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SUPPLEMNTARY MATERIAL
A1. Neon Analysis
After extraction the evolved gases were exposed to a pair of SAES getters (one
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hot, the other cold). Neon was sorbed on charcoal at 32 K and He pumped away through
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a turbomolecular pump. Neon was liberated from the charcoal at 78 K, and analyzed on a
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GV-SFT mass spectrometer. The admitted gas was analyzed for 20Ne, 21Ne, and 22Ne
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using accelerating-voltage controlled peak-hopping at a fixed magnetic field, with all
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isotopes measured on a pulse-counting electron multiplier. The GV-SFT has sufficient
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mass resolution (~750) to pseudo-resolve 20Ne from 40Ar+2, eliminating the need for an
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isobar correction on this isotope. The SFT has a low and very stable CO2 background
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even without a cold trap, so the isobar on 22Ne is fairly small. However, to eliminate its
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effects altogether, for the 22Ne analysis (only) the electron accelerating voltage was
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lowered from a normal setting of 78V to 55V under computer control. The difference in
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electron impact ionization cross-sections for the two mass 22 species is such that the CO2
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isobar is almost completely removed. For all analyses (standards, samples, hot blanks)
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corrections have been made for line blanks; this step ensures removal of any residual
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isobars, both from the vacuum line and resident in the mass spectrometer.
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A2. Fitting the domain size distribution
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For simplicity’s sake we assume a small number of discrete-sized domains, rather
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than a specific type of distribution (e.g., normal or log normal). While either might fit the
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data the former type of distribution is far easier to introduce into a forward model to
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compute expected ages in each domain on arbitrary time-temperature paths. The
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objective is thus to find a (preferably small) number of domains of a given dimension and
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volume fraction that make up the sample. There are several inter-related quantities that
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we could use as the fitting target for this exercise: the Arrhenius array, the individual
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fractional yields for each step, the cumulative yields, or the ln(r/ro) plot. Ultimately we
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found that equally weighting the fractional yield and the cumulative yield converged
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rapidly on a high quality fit to all of these quantities.
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In an MDD model with N discrete domain sizes, the total diffusant yield in step j
is:
𝑁
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𝐹𝑇𝑗 = ∑ 𝑣𝑖 𝐹𝑖𝑗
𝑖=1
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Where vi is the volume faction of domain i and Fij is the yield from domain i in step j.
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The individual Fij values can be forward modeled from the standard release equations
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(Fechtig and Kalbitzer, 1966) assuming:
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𝐷
𝐷𝑜
−𝐸𝑎
2 =
2 exp( 𝑅𝑇 )
𝑎𝑖
𝑎𝑖
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Where ai is the radius of domain i, Ea is the activation energy (e.g., established from the
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measured Arrhenius plot), R is the gas constant, T the Kelvin temperature of the step, and
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Do the diffusivity at infinite temperature. Because we have no way to independently
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establish a, we never separate the convolved quantity D/a2. Thus we simply assume an
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arbitrary value of Do, constant for all domains.
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Using these equations we then simulate the step heat that produced the diffusion data in
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Table S1. Ln(r/ro) is computed from a reference line that essentially goes through the
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first data points on the Arrhenius plot and with activation energy Ea. Note that the exact
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position of this line is irrelevant; different values simply shift the ln(r/ro) plot vertically.
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For an MDD model with N domains there are 2N-1 free parameters (volume fraction and
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size of each domain less the constraint that all volume be accounted for). We used the
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Excel solver function to identify the parameter set that minimizes the mismatch between
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modeled and observed yield data. By trial and error we established that about 7 domains
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are required to match the observations; addition of more domains does not substantially
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improve the misfit at least for this sample. While this is a large number of free
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parameters, our goal is to match the data as well as possible, rather than to describe it in
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the most parsimonious way.
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A3. Assessing cooling paths using HeFTy
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We used HeFTy (Ketcham, 2005) to compute bulk ages and age spectra on arbitrary
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time-temperature paths for comparison with the equivalent measurements. We ran HeFTy
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in the “inversion” mode to compute (and record) results for a large number of randomly
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selected time-temperature paths and for each of the domains associated with each aliquot.
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We used the mean activation energy (157 kj/mol) and assumed it remains constant
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through time (i.e., we assume the absence of radiation damage effects). Because HeFTy
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does not have the capability to reconstruct the aggregate sample by adding the individual
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domains together, we exported the data to a file for further processing.
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To compare the HeFTy output with the measured results, we first computed the bulk age t
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tT for each time-temperature path from the ages of each domain, ti:
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𝑁
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𝑡𝑇 = ∑ 𝑣𝑖 𝑡𝑖
𝑖=1
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Computing the bulk age spectrum is more involved because we must simulate the
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diffusive loss of each domain (smaller domains degas before larger domains) and then
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add them together with their appropriate weighting. The HeFTy model age spectrum for
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each domain size consist of pairs of Fcum and age values, with Fcum incremented by 1%
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between steps. Each of these Fcum values can be mapped to a specific release coordinate
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(Watson et al., 2010); in an isothermal experiment the release coordinate is just Dt/a2
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where t is cumulative time. By normalizing to ai2, we can compute the relative degassing
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time t associated with each of these release fractions in an isothermal experiment. Small
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domains reach high release fractions at short times, while large domains reach
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comparably large release fractions only after longer times. Thus we have a schedule from
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which we can compute when each domain contributes its helium to the aggregate
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synthetic step heat. In practice we make a table of the release times and associated ages
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for each step of all N domains. We then sort this table by increasing release time. A
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model age spectrum for the aggregate is then produced by summing up the volume
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weighted incremental release values for 3He, and the volume weighted average step ages,
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for a series of sequential steps in the table (see Figure A2). We found that adding 15
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sequential entries together produced an adequate resolution (for 7 domains with 100
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model steps each, adding them together in groups of 15 creates 700/15= 46 steps in the
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model age spectrum).
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Figure Captions
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Figure A1. SEM images of Redwall hematite. Note the abundant open pores (black
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regions) and the individual crystallites within and projecting into the pores. EBSD
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revealed only hematite in the regions shown.
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Figure A2. 3He diffusion Arrhenius plots for aliquots A,B, C, and CuOx.
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Figure A3. Construction of the multidomain “sample” from the model age spectra for
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each individual domain. Computed for the reference path and for the domain spectrum
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model of aliquot A.
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