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\begin{document}

\title{Quantifying Uncertainty and Correcting for Systematic Error on
Alpha-Ejection and eU in Apatite (U-Th)/He Chronology Based on Realistic
Grain Sizes and Shapes}



\author[1]{Spencer Zeigler}%
\author[1]{JAMES METCALF}%
\author[1]{REBECCA FLOWERS}%
\author[1]{Jennifer Coulombe}%
\affil[1]{University of Colorado Boulder}%


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  \date{June 01, 2024}


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\begin{abstract}
Apatite (U-Th)/He (AHe) dating is a widely-applied thermochronological
technique used to decipher low-temperature thermal histories. Accurate
dates require that the results are corrected for \selectlanguage{greek}α-\selectlanguage{english}ejection because 4He
atoms travel \textasciitilde{}20 \selectlanguage{greek}µ\selectlanguage{english}m during \selectlanguage{greek}α-\selectlanguage{english}decay and a correction is
required to account for He lost by this effect. Effective uranium
concentrations (eU) are important for accurate AHe data interpretation
because radiation damage scales with eU, which affects He retentivity.
Both \selectlanguage{greek}α-\selectlanguage{english}ejection correction parameter (Ft) and eU are calculated on the
basis of crystal size and assuming an idealized morphology. However, the
uncertainty stemming from the calculations' assumptions depends on how
much the real crystal geometry deviates from that assumed, and this
uncertainty is typically not included in the propagated uncertainties on
AHe data. Our goal for this study was to develop a `rule of thumb' for
Ft and eU uncertainties associated with the full range of commonly
analyzed apatite geometries by comparing manually measured grain size
and actual grain size using nano-computed tomography (nano-CT). Apatite
geometry and roughness were characterized using a Grain Evaluation
Matrix (GEM). The geometry of each grain was described as: A
(prismatic/hexagonal), B (subprismatic), or C (rounded/ellipsoid).
Surface roughness was graded from `least' to `most' using values from 1
to 3. The GEM allows for a single parameter (eg. B2) to succinctly
classify a grain's morphology. High resolution nano-CT scans of
\textasciitilde{}260 grains representative of those usually analyzed for
AHe dates were completed and processed using Dragonfly and Blob3D.
Initial analysis shows that manual grain measurements systematically
overestimate the actual grain size, leading to overestimates in Ft and
eU values. One correction exists for A and B grains (hexagonal) and
another for C grains (ellipsoid). The correction is controlled primarily
by grain size and shape, while the uncertainty on the correction appears
to be controlled primarily by surface roughness. Together, this approach
provides a simple and practical tool for deriving more accurate Ft and
concentration values, and for incorporating this oft neglected geometric
uncertainty into AHe dates.%
\end{abstract}%



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