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^{40}Ar/^{39}Ar dating and errors

*by Alexandra Scherer*

⇒ Introduction

⇒ Argon

⇒ Basics of Ar/Ar dating

⇒ Argon extraction system

⇒ Isotope ratio measurements

⇒ Interference corrections (Ca, K)

⇒ J-value

⇒ Half life / Decay constants

⇒ Excess Argon (Ar-types)

⇒ Conclusions

⇒ References

## Introduction

The ^{40}Ar/^{39}Ar dating method has become a widely used method in the field of isotope geochronology (RENNE 1998b). It is one of the most widely applicable and precise methods in geochronology and has been successfully used for dating the oldest and youngest rocks on earth, for dating lunar samples, bulk rocks and single crystals, and for dating rocks in situ using a variety of lasers systems. However, the increasing number of ages generated by the ^{40}Ar/^{39}Ar dating technique, more and more requires a consistency in the calculation of these ages and particularly their errors (KOPPERS 2002, SCAILLET 2000). The reference age of monitor minerals used and the uncertainties in the ^{40}K decay constants are main sources of systematic errors in ^{40}Ar/^{39}Ar dating, and the atmospheric correction on ^{40}Ar and the J-value determination are important sources of analytical errors (MIN 2000, RENNE 1998b).

## Argon

There are five isotopes of the noble gas argon which have to be measured for Ar-Ar dating. Naturally occuring argon is comprised of 0.337 ± 0.0003 at.% ^{36}Ar, 0.036 ± 0.001 at.% ^{38}Ar and of the major isotope ^{40}Ar (99.6 ± 0.0003 at.%). ^{36}Ar, ^{38}Ar and ^{40}Ar are stable isotopes. Unstable ^{39}Ar and ^{37}Ar are produced from Ca and K during neutron irradiation. ^{39}Ar decays to ^{39}K by beta-emission with a half life of ~ 269 years. Because of this slow decay rate ^{39}Ar can be treated as stable during the short time it is involved in the analysis. ^{37}Ar decays with a half life of ~ 35 days which has to be considered during Ar-Ar analyses.

## Basics of Ar/Ar dating

The ^{40}Ar/^{39}Ar method of dating is based on the decay of ^{40}K to ^{40}Ar with a half life of 1.25 Ga (McDOUGALL & HARRISON 1999). In contrast to the K-Ar dating method, K is not determined by independent analyses, but by a simultaneous measurement of 40Ar and ^{39}Ar from which the latter has been produced from ^{39}K by a nuclear (n,p) reaction during neutron irradiation of samples. The abundance of ^{39}Ar in the irradiated sample is thus a measure for the K content of this sample. The corresponding nuclear reaction is:

where n denotes the neutron capture and p the proton emission (FAURE 1986). The method was first applied by WÄNKE & KÖNIG (1959). The range of applicability is limited by the accumulation of sufficient radiogenic argon (^{40}Ar*). There is no older limit of the method and in general measurements become more precise with increasing age and potassium content. The main limitation is at the younger end of the time scale, involving the detection of a small amount of ^{40}Ar* from a relatively large background of contaminating atmospheric argon (Ar_{atm}). Datable minerals and age ranges are given in Figure 2. Because of the low Ar_{atm} and the high potassium content, alkali feldspars, e. g. sanidine and leucite, are most useful for dating younger rocks. Because of atmospheric argon contamination for particular mineral species, the datable ranges shown in Figure 2 should be taken as an overview only.

The principal advantage of the ^{40}Ar/^{39}Ar dating method in comparison with other techniques lies in the stepwise (incremental) heating technique. At this, the sample is progressively and irreversibly degassed and mass-spectrometrically analyzed during individual but increasing temperature steps (MERRIHUE & TURNER 1966). In contrast to total fusion degassing, this technique results in a series of apparent ages determined on a single sample. In the ideal case, the time of metamorphism (low-temperature release) and the time of initial cooling (high-temperature release) could be distinguished in such Ar-Ar spectra. On the other hand, if the sample behaved as a closed system to argon and potassium since the time of initial cooling, the ^{40}Ar*/^{39}Ar_{K} ratio in each extracted gas fraction and thus the derived age will be constant.

## Argon extraction system

An argon extraction system, in principle, consists of a furnace where the samples get heated, getter systems for purification of the released gas and the mass spectrometer in which the isotopic composition of the argon is measured. Small samples can also be heated by a laser beam instead of the furnace. Because of the presence of argon in the atmosphere, a ultrahigh vacuum system is required for extraction and purification of argon from geological samples. A simplified, schematic diagram of an argon extraction system is shown in Figure 3.

## Isotope ratio measurements

Isotope ratio measurements using mass spectrometry are associated to analytical errors, which are expressed by the standard deviation given for each ratio and calculated from a number of individual measurements of the same gas fraction. The analytical error is directly proportional to the amount of argon released from a sample, which in turn depends on the age and potassium content of the sample. In general, the older a sample and the higher the K-content of a sample is, the higher is the amount of radiogenic Ar and the lower is the analytical error. Dating very young rocks is thus best achieved by usage high-K minerals (e.g. K-feldspars).

## Interference corrections (Ca, K)

From the earliest stages of development of the ^{40}Ar/^{39}Ar dating method it was recognized that the isotopes of argon may be formed by neutron induced nuclear reactions from calcium, potassium, argon and chlorine during sample irradiation. Interfering isotopes that have to be corrected for in Ar-Ar dating are ^{36}Ar, ^{37}Ar and ^{39}Ar produced from Ca, and ^{40}Ar produced from K. To calculate the ^{40}Ar*/^{39}Ar_{K} ratio and thus the age, the following equation of McDOUGALL & HARRISON (1999), whis is identical to the formula given by BRERETON (1970) and MAK et al. (1976), but slightly different from the equations given by DALRYMPLE & LAMPHERE (1971), DALRYMPLE et al. (1981), and McDOUGALL & ROKSANDIC (1974), can be applied:

the subscripts are consistent with the previous usage, where m is measured, Ca denotes the correction factor for neutron induced Ar from calcium, K the correction factor for neutron induced Ar from potassium and * denotes the radiogenic argon. All of the quantities on the right-hand side are know by measuring argon isotopes in the extracted gas from the irradiated sample or are determined correction factors derived from irradiated Ca- and K-salts. For a more detailed derivation see McDOUGALL & HARRISON (1999) pp. 90 - 92.

During neutron irradiation, significant amounts of ^{36}Ar, ^{37}Ar and ^{39}Ar are mainly produced from calcium (McDOUGALL & HARRISON 1999). As ^{37}Ar in a sample results solely from Ca, its amount can be used to correct the measured 36Ar and 39Ar abundance for Ca induced ^{36}Ar and ^{39}Ar. This is done by measuring the Ar isotope composition of a pure irradiated Ca-salt (CaF_{2}) which results in the corresponding correction factors (that represent the constant production rate ratios for the corresponding isotopes:

Because of the significant production of neutron-induced ^{40}Ar from potassium, corrections on measured ^{40}Ar also need to be made. Particularly during the irradation of young samples, the potassium correction factor

becomes increasingly important. In a pure, calcium-free potassium salt (K_{2}SO_{4}) the complete amount of ^{39}Ar will be derived from potassium (^{39}Ar_{m} = ^{39}Ar_{K}) and can be used to determine the correction factor.

^{40}Ar_{atm} must also be corrected for in terrestrial samples which is done by the known ^{40}Ar/^{36}Ar ratio:

All the described interference corrections and correction factors are associated with an analytical error, that must be considered in ^{39}Ar/^{40}Ar dating. With respect to ^{38}Ar, it is widely accepted that 38Ar produced from Ca and K has a negliblible effect on the measurement and that it must only be corrected for in extraterrestrial samples (McDOUGALL & HARRISON 1999).

## J-value

The parameter J reflects the neutron flux (fluence) in the reactor and is determined from a standard sample (monitor) with a known age which is irradiated at the same time as the samples of interest, whose ages will be determined. Before age-calculation, the J-value and its gradient over the radiation container must be determined from the monitor minerals.

By calculating the ^{40}Ar*/^{39}ArK ratio (see eq. (2)) from measured argon isotope abundance in the irradiated standard sample (monitor), the J-value can be easily determined by using the known age of the standard:

where "lambda" is the constant of proportionality (the decay constant), t ist the age, ^{40}Ar* the radiogenic argon and ^{39}Ar_{K} the argon produced from potassium by irradiation. With the known parameter J, the age t of the geological samples that have been irradiated together with the standard can be calculated with the following equation:

To take a closer look to the derivation of age equations see MCDOUGALL & HARRISON (1999), pp. 16 - 19. In some cases, it is possible to determine the J-value to 0.1 % by using a tightly controlled positioning of the fluence monitors in the reactor during irradiation, but a precision of ± 0.5 % is more common (SCAILLET 2000). Applying partial differentiation to the equation (5), the following standard error function associated to the J-value is derived:

where F = ^{40}Ar*/^{39}Ar_{K}, C = exp(lamda*T_{0}), T_{0} is the age of the primary standard, "lambda" the total decay constant of ^{40}K and T_{m} = age of the sample as calculated from eq. (6) (KOPPERS 2002). The first part is reflecting the analytical error in the determination of the ^{40}Ar*/^{39}Ar_{K} ratio. The remaining part reflects the uncertainties in the age standard and "lambda" that can also be used for derivaton of internal and external errors of the parameter J.

## Half life / Decay constants

Like in other dating systems, the accuracy of the ^{40}Ar/^{39}Ar dating technique lags behind the analytical precision, largely because of uncertainties in the decay constants involved (RENNE 1998a; see Figure 5).

Because of the two different modes of ^{40}K decay, i. e. (1) the electron capture to ^{40}Ar followed by emission of gamma-ray and (2) the ß- decay to ^{40}Ca (MIN 2000), the accuracy of ^{40}Ar/^{39}Ar dating depends on the accuracy of two decay constants (RENNE 1998a). ^{37}Ar and ^{39}Ar, which are used for interference corrections, are instable isotopes and before age calculation, their abundances have to be corrected for because of their decay between irradiation and measurement. The uncertainty of their decay constants also imprints an error on the final Ar-Ar age. The half life of ^{39}Ar is 269 ± 3 years (STOENNER et al. 1965) and thus ^{39}Ar can be, treated as a stable isotope during irradiation and measurement, so the correction is negligible. There will be only a small correction of the extracted gas of ~0.3 % on measured ^{39}Ar if the measurement is performed one year after irradiation (McDOUGALL & HARRISON 1999). The decay of ^{37}Ar, in contrast, is significant (McDOUGALL & HARRISON 1999) because of the short half life of 35,1 ± 0.1 days (STOENNER et al. 1965)

## Excess Argon (Ar-types)

Several types of argon with different isotope compositions are found in geological samples. Atmospheric argon has the isotopic composition of the present-day atmosphere. Ar*, the radiogenic argon, has been formed by the decay of ^{40}K. For terrestrial samples it is calculated as follows:

where ^{40}Ar_{total} is the total ^{40}Ar measured, ^{36}Ar_{atm} is the atmospheric argon and 295,5 the constant ratio of ^{40}Ar/^{36}Ar in atmospheric argon. The argon which is trapped in a rock or mineral at the time of formation or during a subsequent event is called trapped argon. Cosmogenic argon is produced by cosmic-ray interactions. It must be corrected for when extraterrestrial samples are dated. The argon produced during irradiation in a nuclear reactor is called neutron-induced argon. There are two types of extraneous argon: First, inherited argon which is introduced into rocks or minerals during their formation by contamination from older material or from an atmospheric component. Second, excess argon (^{40}Ar_{E}), the component of radiogenic ^{40}Ar, apart from atmospheric ^{40}Ar, that was brought into a rock or mineral by processes not related to the in-situ decay of ^{40}K in the sample. Particularly during metamorphic processes, rocks and minerals may incorporate excess argon released from adjacent areas.

Extraneous argon (inherited and excess argon) may sometimes produce Ar/Ar ages that are much older than geologically meaningful or, in some cases, even older than the age of the earth. This effect can sometimes be detected applying the incremental heating technique, which then may result in specific, e.g. "saddle-shaped" age spectrums. Such patterns have been reported for biotite, pyroxenes, hornblende and plagioclase (LAMPHERE & DALRYMPLE 1976, HARRISON & McDOUGALL 1981) and are attributed to the presence of excess argon. A spectacular example of this effect is a biotite separated from the Isua supracrustal rocks of West Greenland with an apparent age of 5.2 Ga (PANKHURST et al. 1973).

## Conclusions

This paper outlines a brief insight into the wide variety of problems associated to the ^{40}Ar/^{39}Ar dating method. Interferences on ^{36}Ar and ^{39}Ar, that result from neutron irradiation of calcium, potassium, argon and chlorine have to be corrected and the errors imprinted have to be accurately monitored. Errors that result from uncertainty in the determination of the J-values must also be considered before calculating reliable Ar-Ar ages. The largest problem, not only for Ar/Ar dating, however, is the uncertainty of the decay constants involved, which must be carefully taken into account in ^{40}Ar/^{39}Ar dating. In conclusion, even for minimizing all potential error sources, absolute radiogenic ages will never be exactly.

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