Ar/ Ar dating and errors - Institut für Geologie

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Oberseminar 09.01.2007
40
Ar/39Ar dating and errors
Alexandra Scherer, Weingasse 13, 09599 Freiberg
Supervisor: Dr. Jörg Pfänder, Institut für Geologie, TU Bergakademie Freiberg,
Bernhard-von-Cotta-Str. 2, 09599 Freiberg
ABSTRACT
Calculation of an
40
Ar/39Ar age involves several errors. Important sources of errors arise from
the uncertainty in the
40
K decay constants, the variation in the neutron flux during irradiation
and the interferences of
36
Ar and
40
Ar produced from calcium and potassium during
irradiating a geological sample. Also, the existence of excess argon and recoil argon are
large problems when ages are calculated. These problems are discussed in this paper and it
will be shown, that an error estimate for Ar-Ar ages can be calculated from the individual
analytical uncertainties.
1.
The
Introduction
40
Ar/39Ar 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/39Ar 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
systematic errors in
40
40
K decay constants are main sources of
Ar/39Ar dating, and the atmospheric correction on
40
Ar and the J-value
determination are important sources of analytical errors (MIN 2000, RENNE 1998b).
1
2.
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.%
and of the major isotope
40
Ar (99.6 ± 0.0003 at.%).
36
36
Ar, 0.036 ± 0.001 at.%
38
Ar,
Ar and
38
Ar
40
Ar are stable isotopes.
Unstable 39Ar and 37Ar 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. 37Ar decays with a half
life of ~ 35 days which has to be considered during Ar-Ar analyses.
Figure 1: Isotopic abundance of argon. Data form Lawrence Berkeley National Laboratory.
3.
The
Basics of Ar/Ar dating
40
Ar/39Ar 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
from which the latter has been produced from
irradiation of samples. The abundance of
40
Ar and
39
Ar
39
K by a nuclear (n,p) reaction during neutron
39
Ar in the irradiated sample is thus a measure for
the K content of this sample. The corresponding nuclear reaction is:
39
19
K (n, p )
39
18
Ar
(1)
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 (40Ar*). There is no older limit of the method and
in general measurements become more precise with increasing age and potassium content.
2
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
(Aratm). Datable minerals and age ranges are given in Figure 2. Because of the low Aratm 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.
Figure 2: Schematic diagram showing the approximate age range of applicability of various types of sample
materials which are commonly used in
40
Ar/39Ar dating. Dashed lines towards the younger limit are achievable
only under favourable circumstances. (McDOUGALL & HARRISON 1999, modified after DALRYMPLE &
LAMPHERE 1969)
The principal advantage of the
40
Ar/39Ar 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*/39ArK ratio in each extracted gas fraction and thus the derived age will be
constant.
4.
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
3
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.
Figure 3: Schematic diagram of an argon extraction system. The samples can be heated in a furnace or in a laser
cell and the system is directly connected to the mass-spectrometer (right). (Modified after G. E. BATT, from
McDOUGAL & HARRISON 1999)
5.
Sources of errors
5.1
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).
5.2
Interference corrections (Ca, K)
From the earliest stages of development of the 40Ar/39Ar 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
4
from K. To calculate the
40
Ar*/39ArK 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:
40
Ar *
=
39
ArK
⎛
⎜
⎜
⎝
Ar ⎞
⎛ 36 Ar ⎞
⎛ 36 Ar ⎞
⎟
⎜
⎟
⎜⎜ 37 ⎟⎟
−
+
295
.
5
295
.
5
39
⎜ 39 Ar ⎟
Ar ⎟⎠
⎝
⎠m
⎝ Ar ⎠ Ca
m
⎛ 39 Ar ⎞ ⎛ 37 Ar ⎞
1 − ⎜⎜ 37 ⎟⎟ ⎜⎜ 39 ⎟⎟
⎝ Ar ⎠Ca ⎝ Ar ⎠ m
⎛ 37 Ar ⎞
⎜⎜ 39 ⎟⎟
⎝ Ar ⎠ m
40
⎛ 40 Ar ⎞
− ⎜⎜ 39 ⎟⎟
⎝ Ar ⎠ K
(2)
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 Ksalts. For a more detailed derivation see McDOUGALL & HARRISON (1999) pp. 90 – 92.
During neutron irradiation, significant amounts of
36
from calcium (McDOUGALL & HARRISON 1999). As
Ar,
37
Ar and
39
Ar are mainly produced
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 36Ar
and
39
Ar. This is done by measuring the Ar isotope composition of a pure irradiated Ca-salt
(CaF2) which results in the corresponding correction factors (that represent the constant
production rate ratios for the corresponding isotopes:
⎛ 36 Ar ⎞
⎛ 39 Ar ⎞
⎜⎜ 37 ⎟⎟ and ⎜⎜ 37 ⎟⎟
⎝ Ar ⎠Ca
⎝ Ar ⎠Ca
Because of the significant production of neutron-induced
measured
40
Ar from potassium, corrections on
40
Ar also need to be made. Particularly during the irradation of young samples, the
potassium correction factor
⎛ 40 Ar ⎞
⎜⎜ 39 ⎟⎟ =
⎝ Ar ⎠ K
(
40
Arm − 36Arm × 295.5
39
Arm
)
(3)
5
becomes increasingly important. In a pure, calcium-free potassium salt (K2SO4) the complete
amount of
39
Ar will be derived from potassium (39Arm =
39
ArK) and can be used to determine
the correction factor.
40
Aratm must also be corrected for in terrestrial samples which is done by the known
40
Ar/36Ar
ratio:
⎛ 40 Ar ⎞
⎜⎜ 36 ⎟⎟ = 295 .5
⎝ Ar ⎠ atm
(4)
All the described interference corrections and correction factors are associated with an
analytical error, that must be considered in 39Ar/40Ar dating.
With respect to
38
Ar, it is widely accepted that
38
Ar 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).
5.3
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.
Figure 4: Plot illustrating the flux gradient, reflected in the irradiation parameter J. It could be easily seen that the
J-value differs with he distance to the reactor core. Position 1 was closest to the reactor core during irradiation.
(McDOUGALL & HARRISON 1999, after McDOUGALL 1974)
6
By calculating the
40
Ar*/39ArK 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:
J=
e λt − 1
40
Ar *
39
ArK
(5)
where λ is the constant of proportionality (the decay constant), t ist the age,
radiogenic argon and
40
Ar* the
39
ArK 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:
t=
⎛
ln ⎜⎜1 + J
λ ⎝
1
40
39
Ar * ⎞
⎟
ArK ⎟⎠
(6)
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:
⎡ C − 1⎤ 2 ⎡ λC ⎤ 2 ⎡ TmC ⎤ 2
= ⎢
σ F + ⎢ ⎥ σ T0 + ⎢
⎥ σλ
⎣ F ² ⎥⎦
⎣ F ⎦
⎣ F ⎦
2
σ
2
J
where F =
2
2
(7)
40
Ar*/39ArK, C = exp(λT0), T0 is the age of the primary standard, λ the total decay
constant of 40K and Tm = age of the sample as calculated from eq. (8) (KOPPERS 2002). The
first part is reflecting the analytical error in the determination of the
40
Ar*/39ArK ratio. The
remaining part reflects the uncertainties in the age standard and λ that can also be used for
derivaton of internal and external errors of the parameter J.
5.4
Half life / Decay constants
Like in other dating systems, the accuracy of the
40
Ar/39Ar dating technique lags behind the
analytical precision, largely because of uncertainties in the decay constants involved
(RENNE 1998a; see Figure 5).
7
Figure 5: Error in age (at a 95 % confidence level) due to decay constant uncertainties as a function of time. Solid
lines show results of propagating error calculations from experimental data used by geochronologists. (Modified
after: RENNE 1998a)
Because of the two different modes of 40K decay, i. e. (1) the electron capture to 40Ar followed
by emission of γ-ray and (2) the ß- decay to 40Ca (MIN 2000), the accuracy of 40Ar/39Ar 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 ArAr 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)
5.5
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:
8
40
Ar* = 40Artotal – (36Aratm x 295.5)
where
40
Artotal is the total
constant ratio of
(8)
40
36
Ar measured,
Aratm is the atmospheric argon and 295,5 the
40
Ar/36Ar 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 (40ArE), the
Ar, apart from atmospheric
40
mineral by processes not related to the in-situ decay of
40
component of radiogenic
40
Ar, that was brought into a rock or
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).
6.
Conclusions
This paper outlines a brief insight into the wide variety of problems associated to the 40Ar/39Ar
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 40Ar/39Ar dating. In conclusion, even for minimizing all potential
error sources, absolute radiogenic ages will never be exactly.
9
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Ar/39Ar dating method.
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10
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