3  The U–Th–Pb isotope system

Authors

Katrin Westner

Sabine Klein

Published

June 19, 2024

3.1 Learning objective

By the end of the unit, you will understand the origins of the different lead isotope ratios. Further, you can summarise which information they can provide about geological processes and relate them to the theoretical background for the application of lead isotopes in archaeological research.

3.2 Prior knowledge

This unit expects that you already know:

3.3 Material

The unit combines text with an expert interview.

3.4 Learning content

Pb has four long-time stable isotopes - 208Pb (52.4 %), 207Pb (22.1 %), and 206Pb (24.1 %), which are continuously produced by radiogenic decay of 232Th, 235U and 238U, respectively. 204Pb (1.4 %) is primordial and its abundance therefore is constant. Other naturally occurring isotopes of Pb are short-lived; for example 210Pb only has a half-life of 22.3 years. The abundances of 208Pb, 207Pb, and 206Pb vary as a function of the U–Th–Pb contents of the parental source(s) and the system closure time. By relating the radiogenic isotopes to the primordial 204Pb, these relationships can be deduced and are described by the following equations:

\[ \left(\frac{^{206}Pb}{^{204}Pb}\right) = \left(\frac{^{206}Pb}{^{204}Pb}\right)_0 + \left(\frac{^{238}U}{^{204}Pb}\right) \cdot \left(e^{\lambda_{238} \cdot t}-1\right)\]

\[ \left(\frac{^{207}Pb}{^{204}Pb}\right) = \left(\frac{^{207}Pb}{^{204}Pb}\right)_0 + \left(\frac{^{235}U}{^{204}Pb}\right) \cdot \left(e^{\lambda_{235} \cdot t}-1\right)\]

\[ \left(\frac{^{208}Pb}{^{204}Pb}\right) = \left(\frac{^{208}Pb}{^{204}Pb}\right)_0 + \left(\frac{^{232}Th}{^{204}Pb}\right) \cdot \left(e^{\lambda_{232} \cdot t}-1\right)\]

The subscript \(_0\) denotes the initial Pb at the start of the model \(t\). It is the ratio of the isotopic composition of Pb when the system closed (e.g., crystallisation of a mineral). Isotope ratios without subscripts denote the measured lead isotope composition, i.e. today’s ratios (\(t=0\)). The decay constants of 238U, 235U and 232Th are:

\[λ_{238}=4.468\cdot10^9\ a\]

\[λ_{235}=0.704\cdot10^9\ a\]

\[λ_{232}=14.1\cdot10^9\ a\]

Therefore, different geological environments (e.g., mantle, crust) and tectonic processes result in distinct Pb isotope ratios. These relationships often are assessed on the basis of model parameters – the model age, µ (235U/204Pb) and κ (232Th/235U) – which are calculated from the 204Pb-based isotope ratios. Different models have been developed, of which the most widely used are the two-stage models of Stacey and Kramers (1975) and Albarède and Juteau (1984).

Pb isotope ratios are applied in ore deposit geology to reconstruct the metal sources and formation processes of ore mineralisations. Grögler et al. (1966) and Brill and Wampler (1967) first analysed Pb isotope ratios of archaeological metal objects to determine from which ore deposits the raw material might have potentially been sourced. The direct comparison between the isotope signatures of archaeological objects and ore mineralisations is possible since the effect of pyrometallurgical and weathering processes on Pb isotope ratios is typically negligible. Nowadays, Pb isotopes are therefore a key method for assessing the potential raw material provenance of various Pb-bearing archaeological materials such as metals and alloys, glass, glazes, pigments and ceramics.

3.5 Self check

Now you can provide answers to the following questions:

  • Which Pb isotopes are stable, radiogenic, and radioactive? And what is the difference?
  • Do I need to measure U and Th isotopes to determine the lead isotope ratios or to calculate the lead isotope age of a material?
  • What generates variations in Pb isotope ratios?
  • Why are Pb isotopes useful for investigating archaeological artefacts?
  • What archaeological materials can be investigated with Pb isotopes?
  • Which Pb isotope ratios are used for the calculation of model parameters?
  • Which Pb isotope ratio is proportional to a) the model age, b) µ, and c) κ?

3.6 Further reading

3.6.1 General

  • Faure G (1986) Principles of isotope geology, 2nd edn. Wiley, New York, Chichester.
  • Huston DL, Champion DC (2023) Applications of Lead Isotopes to Ore Geology, Metallogenesis and Exploration. In: Huston D, Gutzmer J (eds) Isotopes in Economic Geology, Metallogenesis and Exploration. Springer, Cham, 155-187. https://doi.org/10.1007/978-3-031-27897-6_6
  • Köppel V, Grünenfelder M (1979) Isotope geochemistry of lead. In: Jäger E, Hunziker JC (eds) Lectures in isotope geology. Springer, Berlin, pp 134–153. https://doi.org/10.1007/978-3-642-67161-6_9
  • Schoene B (2014) 4.10 - U–Th–Pb Geochronology. In: Holland HD, Turekian KK (eds) Treatise on geochemistry, 2nd edn., vol 4. Elsevier, Amsterdam, pp 341–378. https://doi.org/10.1016/B978-0-08-095975-7.00310-7 (read online)
  • Tosdal RM, Wooden JL, Bouse RM (1999) Pb Isotopes, Ore Deposits, and Metallogenic Terranes. In: Lambert DD, Ruiz J (eds) Application of Radiogenic Isotopes to Ore Deposit Research and Exploration. Society of Economic Geologists, Littleton, pp 2–28. https://doi.org/10.5382/Rev.12.01
  • Weis D (2018) Lead Isotopes. In: White WM (ed) Encyclopedia of Geochemistry: A Comprehensive Reference Source on the Chemistry of the Earth. Springer, Cham, pp 1–5. https://doi.org/10.1007/978-3-319-39312-4_293

3.6.2 Age models