Geoscience Reference
In-Depth Information
Table 6.3
Broad estimates of concentrations of radioactive and common
daughter elements in rocks
U
(ppm)
Th
(ppm)
Pb
(ppm)
K
(%)
Rb
(ppm)
Sr
(ppm)
Sm
(ppm)
Nd
(ppm)
Granitoid
4
15
20
3.5
200
300
8
44
Basalt
0.5
1
<
4
0.8
30
470
10
40
Ultramafic
0.02
0.08
0.1
0.01
0.5
50
0.5
2
Shale
4
12
20
2.7
140
300
10
50
Source
: After York and Farquhar (1972) and Faure (1986).
daughter lead present in the rocks would result in an overestimation of their
age. As another example consider argon, a gas, which is the daughter product
of
40
K decay. Although argon is not likely to have been present in the rock
initially, it cannot be retained in minerals until they have cooled to below their
closure temperatures
(about 300
◦
C for biotite and 550
◦
C for hornblende). These
are informal estimates; actual temperatures depend on local conditions. Thus, a
potassium-argon date of, say, a granite is not the date of its intrusion but the
time at which the minerals in the granite cooled below their particular closure
temperatures. If, after cooling, the granite were reheated to temperatures above
the closure temperatures, then argon would be lost. A potassium-argon date,
therefore, dates the last time that the sample cooled below the closure temperature.
Table 6.4 is an informal compilation of closure temperatures for various dating
methods.
The relationship between the closure temperature of a mineral and its cooling
history can be put onto a more rigorous footing by the use of thermodynamics.
Since the diffusion of any species in a solid mineral is controlled by temperature,
the
diffusion coefficient D
can be defined as
D
=
D
0
e
−
E
/
(
RT
)
(6.24)
where
D
0
is the diffusion coefficient of the particular species and mineral involved
at infinitely high temperature,
E
the activation energy of the diffusion process,
R
the gas constant and
T
the temperature. This is the
Arrhenius equation
. Clearly
D
, the diffusion coefficient, is very dependent on temperature; a small change in
T
can produce an order-of-magnitude change in
D
(Fig. 6.1). An expression for
the closure temperature
T
c
(sometimes referred to as the blocking temperature)
is
−
E
RT
c
=
log
e
AD
0
RT
c
t
T
=
T
c
(6.25)
α
2
E
∂
T
/∂
