5.3 Common (whole-rock) Pb)Pb dating
The whole rock Pb)Pb dating method is based on
rearranging the U)Pb decay equations [5.5] and [5.4] to bring the Pb/Pb terms to the left-hand side:
(207Pb) (207Pb) 235U
())))) ! ()))))
= ))))
(e8235 t ! 1) [5.9]
(204Pb)P (204Pb)I 204Pb
(206Pb) (206Pb) 238U
())))) ! ()))))
= ))))
(e8238 t ! 1) [5.10]
(204Pb)P (204Pb)I 204Pb.
Nier et al.
(1941) showed that if these two equations refer to the same system, equation
[5.9] can be divided by [5.10], and the 204Pb terms in the
right-hand side of the equations cancel out, leaving the term 235U/238U
(which has a constant value of 1/137.88 throughout the solar system). This
yields the simplified equation:
(207Pb) (207Pb) [5.11]
()))))
! ()))))
(204Pb)P (204Pb)I 1 (e8235 t ! 1)
)))))))))))))))
= )))))
@ )))))))
(206Pb) (206Pb) 137.88 (e8238 t ! 1)
()))))
! ()))))
(204Pb)P (204Pb)I
If
we consider a number of systems which have the same age and initial isotopic
composition (e.g. whole-rock samples of a granite)
then it can be seen from equations [5.9] and [5.10] that they will develop
different Pb isotope compositions, according to their
U/Pb ratios, at the present day. Therefore, if the
present-day Pb isotope compositions of this suite are
plotted (left-hand side of equation [5.11]), they should form a straight-line
array, provided that they have remained closed systems. The slope of this
array, which was first termed an ‘isochrone’ by Houtermans (1947), depends only on t, and does not require any knowledge of the U and Pb concentrations in the samples. It should be noted that
the isochron equation [5.11] is ‘transcendental’. In
other words the term on the right-hand side (equal to the slope), cannot be
solved algebraically to yield the age, t,
but must therefore be solved iteratively by computer.
Since
the closed U)Pb system requirement remains, it might be
wondered what advantage this method offers over the discredited whole-rock U)Pb isochron
method (section 5.1), in view of the known high mobility of uranium. However, this
question can be answered empirically. Fig. 5.25 shows a whole-rock Pb)Pb isochron
diagram for the
Fig. 5.25. Pb)Pb
isochron diagram for whole-rock and mineral samples
of the
5.3.1 The geochron
The first application of the common Pb)Pb dating technique was actually to
meteorites rather than terrestrial rocks. In this study, Patterson (1956)
calculated a Pb)Pb age of 4.55 " 0.07 Byr
on a suite of three stony meteorites and two iron meteorites (Fig. 5.26). The
least radiogenic of these samples was troilite (
Fig. 5.26. Pb)Pb isochron
diagram for iron and stony meteorites ( # , Q ) and a ‘Bulk Earth’ sample of
oceanic sediment ( ! ), showing that the Earth lies on the meteorite isochron,
therefore also called the ‘geochron’. After Patterson
(1956).
Patterson
also solved a problem that had occupied geochronologists for decades, namely
the age of the Earth. A sample of recent oceanic sediment, regarded as the best
estimate of the Bulk Earth Pb isotope composition,
lay on the meteorite isochron, and furthermore had
the appropriate U and Pb concentrations to be
generated by radiogenic Pb growth from the Canyon
Diablo composition in 4.55 Byr. This finding provided
good evidence that the Earth has both the same age and the same ultimate origin
as meteorites. The meteorite isochron was therefore
termed the Geochron.
Subsequent
work has shown that the interpretation of pelagic sediment as a Bulk Earth
composition is only a rough approximation to the complexities of terrestrial Pb isotope evolution. Therefore the apparent Pb)Pb age of the Earth must now be revised downwards
slightly (section 5.4.3). However, the new value is almost within experimental
error of the determination of Patterson.
Because
235U was relatively abundant in the early Solar System, and because
of its relatively short half-life of 704 Myr, Pb-Pb dating on meteorites can provide very accurate ages
for the early evolution of the Solar System. Based on evidence from extinct
nuclides (section 15.4.1) calcium–aluminium inclusions (CAIs)
from the Allende chondrite
are regarded as the oldest Solar System objects, and are therefore of
particular interest in dating the early evolution of the Solar System.
Inclusions and chondrules both have high U/Pb ratios, but a significant common Pb
component rules out direct application of the U–Pb
method. Several Pb–Pb
dating studies have therefore been performed, mostly on mixed suites of chondrules and inclusions. However, Chen and Wasserburg (1981) obtained the first precise age from
inclusions alone, which gave an age of 4568 " 5 Myr.
Two-point
isochrons between Canyon Diablo and any individual
inclusion can be calculated. These are termed model 207/206 ages because they
rely on the assumption that initial lead in the inclusion was the same as
Canyon Diablo. However, Allegre et al. (1995a) showed that
the 207/206 ages in the inclusions were correlated with the 206Pb/204Pb
ratio, which measures the amount of common Pb in each
sample (Fig. 5.27). This suggests that the inclusions were contaminated with
extraneous common Pb from outside the chondrules that did not match Canyon Diablo Pb. Therefore, Allegre et al. utilised a progressive leaching
procedure to remove the common Pb component. The
results of this procedure gave 207/206 ages within error of the most radiogenic
data of Chen and Wasserburg, with an improved age of
4566 +2/–1 Myr.
Fig. 5.27. Plot of 207/206 ages for Allende calcium-aluminium inclusions (CAIs)
showing an inverse correlation with common Pb
content. ( " ) = bulk samples; ( ! ) = leached. After Allegre et al. (1995a). (NOTE: the age
should read 4566 Myr, not 4561 Myr).
A
similar approach was used by Amelin et al. (2002) to achieve a high quality Pb–Pb isochron
on acid-washed whole-rock chondrules from the Acfer chondrite. The data are
shown in Fig. 5.28 on an alternative form of the Pb–Pb isochron diagram which is the
same as the third dimension in the Total-Pb/U isochron diagram (Fig. 5.21). On this diagram the intercept
indicates the 207/206 age for an infinitely radiogenic sample. Because the
samples analysed by Amelin et al. were very radiogenic, they gave an excellent intercept,
corresponding to an age of 4564.7 " 0.6 Myr for chondrule formation (MSWD = 0.5). Acid washed whole-rock fragments of two CAIs from the Efremovka chondrite also gave excellent Pb–Pb isochrons (MSWD = 0.9 and 1.1)
with an average intercept age of 4567.2 " 0.6 Myr
which is 2.5 Myr older than the chondrite
isochron. This age difference is consistent with the
age differences between CAIs and chondrules
determined from extinct nuclide (26Al—26Mg) systematics (section 15.4.1). Hence, this evidence provides
a reliable anchor for the chronology of the early Solar System.
Fig. 5.28. Alternative Pb–Pb isochron diagram showing
207/206 (intercept) ages for acid-washed chondrules
(open ellipses) and calcium-aluminium inclusions (= CAIs,
solid ellipses). After Amelin et al. (2002).
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