K
K/Ar AND Ar/Ar DATING
R M Twyman, University of York, York, UK
ª
2007 Elsevier B.V. All rights reserved.
Introduction
Radiometric dating methods measure the decay of
naturally occurring radioactive isotopes, and are
used to determine the ages of rocks, minerals, and
archaeological artifacts. Of the 84 elements found in
nature, there are 70 naturally occurring radioactive
isotopes whose half-lives vary from a few thousand
years (e.g., carbon-14 (14C) 5,730 years) to billions of
years (e.g., samarium-147 (147Sm), 1.06 1011
years). Potassium–argon dating is based on measuring the decay of potassium-40 (40K) to argon-40
(40Ar), a process with a half-life of 1.25 109 years.
This makes the process suitable for dating rocks and
minerals ranging from a few tens of thousands to
more than 1 billion years in age, spanning most geologically relevant time periods is Earth’s history.
Radioactive decay is a nuclear process and is independent of chemical and physical conditions found in
geological processes. It has been shown that radioactive decay is constant over the wide range of temperatures and pressures encountered in geological
events. Consequently, potassium–argon dating is
one of the most widely used geological dating methods. Argon–argon dating is a derivative method in
which samples are bombarded in a fast neutron reactor, converting a proportion of the abundant and
stable isotope 39K into 39Ar. This article describes
the principles and practical aspects of these two
forms of radiometric dating.
Principles of Radiometric Dating
Atomic nuclei are composed of protons and neutrons, only certain combinations of which are inherently stable. Radioactive decay is a property of
unstable nuclei, involving either the ejection or capture of subatomic particles, and resulting ultimately
in the formation of a stable nucleus. The daughter
nucleus formed by radioactive decay may be a different isotope of the same element as the parental
nucleus if the number of protons remains the same,
or a different element may be formed as is the case in
39
K to 39Ar decay. In some cases, radioactive nuclei
decay directly into stable nuclei, whereas in others
the daughter nucleus may itself be unstable, and may
decay further. Radioactive decay may proceed
through several steps until a stable nucleus is formed.
Radiometric dating relies on one of three types of
radioactive decay. The first and most dramatic occurs
predominantly among heavier isotopes and is known
as -decay. During this process, the unstable nucleus
ejects an -particle, which comprises two protons
and two neutrons. The atomic mass of the daughter
nucleus is four units lower than that of the parent
nucleus. More common among lighter isotopes is decay, in which a high-energy electron (-particle) is
ejected from the nucleus, converting a neutron into a
proton, and releasing an antineutrino. Although the
number of protons in the nucleus is increased by one,
the number of neutrons decreases by one and the
atomic mass therefore remains unchanged. The
third form of radioactive decay is known as electron
capture, and is essentially the reverse of -decay.
During this process, an electron from the innermost
electron shell is captured in the nucleus and converts
a proton into a neutron. The atomic number of the
nucleus decreases by one, but because a neutron is
gained there is, again, no overall change in atomic
mass. Electron capture occurs in 39K to 39Ar decay.
The half-life of a radioactive isotope is a measure
of nuclear stability, and reflects the statistical likelihood that a given nucleus will decay in a given time
(see Dating Techniques). This likelihood is expressed
in the form of a decay constant , as shown in the
following equation:
N ¼ N0 e – lt
where N is the number of radioactive parent nuclei
present at any particular time t, and N0 is the number
of such nuclei initially present in the sample. The
1314 K/Ar AND Ar/Ar DATING
half-life (t1=2) is the value of t when N ¼ N0/2, i.e.,
the time taken for half the atomic nuclei in a given
sample to decay.
From a practical standpoint, the above equation is
of little use in radiometric dating because N0 is never
known. However, it can be assumed for any time
point t that N0 is the sum of the parental nuclei (P)
remaining in the sample and the daughter nuclei (D)
formed by radioactive decay. This can be expressed
formally as:
N0 ¼ NP þ ND
We can therefore substitute NP þ ND for N0 in the
original equation to yield:
N ¼ ðNP þ ND Þ e – lt
This can be rearranged to give:
ND ¼ NP ðe – lt þ 1Þ
If this equation is solved for t, it allows the age of a
rock or mineral to be determined by measuring the
relative abundances of the parent and daughter nuclei
in the sample, which is the underlying principle of
radiometric dating:
t ¼ 1=l log e ðND =NP þ 1Þ
More specifically for the subject of this article, the
age of a sample can be described in the simplest terms
by the following equation:
t ¼ 1=l log e ð40Ar=40 K þ 1Þ
It should be emphasized, however, that the above
holds true only if the sample contained no 40Ar at the
time of formation, i.e., if at time t ¼ 0 there was 100%
40
K (the parent radioactive nucleus) and 0% 40Ar (the
stable daughter nucleus). The potassium–argon
method is the only radiometric dating method where
this assumption can generally be made, since any
argon formed by decay prior to the formation of
solid rock will diffuse away, while argon produced
after solidification will accumulate within the rock.
Even so, this requires that the rock cools rapidly. It is
necessary to take into account the possibility of argon
from other sources being present in the rock, for example, diffusing in from the atmosphere or being formed
through the decay of other isotopes. If we call the
number of daughter nuclei present at time zero ND0,
the generic equation can be modified as follows to
correct for the incorporation of argon at formation:
t ¼ 1=l log e ½ðN D – N D0 Þ=N P þ 1
Replacing the generic terms with specific isotopes,
we get the following simplified equation which can
be used to calculate the age of material using the
potassium–argon method:
t ¼ 1=l log e ½ð40 Art – 40 Art ¼ 0 Þ=40 K þ 1
This holds true as long as the sample is a closed
system, i.e., there is no change in the abundance ratio
between the parent and daughter isotopes other than
that caused by radioactive decay. If this condition is not
met, or if external factors influencing the ratio are not
accounted for, then dating using the potassium–argon
method will be inaccurate. Relevant examples may
include the creation of more parental isotope through
the radioactive decay of larger nuclei, the mixing of
samples of different ages over geological timescales, or
the loss of daughter isotope through the leaching of
gaseous argon after the rock has formed. This depends
on the type of sample and the geological conditions
under which it was formed and preserved, and may
need to be evaluated on a case-by-case basis.
Potassium–Argon Dating
The potassium–argon method is based on the decay of
40
K to 40Ar. It is a widely used method not only
because the half-life of the reaction makes it suitable
for the dating of rocks ranging in age from thousands
to billions of years, but also because potassium is very
abundant in rocks and minerals, and is overall the
eighth most common element in the Earth’s crust.
Potassium has one radioactive isotope (40K) and two
stable isotopes (39K and 41K). The relative abundances
are 39K, 92.23%; 40K, 6.73%; and 41K, 0.00118%.
The 40K isotope undergoes two forms of decay
with different likelihoods (Fig. 1). About 11.7% of
decay events involve electron capture and result in
the formation of 40Ar, whereas 88.3% of events
occur through -emission and result in the formation
of calcium-40 (40Ca). The ratio of these events is
known as the branching ratio, and must be taken
into account in potassium–argon dating calculations.
Since 40Ca is formed more frequently than 40Ar, in
might seem logical to measure the calcium daughter
rather than argon. However, this is impractical for
two reasons, first because 40Ca is the most abundant
calcium isotope in rocks making it more difficult to
measure small increments resulting from decay of
40
K, and second because calcium does not diffuse
out of molten rock like argon, so the amount of the
isotope initially present in the rock needs to be
known. Since argon is trapped only when the rock
solidifies, the formation of solid rock fixes the point
at which argon begins to accumulate through 40K
K/Ar AND Ar/Ar DATING
1315
β -emission
neutron becomes proton
+
88.3%
40Ca
20 protons, 20 neutrons
stable
11.7%
40K
electron capture
proton becomes neutron
19 protons, 21 neutrons
unstable
+
40Ar
18 protons, 22 neutrons
stable
Figure 1 The decay of 40K to 40Ca by -emission (88.3% of events) and to 40Ar by electron capture (11.7% of events).
decay, starting the radiometric clock when the rock
first forms. However, argon is an inert gas and will
not combine with other elements. Therefore, if the
rock is heated at some time after formation, argon gas
can escape from the crystal lattices and the radiometric
clock can be reset, making the sample appear younger
than it actually is. The method, therefore, works best
with intrusive igneous and extrusive volcanic rocks that
have crystallized from melts and have not been
reheated. The method does not work well on metamorphic rocks because these rocks have been produced
from other rocks by heat and pressure without being
completely melted, and have probably lost some or all
of the argon that has accumulated since formation.
The simplified equation shown above can be modified to take into account the branching ratio of 40K
decay, which gives the following:
t ¼ 1=ðl40 K ! 40 Ar þ l40 K ! 40 CaÞ
0.063%; and 36Ar, 0.337%. Since this argon can
diffuse into rocks (especially volcanic rocks) when
they form, corrections to dating calculations must
be made for the amount of atmospheric argon in a
sample at the time of formation, and must also take
into account any argon in the apparatus used to
process the sample otherwise the excess argon
makes the sample appear older than its true age.
This correction involves measuring the amount of
36
Ar in the experimental apparatus and multiplying
this by 295.5 which is the 40Ar/36Ar ratio in the
atmosphere, and subtracting this result from the
total amount of 40Ar. What remains is the quantity
we wish to measure, i.e., the amount of radiogenic
40
Ar produced the radioactive decay of 40K.
However, as stated above, excess argon can also
originate from other sources such as the mantle, as
bubbles trapped in a melt, or a xenocryst or xenolith
trapped during emplacement.
log e ð40 Ar=40 K½l40 K ! 40 Ar
þ l40 K ! 40 Ca=l40 K ! 40 Ar þ 1Þ
If values for the decay constants 40K ! 40Ar and
40
K ! 40Ca for are substituted in this equation, we
arrive at:
t ¼ 1:804 109 log e ð9:54340 Ar=40 K þ 1Þ
The distribution of argon isotopes must also be
taken into account. The potassium–argon method
uses a spike of 38Ar mixed with the argon extracted
from the rock/mineral to determine the amount of
40
Ar. Like potassium, argon has three isotopes with
the following abundances in air: 40Ar, 99.60%; 38Ar,
Argon–Argon Dating
The 40Ar/39Ar dating method is a derivative of potassium–argon dating in which the sample is irradiated
in a nuclear reactor with fast neutrons to convert a
fraction of the 39K to 39Ar. Like the conventional
method, argon–argon dating relies on the measurement of 40Ar produced by the radioactive decay of
40
K, but unlike conventional potassium–argon dating, it is unnecessary also to measure the amount of
40
K in the sample. Instead, the 39Ar produced in the
nuclear reactor is used as a substitute for 40K, and the
age is calculated from the ratio or argon isotopes.
This can be determined in a single experiment, rather
1316 K/Ar AND Ar/Ar DATING
than the two separate measurements required for
conventional potassium–argon dating.
As is the case in the conventional method, certain
assumptions need to be made and correction factors
need to be calculated to ensure accurate results. For
argon–argon dating, an important factor is the conversion of 39K to 39Ar. The amount of 39Ar produced in any
given irradiation will not only depend on the amount of
39
K in the sample, but also the duration and intensity of
irradiation, the latter expressed as the neutron flux density. It is virtually impossible to calculate these factors
from first principles so the approach used is to simultaneously irradiate a control sample known as the flux
monitor, whose age has already been determined. The
argon ratios from the flux monitor are used to calculate
a flux constant, J, which is applied to the age calculation
for the experimental sample as follows:
t ¼ 1:804 109 log e ð J40 Ar=39 Ar þ 1Þ
Corrections must be made for atmospheric argon
and for interfering argon isotopes produced by neutron reactions with calcium and other potassium isotopes. These reactions are shown in Table 1.
If an irradiated sample is completely melted, the
argon in the sample is released in a single stage and
provides an age comparable to that derived from
conventional potassium–argon dating, at least when
correction factors have been taken into account.
However, the main advantage of the 40Ar/39Ar
method is that multiple aliquots can be tested from
the same sample, usually using either a laser probe or
by step heating in a furnace to release argon samples
at progressively higher temperatures that can be collected and analyzed separately. Ages calculated for
each temperature increment can be plotted on an agespectrum diagram, which for an undisturbed sample
will yield a horizontal line (i.e., all ages are the same).
For other samples, there is some variation in the
calculated age at different temperatures and the
data can be plotted on an 40Ar/39Ar isochron or
isotope-correlation diagram. The data should fall on
or near a straight line whose slope is equal to the
ratio 40Ar/39Ar and whose intercept is the 40Ar/36Ar
ratio of nonradiogenic argon.
Although potentially more accurate than potassium–argon dating and more applicable to smaller
samples, the method does have some drawbacks.
One is the reliance on an age standard which must
be dated by an alternative method (usually the potassium–argon method) in order to derive the neutron
flux (J) constant. Another is the inherent error in
extrapolating the J constant between samples differing
in structure and homogeneity. This error can be minimized as much as possible by closely matching the
irradiation conditions of the sample and control, and
by using a series of control samples. Some materials
are also subject to a phenomenon known as argon
recoil, in which the kinetic energy gained by 39Ar
during the neutron bombardment is sufficient to eject
it from the sample. This is a significant problem in
grained materials like clay, and may also result in the
redistribution of argon in inhomogeneous samples.
Applications of K-Ar and Ar-Ar dating in
Quaternary Science
Because 40 K has a long half-life, K-Ar dating is most
applicable for determining the age of minerals and
rocks from hundreds of thousands to tens of millions
of years old. However, the technique is also useful for
archaeological applications, e.g., assigning approximate ages to archaeological artifacts at sites rich in
volcanic rock. K-Ar dating has been particularly useful, for example, for dating artifacts at Olduvai
Gorge, a steep ravine approximately 45 km in length
located in the eastern Serengeti Plains in northern
Tanzania, Africa. Olduvai Gorge is one of the most
important sites of prehistoric archaeology in the
world and has contributed much to our understanding of early human development. The deep stratigraphy reveals several layers, or beds, of volcanic material
Table 1 The principle of argon-argon dating is to measure the amount of 39Ar produced from 39K as a proportion of the amount of 40Ar.
However, 39Ar and 40Ar can both be produced in competing reactions involving various isotopes of calcium, chlorine, potassium and
argon present in the same sample. The reactions causing the most interference are identified by sad faces in the table, and correction
factors must be introduced to account for them. Such interfering reactions are monitored using laboratory salts and glasses which are
irradiated along with the sample. Other reactions identified by happy faces are beneficial, because they provide a means to calculate
correction factors. For example, the production of 38Ar from 37Cl allows the amount of chlorine in a sample to be determined.
Argon isotopes
Produced by the irradiation of:
Ca
K
Ar
40
39
36
39
36
Ar
40
37
Ar
38
Cl
Ca
Ca
Ar
42
39
Ar
42
40
Ar
43
Ca
43
Ca, Ca
Ca, 44Ca
K
41
40
40
38
K, K
39
K, K
40
K, 41K
Ar
37
Ar
Cl
40
Ar, Ar
K/Ar AND Ar/Ar DATING
which allow K-Ar dating of the embedded archaeological deposits. This has revealed that tools made from
rocks and pebbles were made by the inhabitants of
Olduvai more than 2 million years ago, while fossils
have been found in rocks which have been dated at 2.5
million years old. Bones discovered in the various beds
of Olduvai rock include modern humans from as
recently as 15–20,000 years ago, back to primitive
homonids such as Australopithecus boisei and Homo
habilis. K-Ar dating has also been used at other
prehistoric African sites with a history of volcanic activity including Hadar, on the Awash River in Ethiopia,
where the 3-million-year-old fossil of Australopithecus
afarensis, named Lucy, was discovered.
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See also: Dating Techniques. Fission-Track Dating.
Radiocarbon Dating: Conventional Method. U-Series
Dating.
References
Dalrymple, G. B., and Lanphere, M. A. (1969). Potassium–Argon
Dating. W. H. Freeman and Company, San Francisco.
Faure, G. (1986). Principles of Isotope Geology, Second edition.
Wiley, New York.
McDougall, I., and Harrison, T. M. (1999). Geochronology and
Thermochronology by the 40Ar/39Ar Method, Second edition.
Oxford University Press, New York.
Wintle, A. G. (1996). Archaeologically-relevant dating techniques
for the next century: small, hot and identified by acronyms.
Journal of Archaeological Science 23, 123–138.