Fig 1.
Principle behind diffusion chronometry.
We use a 1D model to calculate the time since the inception of a given compositional contact in a crystal. We assume an initially infinitely sharp “step function” boundary (indicated as “Initial condition” in the diagram), which becomes progressively less sharp with time (shown as a series of curves). This problem has a well-known solution, with the resulting damped curve being described by a complementary error function (erfc) as shown in the figure. We use a least-squares procedure to find the best-fit erfc function, from which we can extract the value of (); using experimentally determined values of the diffusion coefficient D, we can then calculate the residence time of a given contact and the growth time for the crystal region rimward from the contact. We can also measure the growth distance from our images, from which we calculate average crystal rim growth rates.
Fig 2.
Correlation between CL intensity and Ti concentration in quartz.
Central grayscale image is a detailed cathodoluminescence (CL) image of the rim region of a quartz crystal (fall unit F8 of the Bishop Tuff, following nomenclature of [2]), including the boundary between the bright-CL rim and the duller-CL interior. Color inset is a Ti map obtained using the x-ray microprobe at insertion device beamline of GeoSoilEnviroCARS (Advanced Photon Source, Argonne National Laboratory); color scale corresponds to Ti concentration, as indicated on the top bar. The correlation between CL and Ti concentration is apparent, with largely homogeneous Ti concentrations in the rim and in the interior of the crystal, and a very sharp transition between the two. The bottom diagram shows a quantitative profile across the same boundary in a slightly different position, as indicated in the CL image. The transition between bright-CL, high-Ti rim and interior takes place within one step in the profile, which corresponds to 2 μm; this shows that the diffusional length scale of interest is on the order of 1 μm or less. We obtain a maximum growth time for this contact of 13 years (fitted complementary error function shown in black), which places an upper bound on the growth time for these rims.
Fig 3.
Effect of incident electron beam energy on excitation volume within a quartz crystal.
Results shown are derived from Monte Simulations performed using the software MC X-Ray Lite (version 1.4.6.0, http://montecarlomodeling.mcgill.ca/software/mcxray/mcxray.html), assuming a quartz crystal with density of 2.65 g/cm3; calculations for 1000 electrons are shown as the depth-integrated paths on the plane perpendicular to incidence of the electron beam. Scale is the same for the three images shown. Horizontal bars are for reference; they show the approximate size of the beam at each energy. Notice the very strong effect of beam energy on the diameter of the excited volume, which translates into a strong dependency of maximum possible cathodoluminescence (CL) image resolution with beam energy.
Fig 4.
Comparison of CL images and derived intensity profiles using incident electron beam energies of 15 kV (left panels) and 5 kV (right panels).
(A, C, E, G) Data obtained using 15 kV electron beam. (B, D, F, H) Data obtained using 5 kV electron beam. (A-B) Low-resolution images showing a whole quartz crystal with a distinct bright-CL rim. (C-D) High-resolution images (195 nm per pixel) of the contact between bright rim and duller interior (location within the crystal shown in A-B as white rectangle). (E-H) CL intensity profiles extracted from high-resolution images (locations shown), with best fit error functions displayed as gray curves; the length scale of diffusional relaxation (L) extracted from the fitted curves (assuming an initial step function) are indicated, as well as the derived growth times assuming a temperature of 750°C (following [10]). Estimated errors are less than a factor of 2 (see [28] for details), which, despite relatively large, do not affect any of the interpretations or conclusions. (E-F) Calculations showing profiles resulting in minimum growth times (out of 11 parallel profiles) in each case. (G-H) Calculations showing profiles consisting of median values (out of the same 11 parallel profiles) at each position in each case. Crystal is from fall unit F8 (following the nomenclature of [2]), sample F8-15.
Fig 5.
Timescales of rim crystallization for the Bishop Tuff, CA.
Top panel shows histogram of calculated times. Bottom panel shows cumulative distributions. Notice that bin sizes are on a logarithmic scale on both plots. Crystals from samples F8-15 (fall unit F8), Ib-A1 (flow unit Ig1Eb), and AB-6202 (flow unit Ig2NW) were imaged at 5 kV (red and orange colors), while those from F7-12 and F7-14 (both from fall unit F7) were imaged at 15 kV (blue colors); see text for details. Distribution has a mode at times of 10−2 years (~3 days), and more than 50% of the calculated times are less than 0.1 years (~1 month), particularly so for the crystals imaged at 5 kV.
Fig 6.
Crystal rim growth rates for the Bishop Tuff, CA.
Top panel shows histogram of calculated growth rates. Bottom panel shows cumulative distributions. Notice that bin sizes are on a logarithmic scale on both plots. Distribution has a mode at growth rates of 10−9 m/s (~90 μm/day), and more than 50% of the calculated growth rates are faster than 10−10 m/s (~9 μm/day).
Fig 7.
Summary of estimates of the duration of crystallization for the Bishop Tuff.
Zircon crystallization times are typically on the order of tens of thousands of years. Quartz interiors reveal crystallization timescales on the order of centuries to a few millennia. Quartz and orthopyroxene (Opx) rims have been previously inferred to have crystallized on decadal to centennial timescales. We show in this study that quartz rims mostly crystallized within a year of eruption, with most growth taking place in the days to weeks prior to eruption. Much of the discrepancy between the timescales results from different minerals, or different zones within the same mineral, recording different processes. Zircon records the evolution of the entire magmatic system, including long stages characterized by high crystal contents; quartz interiors and much of zircon crystallized within centuries to millennia of eruption, revealing the lifespan of crystal-poor, eruptible magma bodies; quartz rims reveal the onset of eruptive decompression. SIMS: secondary ionization mass spectrometry; TIMS: thermal ionization mass spectrometry.