U-Pb dating method

Dr. Ahmad Redaa

2024-10-15

What is U-Pb Dating?

U-Pb dating is a radiometric method that measures the decay of uranium isotopes (U-238 and U-235) into lead isotopes (Pb-206 and Pb-207).
Applications: Dates minerals like zircon, apatite, monazite, and titanite … and more

Geochemistry of Uranium

Uranium Isotopes:
- U-238 → Pb-206 (Half-life: ~4.47 billion years).
- U-235 → Pb-207 (Half-life: ~704 million years).
Key Minerals: Zircon (ZrSiO₄), baddeleyite, titanite, monazite.
Behavior in Nature:
- Solubility: Uranium is soluble in oxidizing conditions, especially in the form of U(VI) (uranyl ion \(\text{UO}_2^{2+}\)).
- Oxidation States:
  - U(VI): Uranium in the +6 oxidation state, highly mobile in aqueous solutions.
  - U(IV): Uranium in the +4 oxidation state, less soluble and immobile in reducing environments.
- Compatibility:
  - Uranium is an incompatible element in mafic minerals (like olivine and pyroxene) because it does not easily fit into their crystal structures.
  - Uranium prefers felsic magmas rich in silica, where it concentrates in accessory minerals like zircon, monazite, and titanite during the later stages of crystallization.
- Crystallization Stages:
  - Uranium is usually incorporated in the later stages of crystallization from silica-rich magmas.
  - In mafic rocks, which crystallize earlier from magma and have lower silica content, uranium is not compatible and thus is not typically found in significant concentrations.
- Link to Rock Types:
  - Mafic rocks (rich in magnesium and iron) crystallize early from magma, excluding uranium.
  - Felsic rocks (rich in silica) crystallize later, allowing uranium to become concentrated in accessory minerals like zircon.
- Movement and Leaching: Uranium is mobile in oxidizing environments but becomes immobile in reducing conditions, where U(IV) precipitates.
- Fractionation: Uranium can be fractionated during weathering and hydrothermal processes, leaching out in oxidizing conditions and redepositing in reducing environments.
- Importance: Understanding uranium’s movement and compatibility is important in determining which minerals retain U-Pb isotopic systems for accurate dating.

U-Pb Dating Equations (General Decay)

General Decay Equation: \[ D = D_0 + P \left( e^{\lambda t} - 1 \right) \]
- D = present amount of daughter isotope (Pb)
- D₀ = initial amount of daughter isotope (Pb)
- P = present amount of parent isotope (U)
- λ = decay constant of parent isotope
- t = age
U-238 to Pb-206: \[ \frac{^{206}\text{Pb}}{^{204}\text{Pb}} = \frac{^{206}\text{Pb}_0}{^{204}\text{Pb}} + \frac{^{238}\text{U}}{^{204}\text{Pb}} \left( e^{\lambda_{238} t} - 1 \right) \]
U-235 to Pb-207: \[ \frac{^{207}\text{Pb}}{^{204}\text{Pb}} = \frac{^{207}\text{Pb}_0}{^{204}\text{Pb}} + \frac{^{235}\text{U}}{^{204}\text{Pb}} \left( e^{\lambda_{235} t} - 1 \right) \]

Challenges of U-Pb Dating

Open System: Geological processes (metamorphism, recrystallization) can “open” the system.
Effect: Lead or uranium may escape or enter, causing inaccurate age calculations.
Pb²⁰⁴ is a non-radiogenic isotope with very low natural abundance; therefore, accurate measurement of the measurement is challenging.
Pb²⁰⁴ has isobaric interference with Hg²⁰⁴, which complicate its detection during in-situ analyses (e.g., LA-ICP-MS).

Age Equation for Pb²⁰⁶ (from U²³⁸ decay):

Assuming there is no common lead (i.e., no initial Pb²⁰⁶ is present at the time of sample formation), the relationship between Pb²⁰⁶ and U²³⁸ is given by the equation:

\[ ^{206}\text{Pb} = ^{238}\text{U} (e^{\lambda_{238} t} - 1) \]

Where:
- \(^{206}\text{Pb}\) is the amount of radiogenic lead-206 produced.
- \(^{238}\text{U}\) is the present amount of uranium-238.
- \(\lambda_{238}\) is the decay constant of U²³⁸.
- \(t\) is the age of the sample.

Rearranging this equation to solve for \(t\), we get:

\[ t = \frac{1}{\lambda_{238}} \ln \left( \frac{^{206}\text{Pb}}{^{238}\text{U}} + 1 \right) \]

Age Equation for Pb²⁰⁷ (from U²³⁵ decay):

Similarly, for Pb²⁰⁷ and U²³⁵, the equation is:

\[ ^{207}\text{Pb} = ^{235}\text{U} (e^{\lambda_{235} t} - 1) \]

Where:
- \(^{207}\text{Pb}\) is the amount of radiogenic lead-207 produced.
- \(^{235}\text{U}\) is the present amount of uranium-235.
- \(\lambda_{235}\) is the decay constant of U²³⁵.
- \(t\) is the age of the sample.

Rearranging this equation to solve for \(t\):

\[ t = \frac{1}{\lambda_{235}} \ln \left( \frac{^{207}\text{Pb}}{^{235}\text{U}} + 1 \right) \]

Combining U-238 and U-235 Systems

Concordia Diagram: Combines U-238 and U-235 systems to identify accurate ages even in disturbed systems.
Wetherill Concordia Diagram:
- Plots \(\frac{^{207}\text{Pb}}{^{204}\text{Pb}}\) vs. \(\frac{^{206}\text{Pb}}{^{204}\text{Pb}}\).

Source: (Machado and Simonetti, 2001)

Tera–Wasserburg Concordia Diagram

Tera–Wasserburg Concordia Diagram:
- Plots \(\frac{^{238}\text{U}}{^{204}\text{Pb}}\) vs. \(\frac{^{207}\text{Pb}}{^{204}\text{Pb}}\).

Source: (Machado and Simonetti, 2001)

Discordia Diagram

Discordia Line: Formed when geological processes disturb the U-Pb system.
Interpretation:
- Upper intercept = crystallization age.
- Lower intercept = disturbance (e.g., metamorphism).

Summary

U-Pb dating: Reliable method combining U-238 and U-235 systems.
Concordia diagrams: Useful for accurate dating and detecting disturbances.
Discordia diagrams: Reveal both crystallization and disturbance events in a rock’s history.