36 Ar (essential for the atmospheric correction and
40 Ar
*
content calculation) can be measured in the same way. Thus,
in a single measurement, one can calculate the proportions of
40 K and
40 Ar
* present in a sample, and from this, calculate
its age. In their 1966 article, Merrihue and Turner established the fundamentals in terms of approach and concepts
for the
40 Ar/
39 Ar method. In particular, they showed that the
relative proportions of radioactive parents and radiogenic
daughters can be calculated accurately from a measurement
by mass spectrometry.
In addition, since isotopic ratios can be measured more
precisely than the concentrations of K and Ar, this method
improves the accuracy of the ages and can be used for dating
smaller samples than the
40 K/
40 Ar method does. This same
work laid the groundwork for the application of isochrones
and age spectra (concepts that will be discussed below) to
the
40 Ar/
39 Ar method.
The
40 K/
40 Ar and
40 Ar/
39 Ar methods became very popular in geology as they are applicable to different terrestrial
geological materials, such as terrestrial magmatic rocks
(volcanic, plutonic, metamorphic) and extraterrestrial (meteorites, moon samples) ones. For some measurements, the
40 K/
40 Ar method is also well suited to the dating of clay
minerals. The range of application of these isotopic age
dating methods has an upper limit of 3 billion years and a
lower limit of 10,000 years.
These two methods were used to date major events in the
history of the Earth (fauna and flora of the Mesozoic and
Cenozoic, mass extinctions, origin and evolution of hominids, major volcanic eruptions, genesis and evolution of the
large mountain chains, etc.). They were, and still are, used to
establish and calibrate the geological time scale, including
the time scale of the reversals of Earth’s magnetic field, very
useful tie-points in paleoclimatology.
In the following, we present the main principles and areas
of application of these two methods. For further details, the
reader may refer to the works of Dalrymple and Lanphere
(1969) and McDougall and Harrison (1988).
Principles of the K-Ar Method
Diagram of Radioactive Decay in
40
K
The principle of the
40 K/
40 Ar method is based on the natural
radioactive decay of
40 K in
40 Ar (Fig. 5.1). The decay of
40
K
is complex. At 88.8%, the
40 K decays to
40 Ca by emitting
b
− . At 11.2% it decays to
40 Ar
* , either by emitting b
+
(0.01%), or by direct electronic capture (0.16%) or by
electron capture followed by a c emission (11%). This last
mechanism is the most common. An electron from the atom
is captured, resulting in the formation of a neutron at the
expense of a proton. The
40 Ar atom thus produced is in an
excited state. It then returns quickly to its ground state by
emitting gamma radiation.
The Age Equation
As with the other isotopic clocks, the fundamental law of
radioactive decay applies:
N ¼ N 0 e
Àkt
ð5:1Þ
N: number of radioactive parent atoms (
40 K) at time t, N 0 :
number of radioactive parent atoms at t 0 , k: decay constant.
From Eq. (5.1), we can calculate the number of daughter
atoms (D
à =
40 K +
40 Ca) formed over time t:
N o ¼ Ne
kt
D
Ã
¼ N o À N ¼ Ne
kt
À N ¼ N e
kt
À 1
À
Á
ð5:2Þ
The constants and isotopic abundances required for the
age calculation are listed in Table 5.1.
The age equation is established from Eq. (5.2):
40
Ar
Ã
¼
k
k
40
K e
kt
À 1
À
Á
ð5:3Þ
where
40 Ar
* is the isotope of argon produced from the in situ
decay of
40 K, k the total radioactive decay constant of
40
K
equal to k e + k b . The ratio of proportionality
k
k corresponds
to the fraction of the decay leading to the formation of
40 Ar
*
(and not of
40 Ca
* ).
From Eq. (5.3) we get:
t ¼
1
k
ln
40 Ar
Ã
40 K
k
k
þ 1
ð5:4Þ
with t expressed in years.
40
Ar (ground state)
40
Ca (ground state)
40 K
E=1.46MEV.
11%
γ
E=0.05MEV.
c.e.
E=1.51MEV.
0.16%
c.e.
E=0.49MEV.
0.01%
β +
E=1.32MEV.
88.8%
β -
Fig. 5.1 Diagram of radioactive decay of
40
K
74
H. Guillou et al.
40 Ar
*
content calculation) can be measured in the same way. Thus,
in a single measurement, one can calculate the proportions of
40 K and
40 Ar
* present in a sample, and from this, calculate
its age. In their 1966 article, Merrihue and Turner established the fundamentals in terms of approach and concepts
for the
40 Ar/
39 Ar method. In particular, they showed that the
relative proportions of radioactive parents and radiogenic
daughters can be calculated accurately from a measurement
by mass spectrometry.
In addition, since isotopic ratios can be measured more
precisely than the concentrations of K and Ar, this method
improves the accuracy of the ages and can be used for dating
smaller samples than the
40 K/
40 Ar method does. This same
work laid the groundwork for the application of isochrones
and age spectra (concepts that will be discussed below) to
the
40 Ar/
39 Ar method.
The
40 K/
40 Ar and
40 Ar/
39 Ar methods became very popular in geology as they are applicable to different terrestrial
geological materials, such as terrestrial magmatic rocks
(volcanic, plutonic, metamorphic) and extraterrestrial (meteorites, moon samples) ones. For some measurements, the
40 K/
40 Ar method is also well suited to the dating of clay
minerals. The range of application of these isotopic age
dating methods has an upper limit of 3 billion years and a
lower limit of 10,000 years.
These two methods were used to date major events in the
history of the Earth (fauna and flora of the Mesozoic and
Cenozoic, mass extinctions, origin and evolution of hominids, major volcanic eruptions, genesis and evolution of the
large mountain chains, etc.). They were, and still are, used to
establish and calibrate the geological time scale, including
the time scale of the reversals of Earth’s magnetic field, very
useful tie-points in paleoclimatology.
In the following, we present the main principles and areas
of application of these two methods. For further details, the
reader may refer to the works of Dalrymple and Lanphere
(1969) and McDougall and Harrison (1988).
Principles of the K-Ar Method
Diagram of Radioactive Decay in
40
K
The principle of the
40 K/
40 Ar method is based on the natural
radioactive decay of
40 K in
40 Ar (Fig. 5.1). The decay of
40
K
is complex. At 88.8%, the
40 K decays to
40 Ca by emitting
b
− . At 11.2% it decays to
40 Ar
* , either by emitting b
+
(0.01%), or by direct electronic capture (0.16%) or by
electron capture followed by a c emission (11%). This last
mechanism is the most common. An electron from the atom
is captured, resulting in the formation of a neutron at the
expense of a proton. The
40 Ar atom thus produced is in an
excited state. It then returns quickly to its ground state by
emitting gamma radiation.
The Age Equation
As with the other isotopic clocks, the fundamental law of
radioactive decay applies:
N ¼ N 0 e
Àkt
ð5:1Þ
N: number of radioactive parent atoms (
40 K) at time t, N 0 :
number of radioactive parent atoms at t 0 , k: decay constant.
From Eq. (5.1), we can calculate the number of daughter
atoms (D
à =
40 K +
40 Ca) formed over time t:
N o ¼ Ne
kt
D
Ã
¼ N o À N ¼ Ne
kt
À N ¼ N e
kt
À 1
À
Á
ð5:2Þ
The constants and isotopic abundances required for the
age calculation are listed in Table 5.1.
The age equation is established from Eq. (5.2):
40
Ar
Ã
¼
k
k
40
K e
kt
À 1
À
Á
ð5:3Þ
where
40 Ar
* is the isotope of argon produced from the in situ
decay of
40 K, k the total radioactive decay constant of
40
K
equal to k e + k b . The ratio of proportionality
k
k corresponds
to the fraction of the decay leading to the formation of
40 Ar
*
(and not of
40 Ca
* ).
From Eq. (5.3) we get:
t ¼
1
k
ln
40 Ar
Ã
40 K
k
k
þ 1
ð5:4Þ
with t expressed in years.
40
Ar (ground state)
40
Ca (ground state)
40 K
E=1.46MEV.
11%
γ
E=0.05MEV.
c.e.
E=1.51MEV.
0.16%
c.e.
E=0.49MEV.
0.01%
β +
E=1.32MEV.
88.8%
β -
Fig. 5.1 Diagram of radioactive decay of
40
K
74
H. Guillou et al.