Geoscience Reference
In-Depth Information
a stable isotope. Absolute abundances are often
not known or not treated. This introduces a haz-
ard into statistical treatments and mixing calcu-
lations involving ratios. Ratios cannot be treated
as pure numbers or absolute concentrations. The
means and variances of isotopic ratios are mean-
ingless unless all the samples have the same con-
centrations of the appropriate elements.
Lead has a unique position among the
radioactive nuclides. Two isotopes, lead-206 and
lead-207, are produced from radioactive parent
isotopes of the same element, uranium-238 and
uranium-235. The simultaneous use of coupled
parent--daughter systems allows one to avoid
some of the assumptions and ambiguities associ-
ated with evolution of a single parent--daughter
system. Lead-208 is the daughter of 232-Th (half-
life 14 Gyr); U and Th are geochemically similar
but are separable by processes that occur near
the surface of the Earth.
In discussing the uranium--lead system, it is
convenient to normalize all isotopic abundances
to that of lead-204, a stable nonradiogenic lead
isotope. The total amount of lead-204 in the Earth
has been constant since the Earth was formed;
theuraniumparentshavebeendecreasingby
radioactive decay while lead-206 and lead-207
have been increasing. The U/Pb ratio in various
parts of the Earth changes by chemical fraction-
ation and by radioactive decay. The
238
U/
204
Pb
ratio, calculated as of the present, can be used
to remove the decay effect in order to study the
chemical fractionation of various reservoirs. If
no chemical separation of uranium from lead
occurs, the ratio for the system remains constant.
This ratio is called
multistage or continuous differentiation models
are used, and similar models explain other iso-
tope systems, e.g. fractionation of Rb/Sr, Sm/Nd,
He/U etc.
A melt removed from the primitive reservoir
at
t
0
, will crystallize to a rock composed of min-
erals with different
values. If these minerals
can be treated as closed systems, then they will
have distinctive lead ratios that plot as a straight
line on a
207
Pb/
204
Pb--
206
Pb/
204
Pb plot (Figure 17.1).
This line is an
isochron
because it is the locus
of points that experienced fractionation at the
same time to form minerals with differing U/Pb
ratios. The residual rock will also plot on this
line,ontheothersideofthe
geochron
. The time
at which the rock was fractionated can be cal-
culated from the slope of the isochron. Mixing
lines between genetically unrelated magmas will
also be straight lines, in which case the age will
be spurious unless both magmas formed at the
same time.
In the uranium--lead decay system, the curve
representing the growth of radiogenic lead in
a closed system has marked curvature. This is
because uranium-238 has a half-life (4.47 Gyr)
comparable to the age of the Earth, whereas
uranium-235 has a much shorter half-life (0.704
Gyr). In early Earth history lead-207, the daughter
of uranium-235, is formed at a higher rate than
lead-206. For a late fractionation event
207
Pb/
204
Pb
changes slowly with time.
For isotopic systems with very long half-lives,
such as samarium-142 (106 Gyr) and rubidium-87
(48.8 Gyr), the analogous closed-system geochrons
will be nearly straight lines. Isochrons and mix-
ing lines, in general, are not straight lines. They
are straight in the uranium--lead system because
238
U/
204
Pb and
235
U/
204
Pb have identical fractiona-
tion factors, and mixing lines for ratios are linear
if the ratios have the same denominator.
The initial lead-isotopic composition in iron
meteorites can be obtained since these bodies are
essentially free of uranium, one of the parents.
Galenas are also high in lead and low in uranium
and therefore nearly preserve the lead-isotopic
ratios of their parent at the time of their birth.
Galenas of various ages fall close to a unique
single-stage growth curve. The small depar-
tures can be interpreted as further fractionation
μ
(mu). Some components of
the mantle have high Pb-isotope ratios and are
called HIMU.
Most lead-isotopic results can be interpreted
as growth in a primitive
reservoir
for a certain
period of time and then growth in reservoir with
adifferent
μ
μ
-value from that time to the present.
By measuring the isotopic ratios of lead and ura-
nium in a rock, the time at which the lead
ratios were the same as inferred for the prim-
itive reservoir can be determined, thus giving
the lead-lead age of the rock. This dates the age
of the uranium-lead fractionation event, assum-
ing a two-stage growth model. In some cases
