- Samarium-neodymium dating
**Samarium-neodymium dating**is useful for determining the age relationships of rocks and meteorites, based on decay of a long-lived Sm isotope to aradiogenic Nd isotope. Nd isotope ratios are used to provide information on the source ofigneous melts as well as to provide age data. The various reservoirs within the solid earth will have different values of initial^{143}Nd/^{144}Nd ratios, especially with reference to the mantle.The usefulness of Sm-Nd dating is the fact that these two elements are rare earths. They are thus, theoretically, not particularly susceptible to partitioning during melting of silicate rocks. The fractionation effects of crystallisation of

felsic minerals (see above) changes the Sm/Nd ratio of the resultant materials. This, in turn, influences the^{143}Nd/^{144}Nd ratios with ingrowth of radiogenic^{143}Nd.The mantle is assumed to have undergone

chondritic evolution , and thus deviations in initial^{143}Nd/^{144}Nd ratios can provide information as to when a particular rock or reservoir was separated from the mantle within the Earth's past.In many cases, Sm-Nd and Rb-Sr isotope data are used together.

**m-Nd radiometric dating**Samarium has five naturally occurring isotopes and neodymium has seven.

The two elements are joined in a parent-daughter relationship by thealpha-decay of^{147}Sm to^{143}Nd with ahalf life of 1.06 x 10^{11}years.^{146}Sm is an extinct nuclide which decays via alpha emission to produce^{142}Nd, with a half-life of 1.08 x 10^{8}years.^{146}Sm is itself produced by the decay of^{150}Gd via alpha-decay with a half-life of 1.06 x 10^{11}years.An isochron is calculated normally. As with Rb-Sr and Pb-Pb

isotope geochemistry , the initial^{143}Nd/^{144}Nd ratio of the isotope system provides important information on crustal formation and the isotopic evolution of the solar system.**m and Nd geochemistry**The concentration of Sm and Nd in

silicate minerals increase with the order in which they crystallise from a magma according toBowen's reaction series . Samarium is accommodated more easily intomafic minerals, so a mafic rock which crystallises mafic minerals will concentrate neodymium in the melt phase faster relative to samarium. Thus, as a rock undergoes fractional crystallization from a mafic to a more felsic composition, the abundance of Sm and Nd changes, as does the ratio between Sm and Nd.Thus,

ultramafic rocks have low Sm and Nd and "high" Sm/Nd ratios.Felsic rocks have high concentrations of Sm and Nd but "low" Sm/Nd ratios (komatiite has 1.14ppm Sm and 3.59ppm Nd versus 4.65ppm Sm and 21.6ppm Nd inrhyolite ).The importance of this process is apparent in modeling the age of

continental crust formation.## The CHUR Model

Through the analysis of isotopic compositions of neodymium, DePaolo and Wasserburg [*DePaolo, D. J. and Wasserburg, G. J. (1976). Nd isotopic variations and petrogenetic models. Geophys. Res. Lett. 3, 249)52.*] first discovered that terrestrial igneous rocks closely followed the Chondritic Uniform Reservoir (CHUR) line. Chondritic meteorites are thought to represent the earliest (unsorted) material that formed in the solar system before planets formed. They have relatively homogeneous trace element signatures and therefore their isotopic evolution can model the evolution of the whole solar system and of the ‘Bulk Earth’.After plotting the ages and initial

^{143}Nd/^{144}Nd ratios of terrestrial igneous rocks on a Nd evolution vs. time diagram¸ DePaolo and Wasserburg determined that Archean rocks had initial Nd isotope ratios very similar to that defined by the CHUR evolution line.**Epsilon Notation**Since

^{143}Nd/^{144}Nd departures from the CHUR evolution line are very small, DePaolo and Wasserburg argued that it would be useful to create a form of notation that described^{143}Nd/144Nd in terms of their deviations from the CHUR evolution line. This is called the epsilon notation whereby one epsilon unit represents a one part per 10,000 deviation from the CHUR composition. Dickin, A.P., 2005. Radiogenic Isotope Geology 2nd ed. Cambridge: Cambridge University Press. pp. 76-77 ] . Algebraically, epsilon units can be defined by the equation:

::$epsilon\_\{Nd(t)\}\; =\; left\; [frac\{left(frac\{^\{143\}Nd\}\{^\{144\}Nd\}\; ight)\_\{sample(t)\{left(frac\{^\{143\}Nd\}\{^\{144\}Nd\}\; ight)\_\{CHUR(t)-1\; ight]\; *\; 10000$Since epsilon units are larger and therefore a more tangible representation of the initial Nd isotope ratio, by using these instead of the initial isotopic ratios, it is easier to comprehend and therefore compare initial ratios of crust with different ages. In addition, epsilon units will normalize the initial ratios to CHUR, thus eliminating any effects caused by various analytical mass fractionation correction methods applied.

**Nd Model Ages**Since CHUR defines initial ratios of continental rocks through time, it was deduced that measurements of

^{143}Nd/^{144}Nd and 147Sm/^{144}Nd, with the use of CHUR, could produce model ages for the segregation from the mantle of the melt which formed any crustal rock. This has been termed ‘t-CHUR’. [*McCulloch, M.T. and Wasserburg G.J. 1978. Sm- Nd and Rb-Sr chronology of crustal formation. Science 200, 1003-11*] In order for a T_{CHUR}age to be calculated, fractionation between Nd/Sm would have to have occurred during magma extraction from the mantle to produce a continental rock. This fractionation would then cause a deviation between the crustal and mantle isotopic evolution lines. The intersection between these two evolution lines then indicates the crustal formation age. The T_{CHUR}age is defined by the following equation…

::$T\_\{CHUR\}=(frac\{1\}\{lambda\})ln\; left\; [1+\; frac\{left(frac\{^\{143\}Nd\}\{^\{144\}Nd\}\; ight)\_\{sample\}-left(frac\{^\{143\}Nd\}\{^\{144\}Nd\}\; ight)\_\{CHUR\{left(frac\{^\{147\}Sm\}\{^\{144\}Nd\}\; ight)\_\{sample\}-left(frac\{^\{147\}Sm\}\{^\{144\}Nd\}\; ight)\_\{CHUR\; ight]$

The T_{CHUR}age of a rock, can yield a formation age for the crust as a whole if the sample has not suffered disturbance after its formation. Since Sm/ Nd are Rare Earth Elements (REE), their characteristic immobility enables their ratios to resist partitioning during metamorphism and melting of silicate rocks. This therefore allows for crustal formation ages to be calculated, despite any metamorphism the sample has undergone.**References**

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