4.2 Nd isotope evolution and
model ages
DePaolo and Wasserburg (1976a) made the first
Nd isotope determinations on terrestrial igneous rocks. When they plotted the
ages and initial 143Nd/144Nd ratios of these units on a
diagram of Nd isotope evolution against time, they found that Archean plutons
had initial ratios which were remarkably consistent with the evolution of the
Chondritic Uniform Reservoir (CHUR) observed in meteorites (Fig. 4.13). The
CHUR evolution path is normally drawn as a straight line, but in fact it is a
very gentle curve, due to the finite half-life of 147Sm (ca. 106
Byr).

Fig. 4.13. Diagram of 143Nd/144Nd
against time showing the close correspondence of early Nd isotope analyses of
terrestrial igneous rocks to the chondritic growth line. BCR)1 =
Columbia River basalt, USA. After DePaolo and Wasserburg (1976a).
Because Sm and Nd are rare earth elements (REE)
with atomic numbers only two units apart, their chemical properties are very
similar, and they undergo only slight relative fractionation during crystal)liquid processes. This means that in
terrestrial rocks, departures of 143Nd/144Nd from the
CHUR evolution line are small relative to the steepness of the line (Fig.
4.13). DePaolo and Wasserburg therefore developed a notation whereby initial 143Nd/144Nd
isotopes ratios could be represented in parts per 104 deviation from
the CHUR evolution line, termed epsilon units (, Nd). Mathematically, this notation
is defined as:
|
(143Nd/144Nd)sample (t) |
, Nd (t) = | )))))))))))))
! 1 | @
104 [4.3]
|
(143Nd/144Nd)CHUR (t)
|
where t
indicates the time at which , Nd is calculated. The , notation makes it much easier to compare the initial Nd isotope ratios
of bodies of different ages. Also, by normalising all data to CHUR, it removes
the effects of the different fractionation corrections which have been applied
for Nd analysis as the metal or as the oxide species.
Using
the , notation,
DePaolo and Wasserburg (1976b) presented a larger data set of Nd isotope
analyses on a diagram of , Nd against time (Fig. 4.14). They noted that continental igneous rocks
through time had , Nd values very close to zero. Indeed, for Archean rocks the error bars
overlapped with zero, suggesting that continental igneous rocks were ‘derived
from a reservoir with a chondritic REE pattern, which may represent primary
material remaining since the formation of the Earth.’

Fig. 4.14. Diagram of Nd isotope evolution
against time in the form of deviations from the chondritic evolution line in , units. After DePaolo and Wasserburg
(1976b).
4.2.1 Chondritic model ages
DePaolo and Wasserburg (1976b) argued that if
the CHUR evolution line defines the initial ratios of continental igneous rocks
through time, measurement of 143Nd/144Nd and 147Sm/144Nd
ratios in any crustal rock would yield a model age for the formation of that
rock (or its precursor) from the chondritic reservoir. This is true, providing
that there was sufficient Nd/Sm fractionation during the process of crustal
extraction from the mantle to give a reasonable divergence of crustal and
mantle evolution lines (Fig. 4.15), and hence a precise intersection. The model
age is then given as:
[4.4]
| (143Nd )0 (143Nd )0 |
| ()))))
! ())))) |
1 | (144Nd )sample (144Nd )CHUR |
TCHUR = )) @
ln | 1 + ))))))))))))))) |
8 | (147Sm )0 (147Sm)0 |
| ()))))
! ())))) |
| (144Nd )sample (144Nd )CHUR |
DePaolo
and Wasserburg argued that if the Sm/Nd ratio of a rock sample had not been
disturbed since its separation from the chondritic reservoir (taken to be the
mantle source), then TCHUR
might provide a ‘crustal formation’ age for a wide variety of rocks. Elemental
investigations have indicated the general immobility of REE on a whole-rock
scale during the processes of weathering and low-temperature metamorphism
associated with sedimentary rock formation (e.g. Haskin et al., 1966), and even during high-grade metamorphism (Green et al., 1969). This immobility is
schematically illustrated by the lack of deflection in the evolution line of a
crustal rock sample in Fig. 4.15 during metamorphic and sedimentary events.
Hence, Nd model ages may be able to date crustal formation in rocks that have
been subjected to high-grade metamorphism and even erosion)sedimentation.

Fig. 4.15. Schematic Nd isotope evolution
diagram showing the theory of model ages. Tmet
= age of metamorphic event; Tsed
= age of erosion)sedimentation event; f =
fractionation of sample Sm/Nd relative to Bulk Earth. Dashed vector shows the development
of the depleted mantle as a result of crustal extraction. After McCulloch and
Wasserburg (1978).
These
premises were applied by McCulloch and Wasserburg (1978) in a model age study
aimed at measuring the crustal formation ages of several cratonic rock bodies,
mainly from the
Although
Nd model ages are generally applied to dating the time of crustal separation
from the mantle, other more specialised applications have been made. For
example, Richardson et al. (1984)
investigated the time of diamond formation in the South African mantle
lithosphere by dating garnet inclusions in diamonds. Three samples were
analysed, each consisting of a composite of several hundred sub-calcic garnet
inclusions, and yielding a total of 10 ) 45 ng Nd. The unradiogenic Nd in
these samples gave rise to TCHUR
ages of 3.19 ) 3.41 Byr (Fig. 4.16). When this evidence is combined with evidence of
sub-solidus temperatures for diamond growth (based on equilibrium garnet)olivine inclusions in diamonds), it
suggests that sub-continental lithosphere has existed under the African craton
since the Early Archean. This material may represent the residue from 3.5
Byr-old komatiite extraction (section 7.1).

Fig. 4.16. Nd isotope evolution diagram
showing model age calculations for silicate inclusions in South African
diamonds. The initial ratio of Onverwacht lavas is shown for comparison. After
Richardson et al. (1984).
4.2.2 Depleted mantle model ages
While observing the good fit of Archean plutons
to the CHUR Nd isotope evolution line, DePaolo and Wasserburg (1976b) also
noted that young mid ocean ridge basalts (MORB) lay
Lunar
basalts and troctolites with ages of 3.3 ) 4.3 Byr show a wide range of
initial 143Nd/144Nd ratios, equivalent to a variation
from +7 to !2 , units relative to CHUR (Fig. 4.17;
Lugmair and Marti, 1978). This spread shows that very early Sm/Nd fractionation
occurred in the Moon, and that there was no long-lived uniform magma source
with a chondritic Sm/Nd ratio. In contrast, none of the Archean terrestrial
rocks analysed by 1976 showed any dispersion outside error of CHUR, which led
DePaolo and Wasserburg (1976b) to conclude that the Earth did not undergo early
differentiation, or if it did, that this was re-mixed by convection.

Fig. 4.17. , Nd evolution diagram for lunar
rocks indicating very early Sm/Nd fractionation between lunar reservoirs. After
Lugmair and Marti (1978).
The
paucity of Nd isotope data for the Proterozoic was a serious weakness in this
model, since it left a gap between the Archean CHUR data and the depleted MORB
source (attributed to an elevated Sm/Nd ratio), with questions about the
relationship between the two. An important stage in filling this gap was a
study on Proterozoic metamorphic basement from the Colorado Front Range
(DePaolo, 1981). Four meta-volcanics and two charnockitic granulites from the
Idaho Springs Formation were dated by the Sm)Nd isochron method. In addition, Nd
isotope and Sm/Nd determinations were made on three plutons previously dated by
the Rb)Sr whole-rock
method, (the Boulder Creek, Silver Plume and Pikes Peak granitoids). The
initial 143Nd/144Nd ratios of all these samples are
plotted on an , Nd versus time diagram in
Fig. 4.18.
The
Idaho Springs meta-igneous rocks cluster at , Nd (t) = +3.7 " 0.3, showing them to be derived from a depleted mantle reservoir with
respect to CHUR at 1.8 Byr. Boulder Creek samples also have positive , Nd (+1.7 to +3.5), whereas the
Silver Plume and

Fig. 4.18. Plot of , Nd against time showing Colorado
data relative to a model depleted mantle evolution curve. After DePaolo (1981).
DePaolo
was able to fit a quadratic curve to Idaho Springs and modern island-arc data
(Fig. 4.18), representing the Nd isotope evolution of a progressively depleted
reservoir which was the source area for calc-alkaline (subduction related)
magmatism. This curve begins on the CHUR evolution line in the Early Archean,
but diverges progressively to the present day. The composition of the depleted
reservoir, relative to CHUR, at time T,
is given as:
, Nd (T)
=
0.25 T2 ! 3 T + 8.5 [4.5]
Sm)Nd model ages calculated using this depleted
mantle curve are denoted TDM.
DePaolo argued that TDM
model ages would be a more accurate indication of ‘crustal formation ages’ than
TCHUR ages for studies of
continental evolution. For example, an anomalously low TCHUR age of 0.8 Byr for McCulloch and Wasserburg’s
Grenville composite (section 4.2.1) is revised to a TDM age of 1.3 Byr, within the range expected for
juvenile crust formation during the Grenville orogeny.
Subsequent
to the discovery of Proterozoic depleted mantle by DePaolo (1981), new analyses
have prompted several re-interpretations of the evolution of the depleted
mantle reservoir. An important alternative to DePaolo’s (1981) model was
proposed by Goldstein et al. in 1984
(Fig. 4.19). This model assumes linear depletion of the mantle from , Nd = 0 at 4560 Myr to , Nd = +10 at 0 Myr (the MORB
composition). It also provides a good fit to Early Proterozoic greenstones from
the

Fig. 4.19. Plot of , Nd against time showing two of the
most widely used depleted mantle evolution models. Dashed curve: DePaolo
(1981); Solid line: Goldstein et al.
(1984).
More
recently, Nagler and Kramers (1998) reverted to a model involving essentially chrondritic
mantle evolution until 3 Byr ago, followed by more-or-less linear evolution to , = 8 at the present day. The
resulting evolution curve was fairly close to that of DePaolo (1981) along some
of its length. However, the model of Nagler and Kramers was constrained to fit
the average , Nd values of a wide variety of different rock types, some of which
(e.g. the Stillwater Complex) have been shown to exhibit crustal contamination.
The result is a model which does not seem to be in tune with recent thinking
about depleted mantle evolution in the Archean (section 4.4.3).
There
has been a tendency towards a proliferation of depleted mantle models as new
data for various geographical areas become available. However, an examination
of the literature suggests that the models of DePaolo (1981) and Goldstein et al. (1984) have had the widest
application by other workers. This is illustrated in Fig. 4.20 by a comparison
of citation rates for these two studies, compared with two control papers:
Nelson and DePaolo (1984), discussed above, and Allegre and Rousseau (1984),
who proposed a curved mantle evolution line similar to that of DePaolo (1981).
The durability of citations for DePaolo (1981) and Goldstein et al. (1984) indicates the wide
usefulness of these mantle models, which therefore provide an important basis
for the comparison of different magma suites, even if the absolute values of
the model ages are slightly in error. Hence it is desirable that the TDM and TCR notations should be restricted to the models of
DePaolo (1981) and Goldstein et al.
(1984), while other acronyms can be used to denote different models.

Fig. 4.20. Plot of annual citation rates for
four papers that introduced new depleted mantle evolution models for Nd. Data
from the Science Citation Index, averaged over two-year intervals.
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