Sm-Nd geochronology

¹⁴⁷₆₂Sm → ¹⁴³₆₀Nd:
- ¹⁴⁷Sm decays via alpha decay to produce ¹⁴³Nd.
Decay Constant (λ):
- 6.54 x 10⁻¹² year⁻¹.
Half-Life:
- 106 billion years.
Age Calculation Equation:

\[ \frac{{^{143}\text{Nd}}}{{^{144}\text{Nd}}} = \left( \frac{{^{143}\text{Nd}}}{{^{144}\text{Nd}}} \right)_{i} + \frac{{^{147}\text{Sm}}}{{^{144}\text{Nd}}} \times (e^{\lambda t} - 1) \]

\[ \text{Age} = \frac{ \ln(\text{slope} + 1)}{\lambda} \]

Where:
\[ \text{slope} = \frac{{\frac{{^{143}\text{Nd}}}{{^{144}\text{Nd}}} - \left( \frac{{^{143}\text{Nd}}}{{^{144}\text{Nd}}} \right)_{i}}}{{\frac{{^{147}\text{Sm}}}{{^{144}\text{Nd}}}}} \]

Applications
- Dating Precambrian Mafic Rocks
- High-Grade Metamorphic Rocks
- Garnet Geochronology

Epsilon Nd (εNd)

Epsilon Neodymium (εNd):
- A measure of the deviation of a sample’s ¹⁴³Nd/¹⁴⁴Nd ratio from the Chondritic Uniform Reservoir (CHUR) in parts per 10,000.

\[ εNd(t) = \left( \frac{(^{143}Nd/^{144}Nd)_{sample}}{(^{143}Nd/^{144}Nd)_{CHUR}} - 1 \right) \times 10,000 \]

CHUR: The reference isotopic composition representing the average mantle or primitive Earth.
Positive εNd values: Indicate a depleted mantle source (mantle-derived).
Negative εNd values: Suggest an enriched or crustal source.

Example:

Sample \(^{143}Nd/^{144}Nd = 0.512500\)
CHUR \(^{143}Nd/^{144}Nd = 0.512638\)

\[ εNd = \left( \frac{0.512500}{0.512638} - 1 \right) \times 10,000 = -2.7 \]

K-Ar geochronology

How does Potassium-40 (40K) decay?

40K decays via two main pathways:
- β⁻ decay to 40Ca (major branch).
- Electron capture (EC) decay to 40Ar (minor branch, ~11% of 40K decays).
Decay constants:
- 40Ca branch (β⁻ decay constant): 4.9548 × 10⁻¹⁰ yr⁻¹ (Renne et al., 2011). (half-life: 1397 Ma).
- 40Ar branch (EC decay constant): 0.581 × 10⁻¹⁰ yr⁻¹ (half-life: 11.93 billion years).
Total decay constant (40K): 5.543 × 10⁻¹⁰ yr⁻¹, with a total half-life of 1250 Ma.

Why is K-Ar important in geochronology?

40Ar is a rare gas that accumulates in rocks after 40K decays.
- 99.6% of atmospheric argon comes from this decay.
Since 40Ar does not escape from minerals easily, we can use the K-Ar method to date rocks.
- Especially useful for volcanic and metamorphic rocks.
- Provides information on the timing of volcanic eruptions or metamorphic events.

K-Ar Dating Equations:

General Age Equation:

\[ \frac{^{40}\text{Ar}}{^{36}\text{Ar}}_{\text{total}} = \frac{^{40}\text{Ar}}{^{36}\text{Ar}}_{\text{atm+excess}} + \frac{^{40}\text{K}}{^{36}\text{Ar}} \times \frac{\lambda_{EC}}{\lambda_{EC} + \lambda_{\beta}} (e^{\lambda_{\text{total}} t} - 1) \]

Where:
- 40Ar/36Ar_total = total measured argon isotope ratio.
- 40Ar/36Ar_atm+excess = argon isotope ratio due to atmospheric and excess argon components.
- 40K = potassium-40 content in the sample.
- λ_EC = electron capture decay constant (0.581 × 10⁻¹⁰ yr⁻¹).
- λ_β = beta decay constant (4.962 × 10⁻¹⁰ yr⁻¹).
- λ_total = total decay constant (5.543 × 10⁻¹⁰ yr⁻¹).
- t = age of the sample.

Ar-Ar Geochronology

What is the Ar-Ar Method?

An advanced version of K-Ar dating:
- Instead of directly measuring 40K and 40Ar, the sample is irradiated in a nuclear reactor to convert 39K into 39Ar.
- This allows for both potassium and argon isotopes to be measured in a single step.

How does the Ar-Ar Method work?

Irradiation:
- The sample is irradiated with fast neutrons in a reactor, converting 39K into 39Ar.
Step-Heating:
- The sample is progressively heated in a vacuum, releasing argon gas at different temperatures.
- This allows for the detection of disturbances or mixed ages in the sample.
Isotopic Measurement:
- Both 40Ar (radiogenic) and 39Ar (produced from 39K) are measured using a mass spectrometer.

Advantages of Ar-Ar Over K-Ar:

Higher precision:
- By using step-heating, the Ar-Ar method allows for detailed analysis of argon release, which can reveal age disturbances and offer more precise results.
Smaller sample size:
- Less material is needed compared to K-Ar, and it can be applied to smaller grains.
One-step measurement:
- Both potassium and argon isotopes are measured together, reducing the potential for errors.

Ar-Ar Age Calculation Equations:

Irradiation Factor (J) for the standard:

\[ J = \frac{e^{\lambda t} - 1}{\frac{{^{40}\text{Ar}^{*}}}{{^{39}\text{Ar}}}} \]

Where:
- J = irradiation factor, or “J-value.”
- λ = decay constant (5.543 × 10⁻¹⁰ yr⁻¹).
- t = age of the sample (in years).
- 40Ar* = radiogenic 40Ar.
- 39Ar = argon produced from neutron irradiation of 39K.

General Age Equation:

\[ t = \frac{1}{\lambda} \ln \left( \frac{{^{40}\text{Ar}_{\text{radiogenic}}}}{{^{39}\text{Ar}}} \times J + 1 \right) \]

Where:
- t = age of the sample.
- λ = decay constant (5.543 × 10⁻¹⁰ yr⁻¹).
- 40Ar_radiogenic = radiogenic argon from 40K decay.
- 39Ar = argon produced from neutron irradiation of 39K.
- J = irradiation factor or “J-value” that accounts for the conversion of 39K to 39Ar during neutron irradiation.

Applications:

Dating volcanic, igneous rocks, and metamorphic rocks.
Ideal for resolving complex geologic histories, especially those involving multiple heating or cooling events.

Sm-Nd, K-Ar and Ar-Ar geochronology