The U-Pb system

U and Th are found on the extremely heavy end of the Periodic Table of
Elements. All their isotopes are radioactive and exhibit α-decay and
sometimes even spontaneous fission (see Section 7.2). ^{232}Th, ^{235}U and
^{238}U each form the start of long decay series comprising multiple
α- and β emissions which eventually produce various isotopes of
Pb:

| (5.1) |

Each of these three decay series is unique, i.e. no isotope occurs in more
than one series (Figure 2.2). Furthermore, the half life of the parent isotope
is much longer than any of the intermediary daughter isotopes, thus
fulfilling the requirements for secular equilibrium (Section 2.4). We can
therefore assume that the ^{206}Pb is directly formed by the ^{238}U, the ^{207}Pb
from the ^{235}U and the ^{208}Pb from the ^{232}Th. Several chronometers are
based on the α-decay of U and Th:

Natural Pb consists of four isotopes ^{204}Pb, ^{206}Pb, ^{207}Pb and ^{208}Pb. The
ingrowth equations for the three radiogenic Pb isotopes are given
by:

| (5.2) |

With λ_{238} = 1.55125 ×10^{-10}a^{-1} (t_{1∕2} = 4.468 Gyr), λ_{235} = 9.8485
×10^{-10}a^{-1} (t_{1∕2} = 703.8 Myr), and λ_{232} = 0.495 ×10^{-10}a^{-1} (t_{1∕2} = 14.05
Gyr). The corresponding age equations are:

| (5.3) |

Some igneous minerals (notably zircon) conveniently incorporate lots of
U and virtually no Pb upon crystallisation. For those minerals, the
non-radiogenic Pb can be safely neglected (at least for relatively young
ages), so that we can assume that Pb ≈ Pb^{*}. This assumption cannot be
made for other minerals, young ages, and high precision geochronology.
In those cases, the inherited component (aka ‘common Pb’) needs
to be quantified, which is done by normalising to non-radiogenic
^{204}Pb:

| (5.4) |

where _{∘} stands for the common Pb component for isotope x.
The corresponding age equations then become:

| (5.5) |

U-Pb dating grants access to two separate geochronometers (^{206}Pb/^{238}U
and ^{207}Pb/^{235}U) based on different isotopes of the same parent-daughter
pair (i.e. U & Pb). This built-in redundancy provides a powerful internal
quality check which makes the method arguably the most robust and
reliable dating technique in the geological toolbox. The initial Pb
composition can either be determined by analysing the Pb composition of a
U-poor mineral (e.g., galena or feldspar) or by applying the isochron
method to samples with different U and Th concentrations. As is the case
for any isotopic system, the system needs to remain ‘closed’ in order to yield
meaningful isotopic ages. This sometimes is not the case, resulting in a loss
of Pb and/or U. Such losses cause the ^{206}Pb/^{238}U- and ^{207}Pb/^{235}U-clocks
to yield different ages. Note that isotopic closure is required for all
intermediary isotopes as well. Critical isotopes are the highly volatile ^{226}Rn
(t_{1∕2}=1.6ka) and ^{222}Rn (t_{1∕2}=3.8d). Initially, the U-Pb method was applied
to U-ores, but nowadays it is predominantly applied to accessory
minerals such zircon and, to a lesser extent, apatite, monazite and
allanite.

The ^{207}Pb/^{206}Pb method is based on the U-Pb method and is obtained by
dividing the two U-Pb members of Equation 5.2 (or 5.4), and taking into
account that the average natural ^{238}U/^{235}U-ratio is 137.818:

| (5.6) |

The left hand side of this equation contains only Pb isotopic ratios. Note that these are only a function of time. Equations 5.6 has no direct solution and must be solved iteratively. The Pb-Pb method has the following advantages over conventional U-Pb dating:

- There is no need to measure uranium.
- The method is insensitive to recent loss of U and even Pb, because this would not affect the isotopic ratio of the Pb.

In practice, the Pb-Pb method is rarely applied by itself but is generally
combined with the U-Pb technique. The expected (^{207}Pb∕^{206}Pb)^{*}-ratio for
recently formed rocks and minerals can be calculated from Equation 5.6 by
setting t→0:

| (5.7) |

This ratio was progressively higher as one goes back further in time. It was ≈ 0.6 during the formation of Earth.

It sometimes happens that the U-Th-Pb trio of chronometers does not yield
mutually consistent ages. It is then generally found that t_{208} < t_{206} <
t_{207} < t_{207∕206} which, again, shows that the Pb-Pb clock is least
sensitive to open system behaviour. From Equation 5.2, we find
that:

| (5.8) |

If we plot those ^{206}Pb^{*}/^{238}U- and ^{207}Pb^{*}/^{235}U-ratios which yield the
same ages (t) against one another, they form a so-called ‘concordia’ curve.
The concordia diagram is a very useful tool for investigating and
interpreting disruptions of the U-Pb system caused by ‘episodic lead loss’.
This means that a mineral (of age T_{∘}, say) has lost a certain percentage
of its radiogenic Pb at a time T_{1} after its formation (e.g., during
metamorphism), after which the system closes again and further
accumulation of radiogenic Pb proceeds normally until the present. On the
concordia diagram of multiple aliquots of a sample, this scenario will
manifest itself as a linear array of datapoints connecting the concordant
^{206}Pb^{*}/^{238}U - ^{207}Pb^{*}/^{235}U composition expected at T_{∘} with that
expected at T_{1}. With time, the data shift further away from the origin.
The upper intercept of the linear array (aka discordia line) can be
used to estimate the crystallisation age, whereas the lower intercept
yields the age of metamorphism. The greater the distance from the
expected composition at t, the greater the degree of Pb loss and the
greater the linear extrapolation error on the crystallisation age (Figure
5.1).

Zircon (ZrSiO_{4}) is a common U-Th-bearing accessory mineral in acidic
igneous rocks, which form the main proto-sources of the siliciclastic
sediments. Zircon is a very durable mineral that undergoes minimal
chemical alteration or mechanical abrasion. Therefore, zircon crystals can
be considered time capsules carrying the igneous and metamorphic history
of their proto-sources. The probability distribution of a representative
sample of zircon U-Pb ages from a detrital population can serve as a
characteristic fingerprint that may be used to trace the flow of sand through
sediment routing systems. As a provenance tracer, zircon U-Pb data are less
susceptible to winnowing effects than conventional petrographic techniques.
Using modern microprobe technology (SIMS and LA-ICP-MS, see Chapter
3.1), it is quite easy to date, say, a hundred grains of zircon in a matter
of just a few hours. Due to the robustness of zircons as a tracer
of sedimentary provenance, and the relative ease of dating them,
the use of detrital zircon U-Pb geochronology has truly exploded
in recent years. A literature survey using the keywords ‘detrital’,
‘zircon’, and ‘provenance’ indicates that the proliferation of detrital
zircon studies has followed an exponential trend, with the number of
publications doubling roughly every five years over the past two decades. At
present, nearly a thousand detrital zircon publications appear each
year.

An extensive survey of late Archaean sandstones from the Jack Hills in Australia have revealed a subpopulation of detrital zircons with Hadean (4.1-4.2 Ga) U-Pb ages. These are the oldest terrestrial minerals known to science, predating the oldest igneous rocks by 300 million years. The isotopic composition of oxygen, hafnium and other elements in the zircon represents a unique window into the earliest stages of Earth evolution. They indicate that liquid water was present on the surface of our planet early on in its history. This isotopic evidence is corroborated by the geological observation that the Hadean zircons are preserved in fluvial deposits.