Joint determination of 40K decay constants and 40Ar∗/40K for the Fish Canyon sanidine standard, and improved accuracy for 40Ar/39Ar geochronology
Introduction
The 40Ar/39Ar dating method is one of the most important means of measuring geologic time over most of Earth’s history. In addition to its wide age range of applicability and the existence of internal reliability criteria, this technique is of great importance because it is capable of exemplary precision, better than 0.1%1 of the age in many cases, which is attainable by only the U/Pb method among widely used geochronometers. The 40Ar/39Ar method is especially important in the Cenozoic Era (the past 66 million years), and most currently used Cenozoic time scales (e.g., Cande and Kent, 1995, Aguilar et al., 1996, Gradstein et al., 2004) are calibrated almost exclusively by this method whereas U–Pb data are favored in the pre-Mesozoic. 40Ar/39Ar dating has been employed over the widest temporal range of any dating method, having illuminated important questions in geology, cosmology, archeology, and paleontology through the age of emplacement (i.e., volcanic) or cooling (i.e., plutonic and metamorphic) of rocks.
40Ar/39Ar dating is based on the 40K–40Ar method, which requires knowledge of the decay constants both for the 40K → 40Ar electron capture decay (λε) and the 40K → 40Ca β− decay (λβ). A β+ decay mode was inferred by Beckinsale and Gale (1969) to account for 0.001% of 40K activity, and has subsequently been ignored by other workers – this decay mode has never been detected to our knowledge. The 40Ar/39Ar method requires, in addition, the use of natural standards with either accurately-known 40Ar/40K ratios or independent knowledge of the age. The 40K decay constants in widespread use since 1977 (Steiger and Jäger, 1977) are derived from a compilation of 40K activity data (Beckinsale and Gale, 1969) combined with a revised value for the isotopic abundance of 40K (Garner et al., 1975). Following the suggestion of Steiger and Jäger (1977) the IUGS Subcommission on Geochronology adopted a value for λtot (= λε + λβ) of 5.543 × 10−10 a−1 with a branching ratio of 0.1171 for λε/λβt, but did not consider the uncertainties in these values. Despite its excellent potential age resolution the 40Ar/39Ar method as calibrated by these constants is limited in accuracy to no better than 2% arising mainly from the propagation of systematic errors in the 40K decay constants and the 40K–40Ar data for standards (Min et al., 2000).
Efforts to improve the accuracy of 40Ar/39Ar dating have focused on refining the ages of standards such as the widely used Fish Canyon sanidine (FCs), whose age has been addressed by the following approaches individually or in combination: (i) intercalibration with “first principles” standards (for which K–Ar data were available, e.g., Hurford and Hammerschmidt, 1985, Renne et al., 1998, Lanphere and Dalrymple, 2000, Spell and McDougall, 2003); (ii) comparison with ages based on orbital tuning (Renne et al., 1994, Hilgen et al., 1997, Kuiper et al., 2008); and (iii) comparison with results from coexisting mineral phases and/or different radioisotopic systems (e.g., Baksi et al., 1996, Villeneuve et al., 2000, Lanphere and Baadsgaard, 2001, Schmitz and Bowring, 2001, Bachman et al., 2007). The references cited above are intended to be indicative rather than exhaustive; for a more complete enumeration of data relevant to the age of FCs the reader is encouraged to consult those sources as well as the summary by Dazé et al. (2003).
The results of the various efforts to determine the age of FCs vary by several percent, far beyond what is expected from typical reported precision. Consensus is lacking as to the cause of this dispersion, but it certainly includes systematic errors and inconsistent interlaboratory calibrations as well as real geologic differences between the ages measured by different radioisotopic systems on different materials. Overall, the trend has been that older ages for FCs have been accepted in more recent times, culminating with the unprecedentedly precise age of 28.201 ± 0.023 Ma reported by Kuiper et al. (2008) based on orbital tuning. The result of Kuiper et al. (2008) represented a significant advance in reconciling 40Ar/39Ar ages with those based on other chronometers including orbital tuning, and has achieved wide acceptance.
Despite the progress in determining the ages of standards presented by Kuiper et al. (2008), little progress has been made in refining the 40K decay constants since the synthesis of Beckinsale and Gale (1969), updated by Steiger and Jäger (1977). As is discussed in the following, knowledge of the age of a standard in and of itself is only a partial solution to calibrating the 40Ar/39Ar system because miscalibrated decay constants accrue error as measured isotopic data are extrapolated to samples whose ages differ from that of the standard. Moreover, if we accept the K–Ar isotopic data for 40Ar/39Ar standards (i.e., as summarized by Jourdan and Renne, 2007), the only way to reconcile these data with the orbitally tuned result of Kuiper et al. (2008) is to adjust either or both of the principal 40K decay constants.
Min et al. (2000) and Kwon et al. (2002) observed that one could improve the accuracy of determination of both λtot and the age of the FCs standard (or, in principle, any other standard) by comparing the 40Ar/39Ar ages of volcanic rocks with ages determined for the same samples by independent methods, in most cases by the U–Pb method. The U decay constants, particularly that for 238U, are significantly more precisely known than λtot or the age of FCs, so one can estimate these latter two quantities by finding values for them that best reconcile 40Ar/39Ar and 238U–206Pb∗ ages, as follows.
The 40Ar∗/39ArK isotope ratio of a neutron-irradiated sample is related to these two parameters and to the true age of the sample by:where λtot is the total 40K decay constant, τi is an independently determined age of sample i, and Ri embodies the relationship between sample i and the standard, defined (Renne et al., 1998) by:where 40Ar∗ denotes radiogenic 40Ar and 39ArK indicates 39Ar produced from K by neutron irradiation. A U–Pb age (or other independent determination of the true age) and measurement of Ri for a particular sample thus define a relation between tstd and λtot. Kwon et al. (2002) considered five such pairs and applied a maximum likelihood method (discussed in more detail later) to find values of tstd and λtot that best fit these observations. Graphically, this can be thought of as determining the mutual intersection of a number of curves defined by Eq. (1) for (τi, Ri) pairs.
The approach of Kwon et al. (2002) showed the effectiveness of the basic idea of employing independently dated samples to calibrate the 40Ar/39Ar system, but did not incorporate constraints from activity measurements or isotopic data for the standard. In this work, these constraints are incorporated to determine tstd and both decay constants for 40K. These parameters are related to (τi, Ri) pairs according to:in which Eq. (1) is transformed into a function of κstd, the true (dimensionless) 40Ar∗/40K ratio of the standard, rather than tstd. The (τi, Ri) pairs define relations between λε, λβ, and κ analogous to their relationship to tstd and λtot as employed by Kwon et al. (2002). We use a least-squares solution method similar to that of Kwon et al. (2002) to find values of λε, λβ, and κ that best fit (i) a set of such relations defined by seventeen (τi, Ri) pairs and (ii) independent determinations of λε, λβ, λtot, and κstd. Graphically, this can be thought of as determining the mutual intersection of curved surfaces defined by Eq. (3) for the (τi, Ri) pairs, and planes defined by the independent measurements of λε, λβ, and κ. We show that the estimates of λε, λβ, and κstd derived from this exercise (i) successfully reconcile U–Pb and 40Ar/39Ar ages for our entire data set, (ii) are significantly more precise than those determined from the existing independent measurements alone, and (iii) yield 40Ar/39Ar dates of unprecedented accuracy.
Section snippets
Summary of existing data
A summary of existing constraints on λε, λβ, λtot, and the value of κ for the Fish Canyon sanidine (κFCs), are given in Table 1 and discussed below.
Data analysis
We seek to find values for the parameters λε, λβ, and κFCs that best fit: (i) the relations described by Eq. (3) and the (τi, Ri) pairs described in the Introduction (Section 1) and Section 2.5, as well as (ii) the independent measurements of these parameters described in Sections 2.1 , 2.2 β Activity data, 2.3 Electron capture activity data, 2.4 Liquid scintillation activity data. We adapt the nonlinear regression model of Kwon et al. (2002) for this purpose. First, we rewrite Eq. (3) to
Optimization results
Table 4a, Table 4b, Table 4c show the values of , and that minimize S1, as well as the implied values of . These best-fit values yield S1 = 8.8. Table 4a, Table 4b, Table 4c, Figs. 2 and 3 show the results of the Monte Carlo error analysis. Fig. 4 shows the distribution of the normalized residuals with respect to the input values of τi, Ri, and κFCs; the distribution is indistinguishable from normal. We did not observe any significant relationship between the
Application of the results
Comparison of Table 1, Table 4a shows that our estimates of and are significantly more precise than previously determined values, while the precision of our estimate of remains essentially unchanged.
Conclusions
Here we have found values for the 40K decay constants (λε and λβ), and the 40Ar∗/40K ratio (κFCs) of the FCs standard that best fit: (i) constraints from activity-based measurements of the 40K decay constants, (ii) independent measurements of the age of the FCs standard, and (iii) paired U–Pb and 40Ar/39Ar ages on carefully selected samples. First, these estimates of λε and λβ are significantly more accurate than obtainable from existing disintegration counting data alone. Second, uncertainties
Acknowledgments
This study was funded by the Ann and Gordon Getty Foundation augmented by NSF Grants EAR-9628065, EAR-9614324, EAR-9814378, and EAR-0451802. We thank M. Schmitz and S. Bowring, C. Swisher, and L. Black for providing samples EGB-032, PIT-2, and PaV, respectively; J. Bossi and N. Campal, and W. Sharp, for assistance in collecting samples PR94-7 and PD97-2, respectively. T. Becker, A. Deino and A. Jaouni are thanked for their various contributions to producing the data reported herein. Helpful
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