3 Ma, followed by protracted cooling to ambient crustal temperatures of 150-200 °C over ∼600 Ma.     

Noble gas isotope sites and mobility in mafic rocks and olivine

Important He and Ar isotope studies on rocks and minerals, relevant to the geochemical and degassing history of the Earth, are often hampered by insufficient knowledge of the retentivity of different types of sites in minerals (inclusions, matrix) for these species, and of the relative importance of radiogenic and trapped components and possible differences in their behavior.To identify sites of noble gas isotopes, shed some light on their origin and estimate their residence times in olivine, which is a mineral considered as a good natural sampler, we investigated 2.5 Ga old ultramafic rocks from the Monche Pluton (Kola Peninsula, north-east part of the Baltic shield) using several extraction methods: crushing, fusion, slow step-wise and rapid incremental heating. Previous studies indicated that these rocks contain mainly trapped noble gases; however, to constrain the possible contribution of in-situ generated radiogenic helium, U and Th concentrations were also measured in the samples.The helium release pattern obtained by relatively fast (∼1.5 h long) incremental heating of olivine includes three distinct release peaks for helium: a low-temperature (600 °C) l-peak, a middle (800-1100 °C) m-peak and a high-temperature (∼1400 °C) h-peak. However, helium extraction from a powdered aliquot of the same olivine yields mainly the middle m-peak indicating that gases released in the l- and h-peaks occupy gas-liquid inclusions opened in the course of crushing and grinding. Moreover, slow step-wise heating (14 h) also results in a broad He release peak but in two well-separated l- and h-peaks of non-atmospheric ⁴⁰Ar∗. This feature implies helium migration from l- and h-vesicles into the matrix m during long step-wise heating experiments, whereas less movable Ar remains in inclusions at even relatively high almost-magmatic temperatures.Using a simple phenomenological model envisaging the three different residence sites for noble gases, both fast- and slow-heating release patterns for ⁴⁰Ar∗ and He, including those for the crushed sample, could be reproduced. The diffusion parameters inferred from the modeling of olivine (D₀ = 2.4 × 10⁻² cm² s⁻¹ and Ea = 133 kJ mol⁻¹) are similar to those published by Shuster et al. (2003) and Blard et al. (2008). The high matrix/fluid solubility coefficient for helium, H_He ∼ 0.01, exceeds estimates reported by Trull and Kurz (1993); however, the product D_He(T) × H_He, the “permeability” (that governs He migration in vesicles + matrix composed materials), is very similar to their value. Extrapolation to the ambient temperature (0 °C) gives long and similar helium residence times in l- and h-vesicles, exceeding 10¹⁰ yrs, and even longer time scales ∼10¹⁶ yrs are obtained for the helium residence in the matrix. Therefore, at low temperatures our samples may be considered as excellent samplers of trapped volatile species, including helium.     

Constraints on the loss of matrix-sited helium during vacuum crushing of mafic phenocrysts

Vacuum crushing is an efficient technique to selectively release the mantle-derived helium component trapped within olivine and pyroxene phenocrysts. However, contrary to previous assumptions, recent studies have shown that this method may liberate significant matrix-sited cosmogenic ³He (³He_c) or radiogenic ⁴He (⁴He^∗). Because this loss may bias both the determination of magmatic ³He/⁴He ratios and the accuracy of ³He_c measurements, it is essential to understand what mechanism is responsible and under what conditions matrix helium loss is manifest. To address this question, olivines and pyroxenes with various amounts of matrix-sited ³He (from 10⁷ to 10¹¹ at. g⁻¹) were crushed in air or in vacuum using several crushing devices. Sample temperature was controlled during each crushing experiment, and ranged from 25 to 325 °C. The resulting powders were then sieved to obtain several homogeneous grain fractions ranging between <10 and >300 μm. The ³He_c concentrations measured in each fraction clearly show that significant ³He_c loss (>20%) affects only the finest fraction (<10 μm) and, importantly, only under hot conditions (here T ?300 °C). Even the smallest fractions (<10 μm) quantitatively retain matrix-sited ³He_c when crushed under cold conditions (T ?25 °C), regardless of the duration and energy of crushing. These results invalidate the model previously proposed by (Yokochi R., Marty B., Pik R. and Burnard P. (2005) High ³He/⁴He ratios in peridotite xenoliths from SW Japan revisited: evidence for cosmogenic ³He released by vacuum crushing. Geochem. Geophys. Geosyst.6, doi:10.1029/2004GC000836) that involved spallation tracks and implied that the magnitude of loss was mainly controlled by the grain size. Moreover, new diffusion experiments were carried out to constrain the diffusivity of matrix-sited helium in crushed olivines. When used to model diffusive ³He_c loss as a function of grain size during crushing, these new data predict the observed release fairly well. Therefore, we conclude that temperature-enhanced volume diffusion is one of the main mechanisms controlling the release of ³He_c during crushing. For future applications, special attention should thus be paid to control the grain size, the crushing duration, and the temperature of the sample.     

Diffusion kinetics of proton-induced Ne, He, and He in quartz

A natural quartz sample free of mineral and fluid inclusions was irradiated with a 200 MeV proton beam to produce spallogenic ²¹Ne, ³He and ⁴He. Temperature-dependent diffusivities of these three nuclides were then determined simultaneously by high precision stepped-heating and noble gas mass spectrometry. The outward mobility of proton-induced nuclides reflects diffusion through the quartz lattice. In the studied range of 70 to 400°C the helium diffusion coefficients exceed those of neon by 5-7 orders of magnitude. The implied diffusion parameters E_a = 153.7 ± 1.5 (kJ/mol) and ln(D_o/a²) = 15.9 ± 0.3 (ln(s⁻¹)) and E_a = 84.5 ± 1.2 (kJ/mol) and ln(D_o/a²) = 11.1 ± 0.3 (ln(s⁻¹)) for proton-induced ²¹Ne and ³He, respectively, indicate that cosmogenic neon will be quantitatively retained in inclusion-free quartz at typical Earth surface temperatures whereas cosmogenic helium will not. However, the neon diffusion parameters also indicate that diffusive loss needs to be considered for small (<1 mm) quartz grains that have experienced elevated temperatures. Since natural quartz often contains fluid inclusions which may enhance noble gas retentivity, these parameters likely represent an end-member case of purely solid-state diffusion. The ∼70 kJ/mol higher activation energy for neon diffusion compared to helium diffusion likely represents an energy barrier related to its ∼13% greater diameter and provides a fundamental constraint with which to test theories of solid state diffusion. The diffusion parameters for proton-induced ⁴He are indistinguishable from those for ³He, providing no evidence for the commonly expected inverse square root of the mass diffusion relationship between isotopes. We also find preliminary indication that increased exposure to radiation may enhance neon and helium retentivity in quartz at low temperatures.