Potassium isotopic variability and implications for 40 K-based geochronology

40Ar/39Ar and K-Ar geochronology assume that 40K/K values are invariant among the sample of interest, the coirradiated neutron fluence monitor (“standard”), and the material used to measure decay constants. Until recently, this assumption was reasonable due to the small K isotope (41K, 40K, 39K) variability found in many terrestrial samples and the negligible effect of any variation relative to the precision of the determined age. The recent discovery of measurable d41K 10 variability in terrestrial samples now questions this assumption. Although d41K values for some neutron fluence monitors have now been reported, potassium isotopes are not routinely measured on samples dated by the 40Ar/39Ar method even though a wide range of silicate materials were found to vary by >2.5‰. Further, the 40K decay constants used in 40Ar/39Ar geochronology are based on activity counting of radioactive decay in K-rich salts. These salts have not been measured for d41K, yet evaporites have been shown to vary by >1‰ from the mean value of silicates. The potential effects of d41K variability on 40Ar/39Ar ages 15 are illustrated using the case of the ca. 28.2 Ma Fish Canyon sanidine (FCs) and the ca. 99 Ma Mt. Dromedary Biotite (GA1550). If the two standards have d41K values as measured and the material used to determine decay constants is appropriately represented by d41K of evaporites, the age of FCs is underestimated by ca. 7 ka (0.25‰). Although this is a small effect, such bias is becoming important as the analytical precision and accuracy of isotopic measurements and calculation of 40Ar/39Ar ages continue to improve. 20 1 40Ar/39Ar geochronology The 40Ar/39Ar system is a variant of K-Ar geochronology, where 40K decays to 40Ar with a half-life of ca. 1.25 Ga (Merrihue and Turner, 1966). When applying the K-Ar method, potassium and argon concentrations are typically measured on separate aliquots of sample. Values for the branched decay constant of 40K to 40Ar and 40Ca (e.g. Steiger and Jäger, 1977) are combined with the concentration measurements to calculate an age (Eq. (1)). 25 The 40Ar/39Ar geochronology method requires unknown samples to be co-irradiated alongside neutron fluence monitors (often called “mineral standards”) to convert some 39K to 39Ar (Dalrymple et al., 1981). By assuming a fixed 40K/39K value, the 39Ar measured by mass spectrometry can be used as a proxy for the parent isotope 40K. Age calculations using the 40Ar/39Ar method rely on the measured 40Ar/39Ar isotopic ratios in both sample and mineral standard, in addition to values for the total 40K decay 30 https://doi.org/10.5194/gchron-2020-18 Preprint. Discussion started: 19 June 2020 c © Author(s) 2020. CC BY 4.0 License.

variability in terrestrial samples now questions this assumption. Although d 41 K values for some neutron fluence monitors have now been reported, potassium isotopes are not routinely measured on samples dated by the 40 Ar/ 39 Ar method even though a wide range of silicate materials were found to vary by >2.5‰. Further, the 40 K decay constants used in 40 Ar/ 39 Ar geochronology are based on activity counting of radioactive decay in K-rich salts. These salts have not been measured for d 41 K, yet evaporites have been shown to vary by >1‰ from the mean value of silicates. The potential effects of d 41 K variability on 40 Ar/ 39 Ar ages 15 are illustrated using the case of the ca. 28.2 Ma Fish Canyon sanidine (FCs) and the ca. 99 Ma Mt. Dromedary Biotite (GA-1550). If the two standards have d 41 K values as measured and the material used to determine decay constants is appropriately represented by d 41 K of evaporites, the age of FCs is underestimated by ca. 7 ka (0.25‰). Although this is a small effect, such bias is becoming important as the analytical precision and accuracy of isotopic measurements and calculation of 40 Ar/ 39 Ar ages continue to improve. 20 1 40 Ar/ 39 Ar geochronology The 40 Ar/ 39 Ar system is a variant of K-Ar geochronology, where 40 K decays to 40 Ar with a half-life of ca. 1.25 Ga (Merrihue and Turner, 1966). When applying the K-Ar method, potassium and argon concentrations are typically measured on separate aliquots of sample. Values for the branched decay constant of 40 K to 40 Ar and 40 Ca (e.g. Steiger and Jäger, 1977) are combined with the concentration measurements to calculate an age (Eq. (1)). 25 The 40 Ar/ 39 Ar geochronology method requires unknown samples to be co-irradiated alongside neutron fluence monitors (often called "mineral standards") to convert some 39 K to 39 Ar (Dalrymple et al., 1981). By assuming a fixed 40 K/ 39 K value, the 39 Ar measured by mass spectrometry can be used as a proxy for the parent isotope 40 K. Age calculations using the 40 Ar/ 39 Ar method rely on the measured 40 Ar/ 39 Ar isotopic ratios in both sample and mineral standard, in addition to values for the total 40 K decay 30 constant and the known age of the mineral standard. Often unrecognized, but integral to both the 40 Ar/ 39 Ar and K-Ar geochronology methods, is the assumption that potassium isotopic ratios (often known as 40 K/K) are invariant between three materials: (1) samples, (2) mineral standards (including any primary standards that secondary standards are intercalibrated with), and (3) materials on which the decay constant was measured. While this assumption has previously been reasonably founded in the consistency of terrestrial stable K isotopic ratios (Humayun and Clayton, 1995), more recent work (e.g. Li et 35 al., 2016;Morgan et al., 2018;Ramos et al., 2018;Wang and Jacobsen, 2016) has identified terrestrial stable K isotopic variability and underscores the need to revisit the issue.
One small but important effect of these results is the need to revisit the atomic weight of K, which is determined by the International Union of Pure and Applied Chemistry. Morgan et al. (2018) suggested the need to update this value for bulk earth 55 from 39.0983 to 39.0982. This change will not appreciably affect most geochronology samples, but the ability to account for variable atomic weight is provided in the equations below.

Calculating the effects of potassium isotope variability
Determining the effects of potassium isotopic variability requires an understanding of the parameters involved in calculating an 40 Ar/ 39 Ar age. The method ultimately relies on the K-Ar age equation: 60 where tstd is the K-Ar age of a standard, l and le are the total and electron capture branches of the 40 K decay constant, 40 Ar * std is the abundance of radiogenic 40 Ar in the standard, and 40 Kstd is the abundance of 40 K in the standard. Values for calculating 40 Kstd can be substituted in Eq. (1): where atwtK = atomic weight of K, wK = weight fraction of K in the neutron fluence monitor, and f = 40 K/K (previously assumed to be constant, subscript 'G' indicates value from Garner et al. (1975)). 65 The The age of a sample can be calculated using the 40 Ar/ 39 Ar age equation, updated with new l, atwtK, and f values, including R = Fsample/Fstandard (Renne et al., 1998) where F = ( 40 Ar*/ 39 ArK). We also define r = fsample/fstandard to account for the difference 80 in f ( 40 K/K) between samples and neutron fluence monitors:

Effects of potassium isotope variability
Although f values have not been measured on materials used to determine decay constants (e.g. Beckinsale and Gale, 1969) and those for most samples are not commonly measured directly, we can use values for silicate materials (in some cases directly relevant to 40 Ar/ 39 Ar geochronology) and evaporite materials to estimate the likely effects of potassium isotope variability on 85 40 Ar/ 39 Ar ages. One method for calculating the 40 Ar/ 39 Ar age of Fish Canyon sanidine (FCs) is based on an intercalibration with primary neutron fluence monitor GA1550 (Renne et al., 1998) Based on the above assumptions, the most likely scenario is that the K-Ar age of GA1550 is older than previously believed by ca. 35 ka, and the 40 Ar/ 39 Ar age of FCs (based on the age of GA1550) is older than previously believed by ca. 7 ka. Although 95 these effects are small, they are within range of existing uncertainties in the 40 Ar/ 39 Ar system and should now be considered.
Uncertainties in d 41 K will ultimately require propagation into the 40 Ar/ 39 Ar age equation, as part of continuing work on refining the 40 K decay constant, as well as 40 Ar and 40 K abundances in neutron fluence monitors.
Of course, most unknown sample materials used for 40 Ar/ 39 Ar geochronology are not FCs and may have a range of potential 100 fsample values. Given the range of d 41 K values for silicates measured by Morgan et al. (2018), we can allow fsample to vary between values for d 41 K ranging from -1.5‰ to +1.5‰. Figure 2 shows the resulting 'sample' age for FCs over this range of d 41 Ksample values (left axis), the difference in sample age from the 'most likely scenario' described above (outside right axis), and the https://doi.org/10.5194/gchron-2020-18 Preprint. Discussion started: 19 June 2020 c Author(s) 2020. CC BY 4.0 License. relative effect on sample age (inside right axis). Variance over the range of most silicates, with d 41 K of -1 to 0‰, yields an effect on sample ages (for this example, sample of ca. 28 Ma) of ca. 0.5‰. 105 The potential for variability in the d 41 K value of the material on which decay constants are measured can also be considered. Figure 3 shows the effects of d 41 K variability in both the sample and the decay constant material. Sample variability is discussed above, but variability in d 41 K of decay constant materials is unknown for published measurements (e.g. Beckinsale and Gale, 1969;Kossert and Günther, 2004;Malonda and Carles, 2002;Steiger and Jäger, 1977). Because all these measurements have 110 been made on K-rich salts such as KCl and KNO3, assuming that d 41 K of evaporites can represent likely d 41 K values for these materials is reasonable. Measuring the 40 K decay constants explicitly includes d 41 K measurements of the relevant materials.

Conclusions
40 Ar/ 39 Ar geochronology currently assumes that 40 K/K values do not vary between samples, neutron fluence monitors, or evaporites on which activity counting was done. Recent high-precision K isotope work has shown this to be a false assumption 115 at the per-mil level. Quantifying the likely effects of potential 40 K/K variability yields a 'most likely' scenario where the age of GA1550 is found to be older by ca. 35 ka, and Fish Canyon sanidine is older by ca. 7 ka. Modeling of potential K isotope variability in samples, as well as standards and evaporites, yields a maximum age effect approaching 1.5‰ for extreme cases, but most silicates will be affected at sub-per-mil levels. Many remaining issues can be addressed by continuing work including K isotope measurements, activity counting, and first principles measurements of 40 K and 40 Ar in common neutron fluence 120 monitors.