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.     

Oxygen isotopic fractionation during inorganic calcite precipitation ― Effects of temperature, precipitation rate and pH

Stable oxygen isotopic fractionation during inorganic calcite precipitation was experimentally studied by spontaneous precipitation at various pH (8.3 < pH < 10.5), precipitation rates (1.8 < log R < 4.4 μmol m^− 2 h^− 1) and temperatures (5, 25, and 40 °C) using the CO₂ diffusion technique.The results show that the apparent stable oxygen isotopic fractionation factor between calcite and water (α_{calcite–water}) is affected by temperature, the pH of the solution, and the precipitation rate of calcite. Isotopic equilibrium is not maintained during spontaneous precipitation from the solution. Under isotopic non-equilibrium conditions, at a constant temperature and precipitation rate, apparent 1000lnα_{calcite–water} decreases with increasing pH of the solution. If the temperature and pH are held constant, apparent 1000lnα_{calcite–water} values decrease with elevated precipitation rates of calcite. At pH = 8.3, oxygen isotopic fractionation between inorganically precipitated calcite and water as a function of the precipitation rate (R) can be described by the expressions

at 5, 25, and 40 °C, respectively.The impact of precipitation rate on 1000lnα_{calcite–water} value in our experiments clearly indicates a kinetic effect on oxygen isotopic fractionation during calcite precipitation from aqueous solution, even if calcite precipitated slowly from aqueous solution at the given temperature range. Our results support Coplen's work [Coplen T. B. (2007) Calibration of the calcite–water oxygen isotope geothermometer at Devils Hole, Nevada, a natural laboratory. Geochim. Cosmochim. Acta 71, 3948–3957], which indicates that the equilibrium oxygen isotopic fractionation factor might be greater than the commonly accepted value.     

Solubility and dissolution rate of silica in acid fluoride solutions

We performed 57 batch reactor experiments in acidic fluoride solutions to measure the dissolution rate of quartz. These rate data along with rate data from published studies were fit using multiple linear regression to produce the following non-unique rate law for quartz

where 10^−5.13 < a_HF < 10^1.60, −0.28 < pH < 7.18, and 298 < T < 373 K. Similarly, 97 amorphous silica dissolution rate data from published studies were fit by multiple linear regression to produce the following non-unique rate law for amorphous silica

where 10^−2.37 < a_HF < 10^1.61, −0.32 < pH < 4.76 and 296 < T < 343 K. Regression of the rates versus other combinations of solution species, e.g.  + H⁺, F⁻ + H⁺, HF + , HF + F⁻, or  + F⁻, produced equally good fits. Any of these rate laws can be interpreted to mean that the rate-determining step for silica dissolution in fluoride solutions involves a coordinated attack of a Lewis acid, on the bridging O atom and a Lewis base on the Si atom. This allows a redistribution of electrons from the Si–O bond to form a O–H group and a Si–FH group.     

Pb and rare earth element diffusion in xenotime

Diffusion of Pb and the rare earth elements Sm, Dy and Yb have been characterized in synthetic xenotime under dry conditions. The synthetic xenotime was grown via a Na₂CO₃–MoO₃ flux method. The sources of diffusant for the rare earth diffusion experiments were REE phosphate powders, with experiments run using sources containing a single REE. For Pb, the source consisted a mixture of YPO₄ and PbTiO₃. Experiments were performed by placing source and xenotime in Pt capsules, and annealing capsules in 1 atm furnaces for times ranging from 30 min to several weeks, at temperatures from 1000 to 1500 °C. The REE and Pb distributions in the xenotime were profiled by Rutherford Backscattering Spectrometry (RBS).The following Arrhenius relations are obtained for diffusion in xenotime, normal to (101):

Diffusivities among the REE do not differ greatly in xenotime over the investigated temperature range, in contrast to findings for the REE in zircon [Cherniak, D.J., Hanchar, J.M., Watson, E.B., 1997. Rare earth diffusion in zircon. Chem. Geol. 134, 289–301.], where the LREE diffuse more slowly, and with higher activation energies for diffusion, than the heavier rare earths. In zircon, these differences among diffusion of the rare earths are attributed to the relatively large size of the REE with respect to Zr, for which they likely substitute in the zircon lattice. With the systematic increase in ionic radius from the heavy to lighter REE, this size mismatch becomes more pronounced and diffusivities of the LREE are as consequence slower. Although xenotime is isostructural with zircon, the REE are more closely matched in size to Y, so in xenotime this effect appears much smaller and the REE diffuse at similar rates. In addition, the process of diffusion in xenotime likely involves simple REE^+ 3 → Y^+ 3 exchange, without charge compensation as needed for REE^+ 3 → Zr^+ 4 exchange in zircon. This latter factor may also contribute to the large activation energies for diffusion of the REE in zircon (i.e., 691–841 kJ mol^− 1, [Cherniak, D.J., Hanchar, J.M., Watson, E.B., 1997. Rare earth diffusion in zircon. Chem. Geol. 134, 289–301.]), in comparison with those for xenotime.For Pb, the following Arrhenius relation is obtained (also normal to (101)):

These measurements suggest that Pb diffusion in xenotime is quite slow, even slower than Pb diffusion in monazite and zircon, and considerably slower than diffusion of the REE in xenotime. Xenotime may therefore be even more retentive of Pb isotope signatures than either monazite or zircon in cases where Pb isotopes are altered solely by volume diffusion. However, because the activation energy for Pb diffusion in xenotime is lower than those for monazite and zircon, Pb diffusion may be somewhat faster at many temperatures of geologic interest in xenotime than in monazite or zircon.     

Magnesite growth rates as a function of temperature and saturation state

Magnesite growth rates and step velocities have been measured systematically as a function of temperature from 80 to 105 °C and saturation state in 0.1 M NaCl solutions using hydrothermal atomic force microscopy (HAFM). The observations indicate that at these conditions magnesite precipitation is dominated by the coupling of step generation via spiral growth at screw dislocations and step advancement away from these dislocations. As these two processes occur in series the slowest of these dominates precipitation rates. At 100 °C magnesite growth rates (r) determined by HAFM are consistent with

r=k(Ω-1)²,

where k is a constant equal to 6.5 × 10⁻¹⁶ mol/cm²/s and Ω is the saturation index with respect to magnesite. This equation is consistent with spiral growth step generation controlling magnesite precipitation rates. Corresponding magnesite precipitation rates measured using mixed-flow reactors are shown to be consistent with both the rates measured by HAFM and the spiral growth theory, confirming the rate limiting mechanism. Step advancement, however, is observed to slow far faster than step generation with decreasing temperature; the activation energy for step advancement is 159 kJ/mol whereas step generation rates have an estimated activation energy of 60 kJ/mol. As such, it seems likely that at ambient temperatures magnesite growth is limited by very slow step advancement rates.     

Calibration of sclerosponge oxygen isotope records to temperature using high-resolution δO data

A revised calibration is presented relating the oxygen isotope composition of the aragonite-secreting sclerosponge Ceratoporella nicholsoni, oxygen isotope composition of seawater, and ambient water temperature. This new relationship has been obtained using high-resolution δ¹⁸O data measured in sclerosponges from the Bahamas and Jamaica compared to ambient temperature measurements and δ¹⁸O values of seawater from the two locations, both measured and published. New data improve an existing calibration which was determined using measurements of salinity rather than directly measured δ¹⁸O values of the seawater and was composed of measurements from different species of sclerosponge and other aragonite-secreting organisms. The updated calibration (n = 12, r² = 0.95) is:

T(°C)=16.1(±3.1)-[6.5(±1.1)](δ_arag-δ_sw),

where T is temperature in degrees Celsius, δ_arag is the δ¹⁸O value of aragonite normalized to VPDB, and δ_sw is the δ¹⁸O value of water normalized to VSMOW. This calibration improves accuracy and precision of Caribbean sclerosponges for reconstructions of temperature as well as δ¹⁸O values of seawater.     

Calcite dissolution kinetics in saline waters

The effect of ionic strength (I), pCO₂, and temperature on the dissolution rate of calcite was investigated in magnesium-free, phosphate-free, low calcium (m_Ca2+ ≈ 0.01 m) simple KCl and NaCl solutions over the undersaturation range of 0.4 ≤ Ω_calcite ≤ 0.8. First-order kinetics were found sufficient to describe the rate data where the rate constant (k) is dependent on the solution composition. Rates decreased with increasing I and were faster in KCl than NaCl solutions at the same I indicating that Na⁺ interacts more strongly with the calcite surface than K⁺ or that water is less available in NaCl solutions. Rates increased with increasing pCO₂ and temperature, and their influences diminished at high I. Arrhenius plots yielded a relatively high activation energy (E_a ≈ 20 ± 2 kJ mol^− 1) which indicated that dissolution was dominated by surface-controlled processes. The multiple regression model (MR) of Gledhill and Morse (2006a) was found to adequately describe the results at high I in NaCl solutions, but caution must be used when extrapolating to low I or pCO₂ values. These results are consistent with the hypothesis that the mole fraction of “free” solvent (X_{“free”H2O}) plays a significant role in the dissolution kinetics of calcite with a minimum value of  45–55% required for dissolution to proceed in undersaturated solutions at 25–55 °C and pCO₂ = 0.1–1 atm. This hypothesis has been incorporated into a modified version of the MR model of Gledhill and Morse (2006a) where X_{“free”H2O} has replaced I and the Ca²⁺ and Mg²⁺ terms have been dropped:

     

Earthquake recurrence on the Calaveras fault east of San Jose, California

Occurrence of small (3 M_L < 4) earthquakes on two 10-km segments of the Calaveras fault between Calaveras and Anderson reservoirs follows a simple linear pattern of elastic strain accumulation and release. The centers of these independent patches of earthquake activity are 20 km apart. Each region is characterized by a constant rate of seismic slip as computed from earthquake magnitudes, and is assumed to be an isolated locked patch on a creeping fault surface. By calculating seismic slip rates and the amount of seismic slip since the time of the last significant (M 3) earthquake, it is possible to estimate the most likely date of the next (M - 3) event on each patch. The larger the last significant event, the longer the time until the next one. The recurrence time also appears to be increased according to the moment of smaller (2 < M_L < 3) events in the interim. The anticipated times of future larger events on each patch, on the basis of preliminary location data through May 1977 and estimates of interim activity, are tabulated below with standard errors. The occurrence time for the southern zone is based on eight recurrent events since 1969, the northern zone on only three. The 95% confidence limits can be estimated as twice the standard error of the projected least-squares line. Events of M 3 should not occur in the specified zones at times outside these limits. The central region between the two zones was the locus of two events (M = 3.6, 3.3) on July 3, 1977. These events occurred prior to a window based on the three point, post-1969 slip-time line for the central region.

H2O diffusion models in rhyolitic melt with new high pressure data

Water diffusion in silicate melts is important for understanding bubble growth in magma, magma degassing and eruption dynamics of volcanos. Previous studies have made significant progress on water diffusion in silicate melts, especially rhyolitic melt. However, the pressure dependence of H₂O diffusion is not constrained satisfactorily. We investigated H₂O diffusion in rhyolitic melt at 0.95–1.9 GPa and 407–1629 °C, and 0.2–5.2 wt.% total water (H₂O_t) content with the diffusion-couple method in a piston-cylinder apparatus. Compared to previous data at 0.1–500 MPa, H₂O diffusivity is smaller at higher pressures, indicating a negative pressure effect. This pressure effect is more pronounced at low temperatures. Assuming H₂O diffusion in rhyolitic melt is controlled by the mobility of molecular H₂O (H₂O_m), the diffusivity of H₂O_m (D_H2Om) at H₂O_t ≤ 7.7 wt.%, 403–1629 °C, and ≤ 1.9 GPa is given by

D_H2Om=D₀exp(aX),

Experimental calibration of oxygen isotope fractionation between quartz and zircon

We report the results of an experimental calibration of oxygen isotope fractionation between quartz and zircon. Data were collected from 700 to 1000 °C, 10–20 kbar, and in some experiments the oxygen fugacity was buffered at the fayalite–magnetite–quartz equilibrium. Oxygen isotope fractionation shows no clear dependence on oxygen fugacity or pressure. Unexpectedly, some high-temperature data (900–1000 °C) show evidence for disequilibrium oxygen isotope partitioning. This is based in part on ion microprobe data from these samples that indicate some high-temperature quartz grains may be isotopically zoned. Excluding data that probably represent non-equilibrium conditions, our preferred calibration for oxygen isotope fractionation between quartz and zircon can be described by:

This relationship can be used to calculate fractionation factors between zircon and other minerals. In addition, results have been used to calculate WR/melt–zircon fractionations during magma differentiation. Modeling demonstrates that silicic magmas show relatively small changes in δ¹⁸O values during differentiation, though late-stage mafic residuals capable of zircon saturation contain elevated δ¹⁸O values. However, residuals also have larger predicted melt–zircon fractionations meaning zircons will not record enriched δ¹⁸O values generally attributed to a granitic protolith. These results agree with data from natural samples if the zircon fractionation factor presented here or from natural studies is applied.