Uranium–lead dating

{{short description|Type of radiometric dating}} '''Uranium–lead dating''', abbreviated '''U–Pb dating''', is one of the oldest<ref name="Boltwood">{{cite journal |doi=10.2475/ajs.s4-23.134.78 |title=Ultimate disintegration products of the radioactive elements; Part II, Disintegration products of uranium |journal=American Journal of Science |volume=23 |issue=134 |pages=78–88 |year=1907 |last1=Boltwood |first1=B. B. |bibcode=1907AmJS...23...78B |s2cid=131688682 |url=https://zenodo.org/record/1450152 }}</ref> and most refined of the [[radiometric dating]] schemes. It can be used to date rocks that formed and crystallised from about 1 million years to over 4.5 billion years ago with routine precisions in the 0.1–1 percent range.<ref>{{cite journal |last1= Schoene |first1= Blair |date= 2014 |title= U–Th–Pb Geochronology |url= https://timslab.princeton.edu/sites/g/files/toruqf2276/files/schoene-treatisegeochemistry-2014.pdf |journal= Princeton University, Princeton, NJ, USA |access-date= 6 August 2022}}</ref><ref>{{cite journal |doi=10.1016/j.chemgeo.2015.02.028 |title=U–Th–Pb zircon geochronology by ID-TIMS, SIMS, and laser ablation ICP-MS: Recipes, interpretations, and opportunities |journal=Chemical Geology |volume=402 |pages=89–110 |year=2015 |last1=Schaltegger |first1=U. |last2=Schmitt |first2=A.K. |last3=Horstwood |first3=M.S.A. |bibcode=2015ChGeo.402...89S |url=http://nora.nerc.ac.uk/id/eprint/510788/1/Schaltegger%20et%20al%20resubmission%20%28last%20version%29.pdf }}</ref>

The method is usually applied to [[zircon]]. This mineral incorporates [[uranium]] and [[thorium]] [[atoms]] into its [[crystal structure]], but strongly rejects [[lead]] when forming. As a result, newly-formed zircon crystals will contain no lead, meaning that any lead found in the mineral is [[radiogenic]]. Since the exact rate at which uranium decays into lead is known, the current ratio of lead to uranium in a sample of the mineral can be used to reliably determine its age.

The method relies on two separate [[decay chain]]s, the [[uranium series]] from [[uranium-238|²³⁸U]] to ²⁰⁶Pb, with a [[half-life]] of 4.47 billion years and the [[actinium series]] from [[uranium-235|²³⁵U]] to ²⁰⁷Pb, with a half-life of 710 million years.

==Decay routes== [[Uranium]] decays to [[lead]] via a series of [[Alpha decay|alpha]] and [[Beta decay|beta]] decays, in which ²³⁸U and its daughter [[nuclide]]s undergo a total of eight alpha and six beta decays, whereas ²³⁵U and its daughters only experience seven alpha and four beta decays.<ref name="Romer">{{cite journal |last1=Romer |first1=Rolf L. |year=2003 |title=Alpha-recoil in U–Pb geochronology: Effective sample size matters |journal=Contributions to Mineralogy and Petrology |volume=145 |issue=4 |pages=481–491 |bibcode=2003CoMP..145..481R |doi=10.1007/s00410-003-0463-0 |s2cid=129763448}}</ref>

The existence of two 'parallel' uranium–lead decay routes (²³⁸U to ²⁰⁶Pb and ²³⁵U to ²⁰⁷Pb) leads to multiple feasible dating techniques within the overall U–Pb system. The term ''U–Pb dating'' normally implies the coupled use of both decay schemes in the 'concordia diagram' (see below).

However, use of a single decay scheme (usually ²³⁸U to ²⁰⁶Pb) leads to the U–Pb isochron dating method, analogous to the [[rubidium–strontium dating]] method.

Finally, ages can also be determined from the U–Pb system by analysis of Pb isotope ratios alone. This is termed the [[lead–lead dating]] method. [[Clair Patterson|Clair Cameron Patterson]], an American geochemist who pioneered studies of uranium–lead radiometric dating methods, used it to obtain one of the earliest estimates of the [[age of the Earth]] in 1956 to be 4.550Gy ± 70My; a figure that has remained largely unchallenged since.

==Mineralogy== Although [[zircon]] (ZrSiO₄) is most commonly used, other minerals such as [[monazite]] (see: [[monazite geochronology]]), [[titanite]], and [[baddeleyite]] can also be used.

Where crystals such as zircon with uranium and thorium inclusions cannot be obtained, uranium–lead dating techniques have also been applied to other minerals such as [[calcite]] / [[aragonite]] and other [[carbonate mineral]]s. These types of minerals often produce lower-precision ages than [[igneous]] and [[Metamorphic rock|metamorphic]] minerals traditionally used for age dating, but are more commonly available in the geologic record.

==Mechanism== During the [[alpha decay]] steps, the zircon crystal experiences radiation damage, associated with each alpha decay. This damage is most concentrated around the parent isotope (U and Th), expelling the [[daughter isotope]] (Pb) from its original position in the zircon lattice.

In areas with a high concentration of the parent isotope, damage to the [[crystal lattice]] is quite extensive, and will often interconnect to form a network of radiation damaged areas.<ref name="Romer" /> [[Fission track]]s and micro-cracks within the crystal will further extend this radiation damage network.

These fission tracks act as conduits deep within the crystal, providing a method of transport to facilitate the leaching of lead isotopes from the zircon crystal.<ref name="Mattinson">{{cite journal |doi=10.1016/j.chemgeo.2005.03.011 |title=Zircon U–Pb chemical abrasion ("CA-TIMS") method: Combined annealing and multi-step partial dissolution analysis for improved precision and accuracy of zircon ages |journal=Chemical Geology |volume=220 |issue=1–2 |pages=47–66 |year=2005 |last1=Mattinson |first1=James M. |bibcode=2005ChGeo.220...47M }}</ref>

==Computation==

Under conditions where no lead loss or gain from the outside environment has occurred, the age of the zircon can be calculated by assuming [[exponential decay]] of uranium. That is :<math>N_{\mathrm{n}} = N_{\mathrm{o}} e^{-\lambda t} \,</math> where * <math>N_{\mathrm{n}} = \mathrm{U}</math> is the number of uranium atoms measured now. * <math>N_{\mathrm{o}}</math> is the number of uranium atoms originally - equal to the sum of uranium and lead atoms <math>\mathrm{U} + \mathrm{Pb}</math> measured now. * <math>\lambda = \lambda_\mathrm{U}</math> is the decay rate of Uranium. * <math>t</math> is the age of the zircon, which one wants to determine. This gives :<math>\mathrm{U} = \left( \mathrm{U} + \mathrm{Pb} \right) e^{-\lambda_\mathrm{U} t} ,</math> which can be written as :<math>{{\mathrm{Pb}}\over{\mathrm{U}}} = e^{\lambda_\mathrm{U} t} - 1.</math>

The more commonly used decay chains of Uranium and Lead gives the following equations: {{NumBlk|::|<math>{{^\text{206}\,\!\text{Pb}^*}\over{^\text{238}\,\!\text{U}}}=e^{\lambda_{238}t}-1,</math>|{{EquationRef|1}}}} {{NumBlk|::|<math>{{^\text{207}\,\!\text{Pb}^*}\over{^\text{235}\,\!\text{U}}}=e^{\lambda_{235}t}-1.</math>|{{EquationRef|2}}}} (The notation <math>\text{Pb}^*</math>, sometimes used in this context, refers to ''radiogenic'' lead. For unaltered zircon, the ''original'' lead content can be assumed to be zero, and the notation can be ignored.) These are said to yield concordant ages (''t'' from each equation 1 and 2). It is these concordant ages, plotted over a series of time intervals, that result in the concordant line.<ref name="Dickin">{{cite book |doi=10.1017/CBO9781139165150 |page=101|title=Radiogenic Isotope Geology|year=2005|last1=Dickin|first1=Alan P.|isbn=978-1-139-16515-0}}</ref>

Loss (leakage) of lead from the sample will result in a discrepancy in the ages determined by each decay scheme. This effect is referred to as discordance and is demonstrated in Figure&nbsp;1. If a series of zircon samples has lost different amounts of lead, the samples generate a discordant line. The upper intercept of the concordia and the discordia line will reflect the original age of formation, while the lower intercept will reflect the age of the event that led to open system behavior and therefore the lead loss; although there has been some disagreement regarding the meaning of the lower intercept ages.<ref name=Dickin/>

[[Image:ConcordiaDiagram.jpg|thumb|500px|center|Figure&nbsp;1: Concordia diagram for data published by Mattinson<ref name=Mattinson/> for zircon samples from [[Klamath Mountains]] in Northern California. Ages for the concordia increase in increments of 100&nbsp;million years.]]

Undamaged zircon retains the lead generated by radioactive decay of uranium and thorium up to very high temperatures (about 900&nbsp;°C), though accumulated radiation damage within zones of very high uranium can lower this temperature substantially. Zircon is very chemically inert and resistant to mechanical weathering – a mixed blessing for geochronologists, as zones or even whole crystals can survive melting of their parent rock with their original uranium–lead age intact. Thus, zircon crystals with prolonged and complicated histories can contain zones of dramatically different ages (usually with the oldest zone forming the core, and the youngest zone forming the rim of the crystal), and so are said to demonstrate "inherited characteristics". Unraveling such complexities (which can also exist within other minerals, depending on their maximum lead-retention temperature) generally requires in situ micro-beam analysis using, for example, ion microprobe ([[Secondary ion mass spectrometry|SIMS]]), or laser [[Inductively coupled plasma mass spectrometry|ICP-MS]].

== Lead correction == For U-Pb isotope ratio's to give a age with geological significance it is important to take into account how much of the measured lead isotopes originate from the uranium that has decayed in the mineral since formation. Initial lead Pb_i or Pb₀ is lead that has been in the mineral since formation. Common lead Pb_c refers to all lead that did not form from uranium decay in the mineral. Notably Pb_c also includes lead measured that originates from lab contamination.<ref name=":0">{{Cite web |title=U–Th–Pb Geochronology {{!}} Thermal Ionization Mass Spectrometer Laboratory |url=https://timslab.princeton.edu/publications/u-th-pb-geochronology |access-date=2026-04-30 |website=timslab.princeton.edu |language=en}}</ref> [[File:Complex_zircon.svg|thumb|BSE image of complex zircon showing a core, rim, fractures and fluid alteration with legend and scale. Zircon originates from a metagranitoid in Bergslagen, Sweden.]]

=== Sources of initial lead === Zircons have the tendency to reject lead during crystalisation while uranium can [[Goldschmidt classification|substitute]] zirconium. However lead can still enter or leave zircons through for example (partial)metamorphic reset, inclusions, cracks or fluid alterations. Because this lead can influence the final U/Pb ratios it is common for every zircon to be studied using backscatter electron imaging that can reveal most alterations.<ref>{{Cite journal |last=Andersen |first=Tom |last2=Elburg |first2=Marlina A. |last3=Magwaza |first3=Boniswa N. |date=2019-10-01 |title=Sources of bias in detrital zircon geochronology: Discordance, concealed lead loss and common lead correction |url=https://www.sciencedirect.com/science/article/pii/S0012825219301382 |journal=Earth-Science Reviews |volume=197 |article-number=102899 |doi=10.1016/j.earscirev.2019.102899 |issn=0012-8252}}</ref>

Other minerals used for uranium lead dating can contain lead from the start such as monazite<ref>{{Cite journal |last=Stern |first=Richard A |last2=Berman |first2=Robert G |date=2001-02-01 |title=Monazite U–Pb and Th–Pb geochronology by ion microprobe, with an application to in situ dating of an Archean metasedimentary rock |url=https://www.sciencedirect.com/science/article/pii/S0009254100002394 |journal=Chemical Geology |series=What are we dating? Understanding the Crystallogernesis of U-Pb |volume=172 |issue=1 |pages=113–130 |doi=10.1016/S0009-2541(00)00239-4 |issn=0009-2541|url-access=subscription }}</ref>, titanite <ref>{{Cite journal |last=Frost |first=B. Ronald |last2=Chamberlain |first2=Kevin R. |last3=Schumacher |first3=John C. |date=2001-02-01 |title=Sphene (titanite): phase relations and role as a geochronometer |url=https://www.sciencedirect.com/science/article/pii/S0009254100002400 |journal=Chemical Geology |series=What are we dating? Understanding the Crystallogernesis of U-Pb |volume=172 |issue=1 |pages=131–148 |doi=10.1016/S0009-2541(00)00240-0 |issn=0009-2541|url-access=subscription }}</ref>and apatite<ref>{{Cite journal |last=Chamberlain |first=Kevin R. |last2=Bowring |first2=Samuel A. |date=2001-02-01 |title=Apatite–feldspar U–Pb thermochronometer: a reliable, mid-range (∼450°C), diffusion-controlled system |url=https://www.sciencedirect.com/science/article/pii/S0009254100002424 |journal=Chemical Geology |series=What are we dating? Understanding the Crystallogernesis of U-Pb |volume=172 |issue=1 |pages=173–200 |doi=10.1016/S0009-2541(00)00242-4 |issn=0009-2541|url-access=subscription }}</ref>. The uranium, thorium and lead content can vary significantly between and within individual crystals.

=== Lead correction === When there is initial lead in the system there are several techniques to mitigate this.

* '''Tera-wasserburg Concordia diagram''' - A type of Concordia diagram where ²⁰⁷Pb/²⁰⁶Pb is plotted against ²³⁸U/²⁰⁶Pb. The advantage of plotting the lead/lead ratio is that when a regression is done of a sample population not only an intercept age is given but also a calculated Pb_i ratio. This combines the strength of the Concordia diagram with the Isochron method.<ref name=":0" /><ref>{{Cite journal |last=Tera |first=Fouad |last2=Wasserburg |first2=G. J. |date=1972-04-01 |title=U-Th-Pb systematics in three Apollo 14 basalts and the problem of initial Pb in lunar rocks |url=https://www.sciencedirect.com/science/article/pii/0012821X72901288 |journal=Earth and Planetary Science Letters |volume=14 |issue=3 |pages=281–304 |doi=10.1016/0012-821X(72)90128-8 |issn=0012-821X|url-access=subscription }}</ref> * '''[[Isochron dating|Isochron intercept age]]''' - This method can be used when there is a variety of uranium and lead content in the data. The isochron is a line through the datapoints with high U/Pb and low U/Pb giving an Pb_i specific to that sample that intersect to an event age. * Initial lead estimation based on '''Stacey-Kramer model''' - If there is insufficient data or if the data is not spread out enough for a regression to be attempted to calculate the age using an estimation of the initial lead ratio. Stacey and kramer made a two-stage model of how this ratio changed during the history of the earth.<ref>{{Cite journal |last=Stacey |first=J. S. |last2=Kramers |first2=J. D. |date=1975-06-01 |title=Approximation of terrestrial lead isotope evolution by a two-stage model |url=https://www.sciencedirect.com/science/article/pii/0012821X75900886 |journal=Earth and Planetary Science Letters |volume=26 |issue=2 |pages=207–221 |doi=10.1016/0012-821X(75)90088-6 |issn=0012-821X|url-access=subscription }}</ref> To use this model it is necessary to estimate the rough age based on the surrounding geology and ([[Biostratigraphy|bio]])[[stratigraphy]].

==References== {{Wikibooks |Historical Geology|Other isochron methods}} {{Wikibooks |Historical Geology|U-Pb, Pb-Pb, and fission track dating}} {{reflist}}

{{Chronology}}

{{DEFAULTSORT:Uranium-Lead Dating}} [[Category:Radiometric dating]]