The determined R values and calculated absolute ages of ACs, AM-1, and MDP-1 are concordant with literature values (table S2) and provide the proof of concept for dating samples using the HFNG. The larger age uncertainties of our one to four aliquots as compared with previous work from experiments with several dozen aliquots are a statistical effect and not representative of the ultimately higher precision and accuracy achievable with the HFNG. This ultimately higher accuracy of the HFNG is anticipated on the basis of avoiding or reducing the need for correction of interfering reactions, with the most significant being 42 Ca(n,nα) 36 Ar for high Ca/K samples ( 11 ).

The aliquots of the control fraction of sample MDP-1 in 10 holes display little spatial variation in F value ( 39 Ar K production rate) outside uncertainty with one exception ( Fig. 1 ). The F value of hole 17 exceeds the average by 25% and outside 2σ uncertainty. We can only speculate on the reasons: Most likely, a grain of the neighboring K-rich glass contaminated this sample unnoticed. Hole 17 aside, our experiment shows that the setup used with a multi-aperture extraction plate can create 39 Ar K production rates that vary in the single-digit percent range over >4 cm 2 . This is on the higher side of gradients commonly observed in fission reactors ( 21 ) but sufficient for high-precision 40 Ar/ 39 Ar geochronology.

Recoil

The potential effect of recoil on 40Ar/39Ar geochronology was first recognized by Turner and Cadogan (22). Subsequent studies contributed to the understanding and quantification of Ar recoil by either theoretical estimation or experimental studies of different grain sizes of one mineral separate or vacuum encapsulation of mineral grains. Onstott et al. (23) calculated a theoretical estimate of 39Ar recoil ranges by calculating 39Ar recoil energies based on a fission flux spectrum and a smoothed 39Ar(n,p)39Ar cross section function and by simulating the transport range of 39Ar ions with the resulting energies in silicate glass. A caveat of such a theoretical estimate of recoil energies is its limited transferability because the neutron flux spectrum is an important input to the calculation, but is specific to reactor and irradiation position, varies over time, and is not a smooth function, because cross section functions of moderating materials are not necessarily smooth [cf. Figure 1 of (21) for a simulated neutron spectrum for a 40Ar/39Ar irradiation position]. While neutron moderation will generally decrease recoil energies, it is difficult to accurately predict how the complex structure of the 39K(n,p)39Ar cross section function affects the resulting average recoil energies when it is convolved with a complex neutron energy spectrum. In any case, we estimate 39Ar recoil reduction with D-D neutrons by comparing ~2.7 MeV with the average neutron energy in fission reactors performing the 39K(n,p)39Ar reaction, which is the average of the convolution of the neutron energy flux spectrum and the 39K(n,p)39Ar cross section. This is relevant because the recoil of 39Ar depends primarily on the energy of the neutron and, only to a much lesser extent, on the emission of the proton (22). We convolved the smoothed Evaluated Nuclear Data File (ENDF) cross section (14) with a Watt thermal fission flux spectrum and derived an average neutron energy of 4.1 MeV performing 39K(n,p)39Ar. This suggests a reduction of average recoil energies by a factor of 0.65 when 2.7-MeV neutrons are used. The estimate of a reduction by a factor 0.3 by Renne et al. (11) was based on the erroneous assumption that calculations for a perfectly inelastic collision provide the maximum recoil energy. Our approach cannot capture the complexity in cross section structure and flux spectrum discussed above, nor can any approach until details of these features are resolved. Notably, average recoil energies are compared, which may oversimplify the complexity of loss and redistribution when recoil energies and, thus, recoil distances range over an order of magnitude (23). These caveats highlight the advantages of a quasi-monoenergetic neutron source that allows an accurate theoretical prediction of recoil energy and allows well-controlled experiments to test it.

The experimental approach to recoil quantification chosen in this study is to assess 40Ar*/39Ar K differences as a function of the grain SAV (7, 12). This approach is regarded to mostly capture 39Ar recoil loss through grain surfaces but may contain effects of loss from low-retentivity sites as a function of irradiation temperature or short circuit diffusion pathways that are grain size dependent (12). These processes are invoked by Jourdan et al. (12) to explain the difference between their sanidine data and the biotite data of Paine et al. (7) that indicate about a factor 5 more apparent recoil per SAV (Fig. 2). Another complicating factor is the reimplantation of recoiled 39Ar into neighboring grains that makes the experiments difficult to compare: The biotite grains of Paine et al. (7) were separated by millimeter-thick aluminum, while in our experiment and the experiment of Jourdan et al. (12), multiple sanidine grains were irradiated in contact.

A more direct experimental approach is the vacuum encapsulation of samples during irradiation, in which recoiled 39Ar is captured and can be analyzed separately. This method showed that clay minerals may lose ~30%; hornblende and biotite around 0.4%, but up to 1.2%; and sanidine 0.04 to 0.18% of the produced 39Ar (6, 24). Considering the grain geometries, these amounts exceed the expected recoil loss through surfaces and indicate mineral-dependent loss from nonretentive sites that, in many phases, exceeds loss from surface ejection (6, 24).

Our experiment indicates that fine multigrain separates down to <15 μm can be irradiated without currently resolvable apparent 39Ar recoil loss in the HFNG. It remains unclear how much reimplantation into neighboring grains contributes to this outcome. Our experiment, which was tailored around the current relatively low neutron flux capability of the HFNG, needs to be considered as a starting point for further investigation. Once the necessary neutron fluences can be achieved by the HFNG in acceptable irradiation time, experiments investigating Ar recoil from single encapsulated grains need to be carried out to quantify recoil loss through nonretentive sites and quantify possible reimplantation. These experiments can serve as a benchmark for simulation of recoil distances because the spectral character complicating the recoil energy calculation for fission spectrum neutrons becomes irrelevant.

Moreover, the HFNG’s anisotropic neutron flux—sourcing from a disc-shaped region next to the samples—can allow previously inconceivable experiments such as the semidirectional neutron irradiation of grains with planar inhomogeneities (e.g., exsolutions) or advancement of implantation experiments [e.g., (25)] to determine oriented recoil distances. These could, for example, quantify phase-dependent recoil distance, test the effect of 39Ar ion channeling, and improve our understanding of the degassing behavior of mixed phases.