Recoil refinements: Implications for the ⁴⁰Ar/³⁹Ar dating technique

Integration of the neutron energy distribution for a water-moderated reactor with the most recent cross-section data yields mean recoil energies of 177 keV for ³⁹K (n, p) ³⁹Ar, 969 keV for ⁴⁰Ca (n, α) ³⁷Ar, and 140 eV for ³⁷Cl (n, γ) ³⁸Cl (β) ³⁸Ar. These estimates are insensitive to the anisotropy of reaction products. Utilizing Monte Carlo simulations of collision cascades, we calculate a mean recoil range of 1620 Å for ³⁹K (n, p) ³⁹Ar, 3780 Å for ⁴⁰Ca (n, α) ³⁷Ar, and 11 Å for ³⁷Cl (n, γ) ³⁸Cl (β) ³⁸Ar. Rutherford backscatter (RBS) measurements of argon implantation experiments into albite confirm the veracity of these estimates. Integration of the recoil range distributions yields a mean depletion depth in a semi-infinite medium of 820 Å for ³⁹Ar, 1950 Å for ³⁷Ar, and 6 Å for ³⁸Ar. The concentration gradients generated by recoil-redistribution between thin slabs were then incorporated into standard diffusion equations. If the exsolution lamellae are the effective diffusion dimension for argon, then the calculations indicate that the argon release rates and ⁴⁰Ar/³⁹Ar age spectrum derived from incremental heating of minerals exsolved at the micron to submicron scale are significantly affected by recoil-redistribution. The age spectra will be discordant even if the feldspar has not experienced a complex or slow cooling history. Incremental step apparent ages will increase with the fraction of ³⁹Ar released as the potassium poor lamellae degas. The age spectra will exhibit decreasing apparent ages with increasing fraction ³⁹Ar released as the potassium feldstar lamellae degas. The overall profile of the age spectrum will depend upon the composition of the feldspar and the size distribution of the lamellae, if the lamellae are the effective argon diffusion dimension. In principal, these calculations can be used to discriminate between different models for argon diffusion in minerals. Finally, the 11 Å mean recoil distance calculated for ³⁸Ar indicates that it is not a proxy for anion-sited excess argon. Instead, published correlations of ³⁸Ar with excess ⁴⁰Ar probably reflect the degassing of fine-grained, Cl-rich inclusions.