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the
182
Hf/
180
Hf ratio of the gas at the time the system formed. The
182
Hf/
180
Hf ratio of the
solar nebula at the time the sample formed is obtained from:
182
Hf
180
Hf
spl
=
SN
182
Hf
180
Hf
SN
e
−
λ
182
Hf
t
=
=
(12.14)
t
0
182
W
183
W
spl
today
−
182
W
183
W
SN
today
/
/
(12.15)
180
Hf
183
W
spl
today
−
180
Hf
183
W
SN
today
/
/
If the
182
Hf/
180
Hf ratio of the solar nebula at the reference time
t
0 is assumed, the
result can be converted into an age. This age dates the time at which the dated sample
shared the same
182
Hf/
180
Hf ratio as the solar nebula. If no history of the
182
Hf/
180
Hf ratio
is assumed for the solar nebula, dividing this equation for one sample by the same equation
for a second sample gives the age difference between the two samples.
Similar equations hold for a number of extinct short-lived chronometers, which each
provide a time scale for different planetary phenomena:
=
1. The
26
Al-
26
Mg system (
T
1
/
2
=
0.75 Ma) dates the Al/Mg fractionation events associ-
ated with the condensation of high-temperature minerals (oxides, aluminates, pyroxenes
from the refractory inclusions) from the solar nebula.
2. The
182
Hf-
182
Wsystem(
T
1
/
2
=
8.9 Ma) dates the segregation of the siderophile ele-
ment W from the lithophile element Hf, i.e. the formation of planetary cores, such as
for the Earth-Moon system and for Mars, at
≈
30 Ma after the formation of the Solar
System (
Fig. 12.14
).
3. The
53
Mn-
53
Cr system (
T
1
/
2
=
3.7 Ma) dates the mantle-core differentiation of
planetary objects.
4. The
146
Sm-
142
Nd system (
T
1
/
2
=
103 Ma): the 20 ppm difference in
142
Nd abundances
between the terrestrial mantle-crust system and chondrites demonstrates the existence
of a magma ocean very early in the history of the Earth. There is a small excess of
142
Nd in early Archean samples, such as those from the 3.85-Ga-old terranes from west
Greenland, with respect to modern samples. Coupling these anomalies with the more
conventional
147
Sm-
143
Nd in much the same way as
238
U-
206
Pb and
235
U-
207
Pb are
coupled dates the end of the magma ocean episode a few tens of Ma after the formation
of the Solar System.
5. The
129
I-
129
Xe system (
T
1
/
2
=
15.7 Ma) came historically first. Its low closure tem-
perature makes it susceptible to metamorphic perturbations. The presence in MORB of
excess
129
Xe with respect to the atmosphere indicates that the mantle was outgassed,
i.e. the parent-daughter I/Xe reduced, while
129
I was still extant (
<
75Ma after the
accretion of the Solar System).
6. The
60
Fe-
60
Ni system (
T
1
/
2
=
1.5 Ma) is very particular since
60
Fe is the only undis-
puted nuclide inherited from supernovae. This controversial system therefore dates the
injection of stellar material into the nascent Solar System.
To some extent,
235
U nearly qualifies as an extinct radioactivity!
Applications of these chronometers to the Earth and the early Solar System have recently
produced startling results. Historically, differences in the isotopic abundances of
129
Xe
