Neutron-induced 37Ar recoil ejection in Ca-rich minerals and implications for 40Ar/39Ar dating

Abstract The 40Ar/39Ar dating technique requires the transformation of 39K into 39Ar by neutron activation. Neutron activation has undesirable secondary effects such as interfering isotope production, and recoil of 39Ar and 37Ar atoms from their (dominant) targets of K and Ca. In most cases, the grains analysed are large enough (>50 μm) such that the amount of target atoms ejected from the grains is small and has a negligible effect on the ages obtained. However, increasing needs to date fine-grained rocks requires constraining, and in some cases correcting for, the effect of nuclear recoil. Previous quantitative studies of recoil loss focus mostly on 39Ar. However, 37Ar loss can affect the ages of Ca-rich minerals via interference corrections on 36Ar (and, to a lesser extent, 39Ar), yielding lower 40Ar*/39ArK and, thus, an age spuriously too young. New results focused on 37Ar recoil by measuring the apparent age of multi-grain populations of Ca-rich minerals including Fish Canyon plagioclase (FCp) and Hb3gr hornblende, with discrete sizes ranging from 210 to <5 µm. We use previous result on sanidine grains to correct for the 39Ar recoil loss. For the finest fractions, FCp and Hb3gr apparent ages are younger than the 39Ar recoil-corrected ages expected for these minerals, with a maximum deviation of −40% (FCp) and −21% (Hb3gr) reached for grains below 5 μm. We calculate 37Ar-depletion values ranging from approximately 30 to 91% and from approximately 28 to 98% for plagioclase and hornblende, respectively. This results in x0 values (mean thickness of the partial depletion layer) of 3.3±0.4 μm (2σ; FCp) and 3.6±1.4 μm (Hb3gr), significantly higher than suggested by current models. The reason for the substantial 37Ar loss is not well understood, but might be related to the radiation damage caused to the mineral during irradiation. x0 (39Ar) and x0 (37Ar) values obtained in this study, along with crystal dimensions, can be used for correcting 40Ar/39Ar ages from 39Ar and 37Ar recoil loss. We also discuss the relevance of our results to vacuum-encapsulation studies and isotopic redistribution in fine-grained minerals. Supplementary material: Annex 1, 2 and 3 are available at www.geolsoc.org.uk/SUP18610. Annex 1 and 2: Raw argon data corrected for blank, mass discrimination and radioactive decay for Fish Canyon plagioclase (Annex 1) and Hb3gr hornblende (Annex 2). Annex 3: Step-heating 40Ar/39Ar age spectra for FCp (Fig. A3.1) and Hb3gr (Fig. A3.2).


39
Ar irradiation-induced recoil The 40 Ar/ 39 Ar dating technique is one of the most trusted dating techniques in the geological community. One of the downsides of 40 Ar/ 39 Ar dating, however, is the necessity to bombard 39 K with fast neutrons to convert the former into 39 Ar via the reaction ( 39 K(n, p) 39 Ar). This reaction has an undesirable effect as it recoils the daughter atom over a short distance (Turner & Cadogan 1974;Foland et al. 1984). This effect is well known and has been studied over more than three decades through experimental measurements (e.g. Turner & Cadogan 1974;Hess & Lippolt 1986;Villa 1997;Paine et al. 2006;) and theoretical modelling (Onstott et al. 1995;Renne et al. 2005). In theory, the effect of 39 Ar recoil on 40 Ar/ 39 Ar ages becomes noticeable when the grains analysed are smaller than approximately 50 mm (e.g. Paine et al. 2006). 39 Ar recoil is responsible for the ejection of 39 Ar out of the grains, yielding spuriously older ages, and/or 39 Ar redistribution within the lattice of the grain, yielding complex age spectra. 39 Ar recoil makes dating fine-grain material, such as cryptocrystalline rocks, altered minerals and clay material, a challenge (e.g. Foland et al. 1993;Hall et al. 1997;Haines & van der Pluijm 2008).
In order to quantify recoil, Turner & Cadogan (1974) introduced the x 0 value, which corresponds to the thickness of the partial depletion layer surrounding the grain affected by recoil ejection loss. A similar method of quantifying recoil has been proposed by  with the d 0 value; d 0 is the thickness of the nominal outer boundary layer completely depleted by recoil loss and is represented as a virtual 0-concentration layer in the outermost part of the grain. The benefit of d 0 over x 0 is that the former allows the calculation of the proportion of 39 Ar lost for any size fraction and mineral shape directly. A relationship between the two values is given by: Experimental and theoretical studies suggest a mean thickness of the partial depletion layer (x 0 ) of approximately 0.08 mm (e.g. Turner & Cadogan 1974;Onstott et al. 1995) for silicates. This value corresponds to a mean recoil distance for the 39 Ar atoms of approximately 0.16 mm, with values ranging from 0.14 to 0.18 mm depending on the mineral compositions (Renne et al. 2005). More recently, Paine et al. (2006) and  directly measured the recoil-induced loss in biotite and sanidine grains, with a size ranging from about 210 to ,5 mm. These studies showed that the loss effect is dependent on the mineral analysed. The x 0 value of 0.070 + 0.024 mm measured for sanidine is in excellent agreement with previous estimations. The x 0 value of biotite is about an order of magnitude higher than sanidine, with a x 0 value of 0.92 + 0.12 mm (cf. discussion in . A comprehensive description of the 39 Ar recoil effect is given, for instance, by Onstott et al. (1995), Renne et al. (2005) and .

The specific case of 37 Ar recoil
One overlooked effect of the neutron activation is the recoil of 37 Ar (e.g. Jourdan et al. 2007 and references therein). 37 Ar is produced from calcium by the reaction [ 40 Ca(n, a) 37 Ar]. 37 Ar Ca is unstable and decays with a half-life of 35.1 days (Renne & Norman 2001). Monitoring the 37 Ar is crucial in Ca-rich samples as it allows for the correction for Ca-induced interferences on 36 Ar produced by [ 40 Ca(n,na) 36 Ar] and 39 Ar [ 42 Ca(n, a) 39 Ar]. ( 36 Ar/ 37 Ar) Ca is constant for a given neutron energy spectrum as both activation products derive from the same Ca isotope ( 40 Ca), whereas ( 39 Ar/ 37 Ar) Ca may vary between samples due to small enrichments of 40 Ca* in old, K-rich samples.
Fortunately the latter effect is negligible in all but extreme cases. Values of ( 39 Ar/ 37 Ar) Ca and ( 36 Ar/ 37 Ar) Ca of (7.60 + 0.09) × 10 24 and (2.70 + 0.02) × 10 24 , respectively, for the TRIGA reactor (Oregon State University, USA) have been determined reproducibly for over more than a decade (Renne et al. 2005). These ratios are obtained by using reference material usually irradiated along with the standards and samples. The assumption is made that all the 37 Ar is derived from calcium.
The 39 Ar K corrected for the 39 Ar Ca contribution is given by: 39 Ar K = 39 Ar m − 37 Ar Ca 39 Ar 37 Ar Ca (2) where 39 Ar K is the 39 Ar produced from 39 K, 39 Ar m is the total 39 Ar measured, and 37 Ar Ca is the total 37 Ar raw measured and decay-corrected back to the time of irradiation. ( 39 Ar/ 37 Ar) Ca is the production ratio determined from irradiated standard materials.
The 36 Ar atm is corrected for the 36 Ar Ca contribution and is particularly important for the correction on trapped atmospheric argon given by the following combined equation: 40 where 40 Ar* is the radiogenic 40 Ar, m denotes measured, ( 40 Ar/ 39 Ar) K is the production ratio of K and ( 40 Ar/ 36 Ar) atm is the argon atmospheric composition. During this study, we used a value of 295.5 (Nier 1950) in our calculations (mass spectrometer discrimination and air corrections). We note that a more accurate value of 298.6 + 0.3 has recently been determined by Lee et al. (2006), but using either value will have no influence on the results of our experiments .
( 36 Ar/ 37 Ar) Ca is the production ratio of Ca. Based on preliminary recoil-experiment results on a plagioclase -sanidine mixture,  suggested that 37 Ar recoil effects might be much more important than their 39 Ar counterparts for very fine-grain Ca-rich material, and might bias the age towards younger ages through interference correction disturbances. In addition, they showed that the Q value (energy measurement) of 1.7483 MeV involved in the 40 Ca(n, a) 37 Ar nuclear reaction indicates that this reaction is much more prone to recoil than the 40 Ca(n, na) 36 Ar reaction, with a Q value of 26.9912 + 0.0005 MeV (see the values compiled by Renne et al. 2005). The decoupling of the 37 Ar Ca and 36 Ar Ca concentration within the grain due to ejection loss of 37 Ar Ca by recoil will, therefore, produce spurious corrections to the 40 Ar*. Equations (2) and (3) show that 37 Ar recoil loss will induce an anomalously low 40 Ar*/ 39 Ar K ratio and, thus, bias the age towards younger values.
Here, we carried out 40 Ar/ 39 Ar measurement on Ca-rich minerals to test the effect of the 37 Ar recoil loss on 40 Ar/ 39 Ar ages. We studied multi-grain aliquots of hornblende and plagioclase with discrete sizes ranging from 210 to ,5 mm, and we calculated the d 0 and x 0 values of 37 Ar for these two minerals.

Fish Canyon plagioclase (FCp)
FCp comes from the same tuff as widely used Fish Canyon sanidine (FCs) standards (e.g. Renne et al. 1998). The plagioclase grains are slightly zoned and have a homogenous composition of An33+1 (e.g. Johnson & Rutherford 1989), although some An 60 zones have been detected (Bachmann et al. 2002). The plagioclase has a CaO and K 2 O mean composition of 6.60 wt% and 0.79 wt%, respectively, and a Ca/K atomic ratio of approximately 7 (Johnson & Rutherford 1989). Recent 40 Ar/ 39 Ar measurements by Bachmann et al. (2007) yielded an apparent plateau age of 28.26 + 0.20 Ma (2s) and an apparent total fusion mean age of 28.31 + 0.22 Ma (n ¼ 3), relative to FCs at 28.02 Ma (Renne et al. 1998) and using the decay constants of Steiger & Jäger (1977). However, these ages were interpreted as reflecting minor inherited 40 Ar* in FCp and not the true age of the plagioclase and Fish Canyon tuff eruption. As a side product of this study, we have measured the age of FCp relatively to FCs. We used 10 multi-grain aliquots of the three coarsest plagioclase fractions, with grains ranging between .150 and 85 mm (n ¼ 10). These grain sizes are considered large enough to remain unaffected by the effect of recoil loss (Paine et al. 2006;). The 10 FCp aliquots yielded apparent ages ranging from 27.83 + 0.26 to 28.12 + 0.25 Ma (2s). These data are largely concordant within error, with a MSWD of 0.46 and P of 0.90, and yield a weighted mean age of 28.00 + 0.08 Ma (2s), indistinguishable from the age of the FCs monitor. Interestingly, our particular batch of FCp does not contain any inherited 40 Ar* compared to FCp investigated by Bachmann et al. (2007), and shows that, in this case, plagioclase and sanidine both record the age of the Fish Canyon tuff eruption.
Using the recently published value of the K decay constants (Renne et al. , 2011 yields an absolute age of 28.29 + 0.08 Ma. Nevertheless, the accurate age of FCp is not essential for this study as the ages obtained for the various fractions is normalized to the mean age obtained for the three coarser fractions, and only the departure from this baseline value will be of interest to study recoil effects.

Hb3gr hornblende
The Hb3gr hornblende comes from the Lone Grove pluton (Texas, USA) and is used as a fluence monitor for dating samples generally older than few hundred million years (e.g. Zartman 1964;Turner et al. 1971). The Hb3gr standard has been selected in this study as the hornblende shows a homogenous chemical composition with constant K 2 O (1.46 + 0.06 wt%) and CaO (10.49 + 0.22 wt%) values, Ca/K ratio (6.19 + 0.25)  and is homogenous in age at the single-grain level, with a good reproducibility from grain to grain and with a F value ( 40 Ar*/ 39 Ar K ) mean standard deviation of 0.49%. Hb3gr yielded a 40 Ar/ 39 Ar age of 1074 + 11 Ma (2s; Jourdan et al. 2006) using the decay constant of Steiger & Jager (1977) and relative to FCs at 28.02 Ma. The adopted age is in agreement with a primary K/Ar age of 1072 + 14 Ma (Turner et al. 1971). As for FCs, the apparent age of the Hb3gr standard has been recently revised using a new set of decay constants  and has an absolute age of 1081.4 + 2.2 Ma, but, as explained for FCp, this is not directly relevant to this study.

Sample preparation
FCp comes from a 250-500 mm plagioclase separate (BYO-Nov97) isolated during the initial preparation of the FC sanidine standard at the Berkeley Geochronology Center, using heavy liquids. Plagioclase grains were further hand-picked, using a binocular microscope, in order to select the more transparent and alteration-and inclusion-free grains. To obtain a pure plagioclase (sanidine-free) fraction, we further picked the plagioclase in clove oil (nominal refractive index of 1.535) under plane polarized light. Under clove oil, plagioclase is easily distinguished from sanidine by using the Becke line test. The plagioclase grains were leached in dilute HF acid (2N) for 5 min and rinsed in distilled water for 20 min. We used a total of 400 mg for this experiment.
The hornblende grains come from a cleaned version of the original Hb3gr provided by C. Roddick and named PP-20. The grains range in size from 200 to 250 mm. White inclusions with an age approximately 7.5% younger (c. 990 Ma) than the nominal age of Hb3gr have been reported by Zartman (1964). However, the inclusion-bearing grains were further removed by stringent handpicking.
Both FCp and Hb3gr grains were crushed and sieved in discrete size fractions ranging from 150 to ,5 mm and from 250 to ,5 mm for plagioclase and hornblende, respectively. Below 50 mm, sieving was performed in alcohol to facilitate percolation of the grains through the sieve-cloth. All FCp fractions were analysed as multi-grain aliquots, whereas Hb3gr grains were analysed as single grains from 250 to 150 mm, and as multigrains below 150 mm to obtain sufficiently large Ar ion beams for optimal precision in the measurement of Ar isotopes. For Hb3gr, each sieved fraction was further immersed in heavy liquid with a density of 3 g/cm 3 in order to get rid of potential microcline inclusions (i.e. density of 2.6 g/cm 3 ) not removed by hand-picking. Each fraction of FCp and Hb3gr includes between two and eight aliquots each, with a variable volume of material depending on the nature of the experiment.

Irradiation
Two irradiations of 10 h (irr. 346-FJ; FCp) and 90 h in duration (irr. 342-FJ; Hb3gr) were performed in the Cd-shielded (to minimize undesirable isotopic interference reactions caused by thermal neutrons) CLICIT facility of the TRIGA reactor at the Oregon State University, USA. For irradiation 346-FJ and 342-FJ, sample batches were loaded into wells within, respectively, three and two aluminium discs of 1.9 cm diameter and 0.3 cm depth. Each batch was loaded separately in onesix individual wells. FCs grains (250 -500 mm) were used as the neutron fluence monitor and were loaded in five wells bracketing the fractions of FCp. Grains of Hb3gr (210 -250 mm) were loaded into five wells bracketing the various fractions of Hb3gr. Each of the discs was wrapped in Al-foil and placed in a silica tube. Each of the tubes was sealed at atmospheric pressure and sent for irradiation with other unknown samples.
We calculated the J values relative to FCs at 28.02 Ma (Renne et al. 1998) and Hb3gr at 1072 Ma (Turner et al. 1971), and used the decay constants of Steiger & Jager (1977). The J values consist of the weighted mean and standard deviation of J values from bracketing wells across the entire disc. The J values of disc 1 and 2 vary from 0.002652 + 0.000004 to 0.002656 + 0.000004 for the FCp experiment, and the J values of the three discs vary from 0.023654 + 0.000059 to 0.023690 + 0.000065 for the Hb3gr experiment. The correction factors for interfering isotopes correspond to the weighted mean of 10 years of measurements of K -Fe and CaSi 2 glasses, and CaF 2 fluorite, in the TRIGA reactor: they are ( 39 Ar/ 37 Ar) Ca ¼ (7.60 + 0.09) × 10 24 ; ( 36 Ar/ 37 Ar) Ca ¼ (2.70 +0.02) × 10 24 ; and ( 40 Ar/ 39 Ar) K ¼ (7.30 + 0.90) × 10 24 .
Analytical technique 40 Ar/ 39 Ar analyses were performed at the Berkeley Geochronology Center between 5 and 6 months after irradiation. The grains were degassed using a CO 2 laser, and the gas was purified in a stainless steel extraction line using two C-50 getters and a cryogenic condensation trap. Ar isotopes were measured in static mode using a MAP 215-50 mass spectrometer with a Balzers electron multiplier, mostly using 10 cycles of peak-hopping. A more complete description of the mass spectrometers and extraction line is given in Renne et al. (1998). Blank measurements were generally obtained every three samples. All of the results here were obtained by using the conventional 40 Ar/ 369 Ar value of 295.5 + 0.5 (Nier 1950) to correct for the instrumental mass discrimination and 40 Ar atmospheric contamination. Mass discrimination was monitored every nine steps using an automated air pipette, and yielded mean values of 1.0051 + 0.0022 and 1.0078 + 0.0024 daltons (Da) for the FCp and Hb3gr experiments, respectively.
Our criteria for the plateau and mini-plateau ages are as follows: plateaus and mini-plateaus must include at least 70 and 50% of 39 Ar released, respectively, distributed over a minimum of three consecutive steps and a probability of fit of at least 0.05. In this study, they are both given the same validity. Plateau and mini-plateau ages are calculated using the mean of all the plateau steps, each weighted by the inverse variance of their error. Integrated ages (that compare with total fusion ages) are calculated using the total gas (i.e. summed volumes) for each Ar isotope.

Fish Canyon plagioclase (FCp)
For each fraction, we obtained total fusion ages for two -eight aliquots. A weighted mean age and associated error were calculated for each size fraction, and are given in Table 1. Total fusion weighted mean ages range from 27.97 + 0.17 Ma (2s) for the coarsest fraction (150 mm) to 17.58 + 0.69 Ma for the smallest fraction (,5 mm). From 210 to 85 mm, the weighted mean age of each of the three fractions have been used to determinate the age of FCp at 28.00 + 0.08 Ma (Fig. 1). From 85 to 28 mm, the apparent ages of FCp are mostly indistinguishable from the nominal age of FCp, although we note that the centre of mass of the age tends to be older. We calculated the deviation (D FCp ) from the nominal value by including both the uncertainty on the measured age and on the age of FCp (28.00 + 0.08 Ma; 2s). D FCp ranges from 0.25 + 0.64% to 1.46 + 0.85%. However, previous studies of 39 Ar recoil showed that 39 Ar loss is proportional to the size of the grains below 50 mm; as the grain size diminishes, measured ages will become increasingly older than the nominal age. Recoil loss age correction has been calculated using the correction equation for feldspar rearranged from Jourdan et al. (2007): where t c is the age of FCp corrected to account for 39 Ar recoil loss, t FCp is the nominal age of FCp at 28.0 Ma and h is the mean length of a parallelepiped grain with dimensions of h:1.2h:1.5h adopted for feldspar. Note that these equations are approximations and are used for graphical representation only (see the figures in this section).
The apparent ages measured for FCp match to a better extent the theoretical age of FCp if the latter is corrected for 39 Ar recoil loss (Fig. 1), with a D FCp (corr.) ranging from 20.05 + 0.57 to 1.08 + 0.80% (Table 1), overlapping within uncertainty with the age of FCp except for the 53 -38 mm fraction. Measurements on eight aliquots of the 53-38 mm fraction show rather scattered ages ranging from 28.09 + 0.14 to 28.85 + 0.15 Ma, with two groups of ages and with a large MSWD of 13 suggesting that an unidentified problem has affected some aliquots of this fraction. We note that if the youngest group of ages is selected (n ¼ 5), the weighted mean age of this fraction becomes 28.26 + 0.12 Ma, statistically indistinguishable from the 39 Ar recoil-corrected age of FCp (28.11 + 0.08 Ma). From 28 to 5 mm, weighted mean ages from the four fractions behave more erratically, with a deviation ranging from 1.5 + 1.5% to 24.3 + 7.2% and from 0.5 + 1.5% to 25.6 + 7.1% (Table 1) from the FCp nominal age and FCp recoil-corrected age, respectively (Fig. 1). We note that the variation in deviation is not correlated with the fraction size. The smallest fraction that includes grains with size smaller than 5 mm yielded a much younger age of 17.6 + 0.7 Ma compared to other fractions, which corresponds to deviations of 237+4 and 240 + 4% from the nominal age [D FCp ] and recoil-corrected [D FCp (corr.)] age of FCp, respectively. Among the five smallest fractions, four of them show a negative D FCp (corr.), with three of them distinct at the 2s level with the 39 Ar recoil-corrected age of FCp.
The [Ca/K] Ar ratio (derived from 37 Ar Ca / 39 Ar K ) for all fractions above 22 mm is relatively constant (Fig. 2)

Hb3gr Hornblende (Hb3gr)
For each fraction, we analysed between three and seven aliquots. A weighted mean age and its error were calculated for each fraction, and are given in Figure 3 and Table 2.
Twelve fractions between 212 and 28 mm yielded weighted mean ages ranging from 1065 + 7 Ma to 1079 + 7 Ma. These apparent ages are indistinguishable from the nominal age of Hb3gr (1072 + 10 Ma), with a D Hb3gr ranging from 20.7 + 1.1% to 0.7 + 1.1% (Fig. 4b). Similarly to D FCp , the uncertainty on the D Hb3gr includes both the uncertainty on the age of FCp and the uncertainly on the age measured for a given fraction. As for FCp, the age of Hb3gr must be corrected from 39 Ar recoil loss. Recoil loss age correction using equation (4) yielded a D Hb3gr (corr.) ranging from 21.0 + 1.2% to 0.4 + 1.2% (Table 2) and ages indistinguishable from the recoil-corrected model ages.
From 28 to 10 mm, weighted mean ages measured for Hb3gr range from 1044 + 46 to 1065 + 41 Ma. This results in a D Hb3gr ranging from 22.6 + 4.4% to 0.7 + 3.9%, with all of the fractions within error of Hb3gr. D Hb3gr (corr.) ranges from 23.3 + 4.4% to 22.0 + 3.9%, being indistinguishable from the age of Hb3gr corrected for 39 Ar recoil, although we note that all of the ages have a centre of mass that is younger than the 39 Ar recoil-corrected age of Hb3r (Fig. 3, Table  2). The 10 -5 mm fraction yielded an age of 1069 + 15 Ma; indistinguishable from the nominal age of Hb3rg (D Hb3gr ¼ 20.3 + 1.7%), but statistically distinct (D Hb3gr (corr.) ¼ 22.5 + 1.7%) from the 39 Ar recoil-corrected age of Hb3gr (1096 Ma). Below 5 mm, the weighted mean age is much younger than the age obtained for other fractions, with an age of 909 + 27 Ma corresponding to D Hb3gr and D Hb3gr (corr.) of 215+3 and 221 + 2%, respectively. The [Ca/K] Ar range from 21+7 to 9+4 (n ¼ 66: Fig. 2b) with a MSWD and P values of 1.16 and 0.18, respectively, suggesting that the Ca/K composition is homogenous among all aliquots. The [Ca/K] Ar ratios are indistinguishable from the Hb3gr [Ca/K] EMP microprobe values, ranging from 5.1 to 6.8 . No correlation between [Ca/K] Ar and the grain size is observed, although a scatter is present. We note that the 37 Ar m measured (before correction of 37 Ar i decay) shows a very low ion beam signal for most fractions, rendering the calculation of [Ca/ K] Ar a difficult task. Below 5 mm, the [Ca/K] Ar ratio shows values with large error bars due to a 37 Ar m with a value close to 0 due to the small quantity of material analysed at this size fraction.

Discussion
Recoil in Fish Canyon plagioclase (FCp) 37 Ar recoil loss. The 28 -22 mm, 10 -5 mm and, especially, the ,5 mm fractions show ages statistically younger than what would be expected for ages affected by recoil-induced 39 Ar loss alone. As proposed by , this effect is likely to be due to 37 Ar loss caused by the recoil-induced ejection of 37 Ar atoms following the reaction [ 40 Ca(n, a) 37 Ar]. 37 Ar Ca loss causes undercorrection of the 39 Ar Ca and especially 36 Ar Ca interferences, ultimately yielding a low 40 Ar*/ 39 Ar K ratio and a younger age (see the detail in ). To estimate the proportion of 37 Ar lost from the grains, we assume that the age shift is entirely due to 37 Ar loss and we use the equations of , indicated below and adapted for any 40 Ar/ 36 Ar atmospheric ratios.    where D f ( 39 Ar) corresponds to the 39 Ar depletion factor and F( 39 Ar) corresponds to the relative fractional loss of 39 Ar. Both values are related and calculated for a given fraction size, shape and mineral composition. Note that the D f ( 39 Ar) values reported by  correspond, in fact, to F( 39 Ar) as per equation (6). In this study, we use the F( 39 Ar) values obtained for sanidine crystals, which should represent a good estimate for plagioclase and hornblende crystals, and can be approximated by: The relative loss of 37 Ar is then given by: Relative 37 Ar fractional loss Ar t − 37 Ar m 37 Ar t .
The 37 Ar c corrected (equal to the above theoretical 37 Ar t ) for recoil-induced depletion for a given size fraction, rearranged from equation (8), is given by: where F( 37 Ar) FCp can be approximated by the following relationship fitted to the depletion trend given by the present data (Fig 4a): We calculated the F( 37 Ar) for the four fractions with negative DFCp(corr.); namely 28-22, 15 -10, 10-5 and ,5 mm. F( 37 Ar) weighted mean values are accompanied by their uncertainty, expressed as the standard error of the mean (i.e. the standard deviation divided by the square root of the number of samples) (Fig. 4a). F( 37 Ar) is inversely proportional to the size of the grain fractions, with F( 37 Ar) ranging from 29 + 4% (28-22 mm) to 91.0 + 1.2% (,5 mm: Table 1). As stressed during our previous study on 39 Ar loss , 39 Ar or 37 Ar atoms ejected out of the grains by recoil can be reimplanted at the surface of other grains in close contact and, thus, not lost despite ejection. In addition, 39 Ar and 37 Ar atoms can be displaced in low-retentivity sites (including the reimplanted atoms) and can be lost by thermal diffusion due the temperature reached in the reactor or during the extraction line bake-out (in both cases up to c. 200 8C: Dong et al. 1995;McDougall & Harrison 1999), especially for the very fine fractions. However, simple diffusion calculations using standard D o (Frequency factor) and E a (Activation energy) values for feldspar and amphibole show that spheres of 5 mm diameter heated for 40 and 100 h, respectively, cause a maximum fractional loss of 0.005% for the feldspar and no loss for the hornblende. Nevertheless, the results obtained in this study indicate the total 37 Ar loss directly or indirectly caused by the irradiation process, and that we regroup here under the term 'recoil loss'.

37
Ar total depletion thickness. Based on a simple geometric relation, F( 37 Ar) can be converted into 37 Ar loss from a parallelepiped structure and converted into the thickness (d 0 ) of a 0-concentration layer in the outermost part of the parallelepiped grain ) as: Equation (11) is solvable analytically as a third degree polynomial. L, w and h represent the length, width and height of the grain, respectively: For each grain size, the mean d 0 value corresponds to the average of the individual d 0 value calculated for each batch, weighted by the relative error on the ages associated for each batch. Uncertainties are reported as the standard error of the mean (2s). For each batch, we used a parallelepiped of dimensions h:1.2h:1.5h. Mean d 0 values obtained for FCp ranges from 1.6 + 0.13 to 0.60 + 0.17 mm (2s ; Table 1), and yielded a weighted mean and standard error of the mean of 1.27 + 0.53 mm (Fig. 5a). The MSWD (31) and P (,0.001) values obtained for this group indicate that the data belong to more than one population and that the scatter of the data cannot be explained by individual uncertainty alone. A closer look at the d 0 values suggest that only the 5-10 mm fraction shows a d 0 value (0.6 + 0.1 mm) that departs from an otherwise homogeneous population. If the 5-10 mm fraction is omitted in the calculation, the three other d 0 values give a MSWD of 0.30 and P of 0.74, and a weighted mean and standard error of the mean d 0 ( 37 Ar) FCp of 1.63 + 0.21 mm. We shall see that the result obtained for hornblende is similar to this value, further justifying rejection of the d 0 obtained on the 5 -10 mm fraction. The weighted mean of the d 0 value has been tested against the data in Figure 6a. We modelled the relative 37 Ar loss of a parallelepiped with a volume of h:1.2h:1.5h for h ranging from 50 to 2 mm. We used d 0 values of 1.63 + 0.21 and 1.27 + 0.53 mm as widths of constant 0-concentration layers on the outer edge of a grain. Figure 6a shows that both d 0 values match well the relative 37 Ar loss of each fractions from which they are derived.
The problem of the increasing [Ca/K] Ar . As illustrated by the modelled 37 Ar-and 39 Ar-depletion curve in Figure 2a (+15% increase) for the ,5 mm fraction. Even if no 37 Ar loss were to occur, the Ca/K of homogenous plagioclase should remain sub-stationary, as the 39 Ar depletion is only 3%. In any case, nuclear physics laws imply that the recoil distance of 37 Ar Ca atoms must be at least 2-3 times the recoil distance of 39 Ar due to the energy of the reaction (e.g. Turner & Cadogan 1974;Onstott et al. 1995;Renne et al. 2005).
At this stage, two hypotheses are possible: (1) the decreasing age with decreasing fraction is not due to 37 Ar loss but by contamination by a Ca-rich phase with a composition similar to FCp ([Ca/ K] EMP ≥ 6) but with an age significantly younger than FCp. This would imply that the F( 37 Ar) and d 0 ( 37 Ar) values cannot be calculated for FCp; or (2) a significant part of the 37 Ar Ca is, indeed, ejected from the grain but an extremely Ca-rich phase is progressively enriched in the small fractions and, despite evidence of the young ages, masks the direct loss of 37 Ar Ca . Apatite and sphene inclusions (Ca-rich, K-free phases) along with plagioclase cores with An75 composition (Ca/K of c. 90) and An60 microlites have all been reported to be abundant for the Fish Canyon tuff (Bachmann et al. 2002). All of these phases have the potential to dramatically increase the Ca/K ratios towards fine fractions, especially as the relatively small Ca-rich inclusions and An75 plagioclase cores get liberated and concentrated during the crushing and sieving processes involved in the small fractions. Importantly, these inclusions do not have the potential to reduce the age of FCp as apatite and sphene do not contain any K, and An75 plagioclase has the same age as FCp. Therefore, we conclude that even though inclusions can explain the increasing trend of [Ca/K] Ar , 37 Ar loss is still required to explain the younger ages.

Recoil in Hb3gr hornblende (Hb3gr)
Ar recoil loss. For Hb3gr, the nine smallest fractions ranging from 63 to ,5 mm show negative DHb3gr(corr.) values (i.e. with ages younger than the 39 Ar recoil-corrected ages of Hb3gr) and offer a better continuity than FCp to study the effect of 37 Ar recoil loss for small fractions (Fig. 3). In the case of Hb3gr, the closure temperature of hornblende (c. 550 8C) is too high to allow any diffusion of 37 Ar due to the temperatures attained within the reactor and during the bake-out of the extraction line.
We calculated the relative 37 Ar loss (F( 37 Ar)) from all aliquots of the different size fractions using equations (5) -(8), assuming that the decrease in age is entirely due to 37 Ar loss. The weighted mean and standard error of the mean of the F( 37 Ar) values range from 28 + 9% to 98 + 4% (Fig. 4b, Table 2). The F( 37 Ar) values of all but one fraction are proportional to the grain size, and can be approximated by a power-law curve fitted to the data and defined by the following equation: where h is the mean size (in mm) of the grains of a given aliquot. The 22 -28 mm fraction (80 + 14%) lays well above the trend defined by the other eight fractions and is considered here to be an outlier. The smallest fraction (,5 mm) shows almost an entire depletion of the 37 Ar within the grain with the ejection of 98 + 4% of 37 Ar atoms.

37
Ar total depletion thickness. We calculated the d 0 values for each fraction below 63 mm. d 0 ranges from 1.4 + 0.3 to 3.5 + 5.9 mm (Fig. 5b, Table 2). As mentioned above, the 22-28 mm fraction behaves like an outlier compared to an otherwise homogenous population, and as been excluded from the final calculation of d 0 ( 37 Ar) Hb3gr . Weighted mean and standard error of the mean of d 0 (Hb3gr) is 1.78 + 0.67. MSWD and P values of 1.7 and 0.10, respectively, indicate that some scatter is present but still suggest that these data might belong to a single population. We further tested the d 0 ( 37 Ar) Hb3gr value by modelling the relative 37 Ar loss of a parallelepiped with dimensions of h:1.2h:1.5h, for h ranging from 63 to 0 mm, and a constant 0-concentration layer with a d 0 thickness of 1.78 + 0.67 mm. Figure 6b shows that the model curve offers a reasonable match with the data within uncertainty, in particular with the smallest fractions, whereas the largest fractions show slightly higher F( 37 Ar) than expected from the model alone. Varying the shape of the parallelepiped does not much affect the model curve, although a slightly better match on coarser fractions is reached for square-shaped grains.
[Ca/K] Ar . Hb3gr shows rather scattered [Ca/K] Ar values oscillating around 5. The [Ca/K] t theoretical curve with 37 Ar c and 39 Ar c corrected for recoil loss, using equations (6) and (9), predicts a decrease in Ca/K with decreasing fraction size (Fig. 2b).
[Ca/K] t is indistinguishable from the [Ca/K] Ar measured down to 15 mm. Only the 15-10 and 10 -5 mm fractions show some significant departure from the curve, with [Ca/K] Ar .[Ca/K] t . The ,5 mm fraction shows [Ca/K] Ar ≈ [Ca/K] t ≈ 0. 37 Ar raw beams measured for all fractions and before applying the decay correction show values ranging from 20.00005 to 0.0009, (i.e. close to 0), which makes it hard to assess the reliability of the [Ca/K] Ar ratio in this case. The low 37 Ar raw values are certainly a major cause of the large error associated with d 0 ( 37 Ar) Hb3gr of 1.78 + 0.68 mm.
Comparison with the theoretical estimation of 37 Ar recoil observed for plagioclase and hornblende are much larger than predicted by theoretical models for this type of silicate.
If correct, then why is so much 37 Ar lost from the grains compared to 39 Ar? The total recoil distance of inelastic collisions is a function of the energy of incident neutrons, the stopping power of the medium and the energy involved in the reaction. In the case of plagioclase and sanidine, the stopping power of the medium can be considered as equal, which makes the recoil energy directly dependent on the energy of the incident neutron required for the reactions on 40 Ca and 39 K, and the energy of these reactions. The physics behind these reactions are well known. Accordingly, one of the most straightforward explanations is that ejection due solely to pure nuclear recoil is not the only cause for the 37 Ar loss.
In the case of x 0 ( 39 Ar) biotite being more than 10 times larger than x 0 ( 39 Ar) sanidine , the favoured explanations for such a difference were related to the structure of the mineral itself. Biotite being a sheet silicate, it will have much more abundant fast pathways (e.g. between sheets) than compact tectosilicate, with these pathways acting as shortcircuit diffusion for 39 Ar (Paine et al. 2006). In the case of plagioclase and hornblende, the compact structure of these mineral is similar enough to sanidine to rule out a similar explanation for the large x 0 ( 37 Ar)/x 0 ( 39 Ar) value. Another possible explanation is that Ca-rich material has a longer stopping distance than Ca-poor material. However, SRIM 2003 simulations used to calculate the stopping range of recoiled 39 Ar and carried out on a variety of slab compositions, albeit with amorphous structure, suggest that Ca-rich and dense material, such as hornblende and anorthite, have a similar if not slightly shorter stopping distance than sanidine for 39 Ar recoil (Renne et al. 2005). As the same behaviour is expected for 37 Ar atoms, the composition is unlikely to play any role in the x 0 ( 37 Ar) value.
A possibility is that the external layer of the grains might become amorphous due to significant structural radiation damage caused by the nuclear collisions, especially for 37 Ar as the energy of the reaction is exoergic with a Q value of 1.75 MeV. As a consequence, the amorphous external layer could be prone to significant thermal diffusion of the 37 Ar atoms displaced in this layer by recoil, but this effect would certainly also result in an enhanced loss of 39 Ar and, hence, does not seem to provide a suitable explanation.
The exact reason(s) for a large x 0 ( 37 Ar) value is currently unknown. The physics behind the nuclear recoil process is generally well understood. Yet, our measurements show that a quantity of 37 Ar much larger than expected from recoil alone is lost from the grains, somewhere between the irradiation time and the analysis in the mass spectrometer. Our results are unlikely to be a biased experimentally as two distinct minerals with two distinct irradiation durations (i.e. 10 and 90 h) and distinct neutron doses, and carried out at different times, produced similar results. Our new results are also in agreement with the FCs-p experiments , where a d 0 ( 37 Ar) upper-limit value of ,3 mm was calculated (i.e. x 0 , 6 mm). Similarly, the good fit between experiment and model for 37 Ar lost from plagioclase and hornblende seems to preclude a bias of the experiments. The rather unexpected results obtained during this study warrant further investigation of the 37 Ar recoil loss. One of the possible approaches to directly cross-check our results will be to vacuum-encapsulate all of the mineral fractions (e.g. see the detail in Foland et al. 1992) and to carry out complementary experiments by: (1) directly measuring all of the 37 Ar ejected from the various grain fractions and trapped in the capsules; and (2) measuring the isotopic composition of each fraction similar to the present study. However, the downside of these experiments is that the irradiation of the grains must occur under vacuum conditions and will thus produce F( 37 Ar) and d 0 ( 37 Ar) values significantly lower than the ones reported in this study due to the re-implantation of the 37 Ar (and 39 Ar) in neighbouring minerals.
37 Ar and 39 Ar recoil age correction According to our experiments, a measurable proportion of 37 Ar is lost due to the direct and indirect effects of recoil at small fraction size (Fig. 4), albeit the exact mechanism explaining the large amount of 37 Ar loss is not well understood. In addition, 39 Ar loss has been shown by Paine et al. (2006) and  to be mineral dependent, and seems to affect the age results below 50 mm. Therefore, in order to accurately determinate the age of minerals of a given size range below the 50 mm threshold, one needs to correct for 39 Ar and 37 Ar loss.
The general 40 Ar/ 39 Ar age equation is given by: 40 Ar* and 39 Ar K need to be corrected from 39 Ar and 37 Ar recoil losses that have a direct ( 39 Ar) or indirect effect ( 37 Ar) on these isotopes. 40 Ar* and 39 Ar K can be directly corrected from the effects of recoil by combining the general equation (3.42) of McDougall & Harrison (1999), and equations (6) and (9) of the present study: 40  where the calculation of F( 39 Ar) for a range of crystal size of fixed proportion has been given in , and where the same equations can be used to calculate F( 37 Ar) using the appropriate d 0 ( 37 Ar).

39
Ar and 37 Ar recoil-corrected age can then be calculated by combining equations (14) and (15). If the mineral is calcium-free, then equation (15) is equivalent to equation (9) given by .
The age correction calculation proposed here can be applied to loose minerals irradiated in an air-filled capsule, as is usually the case for conventional 40 Ar/ 39 Ar dating. If fine-grained minerals are irradiated as a single compressed pellet or under vacuum, significant amounts of ejected 37 Ar and Implication for 40 Ar/ 39 Ar geochronology of Ca-rich material Age determination. 39 Ar recoil-induced loss in minerals can become problematic when it comes to dating fine-grained minerals of ,50 mm (Paine et al. 2006;). 37 Ar recoil adds one layer of complexity to the problem for calciumrich minerals as they will suffer from both 39 Ar and 37 Ar recoil. Until a more sophisticated sample  Paine et al. 2006); green curve, x 0 ( 37 Ar) plagioclase-Hornblende ¼ 3.3 + 0.4 mm; and blue curve, x 0 ( 37 Ar) theoretical ¼ 0.2 mm (Turner & Cadogan 1974;Onstott et al. 1995). irradiation method is available (e.g. Deuteron-Deuteron fusion reactor: Renne et al. 2005), neutron-induced recoil loss has to be taken into account for small grain size. Paradoxically, our results show that the 37 Ar loss will result in a younger age but will, to some extent, compensate the opposite effect of 39 Ar recoil loss. As a result, the measured age of Ca-rich minerals will be close to the nominal age of a mineral at least down to a size fraction of about 10 mm (Figs 1 & 3), but note that this is a first-order approximation only.
Vacuum encapsulation and age correction. Ultimately, because of the complexity of the correction problem and the magnification of the uncertainties associated with the recoil correction of grains with a size below 5 mm, dating of fine-to veryfine-grained minerals (e.g. clay and glaucony grains) will require encapsulation of the samples following a standard vacuum-encapsulation method (e.g. Foland et al. 1992;Haines & van der Pluijm 2008). The downside of this approach is that the benefits of age spectrum analysis are sacrificed. This, however, can be circumvented by using samples with different grain sizes or fractions with a different range size, provided that, for each size fraction, the recoil-corrected age can be calculated and then compared to the measured integrated age. If the 40 Ar* distribution in each grain is homogenous, then for each fraction: where t c is given by combining equations (14) and (15), and t int is the total gas age obtained by integrating the gas measured in the capsule and the sample. This implies that d 0 ( 37 Ar) and d 0 ( 39 Ar) values are known for samples irradiated under vacuum condition with d 0 ( 3x Ar) atm . d 0 ( 3x Ar) vacuum for 37 Ar and 39 Ar. If the distribution of 40 Ar* is heterogeneous due to excess 40 Ar* or alteration discretely distributed within the grains, then it is expected that the  (Jourdan unpublished). Errors are quoted at 2s. The black arrow illustrates the theoretical redistribution of 39 Ar from K-rich to K-poor domains, and the grey arrow shows the 37 Ar redistribution from Ca-rich to Ca-poor sites. Note that neither the low-nor the high-temperature flat sections of the age spectrum are likely to represent the formation age of this rock due to 39 Ar and 37 Ar redistribution within the sample (cf. the discussion in the text). different size fractions will not follow a recoilinduced power-law age pattern, such as shown in equation (4). At this stage, the validity and applicability of this method remains to be seen and thoroughly tested.
Note on 39 Ar and 37 Ar redistribution in groundmass. Irradiation-induced recoil not only affects minerals with size ,50 mm through 39 Ar and 37 Ar loss, but can also seriously hamper age determination through recoil redistribution of these isotopes within the structure of the minerals or rocks. Any fine-grained structure will undergo recoil redistribution of the 39 Ar and 37 Ar isotopes. In principle, most of 39 Ar is released from K-rich sites at low to middle temperatures, whereas the 37 Ar is produced by Ca-rich sites and released mostly at high temperatures. In a fine-grain basaltic groundmass, recoil redistribution will cause part of 39 Ar K to move in Ca-rich sites (e.g. pyroxene) causing the low-and mid-temperature steps to yield apparent ages too old, whereas the 39 Ar K re-implanted in Ca-rich phases will cause the high-temperature steps to be too young (Fig. 7). 37 Ar Ca recoil will exacerbate this effect by enriching the low-and mid-temperature steps in 37 Ar Ca causing overcorrection of 39 Ar and 40 Ar (again yielding spuriously old age) and depleting the Ca-rich sites of 37 Ar Ca , with a result similar to that observed during 37 Ar loss (Fig. 8). As a consequence, when recoil redistribution affects the argon isotopes in the groundmass, this will result in a tilde-shaped spectrum such as the one exemplified in Figure 8. In most cases, two pseudo-flat sections will be formed with a relatively old mid-temperature section and a younger high-temperature section. As seen previously, none of these sections will reflect the true age of the groundmass with mid-and hightemperature 'mini-plateau' being too old and too young, respectively.

Conclusion
We carried out total fusion and step-heating Ar isotope measurements on multi-grain populations of Fish Canyon plagioclase (FCp) and Hb3gr hornblende, with discrete sizes ranging from 210 to ,5 mm. Our results show that the smallest fractions yielded younger ages than expected for minerals affected by 39 Ar recoil loss alone. We propose that 37 Ar loss may seriously bias the age measured for a mineral towards younger ages through the interference of correction disturbances on 39 Ar and 36 Ar isotopes. For both FCp and Hb3gr, the smallest fraction (,5 mm) shows the highest departure from the theoretical 39 Ar recoil-corrected age, with DFCp(corr.) of 240 + 4% and DHb3gr(corr.) of 221 + 2%. The age deviations are best explained by ejection of 37 Ar out of the grains during nuclear reactions or subsequent loss of the displaced atoms by diffusion. Relative 37 Ar loss calculated for each mineral is proportional to the grain size, and ranges from approximately 30 to 91% for FCp and from about 28 to 98% for Hb3gr. The 37 Ar loss is used to calculate the mean size of a partial depletion layer x 0 ( 37 Ar) with two concordant values of 3.3 + 0.4 (FCp) and 3.6 + 1.4 mm (Hb3gr). The reason for such a massive 37 Ar loss is not well understood. It can tentatively be attributed to the formation of an external amorphous layer as the result of significant structural radiation damages, and prone to significant thermal diffusion of the 37 Ar atoms displaced into this layer by recoil. The extreme depletion values obtained in this study warrant further investigation of Ca-rich crystals. In any case, using x 0 ( 39 Ar) and x 0 ( 37 Ar), and approximate crystal dimensions, the age of a given mineral can be corrected from the effects of 39 Ar and 37 Ar loss. We also propose a method based on our approach to test the validity of ages obtained via the vacuum-encapsulation method. Finally, our results highlight the problem of 37 Ar (and 39 Ar) redistribution in fine-grained Ca-rich samples.