A revised alpha-ejection correction calculation for (U–Th) ∕ He thermochronology dates of broken apatite crystals

<p>Accurate corrections for the effects of alpha ejection (the loss of daughter <span class="inline-formula">He</span> near grain or crystal surfaces due to long alpha stopping distances) are central to <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><mo>(</mo><mi mathvariant="normal">U</mi><mo>-</mo><mi mathvariant="normal">Th</mi><mo>)</mo><mo>/</mo><mi mathvariant="normal">He</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="58pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="26d53101b6c836ab0b6ef325d9bca65f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-4-629-2022-ie00003.svg" width="58pt" height="14pt" src="gchron-4-629-2022-ie00003.png"/></svg:svg></span></span> thermochronometry. In the case of apatite <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><mo>(</mo><mi mathvariant="normal">U</mi><mo>-</mo><mi mathvariant="normal">Th</mi><mo>)</mo><mo>/</mo><mi mathvariant="normal">He</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="58pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="c9cf0718e10396f6e2182a01dacbca3e"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gchron-4-629-2022-ie00004.svg" width="58pt" height="14pt" src="gchron-4-629-2022-ie00004.png"/></svg:svg></span></span> dating, alpha-ejection correction is complicated by the fact that crystals are often broken perpendicular to the <span class="inline-formula"><i>c</i></span> axis. In such cases, the correction should account for the fact that only some parts of the crystal are affected by alpha ejection. A common current practice to account for such broken crystals is to modify measured lengths of broken crystals missing one termination by a factor of 1.5, and those missing both terminations by a factor of 2. This alpha-ejection “correction correction” systematically overestimates the actual fraction of helium lost to alpha ejection, and thus overcorrects the measured date relative to that determined for an otherwise equivalent unbroken crystal. The ratio of the alpha-ejection-affected surface area to the volume of a fragmented crystal is equivalent to the surface-area-to-volume ratio of an unbroken crystal that is either twice as long (for fragments with one termination) or infinitely long (for fragments with no termination). We suggest that it is appropriate to revise the fragmentation correction to multiply the lengths of crystals missing one <span class="inline-formula"><i>c</i></span>-axis termination by 2, and those missing both <span class="inline-formula"><i>c</i></span>-axis terminations by some large number <span class="inline-formula">≳20</span>. We examine the effect of this revised correction and demonstrate the accuracy of the new method using synthetic datasets. Taking into account alpha ejection, the rounding of the <span class="inline-formula">He</span> concentration profile due to diffusive loss, and the accumulation of radiation damage over a range of thermal histories, we show that the revised fragmentation alpha-ejection correction proposed here accurately approximates the corrected date of an unbroken crystal (“true” date) to within <span class="inline-formula">&lt;0.7</span> % on average (<span class="inline-formula">±4.2</span> %, 1<span class="inline-formula"><i>σ</i></span>), whereas the former method overcorrects dates to be <span class="inline-formula">∼3</span> % older than the “true” date on average. For individual grains, the former method can result in dates that are older by a few percent in most cases, and by as much as 12 % for grains with aspect ratios of up to <span class="inline-formula">1:1</span>. The revised alpha-ejection correction proposed here is both more accurate and more precise than the previous correction, and does not introduce any significant systematic bias into the apparent dates from a sample.</p>