9.5 The K)Ca system

The K)Ca couple was actually the first isotopic system to be suggested as a geochemical tracer for granite petrogenesis (Holmes, 1932). However, this was on the assumption that the major isotope of potassium, ⁴¹K, was the radioactive nuclide. (Fortunately this is not really the case or the Earth would have melted from the heat.) When it was realised that ⁴⁰K was actually the radioactive nuclide, the idea of pursuing the K)Ca system was abandoned, since it was expected that radiogenic ⁴⁰Ca would be swamped by the dominant non-radiogenic ⁴⁰Ca component. The method finally became viable with the development of modern high-precision mass spectrometers, but has not been applied widely.

Russell et al. (1978) used Ca isotope analysis to investigate mass-dependent fractionation processes, but the first geochronological application of the method was made by Marshall and DePaolo (1982). Because of the large relative differences between Ca nuclide masses, isotope ratios must be corrected for natural and instrumental mass fractionation using a more complex procedure than the simple linear law (section 2.2.3). In practice, an exponential mass fractionation correction was used in the two studies mentioned above. Marshall and DePaolo quoted their Ca isotope data as ⁴⁰Ca/⁴²Ca ratios, corrected by reference to a value of 0.31221 for the non-radiogenic ⁴²Ca/⁴⁴Ca ratio.

A variety of meteorites, lunar samples, and mantle-derived materials was analysed by Russell et al. (1978) and Marshall and DePaolo (1982). When age-corrected to yield initial Ca isotope ratios at various times between 1.3 and 4.6 Byr ago, all of the measurements fell within analytical uncertainty of a ⁴⁰Ca/⁴²Ca ratio of 151.016. This tells us that, because of its very low K/Ca ratio, the Earth’s mantle demonstrates negligible growth of radiogenic Ca with time.

Rather than quoting raw isotope ratios, Ca isotope compositions can be reported in terms of , units (part per 10⁴ deviation from the mantle composition). However this is more a matter of convenience than necessity, in view of the zero Ca isotope evolution of the mantle reservoir with time. In contrast, granitic crustal reservoirs have high K/Ca ratios of around 5 ) 10 which can generate appreciable ⁴⁰Ca growth with time. For reservoirs more than 1 Byr old these may give rise to isotope ratios outside error of the mantle value (Fig. 9.30). Because of the relatively short half-life of ⁴⁰K compared with the age of the Earth, isotopic growth lines are curved in this diagram.

Fig. 9.30. Plot of Ca isotope evolution against time in terms of , units (part per 10⁴ deviation from the constant mantle composition). Growth lines are shown for intermediate crust (K/Ca = 1) and granitic crust (K/Ca = 5). After Marshall and DePaolo (1982).

Bearing in mind the branched decay of ⁴⁰K, we can substitute into the general decay equation [1.10] to derive the following isochron equation for the K)Ca system:

⁴⁰Ca (⁴⁰Ca) ⁴⁰K 8_$

))) = ()))) + )) @ ))) (e^{8total t} ! 1) [9.6]

⁴²Ca (⁴²Ca)_I ⁴²Ca 8_total

The branching ratio of $ to total decays is 0.8952, and the total decay constant is 5.543 H 10^!10 yr^!1 (section 10.1).

Marshall and DePaolo tested the K)Ca system as a dating tool by analysing a small suite of separated minerals from the Pikes Peak batholith of Colorado. Plagioclase, whole-rock, K-feldspar and biotite define an isochron array (Fig. 9.31), whose slope yields an age of 1041 " 32 Myr (2F). This is within error of other age determinations on this largely unmetamorphosed pluton. The initial ratio of the Pikes Peak batholith (151.024) is within error of the mantle value.

Fig. 9.31. K)Ca isochron plot for separated minerals from the Pikes Peak batholith. Note erroneous results of spiking aliquots ( " ) rather than the whole dissolution ( ! ). After Marshall and DePaolo (1982).

One severe analytical problem that was encountered during this work (other than the mass fractionation behaviour mentioned above) was that samples divided into aliquots before mixing with spike gave erroneous K/Ca ratios. Marshall and DePaolo speculated that this might have been due to some precipitation of potassium from the rock solutions. It is avoided by spiking the whole sample before dissolution.

Marshall and DePaolo (1989) went on to apply the K)Ca method as a petrogenetic tracer in a study of Cenozoic plutons from the western USA. Granites emplaced into Paleozoic crust on the continental margin had a similar range of Ca isotope ratios to island-arc volcanics, from values within error of the MORB composition to just outside error (see also Nelson and McCulloch, 1989). In contrast, granites emplaced into Lower Proterozoic basement exhibited larger Ca isotope enrichments which were correlated with , Nd (Fig. 9.32). Hence, the Ca isotope ratios of the plutons must be inherited from the crustal source at depth.

Fig. 9.32. Plot of , Nd against , Ca showing compositions of Cenozoic granitoids emplaced into young basement ( Î ) and old basement ( ! ), relative to island-arc volcanics and MORB. Curves show model K/Ca ratios for basement with ¹⁴⁷Sm/¹⁴⁴Nd = 0.1 . After Marshall and DePaolo (1989).

Marshall and DePaolo compared the , Ca ) , Nd compositions of the plutons with crustal evolution models shown by dashed curves in Fig. 9.32. Given a crustal ¹⁴⁷Sm/¹⁴⁴Nd ratio of 0.1 (determined using the known Nd isotope signature of Colorado basement), Ca)Nd isotope evolution curves were drawn for various crustal K/Ca ratios. If we assume the granites to be total crustal melts, then data in Fig. 9.32 imply a K/Ca ratio of about unity in the source. However, this is higher than most estimates for bulk crust, so a more likely explanation is that , Ca ratios were fractionated during the melting processes by preferential extraction of the most fusible components of the crust. The usefulness of these constraints for petrogenetic modelling suggests that Ca isotopes have promise as a tracer for crust)mantle mixing, and may find more exploitation in the future.

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