Interpreting and reporting ⁴⁰Ar/³⁹Ar geochronologic data

Since 2003, the international EARTHTIME Initiative (www.earth-time.org) has focused on enhancing the precision and accuracy of commonly used geochronologic methods, which has resulted in community-wide improvements in metrologic traceability, interlaboratory reproducibility, precision, accuracy, and intercalibration between the ⁴⁰Ar/³⁹Ar method and other dating methods (e.g., U-Pb zircon ages, astronomical time scale). These advances have enabled the expansion of opportunities for ⁴⁰Ar/³⁹Ar dating to provide useful constraints for many geologic processes spanning a wide range of time periods. However, the level of analytical uncertainty (∼0.1%) for dates obtained from a new generation of mass spectrometers—as well as the high spatial resolution afforded by excimer laser microsampling techniques—has led to increasingly dispersed data sets for individual minerals or hand samples, including fluence monitors (Phillips and Matchan, 2013; Mercer et al., 2015; Rivera et al., 2016; Andersen et al., 2017; Yancey et al., 2018). Identification of this complexity, in turn, demands a deeper consideration of the processes (e.g., geologic, analytical, reactor-induced) responsible. Here, we provide example ⁴⁰Ar/³⁹Ar interpretations from a variety of geologic environments and rock types to illustrate possible complexities to nonspecialists. We bolster previous recommendations for minimum reporting requirements for ⁴⁰Ar/³⁹Ar metadata (Renne et al., 2009), along with added criteria, including the requirement that metadata files are made machine-readable to facilitate automated archiving and interdisciplinary usage of data.

The ⁴⁰Ar/³⁹Ar dating method is a variant of conventional K-Ar geochronology (Merrihue and Turner, 1966), whereby the radioactive parent isotope ⁴⁰K (t_1/2 ≈ 1.25 Ga) undergoes branched decay to two stable daughter products, ⁴⁰Ca (∼89%) and ⁴⁰Ar (∼11%), via beta emission and electron capture, respectively (Beckinsale and Gale, 1969; Steiger and Jäger, 1977; Min et al., 2000). The decay branch of interest for ⁴⁰Ar/³⁹Ar geochronology is the production of stable radiogenic Ar (⁴⁰Ar*). ⁴⁰Ar* can be measured in K-bearing materials with ages that range from historical to beyond the Archean. K-Ar geochronology is a first-order dating technique that relies on the quantitative isotopic analysis of separate sample aliquots for potassium and argon using different instruments/techniques. Potassium analyses (assuming a constant ⁴⁰K/³⁹K ratio of 0.01167; Garner et al., 1975) are conducted by flame photometry, X-ray fluorescence (XRF), or isotope dilution, whereas Ar analyses are performed by isotope-dilution noble-gas mass spectrometry. Comparatively, the ⁴⁰Ar/³⁹Ar dating technique is a relative geochronometer that requires the neutron irradiation of samples along with a “known age” fluence monitor. Typically, the five isotopes of argon (⁴⁰Ar, ³⁹Ar, ³⁸Ar, ³⁷Ar, and ³⁶Ar) are measured by noble-gas mass spectrometry (for a more detailed discussion, see Dalyrmple et al., 1981; McDougall and Harrison, 1999; Kelley, 2002; Reiners et al., 2018). The data produced by the ⁴⁰Ar/³⁹Ar method can then be evaluated using the age-spectrum plot, isotope correlation diagrams, Ar diffusion using Arrhenius plots of the Ar isotopes, and direct observation of possible intracrystalline variations in ⁴⁰Ar* through laser-ablation microprobe mapping.

⁴⁰Ar/³⁹Ar dates commonly represent the time since a sample last became closed to isotope exchange of ⁴⁰K and ⁴⁰Ar loss, be it due to crystallization, retrogression, alteration, deformation, or thermal diffusion. In rapidly cooled, unaltered volcanic rocks, ⁴⁰Ar/³⁹Ar dates are commonly interpreted as the eruption age. In metamorphosed, metasomatized, or retrogressed samples, they often represent the age of reaction in a chemically open system. For samples precipitated from sedimentary or weathering solutions, ⁴⁰Ar/³⁹Ar dates record the ages of low-temperature chemical reactions. In samples that preserve petrologic equilibrium achieved at high temperatures, the ⁴⁰Ar/³⁹Ar dates reflect cessation of thermally induced diffusion as the sample cooled. The validity of the closed system of a sample is typically evaluated by conducting an incremental heating experiment, whereby Ar is degassed in a stepwise fashion from low to higher temperatures. The subsequent ⁴⁰Ar/³⁹Ar dates from each step are then plotted on an age spectrum diagram, which allows for the statistical evaluation of concordance, known as an age plateau. An alternative approach to step heating is total fusion of single minerals, for which individual ⁴⁰Ar/³⁹Ar dates are then compiled to determine a potentially meaningful geologic age. These are model ages because a common assumption in the interpretation of ⁴⁰Ar/³⁹Ar dates as eruption or crystallization ages for terrestrial samples is that the trapped or “initial” Ar has an atmospheric composition (⁴⁰Ar/³⁶Ar ratio of ∼300; Nier, 1950; Lee et al., 2006; Renne et al., 2009; Valkiers et al., 2010; Mark et al., 2011), and that samples have retained all ⁴⁰Ar* derived from in situ ⁴⁰K radioactive decay. These assumptions must be tested for each sample, because: (1) ⁴⁰Ar* may diffuse out of crystal structures during cooling or prograde reheating events; (2) K and ⁴⁰Ar* can be removed or added from glasses or minerals by aqueous alteration or metasomatism (e.g., weathering; Cerling et al., 1985); and (3) nonradiogenic ⁴⁰Ar may be incorporated into minerals and glasses during their formation (i.e., trapped Ar). Trapped Ar with ⁴⁰Ar/³⁶Ar greater than the modern atmospheric composition is termed “extraneous Ar” (e.g., Lanphere and Dalrymple, 1976) and may be sequestered in melt or fluid inclusions from the mantle, magmas, or deep crustal fluids. However, even if it is nonatmospheric, the initial ⁴⁰Ar/³⁶Ar ratio of a sample may be evaluated by the isochron method. For example, plutonic and volcanic rocks may (1) contain inherited Ar in antecrysts (e.g., Andersen et al., 2017) or xenocrysts (e.g., Chen et al., 1996; Singer et al., 1998; Renne et al., 2012), which reflect the pre-eruptive/pre-intrusive history of radioisotopic decay, and (2) have incorporated trapped Ar with a ⁴⁰Ar/³⁶Ar ratio lower than the current atmospheric ratio due to kinetic fractionation upon emplacement (Matsumoto and Kobayashi, 1995; Renne et al., 2009; Morgan et al., 2009). The power of the ⁴⁰Ar/³⁹Ar method lies in the ability to evaluate all assumptions within the context of a sample’s geologic history and to identify nonideal behavior (K and Ar gain or loss) by identifying the carrier phases of Ar by their Cl/Ca/K signatures (e.g., Kelley and Turner, 1991).

The ⁴⁰Ar/³⁹Ar method involves placing K-bearing samples in a nuclear reactor for irradiation with thermal and fast neutrons, where nucleogenic ³⁹Ar (³⁹Ar_K; t_1/2 = 269 yr) is produced from ³⁹K, ³⁷Ar is produced from Ca, and ³⁸Ar is produced from Cl (Merrihue and Turner, 1966). The neutron flux is quantified by co-irradiating fluence monitors of known age with the samples (Merrihue and Turner, 1966), defining the irradiation parameter J (i.e., the production factor of ³⁹Ar from ³⁹K). After irradiation, the samples and associated fluence monitors are loaded into an ultrahigh-vacuum system, where gases (including Ar) are extracted from the sample using furnace, laser, or crushing techniques, some of which are discussed below. After extraction, the gases are purified to remove reactive species (e.g., H₂O, CO₂, Cl) using a combination of cold traps and/or getter pumps. The remaining gases, including argon and other noble gases, are introduced into a static gas-source mass spectrometer for isotopic analysis.

Acquisition of ⁴⁰Ar/³⁹Ar data is time- and labor-intensive, with the main time-limiting step being the irradiation process (2–6 mo; Fig. 1), which depends on the irradiation duration as well as the reactor queue (Fig. 1). For a comprehensive list of commonly used nuclear reactors, see table 3-3 (p. 56) of McDougall and Harrison (1999). The optimal duration of the irradiation process is determined by the neutron flux, which is related to reactor power, proximity to the reactor core, and local shielding, as well as the age of the samples, where longer irradiations are required for older samples to achieve optimal ⁴⁰Ar*/³⁹Ar ratios (typically 1–10; Fig. 1).

Until the 1990s, the most widely used approach to extracting Ar from silicate samples for dating involved incremental heating or total fusion of samples in vacuo using a double-vacuum resistance furnace, followed by the separation of reactive species from the evolved gases using zirconium metal-alloy getter pumps and/or cryogenic devices prior to analysis. The gas purification techniques for ⁴⁰Ar/³⁹Ar analytical systems have changed little over the years, but both the gas extraction and mass spectrometry subsystems have advanced substantially.

Lasers have been used to extract gases from samples for ⁴⁰Ar/³⁹Ar analyses since the 1970s (e.g., Megrue, 1973; York et al., 1981), but they were not widely used until the late 1980s and early 1990s. The variety of lasers used has evolved to address the needs of several distinct Ar extraction techniques. Pulsed lasers (micro- to nanosecond pulses) are typically used for spot analysis, whereas continuous lasers dominate heating and fusion of samples over several seconds to minutes. The range of wavelengths utilizes the variation in laser/sample interaction and variations of absorption with wavelength. The various lasers include: (1) CO₂ lasers, which produce energy in the infrared spectrum at a wavelength of 10.6 μm; (2) infrared Nd:YAG lasers (1.06 μm); (3) infrared diode lasers (typically between 800 nm and 1.0 μm); (4) Ar and visible diode lasers (typically around 530 nm); (5) ultraviolet, frequency-quadrupled (266 nm) or quintupled (213 nm) Nd:YAG lasers; and (6) ultraviolet KrF (248 nm) and ArF excimer lasers (193 nm). The use of lasers producing energy across such a broad segment of the electromagnetic spectrum relates to the different light-matter interactions for specific types of analyses.

Of all the lasers used in ⁴⁰Ar/³⁹Ar laboratories, CO₂ lasers are the most versatile, due to the high absorption of 10.6 μm energy by all minerals and glasses of interest. However, minimum focused beam diameters for CO₂ beams are relatively large compared to other commonly available lasers (minimum diameters attainable are generally 5–10 times the laser wavelength). As a consequence, they are typically used for incremental heating or total fusion experiments.

The energy of other infrared lasers (the 1064 nm Nd:YAG and various diode lasers) is much less effectively absorbed by transparent to subtransparent minerals, including muscovite and feldspar, which may require micro-encapsulation in a metal such as niobium (e.g., Jourdan et al., 2014). Both 1064 nm Nd:YAG lasers and infrared diode lasers are typically used to extract Ar at lower irradiances by heating or melting by expanding the beam focal point or lowering the laser power.

For very high-spatial-resolution studies of individual mineral grains or for in situ targeting, ultraviolet lasers are preferred (e.g., Kelley et al., 1994). The growing availability of ArF excimer lasers in ⁴⁰Ar/³⁹Ar laboratories has spawned great interest in microanalytical studies of rock thin sections and mineral grain mounts using ultraviolet laser-ablation microprobes (UVLAMPs). In particular, the near-complete absorption of 193 nm energy by almost all minerals of interest and the high energy and short pulse duration of ArF excimers result in extremely well-formed ablation pits, minimal redeposition of ablated material, full extraction of gases of interest from the ablated material, and minimal heating of the surrounding sample (Gunther et al., 1997; van Soest et al., 2011). The limiting factor for the optimum size of the laser pit is the necessity to detect the five Ar isotopes and measure their concentrations with a precision deemed sufficient for the intended purpose. UVLAMP technology has been used to constrain ⁴⁰Ar exchange by diffusion and alteration in natural samples (Pickles et al., 1997; Kelley and Wartho, 2000; Smith et al., 2005), the role of deformation and recrystallization in ⁴⁰Ar loss (Cosca et al., 2011; Mulch and Cosca, 2004; Mulch et al., 2002), as well as the ages of multiple fabric-forming events in polymetamorphic tectonites (Chan et al., 2000; Janak et al., 2001; Mulch et al., 2005), pseudotachylytes in fault zones (Condon et al., 2006; Cosca et al., 2005; Fornash et al., 2016; Muller et al., 2002), authigenic K-feldspar growth in sedimentary rocks (Sherlock et al., 2005), and multiple impact-melting events in lunar breccias (Mercer et al., 2015, 2019).

Most ⁴⁰Ar/³⁹Ar data currently produced involve the extraction of gases from single crystals or whole-rock/groundmass aliquots. Some laboratories focus only on the evolving Ar isotopic characteristics during incremental heating when interpreting the geologic significance of dates, and they extract gas stepwise by applying progressively higher laser powers for each increment, using power level as a rough proxy for sample temperature. A more quantitative approach, especially for thermochronologic or diffusion-based studies, is to use a well-calibrated optical pyrometer and use the laser to heat a sample that is encapsulated in a nonreactive (e.g., platinum or tantalum) metal jacket in order to obtain a robust estimation of the temperature (e.g., Jourdan, 2014).

Once the gas is extracted from the sample, it is purified by a Ti sublimation pump or by a series of nonevaporable getters. Getter pumps use high field strength element (e.g., titanium, zirconium, vanadium) alloys to remove active gases, like O₂, H₂, and N₂, and break down hydrocarbon volatiles while not reacting with noble gases such as Ar. Trapping of water and carbon dioxide is often accomplished using a cryogenic trap or cold finger operated at a temperature slightly above the freezing point of Ar (83.8 K). The introduction of “clean” gas into the mass spectrometer is key to (1) ionization efficiency, (2) avoiding measurement of argon plus isobarically interfering species, and (3) preventing “memory” effects in the mass spectrometer/extraction system, all of which could lead to an inaccurate ⁴⁰Ar/³⁹Ar date.

⁴⁰Ar/³⁹Ar measurements depend on magnetic sector mass spectrometers to determine isotopic abundances. Commercially available mass spectrometers today are ubiquitously the multicollector type but are quite diverse in other respects. Multicollector analysis allows for significantly more data to be acquired per unit time than peak-hopping with a single collector but carries the disadvantage of requiring intercalibration of sensitivity and mass bias between detectors. Some multicollector instruments have greater mass resolution compared to older mass spectrometers, whereas others offer improved sensitivity or the ability to measure very small signals. By far the most significant development associated with the newer instruments is the more stable electronics, which translates to less noise and improved ion beam and amplifier stability during analysis. This technological improvement, along with the reduction of blanks and isobaric interferences (H³⁵Cl and 3·¹²C), has led to more precise dates and is expanding the applicability of the already versatile ⁴⁰Ar/³⁹Ar chronometer (Fig. 2). In addition, the rapid multicollection of Ar isotopes has resulted in shorter data acquisition times per analysis, thereby increasing sample throughput in laboratories.

The use of lasers for sample heating coupled with the development of low-volume gas extraction lines has, in most cases, resulted in a drastic reduction in the amount of sample required for analysis. Previously, incremental heating experiments of Pliocene–Pleistocene lavas consisted of a small number of steps (average 8–12) and required several hundred milligrams of sample (e.g., Singer and Pringle, 1996). Now, these experiments can be conducted on as little as 10–30 mg of sample (e.g., Singer et al., 2019), and they can be broken up into many more incremental heating steps (Fig. 2). Moreover, analyses of low-K phases such as latest Pleistocene plagioclase phenocrysts (e.g., Carrasco-Nuñez et al., 2018) and Cenozoic pyroxene (e.g., Ware and Jourdan, 2018; Konrad et al., 2019) are now feasible. Higher precision on smaller and younger detrital grains is improving our understanding of progressive, grain size–specific detrital signal dilution in rivers, and our ability to provide robust provenance signals obtained for sediments located many hundreds of kilometers away from their source rocks (e.g., Blewett et al., 2019; Gemignani et al., 2019; Hereford et al., 2016).

To compute an ⁴⁰Ar/³⁹Ar date for a sample of unknown age, the following parameters and their estimated uncertainties are required:

• (1) the corrected relative abundances of Ar isotopes measured for the unknown (see “Data Corrections and Factors Contributing to Uncertainties” section later herein);

• (2) the corrected relative abundances of Ar isotopes measured for a co-irradiated fluence monitor used to calculate a J value;

• (3) the assumed age, or the ⁴⁰Ar*/⁴⁰K ratio of the co-irradiated fluence monitor; and

• (4) the values of the ⁴⁰K decay constants (Table 1).

While the first two data items are measured experimentally during each ⁴⁰Ar/³⁹Ar study, the latter two are typically based on the results of dedicated studies published in the literature. Items 2, 3, and 4 are used to compute the irradiation parameter J, which is then combined with items 1 and 4 to compute a date for a sample of unknown age. As the ⁴⁰Ar/³⁹Ar geochronology technique has evolved, so too has documentation of heterogeneities in the chemical composition of irradiation monitor minerals and their atmospheric-corrected ⁴⁰Ar*/⁴⁰K or apparent ages, along with variation of the estimates of the ⁴⁰K decay constants. In other words, the monitor ages and decay constant values used in ⁴⁰Ar/³⁹Ar studies may differ amongst publications from different times and/or laboratory groups. Therefore, when comparing different ⁴⁰Ar/³⁹Ar data sets, it is important that researchers account for these differences. It is also critical to understand the intercalibration histories of the monitor minerals and the set of ⁴⁰K decay constants used (Tables 1, 2, and 3).

The ages or ⁴⁰Ar*/⁴⁰K ratios of the fluence monitor minerals are generally determined by: (1) the K-Ar method, (2) intercalibration with one or more different co-irradiated mineral fluence monitors, the age(s) of which has(have) been determined independently (e.g., Alexander and Davis, 1974; Renne et al., 1998), or (3) evaluation against astronomically dated cyclical sedimentary sequences (e.g., Kuiper et al., 2008). It is relatively straightforward to recompute the monitor mineral age to accommodate different or updated ⁴⁰K decay constants and/or relative K isotope abundances (e.g., Dalrymple, 1979; Min et al., 2000; Mercer and Hodges, 2016). Changes to these parameters (e.g., age, ⁴⁰Ar*/⁴⁰K, decay constants, etc.) for the selected fluence monitor (and any intermediate-derived fluence monitors) will compound nonlinearly to affect the calibration of a given monitor mineral.

The decay constants of long-lived radioactive nuclides have generally been determined by: (1) directly counting the emission of α, β, and γ particles produced by the decay of a known quantity of a radioactive nuclide, (2) measuring the radiogenic ingrowth of daughter products that accumulate from the decay of a well-known quantity of a radioactive nuclide over a prolonged time period (e.g., decades), and (3) intercalibration of multiple mineral isotopic chronometers (where the well-known decay constant for ²³⁸U is commonly taken as the “gold standard”) in a rock that formed “instantaneously” and lacks evidence of any secondary processes (Begemann et al., 2001). The exact nature of the branched decay of ⁴⁰K into ⁴⁰Ar and ⁴⁰Ca has been debated due to numerous natural and experimental challenges associated with the use of the above approaches to determine the total decay constant, λ_tot, and the branching ratios (Begemann et al., 2001; Naumenko-Dèzes et al., 2017). As our understanding of the ⁴⁰K decay constants continues to evolve, researchers using published ⁴⁰Ar/³⁹Ar data sets will need to recalculate both the apparent ages of common monitor minerals (if the ⁴⁰Ar*/⁴⁰K ratios of the monitors were not reported) and the apparent ages of unknowns as newer values are adopted by the geochronology community. The ⁴⁰K decay constants and ⁴⁰Ar*/⁴⁰K ratio reported by Renne et al. (2010, 2011) for the Fish Canyon sanidine (FCs) monitor mineral were determined using data sets that depended on the ²³⁸U decay constant, which requires that error correlations among the parameter values they reported be accounted for when recomputing ⁴⁰Ar/³⁹Ar data sets. Similar care is required for error correlations that arise in the course of other efforts to constrain the ⁴⁰K decay constants by comparing results from multiple mineral isotopic chronometers.

It is common to encounter ⁴⁰Ar/³⁹Ar dates in the literature calibrated using different ⁴⁰K decay constants and ages for the same mineral monitors, reflecting the evolution of our knowledge of these parameters (Tables 1, 2, and 3). To compare ⁴⁰Ar/³⁹Ar dates from different studies directly, they must be recalculated to an internally consistent parameter set (decay constant and monitor age). Convenient open-source software tools for straightforward recalibration of published ⁴⁰Ar/³⁹Ar dates include ArArCALIBRATIONS (Koppers, 2002) and the Java-based ArAR (Mercer and Hodges, 2016). In addition to these recalibration tools, other free and open-source software packages like IsoplotR provide user-friendly plotting and statistical analysis of geochronologic data (Vermeesch, 2018). As an example, Figure 3 shows ⁴⁰Ar/³⁹Ar dates published for sanidine from the IrZ-coal layer in the Hell Creek area of NE Montana (Swisher et al., 1993; Renne et al., 2013) and the C-1 melt rock from the Chicxulub impact crater in Yucatán, Mexico (Swisher et al., 1993). The dates of Swisher et al. (1993) were originally reported using a monitor age of 27.84 Ma and the ⁴⁰K decay constants of Steiger and Jäger (1977), whereas Renne et al. (2013) used the parameter values reported in Renne et al. (2011). Figure 3 shows how these data sets—which represent samples from two of the key deposits used to define the Cretaceous-Paleogene boundary—compare after recalculation to the FCs age recommended by Kuiper et al. (2008) and the ⁴⁰K decay constants of Min et al. (2000).

While shifts in apparent ages reported by Renne et al. (2013) are within 1σ uncertainties, the shifts in apparent ages reported by Swisher et al. (1993) exceed the stated 1σ uncertainties (Fig. 3). This emphasizes the importance of using an internally consistent set of monitor mineral ages and ⁴⁰K decay constants when comparing and making interpretations of geologic significance from multiple ⁴⁰Ar/³⁹Ar data sets. In this regard, the geochronology community is actively working to refine knowledge of these critical parameters to improve the overall precision and accuracy that can be achieved with the ⁴⁰Ar/³⁹Ar method.

For decades, many K-Ar and ⁴⁰Ar/³⁹Ar dates were published without enough supporting metadata, thereby precluding detailed assessment of the dates, recalculation of the data, or recalibration using different monitors or decay constant values. To improve transparency for readers, reviewers, and journal editors and facilitate complete evaluation of dates, Renne et al. (2009) suggested minimum ⁴⁰Ar/³⁹Ar data reporting criteria for publication of ⁴⁰Ar/³⁹Ar dates. The longevity and utility of ⁴⁰Ar/³⁹Ar data sets will be significantly improved by following the recommendations for ⁴⁰Ar/³⁹Ar data reporting first set out by Renne et al. (2009). These reporting norms were acknowledged to be minimum information that would allow recalculations by others, and they were established prior to the implementation of multicollector noble-gas mass spectrometers and modern open data-sharing protocols (see “Announcement: FAIR data in Earth science,” Nature, 2019). Data collection for Ar isotopes with multiple detectors requires methods for calibrating the various detectors and therefore involves laboratory-specific instrument procedures, which introduces additional analytical complexity. Here, we expand upon the initial data reporting guidelines of Renne et al. (2009) and suggest additional metadata be reported when publishing ⁴⁰Ar/³⁹Ar data in peer-reviewed journals (Table 4).

Cyberinfrastructure for data archiving and sharing guided by the principles of findability, accessibility, interoperability, and reusability (FAIR; Wilkinson, 2016) has been improved over the last decade. The FAIR ideals are widely agreed upon as beneficial by scientists, but they carry practical challenges and concerns (e.g., maintenance, copyrights, poaching, misuse, time commitments; Nelson, 2009). To avoid the problem of time-consuming and high-impact dates turning into “dark data”—data not carefully indexed, stored, or visible to the outside scientific community that have a strong potential to be lost (Heidorn, 2008)—the future of geochronology is FAIR data that are easily readable by both humans and computers. Full ⁴⁰Ar/³⁹Ar data sets must be published in consistent, well-documented tabular formats (e.g., CSV, XLS) or structured machine-readable formats (e.g., JSON/XML); it is inadvisable to publish these data sets in supplements as a nonstructured PDF file, which greatly inhibit indexing and reuse. For two examples of appropriately formatted ⁴⁰Ar/³⁹Ar metadata files (J. Ross, 2020, personal commun.; Rose and Koppers, 2019) archived via FAIR principles, see the Supplemental Materials.¹ Another alternative to publishing the full suite of ⁴⁰Ar/³⁹Ar metadata in the supplements of papers is to make that data open source and freely available via an online repository (e.g., github.com/NMGRLData/KvAges).

A key barrier to the widespread adoption of FAIR practices in geochronology is the lack of cyberinfrastructure to support this new emphasis on consistent, interoperable, and discoverable data products. Community-wide discoverability is crucial for data reuse; it is a precondition for envisioned large-scale, data-mining efforts, which can or plan to build aggregate age models from geochronology measurements (e.g., Macrostrat; Peters et al., 2018; MagIC; EarthRef.org Digital Archive [ERDA]; Paleobiology Database [PBDB]). However, geochronologic data often end up stored on local laboratory hard drives and only exposed to the scientific community through publication. The National Science Foundation–funded community archive for geochronologic data, the Geochron database (http://www.geochron.org/),was created as an effort to improve to the availability and interdisciplinary usage of geochronologic data. Yet, the centralized architecture of Geochron (and most traditional databases) relies on researchers themselves to manually import data in a strict format for it to be used and discoverable, a significant workflow hurdle that has caused the resource to remain underutilized. New tools are needed to ensure that laboratories can make their data available without adding additional steps to already complex workflows. The public availability of machine-readable data products can be supported by forward-looking and automated laboratory data management practices. Laboratory analytical software is most useful when supplemented with components to handle management, discoverability, and interoperability; modern data management software such as ArArSUITE (http://geochronology.coas.oregonstate.edu/software/#ArArSUITE), Pychron (Ross, 2019), or Sparrow (https://sparrow-data.org/; Quinn et al., 2019) can assist with the automation of these processes. A limiting factor in the success of ⁴⁰Ar/³⁹Ar data sets to achieve FAIR ideals relies on a scientist’s willingness to follow the requirements set forth in Table 4. Unfortunately, a decade after the introduction of the data reporting norms of Renne et al. (2009), there continue to be widespread examples of published ⁴⁰Ar/³⁹Ar data sets that ignore these requirements. We strongly emphasize the importance of including the full suite of metadata in Table 4 within supplements to complement ⁴⁰Ar/³⁹Ar data within publications. As such, we strongly recommend that editors and reviewers use Table 4 as a checklist to ensure that future ⁴⁰Ar/³⁹Ar data sets contain this required information prior to publication (Supplemental Material, see ^{footnote 1}).

The suggestion to reclassify some values previously regarded as nonessential to required items in Table 4 follows the FAIR initiative. The most notable example is the final model ⁴⁰Ar/³⁹Ar date. Although Renne et al. (2009) suggested that providing ⁴⁰Ar/³⁹Ar dates is optional because they can be derived from relative abundances, we recommend that the calculated model dates be required within ⁴⁰Ar/³⁹Ar tables to greatly increase convenience and improve interpretation of published data. Thus, the burden of calculating model dates need not be placed on the consumer but instead rests with the geochronologist or laboratory that generated them. Reporting final model dates at the 2σ level (or 95% confidence) is common practice among other geochronologic communities, most notably U-Th-Pb (Horstwood et al., 2016; Dutton et al., 2017). With respect to ⁴⁰Ar/³⁹Ar data, it is common practice to report analytical uncertainties for individual analyses at the 1σ level and the final interpreted dates at the 2σ level (e.g., Fig. 2). When reported date uncertainties include decay constant uncertainties, they can be directly compared to results from different isotope systems (e.g., Schmitz, 2012).

During noble-gas mass spectrometry, Ar isotope ion currents are measured over regular time intervals for a duration of a few minutes. The signal intensity changes systematically during the analysis due to the competing effects of gas consumption by the filament and degassing of additional Ar from the internal surfaces of the instrument (the “memory” effect). By convention, all calculations use the isotopic values and associated uncertainties of the intercepts that are determined via regression to “time zero” (t₀). The definition of t₀ varies amongst laboratories and software packages; the most common is the time of gas introduction into the mass spectrometer, but some laboratories use two thirds of the gas-equilibration time. In the following section, we describe each of the factors contributing to ⁴⁰Ar/³⁹Ar age uncertainties:

(1) Baseline measurement and correction: Voltage or current measurements on Faraday collectors have two parts: a baseline and an “on-peak” measurement. The thermal noise of the amplifier that is associated with a Faraday detector, referred to as the Johnson-Nyquist noise, is determined via a baseline measurement of the signal intensity “off-peak,” typically at the “half-mass” position, e.g., halfway between two peaks. For ⁴⁰Ar/³⁹Ar analyses, baselines are measured either just before or after the sample/blank/air analysis. The optimal duration of the baseline versus on-peak measurements depends on the size of the ion beam and the size of the amplifier’s resistor. The uncertainty in the baseline-subtracted intensity measurement is the quadratic sum of the baseline and on-peak uncertainties. Similarly, for signals measured in an ion-counting detector, a baseline measurement, often referred to as “zero” or “dark noise” measurement, is required. The source of the ion-counting detector noise is primarily related to the discriminator settings or implantation of radioactive isotopes. The uncertainty in the “zero” or “dark noise” measurements is propagated with the on-peak uncertainty in quadrature.

(2) Blank correction: The gas extraction system and mass spectrometer will register a detectable background signal that is measured during a separate “blank” run and subtracted from the measured sample signal. This blank incorporates the backgrounds and rise rates of both the mass spectrometer and extraction line measured over some interval. This presents a challenge for making the best estimation of the blank correction because the blank is not measured at the same time as the sample. Finding the best pattern of measurement of samples, monitors, and blanks is thus a key element of making the best-quality age determinations, and the pattern chosen is not the same in all laboratories. However, it is critical that uncertainty arising from the blank correction reflects the variability of blanks rather than the precision with which the blank can be measured.

(3) Detector calibration: Early noble-gas mass spectrometers had a single ion collector, and Ar isotopic measurements were performed by “peak hopping,” where the magnetic field strength of the mass spectrometer was varied to alternate between isotopic masses. In recent years, a new generation of multicollector noble-gas mass spectrometers has been developed, which allow multiple isotopes to be analyzed simultaneously (e.g., Mark et al., 2009). However, the different ion detectors in a multicollector mass spectrometer do not necessarily respond equally to ion beams of equal mass and size. Because many different instruments with different collector configurations exist, detector calibrations are often specific to each laboratory. Some, but not all, mass spectrometers have a stable voltage supply to intercalibrate gains electronically. Collectors can also be calibrated by applying an ion beam of known size across the detectors and monitoring the response relative to the other resistor circuits (e.g., Mark et al., 2009; Turrin et al., 2010), or measuring a “gas cocktail” with an independently known Ar isotope composition (e.g., Coble et al., 2011; Jicha et al., 2016).

(4) Mass fractionation (i.e., instrumental mass bias or mass discrimination): The mass spectrometer itself causes changes to the measured isotope abundances and thus the expected ratios (i.e., Ireland, 2013). Specifically, mass fractionation is partly due to extraction efficiency from the source following ionization (see discussions in Turrin et al., 2010; Mark et al., 2011). Mass bias can also be imposed by detectors, and so the bias is a composite of effects imposed by both source and detector. These effects in general cannot be deconvolved, and thus the relationship between mass difference and bias (e.g., linear, power law, exponential) must be determined empirically (e.g., Renne et al., 2009). The mass fractionation correction can be significant, especially for samples with low radiogenic ⁴⁰Ar signals (i.e., Turrin et al., 2010), and significant errors can result if mass fractionation and its associated uncertainty are not accounted for properly. The mass fractionation factor can be quantified by comparing the measured ⁴⁰Ar/³⁶Ar signal ratio of an air aliquot on several detectors or that of an artificial gas cocktail with known Ar isotopic ratios and associated uncertainties.

(5) Trapped Ar correction: Despite the incompatibility of noble gases within the crystal structure of most minerals (e.g., Kelley, 2002; Jackson et al., 2015; Krantz et al., 2019), nonradiogenic ⁴⁰Ar, co-located with ³⁸Ar and ³⁶Ar, is hosted in mineral and melt inclusions, found in trace quantities in crystal lattices, and adsorbed on mineral surfaces. On Earth and Mars, Ar is a major constituent of the atmosphere, and atmospheric Ar is often observed during sample degassing (e.g., Bogard and Johnson, 1983; Walton et al., 2007). On the Moon, the trapped gas composition reflects implanted parentless ⁴⁰Ar and solar wind Ar (e.g., Eberhardt et al., 1970; Yaniv and Heymann, 1972). On Earth, magmatic minerals that crystallize under a high partial pressure of Ar may incorporate mantle or crustal Ar. Isochron regressions can sometimes be used to deconvolve the isotopic composition of the trapped Ar component from the ⁴⁰Ar*/³⁹Ar_K ratio of a sample, such that an age can be calculated after appropriately correcting for excess argon (Heaton and Koppers, 2019).

(6) Cosmogenic Ar correction: Samples that have resided within meters of planetary surfaces accumulate ⁴⁰Ar, ³⁸Ar, and ³⁶Ar through spallation reactions between cosmic rays, secondary reaction products, and heavier target nuclei of K, Ca, Cl, Fe, Mn, Ni, Cr, and Ti. Thus, most lunar, Martian, and asteroidal samples found on Earth contain cosmogenic Ar because they were exposed to cosmic rays during transit through space. On Earth, the production rate is sufficiently low due to shielding of cosmic rays by the magnetic field and atmosphere such that cosmogenic corrections can be neglected. Although the cosmogenic correction to ⁴⁰Ar is generally insignificant, the correction to ³⁶Ar, which in turn is used to deconvolve trapped and radiogenic ⁴⁰Ar on isochron diagrams, is often significant (e.g., Bogard and Garrison, 1999). Therefore, assumptions and uncertainties in the application of the cosmogenic correction (for a review, see Cassata and Borg, 2016) can hinder attempts to obtain per mil uncertainties on some extraterrestrial samples.

(7) Interference correction: The ⁴⁰Ar/³⁹Ar method pairs the natural radioactive decay of ⁴⁰K to ⁴⁰Ar with synthetic activation of ³⁹K to ³⁹Ar. Neutron activation also produces not only ³⁹Ar but also a host of other Ar isotopes. For example, some ⁴⁰Ar is produced by neutron activation of ⁴⁰K, which is added to that produced from natural radioactive decay of ⁴⁰K; additional ³⁹Ar is produced from ⁴²Ca; and ³⁶Ar is produced from ⁴⁰Ca and ³⁵Cl. Corrections for interfering reactions are achieved by co-irradiating K-doped glass and fluorite and analyzing the full suite of (³⁶Ar, ³⁷Ar, ³⁸Ar, ³⁹Ar, ⁴⁰Ar) isotopic compositions in both the monitors and samples.

(8) Decay correction: Two of the five measured Ar isotopes are radioactive nuclides produced during irradiation: ³⁷Ar (t_1/2 = 34.95 ± 0.08 d; Renne and Norman, 2001) and ³⁹Ar (t_1/2 = 269 ± 3 yr; Stoenner, 1965). A correction is required for the decay of these isotopes during the time elapsed between irradiation and analysis. Also, ³⁶Cl decays to ³⁶Ar with a half-life of ∼300 k.y. and can be a significant correction for young, Cl-rich samples that are analyzed many months following irradiation.

(9) Irradiation parameter (J): The parameter J, which quantifies the production of ³⁹Ar from ³⁹K in the age equation, is determined by analyzing a co-irradiated fluence monitor with accurately known age. The J value varies horizontally and vertically in an irradiation stack due to neutron flux gradients in the reactor (e.g., Rutte et al., 2015), which can be quantified by analyzing numerous fluence monitors interspersed with the samples at known positions relative to each other.

(10) K isotope effects: The ⁴⁰Ar/³⁹Ar system assumes that ⁴⁰K/K values are equivalent for samples, monitors, and materials used for decay constant determinations. Although potassium stable isotopes are typically assumed to be constant in nature due to the lack of variability found by Humayun and Clayton (1995), more recent work (e.g., Morgan et al., 2018) has identified terrestrial variability in δ⁴¹K (defined as variations in ⁴¹K/³⁹K relative to a standard). The effects of this variability are likely negligible for many samples, and δ⁴¹K is not routinely measured on samples undergoing ⁴⁰Ar/³⁹Ar analysis, but for some samples, the effect on ages could exceed 1‰. Unless ⁴⁰K measurements are also made, the apparent effect on ⁴⁰K/K requires an assumption that mass-independent effects are not in play.

Most igneous rocks have a limited range in δ⁴¹K values (±0.2‰), as shown by the work of Wang and Jacobsen (2016), Li et al. (2019), Morgan et al. (2018), and Tuller-Ross (2019). The exceptions to this limited range in δ⁴¹K are pegmatites and some hyperalkaline volcanic rocks (e.g., the Alban Hills of Italy) that have a 2.5‰ range in δ⁴¹K values (Morgan et al., 2018). Another factor that affects most ⁴⁰Ar/³⁹Ar ages is the ∼0.5‰ difference in δ⁴¹K between silicates and evaporites, and the relatively minor (0.26‰) differences found between commonly used fluence monitors. Based on δ⁴¹K measurements from Morgan et al. (2018), the most likely effect of K isotope variability is that the age of fluence monitors GA1550 and FCs is underestimated by 35 k.y. and 7 k.y., respectively. As the precision and accuracy of the ⁴⁰Ar/³⁹Ar system improve, correcting for variable δ⁴¹K on monitors may become routine, and δ⁴¹K measurements on samples may be important in some cases.

(11) Sample averaging: The J parameters and ⁴⁰Ar/³⁹Ar ratios obtained from the previous steps provide all the elements needed to calculate a single ⁴⁰Ar/³⁹Ar date. However, it is usually beneficial to combine multiple analyses together to improve the precision of the dates and assess their reproducibility. These analyses may be total fusion dates or heating steps in an incremental heating experiment. In order to assess the reproducibility of sample or fluence monitor analyses, repeated measurements are recommended whenever possible. The resulting data can be averaged by taking a weighted mean, or by forming a combined isochron from the replicate analyses.

Each step in the ⁴⁰Ar/³⁹Ar data-processing chain involves statistical uncertainty. The effect of the uncertainties from each Ar isotope measurement and the subsequent corrections to it will vary significantly in materials of different ages and compositions. Figure 4 shows the results of a sensitivity analysis performed at the WiscAr geochronology laboratory at the University of Wisconsin–Madison. Measurements were performed using a Nu Instruments Noblesse multicollector mass spectrometer, and data were reduced using the Pychron software package (Ross, 2019). The ³⁶Ar abundance is typically several orders of magnitude smaller than that of ⁴⁰Ar or ³⁹Ar and dominates the uncertainty budget for most materials (Fig. 4). This measurement is critically important for the correction of trapped atmospheric argon. The duration for which a material is irradiated is typically optimized as a function of its presumed age and composition (Turner, 1971) and the power of the reactor, with the goal of producing enough ³⁹Ar such that a ⁴⁰Ar/³⁹Ar ratio of 1 to 50 is achieved (Dalrymple et al., 1981). Consequently, Quaternary samples require relatively short irradiation times, <1 h (at a 1 MWh reactor), whereas Paleogene and older samples might be irradiated for 1 to >50 h (at a 1 MWh reactor). In the case of older sanidine samples, the uncertainty of the ³⁹Ar measurement is more important in the uncertainty budget (Fig. 4C) compared to a young sanidine (Fig. 4A) that spent little time in the reactor. Composition is also relevant, as the sanidine in both examples in Figure 4 (Fig. 4A and Fig. 4C) contained very little Ca, resulting in negligible contributions by the interference corrections to the overall uncertainty budget. Conversely, for a Ca-rich material like plagioclase, the (³⁶Ar/³⁷Ar)_Ca and (³⁹Ar/³⁷Ar)_Ca interference corrections contribute much more to the uncertainty of old samples, which spend tens of hours in the reactor (Fig. 4D). It is important to note that these uncertainty budgets are only examples from a single laboratory and are highly dependent on the type of detectors (in this case, ion counters), and hence instrument, used for analysis, along with irradiation parameters and reactor conditions. However, Figure 4 illustrates that careful optimization of the irradiation duration is required prior to analysis.

Statistical uncertainties are classified into random and systematic components (Renne et al., 1998). Random (or internal) errors originate from electronic noise in the ion detectors, counting statistics, and temporal variability of the blank as a result of changes in the laboratory environment. The uncertainty associated with random errors can be quantified by taking replicate measurements. The standard error of these measurements (, where σ is the standard deviation of n replicate measurements) is a measure of their precision. The standard error can be reduced to arbitrarily low levels by simply averaging more measurements. Systematic (or external) errors are those caused by uncertainty in the assumptions made to calculate a ⁴⁰Ar/³⁹Ar date from analytical data. These include the systematic effects of decay constant uncertainty, the age of the monitor, and the air ratio. In contrast with the random uncertainties, the systematic uncertainties cannot be characterized by repeat measurements, and they cannot be reduced by simple averaging.

Care must be taken when deciding which sources of uncertainty are included in the error propagation. Intersample comparisons of ⁴⁰Ar/³⁹Ar data may legitimately ignore systematic uncertainties as well as those of intercalibration factors. However, when comparing a ⁴⁰Ar/³⁹Ar date with a U/Pb, astrochronologic date, or ¹⁴C date, both random and systematic uncertainties must be considered. The conventional way to tackle both types of comparison is called “hierarchical” error propagation (Renne et al., 1998; Min et al., 2000, Koppers, 2002). Under this paradigm, the random uncertainties are processed first, and the systematic uncertainties are processed afterwards. Vermeesch (2015) showed that the internal and external errors can also be processed jointly, in matrix form. This algorithm solves the problem with hybrid error models, but it has not yet been widely adopted by the ⁴⁰Ar/³⁹Ar community.

To facilitate interpretation of ⁴⁰Ar/³⁹Ar data, we first discuss common statistical tools utilized in ⁴⁰Ar/³⁹Ar geochronology for evaluating dates and data sets. We then focus on some typical approaches for the interpretation of ⁴⁰Ar/³⁹Ar data from: (1) single-crystal fusion data sets, (2) incremental heating data sets for volcanic rocks, (3) incremental heating data sets for plutonic or metamorphic rocks, (4) provenance studies using detrital minerals, and (5) low-temperature processes. This discussion is intended to serve as a guide for the interpretation and understanding of the complexities associated with individual ⁴⁰Ar/³⁹Ar data sets.

where x_i is the i^th (out of n) dates, σ_i is the corresponding analytical uncertainty, df is the number of degrees of freedom, defined as df = n – 1, and is the weighted mean of all n dates. The definition for the MSWD of an isochron is similar but has one fewer degree of freedom (df = n – 2) and involves a few more terms to account for correlated uncertainties between the x and y variables. The following are general MSWD considerations:

• (1) If the analytical uncertainties (σ_i) are the only source of scatter between the n aliquots, and df is reasonably large (for example, n > 20), then MSWD ≈ 1 (Figs. 5A and 5B). For smaller sample sizes, the MSWD has a much wider distribution with an expected value of less than one (Wendt and Carl, 1991; Mahon 1996). The remainder of this section will assume n > 20.

• (2) MSWD values <<1 indicate that analytical uncertainties have been overestimated or have not been propagated correctly (Figs. 5C and 5D). Assigning ages to samples based on underdispersed data must be done with caution.

• (3) MSWD values considerably greater than one indicate that there is some excess scatter in the data, which cannot be explained by the assumed analytical uncertainties alone. This may reflect underestimation of analytical uncertainties, but it usually reflects the presence of some geological overdispersion affecting the data set and/or neutron fluence gradients. Possible causes of such dispersion may include the protracted crystallization history of a sample, variable degrees of inheritance, or partial loss of radiogenic ⁴⁰Ar by retrograde reactions, thermally activated volume diffusion, deformation, or chemical alteration (Figs. 5E and 5F).

where f is the degrees of freedom. Critical MSWD values were also reported in Mahon (1996). Wendt and Carl (1991) demonstrated that the expectation (or mean) value of MSWD is 1, and this is not a function of f; however, the standard deviation of the expectation value for the MSWD decreases with increasing f. A MSWD value for a data set that is greater than the critical MSWD value, calculated as above, indicates with >95% probability that there is more scatter in the data than can be accounted for by the reported uncertainties.

Data sets with MSWD ≈ 1 are not the only data suitable for publication. Trimming an overdispersed data set by selectively rejecting outliers until achieving a MSWD ≈ 1 is also ill-advised because this risks the loss of geologically valuable information and biasing the results. Outlier identification and rejection must always be accompanied by full disclosure of the specific criteria used for such evaluation, and not simply to improve the statistics of a data set. MSWD values >>1 do not necessarily indicate poor data and may simply reflect high analytical precision of the data or underestimation of analytical uncertainties. Increasingly dispersed data sets are likely to become even more prevalent in the future, as a result of the ever-increasing improvements of mass spectrometers with the potential to further increase precision of measurements. In this case, the excess dispersion can be formally assessed with a chi-square test for homogeneity, and its associated p value. However, unpowered statistical hypothesis tests (e.g., p values) have come under criticism in recent years, and scientists are increasingly advised not use them (Wasserstein and Lazar, 2016; Amrhein et al., 2019).

Dispersed data sets need to be evaluated carefully on a case by case basis, and any conclusions based on dispersed data must be made with caution. It is important to consider the potential causes (geologic, analytical, mineralogic, etc.) of the data dispersion (e.g., Verati and Jourdan, 2014; Phillips et al., 2017). In some cases, a subset of a dispersed data set can be used to assign an age for a sample given sufficient geologic context. For example, single-crystal fusion dates from a volcaniclastic layer intercalated within a fluvio-lacustrine succession along the Tiber River, Italy, showed significant dispersion (MSWD = 603; Marra et al., 2019). The volcaniclastic layer has lithologic and mineralogic characteristics that are nearly identical to another volcaniclastic layer located ∼6 km to the northwest that was dated at 327.5 ± 3.5 ka. The youngest six ⁴⁰Ar/³⁹Ar dates of the dispersed data set give a weighted mean age of 328.7 ± 1.6 ka, which led Marra et al. (2019) to conclude that the two dated volcaniclastic layers are indeed identical and have been tectonically displaced by 50 m.

When no potential sources of data dispersion can be confidently identified, it can be assumed that the excess dispersion is multiplicative and scales in proportion to the analytical uncertainty. In this case, the standard error of the weighted mean or isochron intercept may be augmented by multiplying it with the square root of the MSWD. A second option is to parameterize the overdispersion as an additive term and estimate it as a separate parameter (Vermeesch, 2018). Finally, the validity of using the MSWD value to monitor excess scatter relative to the 95% confidence interval is a function of n (Mahon, 1996). That is, for small data sets, there can be significant deviation from MSWD = 1 for data that are normally distributed at the 95% confidence interval.

Isochrons and weighted mean plots are useful for data sets that contain a relatively small number of tightly clustered dates. However, these plots are ill suited for evaluation of distributions, where ages span large time intervals (e.g., detrital or weathering geochronology). In this case, it is not so much the individual dates that contain the geologically meaningful information, but rather the full distribution of the dates. Histograms are one way to visualize such data sets. This visualization requires binning, and the number of apparent age components may vary significantly depending on the size and placement of the bins.

To address this issue, geochronologists introduced the probability density plot (PDP) as a continuous alternative to the histogram. PDPs are also referred to as a type of ideogram in the context of ⁴⁰Ar/³⁹Ar geochronology (Deino and Potts, 1991). They are generated by ranking the dates from youngest to oldest, stacking a Gaussian bell curve on each date, where the standard deviation corresponds to the analytical precision, and summing all the bell curves together to form a single continuous distribution.

We note that when the analytical uncertainty becomes very small compared to the range of dates, the PDP resembles a number of “spikes.” This trend is likely to become ever more prevalent if the trend towards increasing analytical precision continues.

An alternative to PDPs is a kernel density estimation (KDE), which uses a procedure that is broadly similar in construction to PDPs. Like PDPs, KDEs are also constructed by (1) ranking the dates in increasing order, (2) assigning a bell curve (or any other symmetric shape or “kernel”) to each date, and (3) summing all these curves to form one continuous line. However, where PDPs use the analytical precision to set the width of the kernels, KDEs do so using independent statistical means (Fig. 6; Vermeesch, 2015).

⁴⁰Ar/³⁹Ar dating of single minerals hosted in volcanic rocks, either by total fusion or incremental heating, is one way to estimate the eruption age. Single-crystal analyses are typically performed on K-rich mineral phases such as sanidine, anorthoclase, micas, or hornblende, but analysis of plagioclase or other low-K phases is possible. For pyroclastic deposits, analyses of single crystals are preferred because the crystal cargo may consist of minerals with different crystallization and/or alteration/thermal histories. For this reason, multicrystal analyses must be avoided whenever possible.

A first step toward the interpretation of a collection of single-crystal dates from a volcanic rock or tephra is to decide what value to assume for the ⁴⁰Ar/³⁶Ar initial ratio. In many cases, analysts begin with the assumption of a ratio equivalent to that of modern atmosphere and calculate what are commonly referred to as ⁴⁰Ar/³⁹Ar model dates. It is also common practice to plot all of the data on a normal or inverse isotope correlation diagram (Fig. 5) and, if the data define a robust linear relationship (as indicated by the MSWD for the isochron fit), to use the intercept to estimate an initial trapped ⁴⁰Ar/³⁶Ar ratio to use in (re)calculating model dates. The dates can then be plotted on a diagram such as that shown in Figure 7A, and a preliminary inverse-variance-weighted mean for all of the dates—as well as the MSWD for the weighted mean—can be calculated. In an ideal system, all crystals hosted in a volcanic rock will have incorporated no radiogenic or excess Ar prior to eruption due to storage at high temperatures. Therefore, the dispersion in the single-crystal ⁴⁰Ar/³⁹Ar dates for a volcanic sample is expected to reflect solely the analytical uncertainty of the mass spectrometer analyses (assuming no reactor fluence gradients, self-shielding, etc.). In this case, the weighted mean date can be calculated from the entire single-crystal data set, and its MSWD will be lower than the MSWD value deemed acceptable for the total number of analyses at 95% confidence (i.e., critical MSWD, Eq. 2).

In cases where the MSWD is less than the critical MSWD, it is reasonable to interpret the weighted mean date and its uncertainty as representative of the eruption age of the volcanic rock. However, with improved precision in ⁴⁰Ar/³⁹Ar geochronology (e.g., Fig. 2), it has become increasingly commonplace to observe more variability in single-crystal ⁴⁰Ar/³⁹Ar dates from a sample than can be explained by analytical uncertainty alone (e.g., Andersen et al., 2017; Ellis et al., 2017; Stelten et al., 2015; Rivera et al., 2016, 2018; see Figs. 7B and 7C). Under such circumstances, the MSWD calculated for the complete data set will exceed its critical threshold, and the mean for all crystals cannot be interpreted as the eruption age.

In many cases, such data sets will have distributions such as those shown in Figure 7A, with a dominant mode and a tail towards older and/or younger dates. The older single-crystal dates are most commonly interpreted to reflect excess Ar trapped within the crystals (e.g., Ellis et al., 2017) and/or the presence of antecrysts or xenocrysts (routinely diagnosed by mineral chemistry) that have not been fully degassed (e.g., Andersen et al., 2017; Rivera et al., 2016, 2018). A tail towards younger ages may represent variable partial Ar loss from the crystals or the presence of an unrecognized interference during the mass spectrometer analyses (e.g., a hydrocarbon interference may lead to anomalously high ³⁶Ar signal size and therefore a younger date; Fig. 7A). In general, greater dispersion in single-crystal dates is observed in total-fusion experiments relative to incremental heating experiments, because the latter provide an independent means of rejecting grains that display evidence for excess Ar or Ar loss, or that otherwise do not yield plateaus (cf. Rivera et al., 2016; Ellis et al., 2017). Some of the dispersion may also be attributed to flux gradients or self-shielding during sample irradiation, but these issues have yet to be fully understood.

Increased recognition of overdispersion in single-crystal data sets due to enhanced analytical precision has made interpreting the best estimate of an eruption age much more challenging than it was when methods were less precise. Approaches that appear in the literature include the following:

Method 1: Low MSWD weighted mean. This method assumes that the eruption age of the sample is best represented by a group of the youngest single-crystal ⁴⁰Ar/³⁹Ar dates, whereas older dates reflect excess Ar or undegased, inherited crystals. Here, it is assumed that argon loss and young dates due to analytical interferences do not represent significant factors. An inverse-variance-weighted mean date is calculated for the youngest n analyses that yield an MSWD below the critical MSWD. This calculation is performed by ordering the single-crystal ⁴⁰Ar/³⁹Ar dates from youngest to oldest and calculating a running weighted mean and MSWD, starting with the youngest date, until the MSWD acceptance criteria fail (e.g., Gansecki et al., 1996; Ton That et al., 2001; Stelten et al., 2015). The final weighted mean date of this young population with an acceptable MSWD is taken to represent the eruption age of the sample. As noted above, MSWD values that approach zero indicate that analytical uncertainties have been overestimated or have not been propagated correctly. Thus, low MSWD weighted mean ages ought to be used with caution unless otherwise corroborated by other geochronologic or geologic evidence.

Method 2: Weighted mean filter. This method makes the same assumptions as in method 1. This calculation is carried out by ordering the single-crystal ⁴⁰Ar/³⁹Ar dates from youngest to oldest and calculating a running weighted mean. The youngest population of ⁴⁰Ar/³⁹Ar dates, which are interpreted to represent the eruption age, is defined as that for which the difference between the weighted mean age of the youngest group and the next oldest date is greater than zero with 95% confidence (Andersen et al., 2017). One problem with methods 1 and 2 is that they produce weighted mean ages that become younger with increasing sample size.

Method 3: Normality test and goodness-of-fit parameter. This method assumes that the population of single-crystal ⁴⁰Ar/³⁹Ar dates that best represents the eruption age of the sample follows a normal distribution and that the scatter about this eruption age is dominated by analytical uncertainty. Unlike methods 1 and 2, this method does not assume that the youngest ⁴⁰Ar/³⁹Ar ages are the best measure of the eruption age. In turn, young dates, as well as old, may be excluded from the preferred weighted mean age. This calculation can be done by ordering the single-crystal ⁴⁰Ar/³⁹Ar ages from youngest to oldest and testing every combination of contiguous data to find the largest population of data that is consistent with a normal distribution and has an acceptable degree of dispersion based on the MSWD or another goodness-of-fit parameter (e.g., Jicha et al., 2016; Ellis et al., 2017). Testing for the normality of a data set can be done using a number of statistical tests (e.g., chi-squared, Shapiro-Wilk test, Kolmogorov-Smirnov test) and may include constraints on the skewness and kurtosis of the population being examined.

For the calculations presented below, we used the MSWD and the Shapiro-Wilks normality test at a probability threshold of 0.0005 and specified that the skewness must be between –0.2 and 0.2 (using the adjusted Fisher-Pearson coefficient of skewness). To illustrate the differences in these data-filtering methods, we applied each method to single-crystal total fusion data for Mesa Falls Tuff sanidine from Ellis et al. (2017) and single-crystal incremental heating data for Bishop Tuff sanidine from Andersen et al. (2017); see Figures 7B and 7C. Single-crystal ⁴⁰Ar/³⁹Ar model dates for the Mesa Falls Tuff sanidine range from 1.280 Ma to 2.052 Ma and show a large tail towards older ages. Application of the filtering methods described above yielded inverse-variance-weighted mean dates of 1.2985 ± 0.0006 Ma (n = 53/147) for method 1, 1.2957 ± 0.0008 Ma (n = 36/147) for method 2, and 1.3009 ± 0.0006 (n = 55/147) for method 3, respectively (Fig. 7B). The older date calculated via method 3 reflects the fact that the seven youngest analyses were rejected due to a nonnormal distribution. Methods 1 and 2 yielded younger dates because the youngest single-crystal dates are always included in the weighted mean. In this case, Ellis et al. (2017) noted that the inverse-variance-weighted mean date derived from method 3 (1.3009 ± 0.0006 Ma) agrees well with the zircon U/Pb data for this sample, 1.3004 ± 0.0007 Ma, and suggested that this value represents the best eruption age estimate for this sample. The seven youngest single-crystal ages that were excluded from the weighted mean may have experienced Ar loss, or the analyses may have been affected by isobaric interferences.

Bishop Tuff single-sanidine plateau dates (Andersen et al., 2017) also show a distribution with a tail towards older dates. Application of methods 1, 2, and 3 yielded inverse-variance-weighted mean dates of 765.2 ± 0.14 ka (n = 31/49) for method 1, 764.8 ± 0.17 ka (n = 25/49) for method 2, and 765.4 ± 0.13 (n = 32/49) for method 3 (Fig. 7C). The older date calculated via method 3 is due to the rejection of the two youngest analyses. Andersen et al. (2017) argued that because single-crystal incremental heating provides an independent check on Ar loss and/or young dates resulting from analytical interferences, the use of method 2 provides the most robust estimate of the eruption age for this sample. In both of the example data sets, the use of different filtering methods results in inverse-variance-weighted mean dates that differ outside of their 1σ uncertainties (Figs. 7B and 7C), highlighting the importance of the choice of data-filtering method.

Although there is no a priori way to determine which filtering method is best for a given data set, we suggest that the assumptions behind these data-filtering methods should be carefully considered before applying them. Regardless of the method chosen, we suggest that any data filtering be described in sufficient detail such that it may be reproduced by other researchers. For example, if normality tests are performed during data filtering, then it behooves the author to specify the normality test that was performed and if skewness or kurtosis constraints were employed. Finally, it is important to be consistent when selecting a filtering method for multiple volcanic samples within a single study.

Recent improvements in multicollector mass spectrometry for ⁴⁰Ar/³⁹Ar geochronology have led to ever-improving precision on ⁴⁰Ar/³⁹Ar dates and a reduction in the amount of sample required for analysis, thereby leading to the preparation of smaller and likely more homogeneous mineral or groundmass separates. The improved precision, however, has resulted in observation of degassing patterns during incremental heating experiments that are considerably more complicated than the ideal case of a flat (i.e., concordant) age spectrum. For example, a commonly observed age spectrum shape for both individual sanidine crystals and groundmass separates starts at low temperatures with older apparent ages, high K/Ca ratios, and low radiogenic ⁴⁰Ar content, followed by a decrease to younger ages that sometimes form a plateau (e.g., Fig. 8A). The older apparent ages may be the result of degassing of fluid inclusions, ³⁷Ar and/or ³⁹Ar recoil loss, or redistribution from the fine-grained secondary phases in the groundmass or fine-grained groundmass during irradiation (e.g., Turner and Cadogan, 1974; Huneke and Smith, 1976; Hall, 2014; Koppers et al., 2000; Fleck et al., 2014; Jourdan and Renne, 2013).The low-temperature heating steps likely reflect preferential degassing of potassium-rich alteration phases in groundmass or K-rich melt inclusions in sanidine. The same applies to the Cl/K ratios, provided Cd shielding has not been used during irradiation. A more robust method, involving vacuum encapsulation (Villa et al., 1983; Smith et al., 1993; Hall, 2014), allows for precise quantification of recoil losses.

In some samples, the apparent ages calculated for the initial heating steps are younger than the plateau and form a staircase upward pattern towards the plateau (Fig. 8B). This is commonly interpreted to indicate radiogenic ⁴⁰Ar loss from alteration phases degassed at low temperature, but it may also be the result of ³⁷Ar recoil (e.g., Fleck et al., 2014). If a sample records a history of brittle deformation, younger ages at low-temperature steps could reflect Ar loss associated with deformation-recrystallization. High-temperature heating steps can variously trend towards older and younger apparent ages. Degassing of clinopyroxene and plagioclase microphenocrysts within groundmass generally results in lower K/Ca ratios and younger apparent ages due to the recoil loss of ³⁷Ar from these Ca-bearing phases (Fig. 8C; Koppers et al., 2000, 2004; Singer et al., 2019), and due to shock heating in meteorite samples (Cassata et al., 2010, 2011). Progressively older apparent ages in high-temperature steps are often attributed to excess ⁴⁰Ar in the groundmass or the mineral being analyzed or recoil artifacts (e.g., Heath et al., 2018; Fig. 8D).

The ability to step heat samples is the most important attribute in ⁴⁰Ar/³⁹Ar geochronology because it can potentially evaluate underlying assumptions of the method and identify nonideal behavior. For many samples that have simple thermal and mineralogical histories, the age spectrum commonly reveals multiple steps that are concordant at 2σ, and this set of ages, deemed a plateau, yields acceptable MSWD values. We emphasize that the term “plateau” should be held in the highest regard, as it has the connotation of simple age systematics. It should only be used in cases where previously defined criteria have been met. Unless specifically stated otherwise, plateau ages are model ages that assume the trapped initial argon has an atmospheric composition or an initial composition determined by the inverse isochron approach. Numerous criteria have been put forth to evaluate age spectrum quality and to identify steps that can be combined to calculate a plateau age (e.g., Fleck et al., 1977; Sharp and Renne, 2005; Jourdan et al., 2004). These previously published plateau criteria were based on incremental heating experiments that often consisted of ∼5–10 steps. Given the fact that modern incremental heating experiments now consist of many more steps (∼15–40; Fig. 8A), we suggest that a plateau

• (1) consist of at least five or more consecutive steps that comprise at least >50% of the ³⁹Ar released;

• (2) not have a slope (i.e., the majority of consecutive plateau steps do not have ascending or descending ages; Sharp and Renne, 2005); and

• (3) have an isochron regressed through all of the plateau steps with a (⁴⁰Ar/³⁶Ar)_i that is indistinguishable from the atmospheric value at the 95% confidence level (i.e., for terrestrial samples only).

Most incremental heating experiments now yield age spectra showing some level of complexity (Fig. 8). Alternative terms have been used to define data that comprise <50% of the ³⁹Ar released, such as “pseudo-plateau” or “miniplateau.” These terms are misleading and must be abandoned because they are too closely associated with the term plateau. In Figures 8A and 8B, the spectra reveal minor amounts of discordance, but in both cases, a plateau is produced consisting of ∼65% and >90% of the ³⁹Ar released, respectively. In Figures 8C and 8D, the incremental heating experiments yielded sloping plateaus that were likely variably affected by a variety of processes, including recoil, fractionation, excess Ar, and/or thermal or chemical alteration of the mineral phases. Age spectra that do not meet nominal plateau criteria may often still contain geologically meaningful information (e.g., reheating/alteration events) and can still be discussed within the context of other geochronologic or stratigraphic data, but they are simply less reliable than their plateau counterparts. For these types of data, it is more appropriate to discuss the age of a sample with a range of dates or use the integrated age with caution.

It has also become more commonplace to take the trapped (⁴⁰Ar/³⁶Ar)_i intercept from the isochron diagram and use it to recalculate each heating step in an attempt to rectify a partially disturbed spectrum (e.g., Heizler and Harrison, 1988; Heaton and Koppers, 2019). Heath et al. (2018) observed that basaltic lavas with subatmospheric (⁴⁰Ar/³⁶Ar)_i isochron intercepts sometimes yield erroneously old apparent isochron ages, but more experiments are needed to assess this hypothesis.

For cases where the isochron has a (⁴⁰Ar/³⁶Ar)_i value greater than and not within 2σ uncertainty of the atmospheric value, the isochron gives the preferred age in most cases. Alternatively, the heating steps that originally defined a plateau can be recalculated using a supra-atmospheric (⁴⁰Ar/³⁶Ar)_i value instead of the atmospheric ratio (e.g., Heaton and Koppers, 2019), which, if applied correctly, results in a plateau age that is nearly identical to the isochron age within uncertainty, assuming the uncertainty on the (⁴⁰Ar/³⁶Ar)_i value is correctly propagated.

Thermochronology—the use of isotopic dates to trace the temperature-time histories of rocks—has become an important component of many tectonic studies (e.g., Reiners and Brandon, 2006; Hodges, 2014). Researchers have found that an abundance of well-calibrated thermochronometers, including those with moderately high closure temperatures like ⁴⁰Ar/³⁹Ar, can be coupled with other lower-temperature thermochronometers, e.g., (U-Th)/He or fission track, to offer expanded temperature-time histories.

In this equation, A is a constant dependent on the model geometry assumed to best represent ⁴⁰Ar diffusion in the mineral and approximately equals 55 for radial diffusion in a sphere, 27 for radial diffusion in a cylinder, and 8.7 for diffusion across a plane sheet. Variables D_o and E are terms from the Arrhenius equation that describes diffusivity (D) as a function of temperature, i.e., D = D_oexp(–E/RT), where E is the activation energy, D_o is a pre-exponential constant equal to D at infinite temperature (T), and R is the universal gas constant. The parameter a represents the effective dimension over which diffusive loss occurs. Finally, dT/dt is the assumed instantaneous cooling rate at the time recorded by the chronometer. This equation cannot be solved analytically for T_cb, but it is easily solved iteratively; from an initial estimate for T_cb, the equation typically converges on a final result after only a few iterations. An accessible derivation of a slightly different form of Equation 3—with a negative sign before A to account for their preferred use of a negative cooling rate—may be found in Reiners et al. (2018). Table 5 presents notional bulk closure temperatures for a variety ⁴⁰Ar/³⁹Ar chronometers for which experimental diffusion data have been published as calculated from Equation 3, assuming a cooling rate of 10 °C/m.y. (Hodges, 2014). For this table, all closure temperatures were calculated assuming the same effective diffusion dimension of 100 mm and the same cooling rate of 10 °C/m.y. to facilitate comparisons among chronometers.

Calculated values for T_cb are significantly dependent on the choice of a and dT/dt. For example, choosing a value of 500 mm instead of 100 mm for hornblende results in a 12% increase in T_cb to 570 °C. The dependence of T_cb on different values of dT/dt is somewhat less pronounced in most cases; for hornblende, holding a = 100 mm but increasing dT/dt to 50 °C/m.y. (again a fourfold increase) results in only a 6% increase in T_cb to 540 °C. However, the dependence of T_cb on dT/dt becomes more significant for cooling rates of a few degrees or less per million years, such as those that apparently prevailed in the lower and middle crust of many cratonic regions during their thermal stabilization (e.g., Blackburn et al., 2011; Hodges et al., 1994).

It is especially important to recognize that the most appropriate value of a to use for a particular dated mineral can be ambiguous. Many He and Ar diffusion studies for minerals and empirical observations suggest that half of the physical grain size is commonly the effective diffusion dimension for samples that are devoid of alteration, microfractures, and other potential fast-diffusion pathways (Anderson et al., 2019; Cassata and Renne, 2013; Flude et al., 2014; Hodges and Bowring, 1995; Kula and Spell, 2012; Skipton et al., 2017; Wartho et al., 1999). However, for deformed crystals that contain internal subgrain boundaries that may define fast-diffusion pathways (Lee, 1995) or structurally complex feldspars, a may be substantially smaller than the physical grain size would suggest (Lovera et al., 1989, 1991; Cassata and Renne, 2013). Step-heating experiments on slowly cooled K-feldspars frequently yield complex apparent ⁴⁰Ar/³⁹Ar age spectra, which can be attributed to low-temperature recrystallization (Villa, 2006) and/or the existence of multiple diffusion domains within individual crystals (Lovera et al., 1989; Zeitler, 1987). Both models imply that the nominal closure temperatures for K-feldspars listed in Table 5 are best used with caution when making geologic inferences. A better approach, provided the assumptions of the multidiffusion domain model (MDD) are fulfilled, is to use the ⁴⁰Ar/³⁹Ar step-heating data for each K-feldspar to determine Arrhenius parameters and, in conjunction with inversion of the age spectrum, to infer cooling histories over the temperature range defined by the kinetic parameters (e.g., Harrison et al., 2005; Harrison and Lovera, 2014; Lovera et al., 1991). MDD K-feldspar thermochronology has proven to be useful for examining a broad range of tectonic questions because of (1) the wide Ar closure-temperature window (∼150–350 °C) of the system, and (2) the ability to use computational modeling to understand the rate of rock cooling and/or reheating within this temperature range. Temperature must be monitored during step-heating experiments in order to retrieve the ³⁹Ar diffusion characteristics to apply in the diffusion models and to model thermal histories (Fig. 9; Lovera et al., 1993). Traditionally, diffusion experiments have been performed with a double-vacuum resistance furnace, but recently, step heating of samples has been performed using a laser with a thermocouple or optical pyrometer for temperature control (Idleman et al., 2018). There is ongoing debate on the geologic significance of K-feldspar ⁴⁰Ar/³⁹Ar release patterns (Parsons et al., 1999; Villa and Hanchar, 2013). However, it is clear from numerous applications of MDD K-feldspar thermochronology to structural problems (Batt et al., 2004; Benowitz et al., 2011), including comparisons to other thermochronometers from the same rock sample (McDannell et al., 2019), that MDD results can provide very robust regional thermal constraints. A relatively new finding that appears to show great promise for ⁴⁰Ar/³⁹Ar thermochronometry is to extend MDD-style analyses to muscovite (Harrison and Lovera, 2014; Long et al., 2018). The challenge towards taking advantage of this potential opportunity is to demonstrate that the metastability of muscovite in the temperature range of the laboratory degassing experiment does not impact negatively on determining geologically relevant diffusion parameters. Similarly, determination of diffusion parameters and closure temperatures for hydrothermal and supergene alunite may extend the use of thermochronology to sulfates in hydrothermal systems and metamorphic terrains (Ren et al., 2019).

While uncertainties regarding the most appropriate values to use for a and dT/dt, as well as the multiple domain diffusion behavior in certain samples, argue against the rigid assignment of an intrinsic T_cb to specific geochronometers, nominal values are useful guides to the interpretation of ⁴⁰Ar/³⁹Ar dates. For example, a ⁴⁰Ar/³⁹Ar date for a muscovite that crystallized as part of a prograde, amphibolite-facies metamorphic assemblage in a schist is not interpreted by this approach as the age of prograde metamorphism but instead as the approximate time of cooling of that crystal through conditions of roughly 390 °C. On the other hand, a ⁴⁰Ar/³⁹Ar date for a muscovite that grew at temperatures of ∼390 °C—maximum metamorphic conditions for many greenschist-facies samples—might be reasonably interpreted as the approximate age of muscovite crystallization and, by extension, greenschist-facies metamorphism.

The ⁴⁰Ar/³⁹Ar chronometers in Table 5 are listed in order of descending closure temperature and thus the retentivity of radiogenic ⁴⁰Ar in several important rock-forming minerals. This order suggests how ⁴⁰Ar/³⁹Ar data for different minerals might be particularly useful for specific geologic applications. For example, ⁴⁰Ar/³⁹Ar thermochronometers have traditionally been of limited use in studies of the high-temperature cooling paths of granulite-facies metamorphic terranes because the notional closure temperatures of ⁴⁰Ar/³⁹Ar thermochronometers are several hundred degrees lower than peak granulite-facies conditions. However, experimental ⁴⁰Ar diffusion data for pyroxenes (Cassata et al., 2011) imply high notional closure temperatures: 730 °C for clinopyroxene and 600 °C for orthopyroxene. Thus, as noted by Ware and Jourdan (2018), ⁴⁰Ar/³⁹Ar thermochronometry of pyroxenes may yield improved constraints on the temperature-time evolution of exhumed granulite-facies rocks. The same could be said for ⁴⁰Ar/³⁹Ar thermochronometry of the rare cyclosilicate mineral osumilite (Blereau et al., 2019), which can be found in some Mg-rich, granulite-facies metapelites, given that its closure temperature is similar to that of orthopyroxene. Detailed temperature-time paths for eclogite-facies terranes may also be improved through ⁴⁰Ar/³⁹Ar thermochronometry of pyroxenes found in mafic eclogites. A complication that arises with ⁴⁰Ar/³⁹Ar dates for minerals with high closure temperature such as pyroxene is that they can pass through multiple orogenic heating episodes without being fully outgassed, even though the peak temperature exceeds the nominal closure temperature. This phenomenon is illustrated by ages for the mica phengite in ultrahigh-pressure, low-temperature blueschists. Warren et al. (2012a, 2012b) modelled argon loss during short orogenic cycles at subduction zones, showing that it was unlikely that phengites would yield cooling ages, but they would likely retain mixed ages reflecting both prograde and retrograde paths. The same is likely to be true of pyroxene ⁴⁰Ar/³⁹Ar ages, and attention must be paid to the full thermal history of the rocks.

For many years, the hornblende ⁴⁰Ar/³⁹Ar chronometer has been used extensively to constrain ages of amphibolite-facies metamorphic events due to its relatively high closure temperature. In many studies, ⁴⁰Ar/³⁹Ar dates serve as medium-temperature anchors for low-temperature cooling histories constrained by ⁴⁰Ar/³⁹Ar mica and feldspar data, as well as (U-Th)/He and fission-track accessory mineral data. In principle, having so many ⁴⁰Ar/³⁹Ar chronometers with closure temperature estimates ranging between 300 and 400 °C (Table 5) offers the opportunity to combine their use to develop close constraints on the cooling histories of samples over that temperature interval. However, such “multichronometric” studies using ⁴⁰Ar/³⁹Ar chronometers alone are unlikely to yield satisfactory results; even if we knew values for a and dT/dt a priori, uncertainties in the diffusion parameters D_o and E based on experimental data sets are so large that they propagate into practical uncertainties in T_cb values of ±50 °C or more, leading to highly uncertain estimated temperature-time histories across such a narrow temperature interval. Better success comes from the integration of ⁴⁰Ar/³⁹Ar chronometers with (U-Th)/Pb, (U-Th)/He, and fission-track thermochronometers and thus the temperature range of an estimated temperature-time path. For example, a typical granodiorite sample might contain hornblende, biotite, K-feldspar, and plagioclase that can be dated using the ⁴⁰Ar/³⁹Ar method, but also zircon, titanite, and apatite—minerals amenable to (U-Th)/Pb, (U-Th)/He, and fission-track geochronology and thermochronology. Together, these chronometers would permit detailed tracing of the thermal history of a single granodiorite sample from the time of its emplacement to temperature of ∼70 °C (Hodges, 2014).

While many earth scientists understand the utility of ⁴⁰Ar/³⁹Ar dates for thermochronology, fewer appreciate that slowly cooled K-bearing crystals are likely to preserve intracrystalline ⁴⁰Ar diffusive loss profiles that can be used to model temperature-time paths (Hodges, 2014). Dodson (1986) showed that different positions within a cooling crystal that acts as a single diffusion domain have coordinate-specific closure temperatures different from the bulk closure temperature of the whole crystal. Dodson (1986) went on to derive an equation similar to Equation 3 with which to calculate position-dependent closure temperatures.

Studies such as those by Phillips and Onstott (1988) and Kelley and Turner (1991) have demonstrated the possibility of resolving diffusive loss profiles in minerals using a focused laser. For example, Kelley and Turner (1991) showed that hornblende grains found in the Giants Range Granite of northern Minnesota in the United States had lost Ar as a consequence of reheating due to the intrusion of a much younger gabbro nearby. The existence of “closure profiles” in slowly cooled minerals as predicted by Dodson (1986) was confirmed a few years later through laser spot fusion studies of (001) cleavage surfaces in slowly cooled micas from the New England Appalachians and the Proterozoic orogen of the southwestern United States (Hames and Hodges, 1993; Hodges and Bowring, 1995; Hodges et al., 1994). The results were used to make general inferences about the cooling histories of the micas over the core-to-rim closure interval. However, detailed mapping of intracrystalline ⁴⁰Ar distributions was not possible with the laser technologies used because of collateral heating of the sample outside the laser target area. A major advancement in spatial resolution accompanied the development of UVLAMP facilities (Kelley et al., 1994). With increasing use of ultraviolet lasers for very high-resolution apparent-age mapping, it is possible to build more detailed models of cooling histories, while also learning the limitations of conventional thermochronology. For example, while classical thermochronology is predicated on the notion that the region surrounding a crystal is essentially an infinite sink for ⁴⁰Ar lost from a sample by diffusion, many studies—particularly studies of polymetamorphic samples—are now finding clear evidence for inward diffusion of excess ⁴⁰Ar along crystal margins (e.g., McDonald et al., 2018; Pickles et al., 1997; Warren et al., 2011, 2012b). Laser microprobe studies are confirming that other processes in nature, such as thermally activated volume diffusion, recrystallization due to changing thermal regimes, deformation, partial melting, and hydrothermal alteration, influence dates recorded by individual minerals collected from orogenic systems (e.g., Cosca et al., 2011; McDonald et al., 2016; Mulch et al., 2005; Mulch and Cosca, 2004; Putlitz et al., 2005; Warren et al., 2012a).

⁴⁰Ar/³⁹Ar geochronology and thermochronology method on detrital minerals has been used for decades to constrain maximum deposition ages (MDA), sediment provenance, and sedimentary basin thermal histories (Harrison and Be, 1983; Renne et al., 1990; Copeland and Harrison, 1990; Heizler and Harrison, 1991; Pierce et al., 2014; Mulder et al., 2017; Benowitz et al., 2019). Until recently, data collection for these detrital mineral studies was time- consuming because of the slow data acquisition on single-collector mass spectrometers. With the augmentation of multicollector instruments that provide rapid analyses at high precision, detrital mineral studies using the ⁴⁰Ar/³⁹Ar method now have tremendous potential. For the more widely applied U-Pb detrital zircon chronometer, there are at least 10 different methods used to calculated MDAs, which vary in accuracy depending on age population sample size and the controlling geologic process (e.g., tectonic or sedimentary). For a recent detailed review of MDA determinations, see Coutts et al. (2019).

In general, there is no uniform method to calculate an MDA for all data sets, and thus a case-by-case approach seems warranted. Multiple individual detrital dates that form discrete age populations are always desirable, but they are not necessarily required. A low n population can hold valuable and robust MDA and provenance information and should not be discounted based solely on the number of analyses.

Because of their relatively common occurrence in many crystalline and volcanic rocks, the ⁴⁰Ar/³⁹Ar ages of individual detrital hornblende grains in marine sediment cores offshore from current and past ice sheets can provide powerful constraints on the locations from which icebergs calved off ice-sheet margins, and thus they can provide evidence for unstable sectors of past ice sheets. Several studies have used this approach both in the North Atlantic region (for an overview, see Hemming, 2004) and around Antarctica. Uncertainties about how debris gets incorporated into flowing ice and transported, as well as about processes near the terminus of the ice sheet, mean that the interpretations of ice-sheet history from this approach are qualitative. (The processes and approaches to studying glacigenic sediments in Antarctica were reviewed by Licht and Hemming [2017] and Cook et al. [2017].) However, the occurrence of large amounts of ice-rafted detritus (IRD) with provenance requiring long-distance transport requires the coincidence of dramatic iceberg production, extreme sediment entrainment, and increased winds and surface current velocities to move the icebergs more quickly, or cold currents to limit iceberg melting (Cook et al., 2014). All these factors that enhance the abundance of IRD in marine sediments are climate sensitive.

An example of the application of ⁴⁰Ar/³⁹Ar detrital hornblende provenance from Antarctica comes from Ocean Drilling Program (ODP) Site 1165 off Prydz Bay (Fig. 10). A survey of proximal sediment cores around Antarctica (Fig. 10) revealed that there is a distinctive age range on the Wilkes Land margin (the Australian conjugate margin to Antarctica; Roy et al., 2007; Pierce et al., 2011, 2014). At Site 1165, variability in the proportion of locally derived ca. 500 Ma hornblendes and distantly derived ca. 1200 Ma hornblendes (Cook et al., 2014) revealed episodes of large increases of icebergs from the Wilkes Land margin (Williams et al., 2010; Cook et al., 2014) in the late Pliocene. Further, the ⁴⁰Ar/³⁹Ar ages of hornblende and biotite from dropstones found in the Miocene section of Site 1165 also revealed significant occurrences of Wilkes Land–derived icebergs (Pierce et al., 2014).

Detrital sanidine geochronology has the potential for utilization for many Phanerozoic sedimentary deposits (Copeland and Harrison, 1990; Chetel et al., 2011). Recent applications have mostly focused on Paleocene/Late Cretaceous chronostratigraphic studies and river terrace dating in the southwest United States (Hereford et al., 2016; Karlstrom et al., 2017; Leslie et al., 2018a, 2018b; Aslan et al., 2019; Walk et al., 2019). The power of the method lies in the robustness of sanidine to produce ultraprecise and accurate dates by single-crystal total fusion. Additionally, high throughput is accomplished by multicollection mass spectrometry, where about 200 grains can be dated in ∼24 h. This does not reach the throughput of detrital zircon analyses, but sanidine dates are typically 100× more precise than detrital zircon dates, allowing discrete identification of source calderas (e.g., Hereford et al., 2016; Karlstrom et al., 2017). By specifically choosing the sanidine from the bulk K-feldspar population, the chances of finding grains that are subequal to sediment deposition ages are greatly enhanced, especially compared to detrital zircons that are recycled multiple times from older rocks into younger sediments. These young sanidine populations found in terrace deposits of western U.S. river systems are the result of numerous large and young volcanic systems such as Yellowstone and Long Valley. The fact that silicic volcanism has occurred nearly continuously in the western United States during the Cenozoic bodes well for finding juvenile sanidines in most Cenozoic sedimentary rocks and thus makes detrital sanidine ⁴⁰Ar/³⁹Ar dating a potential breakthrough method for chronostratigraphic studies in volcanically active areas. Additionally, Paleozoic and Mesozoic sanidine is found in young sedimentary rocks and thus indicates great potential to apply detrital sanidine geochronology to older systems.

⁴⁰Ar/³⁹Ar dating studies of individual detrital white mica grains are commonly used to track sediment transport during active mountain building. Their resistance to grain-size reduction during erosion and transport, and their platy shapes, which enhance their transport in rivers, have led to their use in provenance studies. Individual grain ⁴⁰Ar/³⁹Ar ages record both midcrustal closure ages (e.g., Carrapa et al., 2003) and (when combined with the age of the enclosing sediment) lag time, indicative of the speed of sediment transport from erosive source to final deposition site (e.g., Szulc et al., 2006). Although the approach is not new (Kelley and Bluck, 1992), it became more commonly used when automated laser systems were able to measure the ⁴⁰Ar/³⁹Ar ages of tens to hundreds of individual grains. The measurements are commonly combined with geochronology of other detrital minerals such as U/Pb of zircon and rutile and apatite fission-track dating (e.g., Najman et al., 2019) to provide an integrated and powerful approach to understanding sediment transport and active orogenic processes.

⁴⁰Ar/³⁹Ar geochronologic analysis of minerals formed at low temperatures can provide age constraints on the formation of soils, weathering profiles, and caves (e.g., Polyak et al., 1998); it can also provide age/rate constraints on landscape evolution (Vasconcelos et al., 1992; Vasconcelos, 1999) along with shallow-crustal faulting (e.g., van der Pluijm et al., 2001; Yun et al., 2010; van der Pluijm and Hall, 2015) and the timing of mineralization (Harbi et al., 2018).

Fault activity dating relies on analysis of either bulk aliquots of the clay gouge (e.g., illite) from fault rocks (e.g., van der Pluijm and Hall, 2015, and references therein), in situ measurement of fault-zone vein material such as pseudotachylyte (e.g., Kelley et al., 1994) or low-temperature strain fringes (e.g., Sherlock et al., 2003), or precipitated and/or recrystallized minerals during fault fluid flow (Davids et al., 2018). Fault gouge clay is thought to be a mixture of two populations: a detrital (2M₁ polytype) wall-rock population, and an authigenic (1 M or 1M_D polytype) population formed in the brittle zone coeval with faulting (Vrolijk and van der Pluijm, 1999; Yan et al., 2001; Haines and van der Pluijm, 2008). Distinction between these two populations is achieved by separating clay gouge into three of four size fractions (<0.02 μm to <2 μm) and analyzing each by X-ray diffraction to determine the crystalline size and diagenetic grade (Środoń, 1980; Reynolds and Reynolds, 1996). Either K-Ar or encapsulated ⁴⁰Ar/³⁹Ar analysis is subsequently performed on each aliquot, with the resulting ages forming a mixing line between the fine-grained authigenic population (i.e., the age of the fault) and the relatively coarser detrital population (Fig. 11). This method, called the illite age analysis (IAA), has been routinely applied to clay gouge of brittle fault rocks (e.g., van der Pluijm and Hall, 2015) along with hydrothermally produced clay (Hall et al., 1997, 2000). For detailed reviews of K-Ar and ⁴⁰Ar/³⁹Ar dating of clay minerals see Clauer et al. (2012) and Clauer (2013). Low-temperature minerals may be very fine grained (micro- to cryptocrystalline) with average grain thicknesses far smaller than the average recoil distance (Turner and Cadogan, 1974; Onstott et al., 1995). This makes quantification of potential ³⁹Ar and ³⁷Ar recoil from these phases extremely important, as up to 30% ³⁹Ar loss is possible (Hall, 2014). In fine-grained clay minerals, the inevitability of recoil is overcome by encapsulating samples in evacuated fused silica vials prior to irradiation. After irradiation, vials are then cracked or lased within an ultrahigh-vacuum system, and the recoil-lost Ar can be accounted for by mass spectrometry analysis prior to incremental heating of the sample (Hess and Lippolt, 1986; Foland et al., 1992; Smith et al., 1993; Onstott et al., 1995).

Weathering geochronology relies primarily on incremental heating ⁴⁰Ar/³⁹Ar dating of K-bearing Mn oxides, particularly cryptomelane and hollandite, and the alunite-group sulfates alunite and jarosite (Vasconcelos, 1999). The ⁴⁰Ar/³⁹Ar geochronologic method applied to weathering minerals faces some of the same challenges encountered in other applications of the ⁴⁰Ar/³⁹Ar method, such as partial argon loss by diffusion or alteration, extraneous argon hosted in mineral contaminants, etc. Weathering geochronology, however, also suffers from a series of challenges particular to the application. For example, some supergene minerals, such as Mn oxides, may form by colloform growth, where fine-scale (∼20-μm-wide) mineral layers precipitate concentrically and progressively through time. A single 1 mm fragment of cryptomelane may contain 50 distinct mineral precipitation events, spanning in excess of 1 m.y. (Vasconcelos et al., 1992; Hénocke et al., 1998). Incremental heating analysis of these phases invariably produces ascending or descending apparent age spectra, depending on the relative Ar retentivity of the various growth bands. Improvements in mass spectrometry make these age progressions more noticeable, and suitable analytical and statistical approaches for retrieving mineral precipitation ages from these phases are required. For example, in situ dating with laser microprobes may resolve ages of precipitation at the microband scale. Minerals precipitated at low temperatures may also be extremely fine grained and suffer from the recoil effects discussed above, and so quantification of potential losses is necessary (Ren and Vasconcelos, 2019a). Finally, minerals generated by low-temperature water-rock interaction may persist on the surface of Earth (e.g., Landis et al., 2005) or Mars for protracted periods of time. Measurements of diffusion parameters and closure temperatures for these phases are needed to determine if they can indeed remain closed to Ar at surface temperatures at billion-year time scales (Kula and Baldwin, 2011; Ren and Vasconcelos, 2019b). Challenges in determining diffusion parameters for hydrous phases include a lack of information on their thermal behavior during heating in vacuum (Gaber et al., 1988; Lee et al., 1991) and the possibility that Ar is released during phase transformation and not by volume diffusion (Vasconcelos et al., 1995). Combining high-resolution ⁴⁰Ar/³⁹Ar geochronology with mineralogical approaches suitable for studying mineral transformation permits the mechanisms of Ar release to be determined and the temperature windows when volume diffusion controls noble-gas release to be identified (Ren and Vasconcelos, 2019b).

The impact of the improved sensitivity and/or higher mass resolution of multicollector mass spectrometers has been overwhelmingly positive for ⁴⁰Ar/³⁹Ar geochronology. However, with higher precision come new challenges. As noted in the previous sections, numerous recent ⁴⁰Ar/³⁹Ar studies of volcanic sanidine and other K-bearing minerals have yielded a large range in dates with overdispersion akin to that observed in many U-Pb zircon studies. To fully understand the sources of the overdispersion in ⁴⁰Ar/³⁹Ar dates, to improve the accuracy of the ⁴⁰Ar/³⁹Ar method, and to make more informed decisions regarding the age of a sample, developments must be made in the following areas:

(1) Nuclear reactions: Part of the overdispersion in ⁴⁰Ar/³⁹Ar dates is likely linked to processes that occur in the reactor during irradiation. Studies similar to those of Rutte et al. (2015, 2019), which are focused on careful characterization of fluence gradients, the effects of self-shielding, and interfering reactions, are highly desirable. It is important to better understand how each of these parameters changes as a function of irradiation time and position in the reactor.

(2) Calibration: The accuracy of ⁴⁰Ar/³⁹Ar dating is ultimately limited by uncertainties in the ⁴⁰K decay constants and the isotopic composition of standards. These two variables are often collectively conflated with the ages of standards, which are dependent on both. Efforts to improve these sources of uncertainty are ongoing, including the intercalibration with the U/Pb system as described by Renne et al. (2010, 2011). An ongoing effort aims to populate a so-called R-matrix (e.g., Niespolo et al, 2017), consisting of intercalibration factors between standards defining a geometric age progression. Plans to populate an R-matrix in conjunction with an initiative to improve the intercalibration approach of Renne et al. (2010, 2011), involving multiple ⁴⁰Ar/³⁹Ar and U/Pb laboratories, were adopted at an Earthrates workshop in 2018, and this work is ongoing as of this writing.

(3) Ar diffusion kinetics: As noted by Reiners et al. (2018), one of the remaining challenges for ⁴⁰Ar/³⁹Ar geochronology is to improve our understanding of the mechanism(s) for incorporation, uptake, and retention of both radiogenic and nonradiogenic Ar by various materials. Andersen et al. (2017) suggested that production of ⁴⁰Ar* in sanidine may outpace diffusive loss in a magma at temperatures less than 475 °C, and that crystals stored at 600 °C could retain pre-eruption ages for several millennia. However, these suggestions were based on theoretical modelling. Additional studies of Ar inheritance/uptake (e.g., Singer et al., 1998; Renne et al., 2012) on a variety of K-bearing minerals are needed to address this issue.

(4) ⁴⁰Ar/³⁹Ar petrochronology: Petrochronology is broadly defined as the pairing of isotopic dates with complementary morphological, elemental, or isotopic data from the same volume of sample aliquot (e.g., Schoene et al., 2010; Kylander-Clark et al., 2013, Kohn et al., 2017). The coupled compositional data can further improve the understanding (e.g., petrologic fingerprinting, robust filtering of antecrysts) of isotopic dates, allowing for more advanced age interpretations. One of the most widely employed minerals utilized in U/Pb petrochronology is zircon, because it can persist through multiple igneous events spanning a wide range of pressures and temperatures, and it often grows in response to changes in these parameters. Although more challenging for noble gases, comparable petrochronologic approaches could be employed on K-bearing minerals for ⁴⁰Ar/³⁹Ar analysis (e.g., Ellis et al., 2017).

(5) ⁴⁰Ar/³⁹Ar analysis of nontraditional phases: Recent advances in our understanding of ⁴⁰Ar diffusion in minerals not traditionally used in ⁴⁰Ar/³⁹Ar chronometry, coupled with analytical advances that permit analysis of minerals that are poor in potassium, are rapidly expanding the spectrum of geologic questions that can be addressed. For example, ⁴⁰Ar diffusion data for pyroxenes (Cassata et al., 2011) provide new opportunities to use these minerals for the ⁴⁰Ar/³⁹Ar dating of mafic and ultramafic rocks (Ware and Jourdan, 2018; Konrad et al., 2019; Zi et al., 2019) and may provide more robust indications of the crystallization ages for weakly metamorphosed or hydrothermally altered samples than more familiar ⁴⁰Ar/³⁹Ar chronometers. The ⁴⁰Ar/³⁹Ar analyses of K-rich metasomatic and hydrothermal alteration phases (e.g., alunite, jarosite; Vasconcelos et al., 1994; Ren and Vasconcelos, 2019b) and ⁴⁰Ar/³⁹Ar dating of fluid inclusions via mechanical crushing (e.g., Xiao et al 2019) have become more commonplace.

The abundance of potassium in Earth’s crust (several weight percent) makes a large variety of rock-forming K-bearing phases suitable for ⁴⁰Ar/³⁹Ar dating, continuing to ensure the versatility and relevance of this dating technique to a broad range of geologic disciplines. The diversity of data sets produced, and the variety of applications utilized in ⁴⁰Ar/³⁹Ar geochronology are dependent on the geologic question of interest, leading to different approaches and methods of data interpretation. In this contribution, we have highlighted strategies for the interpretation of several different types of ⁴⁰Ar/³⁹Ar data sets that will continue to evolve as analytical techniques become more advanced. To ensure that both ⁴⁰Ar/³⁹Ar specialists and a variety of end-users can fully evaluate ⁴⁰Ar/³⁹Ar data sets, the full spectrum of isotopic abundance measurements, analytical procedures, monitor ages and constant values, metadata, and geologic context are required to be reported by FAIR standards. Compliance of ⁴⁰Ar/³⁹Ar data sets to the FAIR principles requires community agreement about (1) a common language with which to describe the data, and (2) a common file format that is readable by both humans and computers. In this contribution, we deliver both with the guidelines set forth in Table 4 (see also Supplementary Material DR1). Thus, ⁴⁰Ar/³⁹Ar data maintain viability and longevity both within and outside the literature, enabling interdisciplinary usage and more robust science.

This work was funded in part by a National Science Foundation EARTHCUBE grant, EAR-1740694. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. government. We appreciate constructive comments from Bob Fleck, Jim Ogg, and one anonymous reviewer.