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.     

Experimental measurements of zircon/melt trace-element partition coefficients

Zircon was grown from trace-element doped hydrous peralkaline rhyolite melts with buffered oxygen fugacities in cold-seal experiments at 0.1 and 0.2 GPa and 800 °C and piston-cylinder experiments at 1.5 GPa and 900-1300 °C. Zircon and glass were present in all run products, and small monazite crystals were present in eight of the 12 experiments. Average diameters of zircon crystals ranged from 5 to 20 μm at 800 °C to 30-50 μm at 1300 °C. Zircon crystals have thin rims, and adjacent glass has a narrow (∼1 μm thick) compositional boundary layer. Concentrations obtained through in-situ analysis of cores of run product zircon crystals and melt pools were used to calculate trace-element partition coefficients D^zircon/melt for P, Sc, Ti, V, Y, La, Ce, Pr, Nd, Eu, Gd, Ho, Yb, Lu, Hf, Th, and U. In most cases Lu was the most (D 12-105) and La the least (0.06-0.95) compatible elements. D values from this study fall within the range of previously measured values for Rare Earth Elements (REE). However, D values measured experimentally show less fractionation than those recently measured using natural phenocryst/matrix pairs. For example, D_Lu/D_La measured experimentally in this study range between 27 and 206 compared to a value of 706,522 for a natural zircon/dacite pair [Sano, Y., Terada, K., and Fukuoka, T. 2002 High mass resolution ion microprobe analysis of rare earth elements in silicate glass, apatite and zircon: lack of matrix dependency. Chem. Geol.184, 217-230]. Although D values from this study show good agreement with the lattice strain model, D values from natural phenocryst/matrix pairs combined with measured zircon compositions better reproduce host-rock (magma) compositions of igneous rocks. They also yield more reasonable estimates of magma compositions when combined with compositions of ‘‘out-of-context” zircons. For example, compositions of the Hadean detrital zircons from Jack Hills, Australia yield LREE-enriched magmas when combined with D values from phenocryst/matrix pairs yields, but yield LREE-depleted magmas when experimentally determined D values are used. We infer that experimentally measured D^zircon/melt values represent disequilibrium partitioning resulting from rapid zircon growth during short laboratory timescales. Rapid growth causes development of observed diffusive boundary layers in the melt adjacent to zircon crystals. D values from phenocryst/matrix pairs are therefore recommended for petrogenetic modeling.     

Diffusion of helium in zircon and apatite

Diffusion of helium has been characterized in natural zircon and apatite. Polished slabs of zircon and apatite, oriented either normal or parallel to c were implanted with 100 keV ³He at a dose of 5 × 10^{15 3} He/cm². Diffusion experiments on implanted zircon and apatite were run in Pt capsules in 1-atm furnaces. ³He distributions following experiments were measured with Nuclear Reaction Analysis using the reaction ³He(d,p)⁴He. For diffusion in zircon we obtain the following Arrhenius relations:

Although activation energies for diffusion normal and parallel to c are comparable, there is marked diffusional anisotropy, with diffusion parallel to c nearly 2 orders of magnitude faster than transport normal to c. These diffusivities bracket the range of values determined for He diffusion in zircon in bulk-release experiments, although the role of anisotropy could not be directly evaluated in those measurements.In apatite, the following Arrhenius relation was obtained over the temperature range of 148–449 °C for diffusion normal to c:

In contrast to zircon, apatite shows little evidence of anisotropy. He diffusivities obtained in this study fall about an order of magnitude lower than diffusivities measured through bulk release of He through step-heating, and within an order of magnitude of determinations where ion implantation was used to introduce helium and He distributions measured with elastic recoil detection.Since the diffusion of He in zircon exhibits such pronounced anisotropy, helium diffusional loss and closure cannot be modeled with simple spherical geometries and the assumption of isotropic diffusion. A finite-element code (CYLMOD) has recently been created to simulate diffusion in cylindrical geometry with differing radial and axial diffusion coefficients. We present some applications of the code in evaluating helium lost from zircon grains as a function of grain size and length to diameter ratios, and consider the effects of “shape anisotropy”, where diffusion is isotropic (as in the case of apatite) but shapes of crystal grains or fragments may depart significantly from spherical geometry.     

A computer simulation study of the accommodation and diffusion of He in uranium- and plutonium-doped zircon (ZrSiO4)

We report the results of an atomistic computational study of He accommodation and diffusion in the Pu⁴⁺- and U⁴⁺-doped zircon (ZrSiO₄). The He-cation potentials derived for this work give results of comparable accuracy to DFT calculations. We have calculated the structural features of doped lattices as well as He solution energies in interstitial sites in the perfect and doped zircon and its diffusion in these lattices. The mode of He accommodation in the perfect zircon is influenced mainly by the topological features of the lattice, promoting site preference of He towards accommodation in the interstitial sites present in the middle of c cylinder channels, whereas the presence of Pu⁴⁺ and U⁴⁺ dopants in the zircon lattice significantly affects the energetics of He accommodation and diffusion in the lattice. Doping causes strong local structural distortions, extending to next nearest-neighbour atoms of the dopants to a radius of up to ∼4 Å, in agreement with experimental results. The presence of dopants in the vicinity of He enhances the solubility of He in the lattice compared to the perfect lattice. The mechanism of diffusion is also affected, where the dopants can create a He trap along the most energetically favourable pathway in the (0 0 1) direction, which may slow down the movement of He along the c direction. The dopants also lower the energy barriers by ∼50% in the octahedral sites.     

The influence of artificial radiation damage and thermal annealing on helium diffusion kinetics in apatite

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 (E_a) and the frequency factor (D_o/a²) of diffusion and yielded a higher He closure temperature (T_c) 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 E_a and ln(D_o/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 T_c was observed, with values becoming lower with increasing temperature and time. For example, reduction of T_c 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 T_c 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 E_a − ln(D_o/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.     

Kinetics of zircon dissolution and zirconium diffusion in granitic melts of variable water content

The experimental dissolution of zircon into a zircon-undersaturated felsic melt of variable water content at high pressure in the temperature range 1,020° to 1,500° C provides information related to 1) the solubility of zircon, 2) the diffusion kinetics of Zr in an obsidian melt, and 3) the rate of zircon dissolution. Zirconium concentration profiles observed by electron microprobe in the obsidian glass adjacent to a large, polished zircon face provide sufficient information to calculate model diffusion coefficients. Results of dissolution experiments conducted in the virtual absence of water (<0.2% H₂O) yield an activation energy (E) for Zr transport in a melt ofM=1.3 [whereM is the cation ratio (Na+K+2Ca)/(Al·Si)] of 97.7±2.8 kcal-mol^?1, and a frequency factor (D ₀) of 980 _?580 ^+1,390 cm²-sec^?1. Hydrothermal experiments provide an E=47.3±1.9 kcal-mol^?1 andD ₀=0.030 _?0.015 ^+0.030 cm²-sec^?1. Both of these results plot close to a previously defined diffusion compensation line for cations in obsidian. The diffusivity of Zr at 1,200° C increases by a factor of 100 over the first 2% of water introduced into the melt, but subsequently rises by only a factor of five to an apparent plateau value of ～2×10^?9 cm²-sec^?1 by ～6% total water content. The remarkable contrast between the wet and dry diffusivities, which limits the rate of zircon dissolution into granitic melt, indicates that a 50 μm diameter zircon crystal would dissolve in a 3 to 6% water-bearing melt at 750° C in about 100 years, but would require in excess of 200 Ma to dissolve in an equivalent dry system. From this calculation we conclude that zircon dissolution proceeds geologically instantaneously in an undersaturated, water-bearing granite. Estimates of zircon solubility in the obsidian melt in the temperature range of 1,020° C to 1,500° C confirm and extend an existing model of zircon solubility to these higher temperatures in hydrous melts. However, this model does not well describe zircon saturation behavior in systems with less than about 2% water.     

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.     

Si diffusion in zircon

Self-diffusion of Si under anhydrous conditions at 1 atm has been measured in natural zircon. The source of diffusant for experiments was a mixture of ZrO₂ and ³⁰Si-enriched SiO₂ in 1:1 molar proportions; experiments were run in crimped Pt capsules in 1-atm furnaces. ³⁰Si profiles were measured with both Rutherford backscattering spectrometry (RBS) and nuclear reaction analysis with the resonant nuclear reaction ³⁰Si(p,γ)³¹P. For Si diffusion normal to c over the temperature range 1,350–1,550°C, we obtain an Arrhenius relation D = 5.8 exp(−702 ± 54 kJ mol⁻¹/RT) m² s⁻¹ for the NRA measurements, which agrees within uncertainty with an Arrhenius relation determined from the RBS measurements [62 exp(−738 ± 61 kJ mol⁻¹/RT) m² s⁻¹]. Diffusion of Si parallel to c appears slightly faster, but agrees within experimental uncertainty at most temperatures with diffusivities for Si normal to c. Diffusion of Si in zircon is similar to that of Ti, but about an order of magnitude faster than diffusion of Hf and two orders of magnitude faster than diffusion of U and Th. Si diffusion is, however, many orders of magnitude slower than oxygen diffusion under both dry and hydrothermal conditions, with the difference increasing with decreasing temperature because of the larger activation energy for Si diffusion. If we consider Hf as a proxy for Zr, given its similar charge and size, we can rank the diffusivities of the major constituents in zircon as follows: D _Zr < D _Si << D _{O, dry} < D _{O, ‘wet’}.     

Geothermochronology based on noble gases: II. Stability of the (U-Th)/He isotope system in zircon

The kinetics of He migration from zircon of variable degree of metamictization was investigated. The migration parameters of He were experimentally determined, the influence of radiation damage and the degree of metamictization on the stability of the (U-Th)/He isotope system was evaluated, the mechanisms of noble gas escape from zircon were investigated, new data on the kinetics of He migration were obtained and compared with previous results for the kinetics of Xe migration from zircon of the same geologic objects. It was shown that He occurs in two energy positions in the zircon lattice: the main position (more than 80% He) with an activation energy of ∼39 kcal/mol and k ₀ = 10¹¹ yr⁻¹ and the second position with an activation energy for migration of 5–10 kcal/mol and k ₀ ∼ 10⁶ yr⁻¹. It was concluded that He migration from the main energy position is better described by a single-jump mechanism. The migration of He from the second energy position is consistent with the diffusion mechanism. It was shown that deviations from the linear dependence in the lnln(He₀/He_t)-1/T coordinates are probably related to the destruction of volume defects containing He atoms at high temperatures (more than 1000°C on the experimental time scale) resulting in a change from the single-jump to diffusion mechanism and the presence of atoms migrating via the diffusion mechanism. It was shown that the peak width in the spectrum of radiogenic He release and the appearance of a second peak also depend on the fraction of atoms migrating in accordance with the diffusion mechanism. It was found that the low activation energy for He release from the second energy position indicates the existence of continuous He loss from the zircon lattice.     

Quantitative characterization of plastic deformation of zircon and geological implications

The deformation-related microstructure of an Indian Ocean zircon hosted in a gabbro deformed at amphibolite grade has been quantified by electron backscatter diffraction. Orientation mapping reveals progressive variations in intragrain crystallographic orientations that accommodate 20° of misorientation in the zircon crystal. These variations are manifested by discrete low-angle (<4°) boundaries that separate domains recording no resolvable orientation variation. The progressive nature of orientation change is documented by crystallographic pole figures which show systematic small circle distributions, and disorientation axes associated with 0.5–4° disorientation angles, which lie parallel to rational low index crystallographic axes. In the most distorted part of the grain (area A), this is the [100] crystal direction. A quaternion analysis of orientation correlations confirms the [100] rotation axis inferred by stereographic inspection, and reveals subtle orientation variations related to the local boundary structure. Microstructural characteristics and orientation data are consistent with the low-angle boundaries having a tilt boundary geometry with dislocation line [100]. This tilt boundary is most likely to have formed by accumulation of edge dislocations associated with a 〈001〉{100} slip system. Analysis of the energy associated with these dislocations suggest they are energetically more favorable than TEM verified 〈010〉{100} slip. Analysis of minor boundaries in area A indicates deformation by either (001) edge, or [100](100) and [001](100) screw dislocations. In other parts of the grain, cross slip on (111), and (112) planes seems likely. These data provide the first detailed microstructural analysis of naturally deformed zircon and indicate ductile crystal-plastic deformation of zircon by the formation and migration of dislocations into low-angle boundaries. Minimum estimates of dislocation density in the low-angle boundaries are of the order of ∼3.10¹⁰ cm⁻². This value is sufficiently high to have a marked effect on the geochemical behavior of zircon, via enhanced bulk diffusion and increased dissolution rates. Therefore, crystal plasticity in zircon may have significant implications for the interpretation of radiometric ages, isotopic discordance and trace element mobility during high-grade metamorphism and melting of the crust.     

Assessment of the Re decay constant by cross calibration of Re-Os molybdenite and U-Pb zircon chronometers in magmatic ore systems

The past decade has seen renewed interest in ¹⁸⁷Re-¹⁸⁷Os geochronology using a variety of matrices including sulfide minerals, shales and meteorites. The most widely used value of the ¹⁸⁷Re decay constant (λ¹⁸⁷Re) is 1.666 ± 0.005 × 10⁻¹¹ a⁻¹ (±0.31%), which is based on cross calibration of Re-Os and Pb-Pb chronometers for certain meteorites [Smoliar M. I., Walker R. J., and Morgan J. W. (1996) Re-Os isotope constraints on the age of Group IIA, IIIA, IVA, and IVB iron meteorites. Science271, 1099-1102]. However, other recent studies have yielded alternate values of λ¹⁸⁷Re, based upon either direct counting experiments or analysis of meteorites. Here, we provide an independent assessment of λ¹⁸⁷Re, using methodology, sample materials, and preparation of Os standard solutions different from those of Smoliar et al. (1996). Combining Re-Os age data for molybdenite formed in magmatic ore deposits, with the U-Pb zircon age of the magmatic rocks, a refined λ¹⁸⁷Re value is determined by averaging 11 individual cross-calibration experiments spanning ca. 2700 Ma of Earth history. Using the U decay constants of Jaffey [Jaffey A. H., Flynn K. F., Glendenin L. E., Bentley W. C., and Essling A. M. (1971) Precision measurement of half-lives and specific activities of 235U and 238U. Phys. Rev.4, 1889-1906], a value for λ¹⁸⁷Re of 1.6668 ± 0.0034 × 10⁻¹¹ a⁻¹ is determined. Using the λ²³⁸U value of Jaffey et al. (1971) and λ²³⁵U value of Schoene [Schoene B., Crowley J. L., Condon D. J., Schmitz M. D., and Bowring S. A. (2006) Reassessing the uranium decay constants for geochronology using ID-TIMS U-Pb data. Geochim. Cosmochim. Acta70, 426-445], a value for λ¹⁸⁷Re of 1.6689 ± 0.0031 × 10⁻¹¹ a⁻¹ is determined. These values are nominally higher (ca. 0.1 and ca. 0.2%) than the value determined by Smoliar et al. [Smoliar M. I., Walker R. J., and Morgan J. W. (1996) Re-Os isotope constraints on the age of Group IIA, IIIA, IVA, and IVB iron meteorites. Science271, 1099-1102], but within calculated uncertainty. Further refinement of λ¹⁸⁷Re by cross calibrating the molybdenite and U-Pb zircon chronometers should be possible by utilizing high precision, single-grain, chemical abrasion zircon U-Pb analyses.     

Experimental constraints on the mobility of Rhenium in silicate liquids

The volatization of Rhenium (Re) from melts of natural basalt, dacite and a synthetic composition in the CaO-MgO-Al₂O₃-SiO₂ system has been investigated at 0.1 MPa and 1250-1350 °C over a range of fO₂ conditions from log fO₂ = −10 to −0.68. Experiments were conducted using open top Pt crucibles doped with Re and Yb. Analysis of quenched glasses by laser ablation-inductively coupled plasma mass spectrometry (LA-ICP-MS) normal to the melt/gas interface showed concentration profiles for Re, to which a semi-infinite one-dimensional diffusion model could be applied to extract diffusion coefficients (D). The results show Re diffusivity in basalt at 1300 °C in air is log D_Re = −7.2 ± 0.3 cm²/s and increases to log D_Re = −6.6 ± 0.3 cm²/s when trace amounts of Cl were added to the starting material. At fO₂ conditions below the nickel-nickel oxide (NNO) buffer Re diffusivity decreases to and to in dacitic melt. In the CMAS composition, . The diffusivity of Re is comparable to Ar and CO₂ in basalt at 500 MPa favoring its release as a volatile. Our results support the contention that subaerial degassing is the cause of lower Re concentrations in arc-type and ocean island basalts compared to mid-ocean ridge basalts.     

Kinetic isotopic fractionation during diffusion of ionic species in water

Experiments specifically designed to measure the ratio of the diffusivities of ions dissolved in water were used to determine . The measured ratio of the diffusion coefficients for Li and K in water (D_Li/D_K = 0.6) is in good agreement with published data, providing evidence that the experimental design being used resolves the relative mobility of ions with adequate precision to also be used for determining the fractionation of isotopes by diffusion in water. In the case of Li, we found measurable isotopic fractionation associated with the diffusion of dissolved LiCl (D_⁷Li/D_⁶Li=0.99772±0.00026). This difference in the diffusion coefficient of ⁷Li compared to ⁶Li is significantly less than that reported in an earlier study, a difference we attribute to the fact that in the earlier study Li diffused through a membrane separating the water reservoirs. Our experiments involving Mg diffusing in water found no measurable isotopic fractionation (D_²⁵Mg/D_²⁴Mg=1.00003±0.00006). Cl isotopes were fractionated during diffusion in water (D_³⁷Cl/D_³⁵Cl=0.99857±0.00080) whether or not the co-diffuser (Li or Mg) was isotopically fractionated. The isotopic fractionation associated with the diffusion of ions in water is much smaller than values we found previously for the isotopic fractionation of Li and Ca isotopes by diffusion in molten silicate liquids. A major distinction between water and silicate liquids is that water surrounds dissolved ions with hydration shells, which very likely play an important but still poorly understood role in limiting the isotopic fractionation associated with diffusion.     

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.     

Li diffusion in zircon

Diffusion of Li under anhydrous conditions at 1 atm and under fluid-present elevated pressure (1.0–1.2 GPa) conditions has been measured in natural zircon. The source of diffusant for 1-atm experiments was ground natural spodumene, which was sealed under vacuum in silica glass capsules with polished slabs of zircon. An experiment using a Dy-bearing source was also conducted to evaluate possible rate-limiting effects on Li diffusion of slow-diffusing REE⁺³ that might provide charge balance. Diffusion experiments performed in the presence of H₂O–CO₂ fluid were run in a piston–cylinder apparatus, using a source consisting of a powdered mixture of spodumene, quartz and zircon with oxalic acid added to produce H₂O–CO₂ fluid. Nuclear reaction analysis (NRA) with the resonant nuclear reaction ⁷Li(p,γ)⁸Be was used to measure diffusion profiles for the experiments. The following Arrhenius parameters were obtained for Li diffusion normal to the c-axis over the temperature range 703–1.151°C at 1 atm for experiments run with the spodumene source:

Dissolution kinetics as a function of the Gibbs free energy of reaction: An experimental study based on albite feldspar

Here we report on an experimental investigation of the relation between the dissolution rate of albite feldspar and the Gibbs free energy of reaction, ΔG_r. The experiments were carried out in a continuously stirred flow-through reactor at 150 °C and pH_(150 °C) 9.2. The dissolution rates R are based on steady-state Si and Al concentrations and sample mass loss. The overall relation between ΔG_r and R was determined over a free energy range of −150 < ΔG_r < −15.6 kJ mol⁻¹. The data define a continuous and highly non-linear, sigmoidal relation between R and ΔG_r that is characterized by three distinct free energy regions. The region furthest from equilibrium, delimited by −150 < ΔG_r < −70 kJ mol⁻¹, represents an extensive dissolution rate plateau with an average rate . In this free energy range the rates of dissolution are constant and independent of ΔG_r, as well as [Si] and [Al]. The free energy range delimited by −70 ? ΔG_r ? −25 kJ mol⁻¹, referred to as the ‘transition equilibrium’ region, is characterized by a sharp decrease in dissolution rates with increasing ΔG_r, indicating a very strong inverse dependence of the rates on free energy. Dissolution nearest equilibrium, defined by ΔG_r > −25 kJ mol⁻¹, represents the ‘near equilibrium’ region where the rates decrease as chemical equilibrium is approached, but with a much weaker dependence on ΔG_r. The lowest rate measured in this study, R = 6.2 × 10⁻¹¹ mol m⁻² s⁻¹ at ΔG_r = −16.3 kJ mol⁻¹, is more than two orders of magnitude slower than the plateau rate. The data have been fitted to a rate equation (adapted from Burch et al. [Burch, T. E., Nagy, K. L., Lasaga, A. C., 1993. Free energy dependence of albite dissolution kinetics at 80 °C and pH 8.8. Chem. Geol.105, 137-162]) that represents the sum of two parallel reactions

R=k₁[1-exp(-ng^m₁)]+k₂[1-exp(-g)]^m₂,     

Retention of biosignatures and mass-independent fractionations in pyrite: Self-diffusion of sulfur

Self-diffusion of sulfur in pyrite (FeS₂) was characterized over the temperature range ∼500-725 °C (∼1 bar pressure) by immersing natural specimens in a bath of molten elemental ³⁴S and characterizing the resulting diffusive-exchange profiles by Rutherford backscattering spectroscopy (RBS). The temperature dependence of the sulfur diffusivity (D_S) conforms to D_S = D_o exp(−E_a/RT), where the pre-exponential constant (D_o) and the activation energy (E_a) are constrained as follows:

     

Acoustic velocity measurements on Na2O-TiO2-SiO2 liquids: Evidence for a highly compressible TiO2 component related to five-coordinated Ti

Longitudinal acoustic velocities were measured at 1 bar in 10 Na₂O-TiO₂-SiO₂ (NTS) liquids for which previous density and thermal expansion data are reported in the literature. Data were collected with a frequency-sweep acoustic interferometer at centered frequencies of 4.5, 5, and 6 MHz between 1233 and 1896 K; in all cases, the sound speeds decrease with increasing temperature. Six of the liquids have a similar TiO₂ concentration (∼25 mol %), so that the effect of varying Na/Si ratio on the partial molar compressibility of the TiO₂ component can be evaluated. Theoretically based models for β_T and (∂V/∂P)_T as a function of composition and temperature are presented. As found previously for the partial molar volume of TiO₂ in sodium silicate melts, values of (13.7-18.8 × 10⁻²/GPa) vary systematically with the Na/Si and Na/(Si + Ti) ratio in the liquid. In contrast values of for the SiO₂ and Na₂O components (6.6 and 8.0 × 10⁻²/GPa, respectively, at 1573 K) are independent of composition. Na₂O is the only component that contributes to the temperature dependence of the compressibility of NTS liquids (1.13 ± 0.04 × 10⁻⁴/GPa K). The results further indicate that the TiO₂ component is twice as compressible as the Na₂O and SiO₂ components. The enhanced compressibility of TiO₂ appears to be related to the abundance of five-coordinated Ti (^[5]Ti) in these liquids, but not with a change in Ti coordination. Instead, it is proposed that the asymmetric geometry of ^[5]Ti in a square pyramidal site promotes different topological rearrangements in alkali titanosilicate liquids, which lead to the enhanced compressibility of TiO₂.     

Water diffusion in dacitic melt

H₂O diffusion in dacitic melt was investigated at 0.48-0.95 GPa and 786-893 K in a piston-cylinder apparatus. The diffusion couple design was used, in which a nominally dry dacitic glass makes one half and is juxtaposed with a hydrous dacitic glass containing up to ∼8 wt.% total water (H₂O_t). H₂O concentration profiles were measured on quenched glasses with infrared microspectroscopy. The H₂O diffusivity in dacite increases rapidly with water content under experimental conditions, similar to previous measurements at the same temperature but at pressure <0.15 GPa. However, compared with the low-pressure data, H₂O diffusion at high pressure is systematically slower. H₂O diffusion profiles in dacite can be modeled by assuming molecular H₂O (H₂O_m) is the diffusing species. Total H₂O diffusivity D_H2Ot within 786-1798 K, 0-1 GPa, and 0-8 wt.% H₂O_t can be expressed as: where D_H2Ot is in m²/s, T is temperature in K, P is pressure in GPa, K = exp(1.49 − 2634/T) is the equilibrium constant of speciation reaction (H₂O_m+O?2OH) in the melt, X = C/18.015/[C/18.015 + (100 − C)/33.82], C is wt.% of H₂O_t, and 18.015 and 33.82 g/mol correspond to the molar masses of H₂O and anhydrous dacite on a single oxygen basis. Compared to H₂O diffusion in rhyolite, diffusivity in dacite is lower at intermediate temperatures but higher at superliquidus temperatures. This general H₂O diffusivity expression can be applied to a broad range of geological conditions, including both magma chamber processes and volcanic eruption dynamics from conduit to the surface.     

Dislocation-assisted diffusion of oxygen in albite

Oxygen diffusion in albite has been determined by the integrating (bulk ¹⁸O) method between 750° and 450° C, for a P _H2O of 2 kb. The original material has a low dislocation density (<10⁶ cm^?2), and its lattice diffusion coefficient (D ₁), given below, agrees well with previous determinations. A sample was deformed at high temperature and pressure to produce a uniform dislocation density of 5 × 10⁹ cm^?2. The diffusion coefficient (D _a) for this deformed material, given below, is about 0.5 and 0.7 orders of magnitude larger than D ₁ at 700° and 450° C, respectively. This enhancement is believed due to faster diffusion along the cores of dislocations. Assuming a dislocation core radius of 4 Å, the calculated pipe diffusion coefficient (D _p), given below, is about 5 orders of magnitude larger than D ₁. These results suggest that volume diffusion at metamorphic conditions may be only slightly enhanced by the presence of dislocations. $$\begin{gathered} D_1 = 9.8 \pm 6.9 \times 10^{ - 6} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 33.4 \pm 0.6(kcal/mole)/RT] \hfill \\ \end{gathered} $$ $$\begin{gathered} D_a = 7.6 \pm 4.0 \times 10^{ - 6} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 30.9 \pm 1.1(kcal/mole)/RT] \hfill \\ \end{gathered} $$ $$\begin{gathered} D_p \approx 1.2 \times 10^{ - 1} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 29.8(kcal/mole)/RT]. \hfill \\ \end{gathered} $$