3.2 Dating igneous rocks
The Rb–Sr method has largely been superceded as
a tool for dating igneous rocks. However, the method provides a good illustration of the
principles of isotope dating, and will therefore be reviewed here to demonstrate
those principles. This application begins from the general equations for
radioactive decay (section 1.4). Hence, the number of 87Sr daughter
atoms produced by decay of 87Rb in rock or mineral since its
formation t years ago is given by
substituting into decay equation [1.10]:
87Sr = 87SrI + 87Rb (e8t ! 1) [3.1]
where 87SrI is the number
of 87Sr atoms present initially. However, it is difficult to measure
precisely the absolute abundance of a given nuclide. Therefore it is more
convenient to convert this number to an isotope ratio by dividing through by 86Sr
(which is not produced by radioactive decay and therefore remains constant with
time). Hence we obtain:
(87Sr) (87Sr) 87Rb
()))) = ()))) + ))) (e8t ! 1) [3.2]
(86Sr)P (86Sr)I 86Sr
The present-day Sr isotope ratio (P) is
measured by mass spectrometry, and the atomic ratio 87Rb/86Sr
is calculated from the weight ratio of Rb/Sr. If the initial ratio (87Sr/86Sr)I
is known or can be estimated then t
can be determined, subject to the assumption that the system has been closed to
Rb and Sr mobility from time t until
the present:
1 { 86Sr | (87Sr) (87Sr) | }
t
= )
ln { 1 + ))) |
()))) ! ()))) |
} [3.3]
8 { 87Rb | (86Sr)P (86Sr)I | }
3.2.1 Sr model ages
When the Rb)Sr method was first used in
geochronology, the poor precision attainable in mass spectrometry limited the
technique to the dating of Rb-rich minerals such as lepidolite. These minerals
develop such high 87Sr/86Sr ratios over geological time
that a uniform initial 87Sr/86Sr ratio of 0.712 could be
assumed in all dating studies without introducing significant errors. Such
determinations are called ‘model ages’ because the initial ratio is predicted
by a model rather than measured directly.
Subsequently,
the Rb)Sr method was
extended to less exotic rock-forming minerals such as biotite, muscovite and
K-feldspar, with lower Rb/Sr ratios. However, discordant dates were often
generated by assuming an initial ratio of 0.712 when the real initial ratio was
higher. This problem was first recognised by Compston and Jeffery (1959), and
overcome by the invention of the isochron diagram (Nicolaysen, 1961). Model
ages subsequently re-appeared in more specialised aspects of Rb)Sr dating such as meteorite chronology,
and as an important approach in the Sm)Nd method (section 4.2).
3.2.2 The isochron diagram
An examination of equation [3.2] shows that it
is equivalent to the equation for a straight line:
y = c
+ x m [3.4]
This led Nicolaysen (1961) to develop a new way
of treating Rb)Sr data, by plotting 87Sr/86Sr (y) against 87Rb/86Sr
(x). The intercept (c) is then the initial 87Sr/86Sr
ratio of the system. On this diagram, a suite of comagmatic minerals having the
same age and initial 87Sr/86Sr ratio and which have since
remained as closed systems define a line termed an ‘isochron’. The slope of
this line, m (= e8t ! 1), yields the age of the minerals.
If one of the minerals is very Rb-poor then this may yield the initial ratio
directly. Otherwise, the initial ratio is determined by extrapolating back to
the y axis a best-fit line through
the available data points (Fig. 3.2). Because 8 87Rb is so small, for
geologically young rocks the slope may be quite accurately approximated by 8t. Such an
approximation does not hold for nuclides with shorter half-lives such as K and
U.
Fig. 3.2. Schematic Rb)Sr isochron diagram for a suite of
comagmatic igneous minerals.
The
isotopic evolution of a suite of hypothetical minerals in the isochron diagram
is illustrated in Fig. 3.3. At the time of crystallisation of the rock, all
three minerals have the same 87Sr/86Sr ratio, and plot as
points on a horizontal line. After each mineral has become a closed system
(effectively at the same instant for the minerals in a high-level, fast-cooling
intrusion) isotopic evolution begins. On a diagram where the two axes have the
same scale (Fig. 3.3), the points move up straight lines with a slope of !1 as each 87Rb decay
increases 87Sr/86Sr and reduces 87Rb/86Sr
by the same amount. Each mineral composition remains on the isochron as its
slope increases with time. In practice, the y
axis is usually very much expanded to display rocks of geological age in a
suitable format, and the growth lines are then nearly vertical.
Fig. 3.3. Rb)Sr isochron diagram on axes of equal
magnitude showing production of 87Sr as 87Rb is consumed
in two hypothetical samples.
Another
development of the Rb)Sr method (Schreiner, 1958), was the analysis of co-genetic whole-rock
sample suites, as an alternative to separate minerals. To be effective, a
whole-rock suite must display variation in modal mineral content, such that
samples display a range of Rb/Sr ratios, without introducing any variation in
initial Sr isotope ratio. In actual fact, perfect initial ratio homogeneity may
not be achieved, especially in rocks with a mixed magmatic parentage. However,
if the spread in Rb/Sr ratios is sufficient, then any initial ratio variations
are swamped, and an accurate age can be determined. Initial ratio heterogeneity
is a greater problem in Sm)Nd isochrons, and is therefore discussed under that heading (section
4.1.2). Schreiner’s proposal actually preceded the invention of the Rb)Sr isochron diagram, but some of his
data are presented on an isochron diagram in Fig. 3.4 to demonstrate the
method.
Fig. 3.4. Rb)Sr whole-rock isochron for the ‘red
granite’ of the Bushveld complex, using the data of Schreiner (1958).
Graphical
calculation of isochron ages was superseded in the 1960s by the application of
least squares regression techniques (section 2.6), but the isochron diagram remains a very useful
tool to assess the distribution of data points about a regression. However,
Papanastassiou and Wasserburg (1970) found that the vertical scale the isochron
diagram was too compressed to allow clear portrayal of the experimental error
bars on their data points. To overcome this problem they developed the , notation, which they defined as the
relative deviation of a data point from the best-fit isochron in parts per 104.
This is given by:
|
(87Sr/86Sr)measured |
, = | )))))))))) !
1 | H 104 [3.5]
|
(87Sr/86Sr)best-fit |
Figure 3.5 shows a combined mineral isochron
diagram and , diagram for an Apollo 11 sample from the
Fig. 3.5. Rb)Sr data for Lunar mare sample 100 17
plotted (a) on a conventional isochron diagram; and (b) on a diagram of , against Rb/Sr. After Papanastassiou
and Wasserburg (1970).
Provost
(1990) has pointed out that isochrons determined on granitic rocks are
dominated by errors in Rb/Sr rather than 87Sr/86Sr (Fig.
3.6a). He developed a new version of the isochron plot (Fig. 3.6b), with
non-linear axes, which attempts to portray both sources of error at once.
Uncertainties in isotope ratio and Rb/Sr ratio both generate vertical or
sub-vertical error bars, but their meaning changes progressively across the
diagram from an error on the initial ratio (left-hand side) to an error on the
age (right-hand side). Unfortunately this diagram is conceptually quite
difficult to understand, so a more practical approach may be to improve the , diagram of Papanastassiou and
Wasserburg by adding error bars which represent the effect of Rb/Sr
uncertainties on each data point, in the form of equivalent errors in e value.
Fig. 3.6. Rb)Sr data for the Agua Branca
adamellite,
3.2.3 Erupted isochrons
A primary basic magma should inherit the
isotopic composition of its mantle source, providing that melting occurs in
equilibrium conditions. Tatsumoto (1966) first suggested, on the basis of U)Pb data, that primitive basic magmas
could also inherit the parent/daughter ratio of their mantle source. If
different magma batches were to sample the elemental and isotopic composition
of different source domains, this might lead to the eruption of an ‘isochron’
suite whose slope would yield the time over which these sources were isolated.
This concept was examined for the Rb)Sr system in alkalic ocean island basalts by
Sun and Hanson (1975).
Average
compositions for 14 different ocean island basalts were plotted on an isochron
diagram (Fig. 3.7). The data are fairly scattered, but form a positive
correlation with a slope age of ca. 2 Byr. Individual ocean islands may also
define arrays with positive slope, but usually with more scatter. Sun and Hanson
attributed the positive correlations between Rb/Sr and isotopic composition to
mantle heterogeneity, suggesting that the apparent ages represented the time
since mantle domains were isolated from the convecting mantle. Brooks et al. (1976a) termed these ages ‘mantle
isochrons’.
Fig. 3.7. Rb)Sr isochron diagram for young
volcanic rocks (mostly alkali basalts) from ocean islands. (Numbers by each
data point can be ignored). After Sun and Hanson (1975).
The
mantle isochron concept was extended to continental igneous rocks by Brooks et al. (1976b). Because these are often
ancient (unlike most ocean island basalts), it was necessary to correct
measured 87Sr/86Sr ratios back to their calculated
initial ratios at the time of magmatism, before plotting against Rb/Sr (e.g.
Fig. 3.8). Hence Brooks et al. termed
these plots ‘pseudo-isochron’ diagrams. They listed 30 examples from both
volcanic and plutonic continental igneous rock suites where the data formed a
roughly linear array. The controversial aspect of this work was that Brooks et al. rejected the possibility that
pseudo-isochrons were mixing lines produced by crustal contamination of
mantle-derived basic magmas. Instead, they believed them to date mantle
differentiation events which established domains of different Rb/Sr ratio in
the subcontinental lithosphere.
Fig. 3.8. Pseudo-isochron for quartz and
olivine norites from Arnage ( " ) and Haddo House ( ! ) in
It
is a fundamental assumption of the mantle isochron model that neither isotope
nor elemental ratios are perturbed during magma ascent through the crust.
However, it is now generally accepted that this assumption is not upheld with
sufficient reliability to attribute age significance to erupted isochrons. For
example, the Haddo House norites of N.E. Scotland (Fig. 3.8) are known to
contain pelitic xenoliths, so this array must document crustal assimilation.
Another pseudo-isochron example from Lower Tertiary lavas of NW Scotland
(Beckinsale et al., 1978) can be
attributed to Sr depletion in the melt by plagioclase fractionation, followed
by crustal contamination (Fig. 3.9). Breakdown of the mantle isochron model can
also be caused by low degrees of melting in the mantle source, leading to
fractionation between Rb, an ultra-incompatible, and Sr, a moderately
incompatible element. Hence it is concluded that only isotope)isotope mantle isochrons (such as
provided by the Pb)Pb system) can reliably be interpreted as dating the ages of mantle
differentiation events.
Fig. 3.9. Pseudo-isochron diagram for Tertiary
lavas from the Isle of Mull, NW Scotland, showing an apparent age of 68 Myr
prior to eruption. Vectors illustrate effects of crystal fractionation and
crustal contamination. Modified after Beckinsale et al. (1978).
3.2.4 Meteorite chronology
Meteorites have been the subject of numerous Rb)Sr dating studies, but some of the
most important Rb)Sr results on meteorites are initial ratio determinations. These have
significance, both as a reference point for terrestrial Sr isotope evolution,
and as a model age tool for estimating the relative condensation times of solar
system bodies.
The
first accurate measurement of meteorite initial ratios was made by
Papanastassiou et al. (1969) on
basaltic achondrites. These differ from chondritic meteorites in showing
evidence of differentiation after their accretion from the solar nebula.
However, they may not have participated in the full planetary differentiation
process which generated iron meteorites. Their low Rb/Sr ratios have resulted
in only limited radiogenic Sr production since differentiation, so an accurate
initial ratio determination is possible.
In
order to make this determination, Papanastassiou et al. analysed whole-rock samples from seven different basaltic
achondrites, yielding an isochron (Fig. 3.10) without any excess scatter over
analytical error. An age of 4.39 " 0.26 Byr was calculated using the old decay
constant (8 = 1.39 H 10!11 yr!1). The initial ratio of 0.69899 " 5 was referred to by Papanastassiou
et al. as the ‘Basaltic Achondrite
Best Initial’ or BABI. This value represents a bench-mark to which other
meteorite initial ratios may be compared. Birck and Allegre (1978) repeated
this study with the addition of separated minerals from Juvinas and Ibitira,
yielding an identical initial ratio, but an improved age determination of 4.57 " 0.13 Byr (same decay constant).
However, Rb)Sr mineral isochrons are not possible for other achondrites due to later
disturbance of the Rb—Sr system.
Fig. 3.10. Rb)Sr isochron diagram for whole-rock
samples of basaltic achondrites showing the determination of ‘BABI’. After Papanastassiou et al. (1969).
The
determination of precise initial ratios for chondritic meteorites is
problematical because of their much higher Rb/Sr ratios than basaltic
achondrites. However, by separating out low-Rb/Sr phosphate minerals,
Wasserburg et al. (1969) and Gray et al. (1973) were able to determine
good initial ratios for the chondrites Guarena and
These
initial ratios can be translated into a relative chronology for meteorite
condensation (Fig. 3.11) by assuming a homogeneous Rb/Sr ratio in the solar
nebula (Papanastassiou et al., 1969).
The results are only ‘model’ ages because they depend on an assumed composition
for the source reservoir (solar nebula), and they would be rendered invalid if
it did not evolve as a homogeneous reservoir. The estimate of the Rb/Sr ratio
in the solar nebula was based on cited spectroscopic measurements from the Sun,
yielding a value of 0.65 which is capable of generating an increase in 87Sr/86Sr
of ca. 0.0001 in 4 Myr.
If
we assume a homogeneous Sr isotope distribution in the solar nebula, the
Allende data suggest it to be the oldest known object in the solar system,
predating the condensation of basaltic achondrites by ca. 10 Myr (Fig. 3.11).
Similarly, Angra dos Reis has a model age ca. 5 Myr older than BABI.
Application of the same model to the high initial ratios of Guarena and
Fig. 3.11. Plot of initial Sr isotope
composition for selected meteorites against model ages for condensation or
differentiation)metamorphism, based on assumed Rb/Sr ratios in major reservoirs. ADOR =
Angra dos Reis. After Gray et al.
(1973).
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