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Lecture 7 Spring 2003
GEOCHRONOLOGY III
THE SM-ND SYSTEM
(^147) Sm decays to 143 Nd by alpha decay with a half-life of 106 Ga (l = 6.54 x 10 -12y-1). Because t h e half-life is so long, the resulting variations in Nd isotopic composition are small and require precise measurement. Sm and Nd are both intermediate rare earth elements (Figure 1). The distinctive fea- ture of the rare earth elements is that inner electron shells (specifically the 4f and 5d shells) are be- ing filled as atomic number increases. Normally an electron is added to the outermost shell when atomic number increases. It is the outer electron shells that dictate the chemical behavior of ele- ments. Since the outer electron shells of the rare earths have identical configurations, we would ex- pect them to behave quite similarly. This is indeed the case. The rare earths generally have a + valence; the most important exceptions being Eu, which is +2 under some conditions, and Ce, which is +4 under some conditions. The primary chemical difference between the rare earth elements is t h e ionic radius, which shrinks systematically from 1.15 Å for La (A=57) to 0.93Å for Lu (A=71). Since the rare earths form predominately covalent bonds with oxygen in the solid earth, their ionic radius is a key factor in their geochemical behavior. Thus there is a systematic variation in their abun- dances in rocks, minerals, and solutions (see box on rare earth plots). The ionic radii of Sm and Nd, which are separated by Pm (an element that has no stable or long-lived isotope), differ by only 0.04Å (Nd=1.08, Sm=1.04). The ionic radii and relatively high charge of the rare earths make them fairly unwelcome in many mineral lattices: they can be considered moderately incompatible, with Nd being slightly more incompatible than Sm. Ce is generally the most abundant rare earth and forms its own phase in rare instances. Some rare earths, particularly the heavier ones, are accommodated in l a t - tice structures of common minerals; for example the partition coefficient of Lu in garnet is in the range of 4-10 (depending on the composition of the magma and the garnet). In mafic minerals, the lighter rare earths, which have the largest ionic radii, tend to be excluded more than the heavies, but in plagioclase, the heavies are the most excluded (though partition coefficients generally do not exceed 0.1). The high valence state of the rare earths results in relatively strong bonds. This, together with their tendency to hydrolyze (that is, surround themselves with OH-^ radicals), results in relatively low solubilities and low mobilities.
La Ce Pr Pm Eu Gd Tb Dy Ho Er Tm Yb Lu
Kr
Po At Rd
Li
K
Rb
Cs
Fr
Be
Sr
Ba
Ra
Mo
W Re
Ag
Au
Cd
Hg
Ga Ge
In Sn
Tl Pb Bi
Ac Th Pa U
Ac
Na Mg
Ca Fe
O
Al Si P
Y
Sc Ti V Cr Mn Co Ni Cu Zn
Zr
Hf
Nb
Ta
H He
C N Ne
Ar
Ru Xe
Os
Rh
Ir
Pd
Pt
B F
S Cl
As Se Br
Tc Sb Te I
La
The Rare Earth Elements
Nd Sm
Figure 7.1. Periodic table highlighting the rare earths (gray background) and Nd and Sm.
Lecture 7 Spring 2003
RA RE EA RTH PLOT S
The systematic contraction in the ionic radii of the rare earth elements leads to systematic variation in their behavior. This is best i llustrated by viewing their abun dances on rare earth, or Masuda-Coryell, plots. The plots are con structed by first "normalizing" t h e concentrations of the rare earth, i.e., dividing but the concentration of t h e element in a standard. Gen erally, this standard is t h e abun dance in chondritic meteorites, but other values are also used (for example, rare earths in sediments and seawater are often normalized to average shale). This normalizing process removes t h e sawtooth pattern t h a tresults from odd-even nuclear effects, and also the effect of decreasing concentration with atomic number. Those con centra- tion variations, illustrated in Figure 7.2, reflect differences in nuclear stability and t h e nucleo- synthetic process, and therefore affect t h e abundances of rare earths in all matter. Removing these effects by nor malization highlights difference s in con- centration due to geo chemical processes. After nor malizing, t h e log of the abun dance of each element is plotted against atomic number, as is i llustrated in Figure 7.3. Figure7.2. Concentrations of t h e rare earths in t h e carbona- ceous chondritic meteorite Orgueil. Figure 7.3. A rare earth plot showing rare earth patterns for orgueil, average upper continental crust, and average mid- ocean ridge basalt (MORB). The rare earths are refractory elements (which is to say they have low vapor pressures or low boil- ing points); what is more relevant is that they form refractory compounds. As is the case with other refractory elements, it can be assumed that their relative abundances in the Earth are the same as in chondritic meteorites. This assumption is strengthened in the case of the rare earths because of t h e general similarity of their chemical behavior: i.e., we do not believe that processes in the early solar system fractionated the rare earths. The important point is we have good reason to believe t h e (^147) Sm/ (^144) Nd ratio of the Earth is the same as the chondritic value, 0.1967, which corresponds to a Sm/Nd of about 0.32. A general assumption is that the solar system was isotopically homogeneous when the Earth formed. This is to say that the initial 143 Nd/^144 Nd ratio of the Earth should be iden- tical to the initial 143 Nd/^144 Nd ratio of other bodies formed 4.55 Ga ago, including meteorite parent bodies. Since the initial ratio and the Sm/Nd ratio of all bodies in the solar system are identical,
Lecture 7 Spring 2003
tively high Sm/Nd ratios. Failing this, inclusion of both plagioclase and pyrox- ene can result in a satisfactory spread in Sm/Nd ratios. Because the range in Sm/Nd ratios tends to be small, even small variations in initial 143 Nd/^144 Nd can result in erroneous ages. There are several such cases in the literature. Perhaps the greatest advantage of Sm/Nd is the lack of mobility of these elements. The Sm-Nd chronometer i s therefore relatively robust with respect to alteration and low-grade metamor- phism. Thus the Sm-Nd system is often the system of choice for mafic rocks and for rocks that have experienced low- grade metamorphism or alteration.
SM-ND MODEL AGES AND CRUSTAL RESIDENCE TIMES
A general assumption about the Earth is that the crust has been created from the mantle by magma- tism. When a piece of crust is first created, it will have the 143 Nd/^144 Nd ratio of the mantle, though it’s Sm/Nd ratio will be lower than that of the mantle (a consequence of Nd being more incompatible and partitioning more into the melt than Sm). Let's make the simplistic assumption that the mantle has the same Nd isotopic history as CHUR. This means a piece of crust will have the same (^143) Nd/ (^144) Nd as the mantle and as CHUR when it is created, i.e., eNd (^) = 0. If we know the present-day Sm/Nd and 143 Nd/^144 Nd ratio of this piece of crust, we can estimate its age. Figure 7.5 illustrates how this is done graphically, let's see how this is done mathematically. What we want to find is t h e intersection of line describing the evolution of the sample and that describing the evolution of t h e mantle. To do so, we simply need to subtract one equation from the other. The closed system isotopic evolution of any sample can be expressed as:
143 Nd / 144 Nd
sam =
143 Nd / 144 Nd
147 Sm / 144 Nd
sam ( e
l t - 1 ) 7.
The chondritic evolution line is:
143 Nd / 144 Nd
CHUR =
143 Nd / 144 Nd
147 Sm / 144 Nd
CHUR ( e
l t - 1 ) 7.
The CHUR model age of a system is the time elapsed, t = t, since it had a chondritic 143 Nd/^144 Nd ratio, assuming the system has remained closed. We can find t by subtracting equation 7.03 from 7.02, which yields:
143 Nd / 144 Nd
sam -
143 Nd / 144 Nd
CHUR =^
147 Sm / 144 Nd
sam -
147 Sm / 144 Nd
{ (^) CHUR }( e
lt - 1 ) 7.
Another way of thinking about this problem is to imagine a 143 Nd/^144 Nd vs. time plot: on that plot, we extrapolate the sample’s evolution curve back to the chondritic one. In terms of the above equations, this intersection occurs at (^143 Nd/^144 Nd) 0. Solving equ. 7.04 for t:
t CHUR =
l
ln
143 Nd / 144 Nd
sam -
143 Nd / 144 Nd
CHUR
147 Sm / 144 Nd
sam -
147 Sm / 144 Nd
CHUR
Ê
Ë
Á
An age obtained in this way is called an Nd model age (the model is that of chondritic evolution of the mantle), or a crustal residence age , because it provides an estimate of how long this sample of Nd has been in the crust. Note that we explicitly assume the sample has remained a closed system, in the sense of no migration in or out of Sm or Nd. Because of the immobility of these elements, the as- sumption generally holds, at least approximately. Figure 7.5. Sm-Nd model ages. The 143 Nd/^144 Nd is ex- trapolated backward (slope depending on Sm/Nd) until it intersects a mantle or chondritic growth curve.
Lecture 7 Spring 2003
We can obtain somewhat better model ages by making more a sophisticated assumption about t h e Nd evolution of the mantle. Since the crust is enriched in Nd relative to Sm, the mantle must be de- pleted in Nd relative to Sm (analyses of mantle-derived rocks confirm this). So the chondritic as- sumption must be wrong. We can assume instead a model of 143 Nd/^144 Nd growth in the mantle that is more rapid than chondritic, i.e., a higher Sm/Nd ratio. Once we decide on Sm/Nd and present-day (^143) Nd/ (^143) Nd ratios for this 'depleted-mantle' (the latter can be estimated from the 143 Nd/ (^143) Nd of MORB, mid-ocean ridge basalts), we can calculate a model age relative to the depleted mantle by substituting the depleted-mantle terms for the CHUR terms in 7.2 and 7.3. To calculate the depleted mantle model age, tD M, we use the same approach, but this time we want the intersection of the sample evolution line and the depleted mantle evolution line. So equation 7. becomes:
t DM =
l
ln
143 Nd / 144 Nd
sam -
143 Nd / 144 Nd
DM
147 Sm / 144 Nd
sam -
147 Sm / 144 Nd
DM
Ê
Ë
Á
The depleted mantle (as sampled by mid-ocean ridge basalts) has an average eNd of about 10, or (^143) Nd/ (^144) Nd = 0.51315. The simplest possible evolution path, and the one we shall use, would be a closed system evolution since the formation of the Earth, 4.55 Ga ago (i.e., a straight line on a (^143) Nd/ (^144) Nd vs. time plot). This evolution implies a 147 Sm/ (^144) Nd of 0.2137. Because the Sm/Nd ratio is so little affected by weathering, and because these elements are so in- soluble, Sm/Nd ratios in fine-grained sediments do not generally differ much from the ratio in t h e precursor crystalline rock. Thus, the system has some power to ‘see through’ even the process of mak- ing a sediment from a crystalline rock. The result is we can even compute crustal residence times from Nd isotope ratio and Sm/Nd measurements of fine-grained sediments. This generally does not work for coarse-grained sediments though because they contain accessory minerals whose Sm/Nd ratios can be quite different from that of the whole rock.
REFERENCES AND SUGGESTIONS FOR FURTHER READING
Dickin, A. 1995. Radiogenic Isotope Geochemistry. Cambridge: Cambridge University Press. DePaolo, D. J. 1988. Neodymium Isotope Geochemistry, an Introduction , Berlin: Springer-Verlag.
