Focus

• Understanding key beta decay systems used in geochronology
• Applications in dating minerals and rocks
• Practical examples using Rb-Sr

Important Beta Decay Systems

• Rb-Sr
• Lu-Hf
• K-Ca
• Re-Os

Rb-Sr Geochronology

• ⁸⁷₃₇Rb → ⁸⁷₃₈Sr:
  • ⁸⁷Rb decays via β⁻ decay to produce ⁸⁷Sr.
• Decay Constant (λ):
  • Old Value: 1.42 x 10⁻¹¹ year⁻¹.
  • Updated Value: Villa et al. (2015) have refined the decay constant to 1.3972 x 10⁻¹¹ year⁻¹.
• Half-Life:
  • The half-life of ⁸⁷Rb is approximately 49.61 billion years.
• Applications:
  • Dating of igneous and metamorphic rocks.
  • Commonly used in minerals like mica and feldspar.
  • Useful for dating rocks and minerals millions to billions of years old.
• Age Dating Equation: \[ \frac{87Sr}{86Sr} = \left(\frac{87Sr}{86Sr}\right)_i + \frac{87Rb}{86Sr} \times (e^{\lambda t} - 1) \] The age can be calculated via the equation: \[ \text{Age} = \frac{\ln(\text{slope} + 1)}{\lambda} \] Where: \[ \text{slope} = \frac{\left(\frac{87Sr}{86Sr} - \left(\frac{87Sr}{86Sr}\right)_i\right)}{\frac{87Rb}{86Sr}} \]

Lu-Hf Geochronology

• ¹⁷⁶₇₁Lu → ¹⁷⁶₇₂Hf:
  • ¹⁷⁶₇₁Lu decays via β⁻ decay to produce ¹⁷⁶₇₂Hf.
• Decay Constant (λ):
  • Decay constant (λ) for ¹⁷⁶Lu: 1.867 x 10⁻¹¹ year⁻¹ (Scherer et al., 2001; Söderlund et al., 2004).
• Half-Life:
  • The half-life of ¹⁷⁶Lu is approximately 37.1 billion years .
• Applications:
  • Important for dating garnet-bearing rocks and mantle processes.
  • Widely used in the study of early Earth evolution.
  • Helps in determining the age and origin of continental crust.
• Age Dating Equation: \[ \frac{176Hf}{177Hf} = \left(\frac{176Hf}{177Hf}\right)_i + \frac{176Lu}{177Hf} \times (e^{\lambda t} - 1) \] The age can be calculated via the equation: \[ \text{Age} = \frac{\ln(\text{slope} + 1)}{\lambda} \] Where: \[ \text{slope} = \frac{\left(\frac{176Hf}{177Hf} - \left(\frac{176Hf}{177Hf}\right)_i\right)}{\frac{176Lu}{177Hf}} \]

K-Ca Geochronology

• ⁴⁰₁₉K → ⁴⁰₂₀Ca:
  • ⁴⁰₁₉K decays via β⁻ decay to produce ⁴⁰₂₀Ca.
• Decay Constant (λ):
  • Decay constant (λ) for ⁴⁰K: 4.9548 x 10⁻¹⁰ year⁻¹ (Renne et al., 2011) .
• Half-Life:
  • The half-life of ⁴⁰K is approximately 1.40 billion years .
• Applications:
  • Useful for dating potassium-rich minerals such as mica and feldspar.
  • Important in dating volcanic rocks and studying the geological history of igneous and metamorphic systems.
• Age Dating Equation: \[ \frac{40Ca}{44Ca} = \left(\frac{40Ca}{44Ca}\right)_i + \frac{40K}{44Ca} \times (e^{\lambda t} - 1) \] The age can be calculated via the equation: \[ \text{Age} = \frac{\ln(\text{slope} + 1)}{\lambda} \] Where: \[ \text{slope} = \frac{\left(\frac{40Ca}{44Ca} - \left(\frac{40Ca}{44Ca}\right)_i\right)}{\frac{40K}{44Ca}} \]

Why is K-Ca Dating Not Common?

• 40Ca is very abundant in rocks (97% of total calcium), making it hard to distinguish radiogenic 40Ca from common calcium.
• Variations in radiogenic 40Ca are very small and difficult to measure accurately.
• K-Ar dating is preferred because 40Ar is a rare gas and easy to detect, making it more practical and accurate for dating.
• Measuring radiogenic 40Ca requires highly precise instruments due to the large amount of common calcium.

Re-Os Geochronology

• ¹⁸⁷₇₅Re → ¹⁸⁷₇₆Os:
  • ¹⁸⁷₇₅Re decays via β⁻ decay to produce ¹⁸⁷₇₆Os.
• Decay Constant (λ):
  • Decay constant (λ) for ¹⁸⁷Re: 1.6668 x 10⁻¹¹ year⁻¹ (Kosler et al., 2003).
• Half-Life:
  • The half-life of ¹⁸⁷Re is approximately 42.3 billion years (Lindner et al., 1989)..
• Applications:
  • Molybdenite (MoS₂): The primary ore-bearing mineral for rhenium, common in high-temperature hydrothermal systems, and porphyry Cu deposits. It substitutes Mo with Re, making molybdenite the most commonly dated mineral in Re-Os geochronology. Molybdenite is highly stable and contains low or no detectable common Os, making it ideal for dating hydrothermal and metamorphic events.
  • Sulfides (Pyrite & Chalcopyrite): These minerals can contain sufficient rhenium for Re-Os dating and are used to date a range of deposits, including porphyry, epithermal, sedimentary, volcanic-hosted massive sulfide (VHMS), and iron oxide copper gold (IOCG) ore deposits. Pyrite and chalcopyrite are useful in directly dating ore formation events due to their ability to incorporate Re in sufficient amounts.
• Age Dating Equation: \[ \frac{187Os}{188Os} = \left(\frac{187Os}{188Os}\right)_i + \frac{187Re}{188Os} \times (e^{\lambda t} - 1) \] The age can be calculated via the equation: \[ \text{Age} = \frac{\ln(\text{slope} + 1)}{\lambda} \] Where: \[ \text{slope} = \frac{\left(\frac{187Os}{188Os} - \left(\frac{187Os}{188Os}\right)_i\right)}{\frac{187Re}{188Os}} \]

Why Use Ratios Instead of Isotopes in Geochronology?

• Normalization for Variability:
  • Using isotope ratios (e.g., 87Sr/86Sr) helps normalise for natural variations in the amount of parent (Rb-87) and daughter (Sr-87) isotopes present in different samples.
  • This makes it easier to compare samples, as the absolute concentrations of isotopes can vary greatly depending on rock type and formation conditions.
• Accounting for Initial Isotope Ratios:
  • Absolute isotope concentrations cannot tell us the initial amount of daughter isotope present. By using ratios, we can account for the initial ratio at the time of rock formation, which is essential for accurate age calculations.
• Improving Precision:
  • Measuring isotope ratios, rather than individual isotopes, improves the precision of geochronological dating methods. This is because ratios are less sensitive to small variations in concentration, giving more reliable results.
• Elimination of Matrix Effects:
  • In analytical techniques like mass spectrometry, isotope ratios are used to minimize the effect of the sample matrix, which can affect ionization efficiency differently for each isotope.

Difficulty of Analysis: Isobaric Interference

What is Isobaric Interference?

• Isobaric interference occurs when two or more isotopes of different elements have the same mass number (e.g., 87Rb and 87Sr).
• This creates difficulties in mass spectrometry analysis because the instrument cannot easily distinguish between isotopes of different elements with the same mass.

Challenges in Isotope Geochronology:

1. Rb-Sr Dating:
   • The presence of 87Rb interferes with the measurement of 87Sr because both have the same mass number (87).
   • This makes it hard to accurately measure the radiogenic 87Sr needed for age calculations.
2. Increased Complexity in Measurement:
   • To correct for isobaric interference, advanced techniques like double-spike isotope dilution or collision cell technology are used, which add complexity to the analysis process.
   • It requires careful correction for the 87Rb contribution before obtaining accurate 87Sr values.
3. Instrument Sensitivity:
   • Isobaric interferences reduce the sensitivity of the instrument and limit its ability to resolve small amounts of isotopes accurately.
   • This leads to higher uncertainty in age calculations.

Techniques to Mitigate Isobaric Interference:

• Chemical Separation: Use of ion-exchange columns to separate Rb from Sr before mass spectrometry analysis.
• Reaction Cell in ICP-MS/MS: Using a reaction cell in ICP-MS/MS enables the in-situ analysis of samples with laser ablation (LA). The reaction cell introduces reactive gases that selectively remove isobaric interferences.

Exercise:

• Using the following dataset, plot the ratios 87Rb/86Sr against 87Sr/86Sr.
• Use the slope of your plot and the decay constant for 87Rb (1.3972 x 10⁻¹¹ year⁻¹) to calculate the age of the sample.
• The age can be calculated using the equation:
  \[ \text{Age} = \frac{\ln(\text{slope} + 1)}{\lambda} \]
• Explain what your results mean in terms of the geological history of the sample.

Data Set: