**
****Chronostratigraphy I:**

**Chronostratigraphy I:**

**Numerical** or **absolute** dating
There are many methods, each with its own strengths and limitations:

- Varves
- Dendrochronology
- Thermoluminescence dating
- Fission track dating
- Cosmogenic nuclide dating
- Amino acid racemization
- Tephrachronology
- Astronomical dating/Milankovitch cycles
- Radiometric dating

### Radiometric dating

**Antoine Becquerel**(1852-1908): Discovered natural radioactivity (1896). In the following years, a large number of radioactive isotopes and their daughter products became known.

**Pierre**(1859-1906) and

**Marie**(1867-1934)

**Curie**: Discovered that the radioactive element

**radium**continuously releases newly generated heat -

**radiogenic heat**. With this discovery, it became clear that the decay of radioactive substances provided a continuous source of new heat that Sir William Thomson (aka Lord Kelvin) hadn't accounted for in his calculations that Earth was 20 - 40 million years old. The Earth might, indeed, be

**much**older than his calculations indicated.

**But how old?**

History:

- At the beginning of the 20th century,
**Ernest Rutherford**and Frederick Soddy developed the concept of the**half-life - For any radioactive substance, there is a specific period of time in which half of a sample will decay to a daughter substance.**E.G., if we have a newly created 1 kg. sample of a substance whose half-life is 10 years, then ten years from its creation, half of the radioactive material will remain in the sample. The other half will be the daughter product. After twenty years, 0.25 kg. will remain (with the rest being daughter product), and after thirty years, 0.125 kg. of the original radioactive substance will remain in the sample. - In 1904, Rutherford made the first attempt to use this principle to estimate the age of a rock using the presence of helium in a rock as a proxy for alpha decay of radium (alpha-particles are helium nuclei). His analysis was technically problematic because of his choice of a gas, helium as a radioactive product (gasses have a way of migrating out of rocks), but it was a start.
- In 1905,
**Bertram Boltwood**noted a specific parent-daughter relationship between an isotope of uranium,^{235}U, a radioactive isotope, and lead (Pb) suggesting that one decayed into the other - the**uranium-lead system**. Because lead is usually found as a solid, this method was more promising. Like Rutherford's, Boltwood's attempt to apply the principle to the dating of rocks was technically flawed but a further step forward. - Beginning in 1911,
**Arthur Holmes**began a long career of applying the concept of radiometric dating to rocks, and is given credit for ironing out the technical issues that hampered earlier attempts. (Note: Holms also first proposed the concept of sea-floor spreading.) - After a century of applying the method we now know that that oldest known Earth rocks are aprox 4.28 billion years old (abbreviated "Ga"). The oldest in the Solar System are 4.56 Ga.

**The current understanding:**

**Radioactive decay** - unstable parent atoms change into more stable daughter atoms. This involves one of the following transformations:

- Loss of neutron(s)
- Loss of proton(s)
- Loss of alpha (α) particles (= 2 neutrons, 2 protons, i.e. He nucleus)
- Loss of beta (β) particle - 1 neutron and 1 electron
- Electron capture - 1 electron joins with a proton to form a neutron (i.e. gamma particle γ)

**Decay constant (λ)**- The probability that a given nucleus will decay at a given time. This is unique to each element. If one assumes that the parent:daughter ratio present in a crystal is determined only by the elapsed time since the parent and daughter were locked into the crystal and neither have escaped

N = N_{0}e^{-λt}

Where:

- N = # radioactive nuclei present
- t = time elapsed
- N
_{0}= # radioactive nuclei present at t=0

**Half-life (t _{1/2})** - increment of time needed for half the parent atoms to decay to daughters

t_{1/2} = 0.693/λ

t = (1/λ) ln(d/p +1)

where:

- t is the age of the rock/mineral
- d is the concentration of the daughter product
- p is the concentration of the parent substance

**Caveats**:

**closure time**when a crystal cooled to solid state and locked radiogenic elements into its structure.

**Potassium ( ^{40}K) → Argon (^{40}Ar)** by electron capture and γ decay.

- t
_{1/2}= 1.3 billion years - Feldspars, micas, ashes
- Benefits: K is extremely common
- Limitations: Ar is an inert gas and diffuses out of minerals. Ar is common in atmosphere and must be accounted for. It is sensitive to metamorphic resetting, and weathering (allows Ar to escape).

**Uranium ( ^{238}U) → Lead (^{206}Pb)** by series of α and β decays.

- t
_{1/2}= 4.5 billion years - Zircon, monazite, badellyite, apatite
- Benefits: Zircons are very stable and withstand weathering, can be sedimentary minerals. Thus we can date things from Earth's earliest times.
- Limitations: detrital zircon records mineral formation age, not sedimentary rock age. Indeed, the oldest known Earth material is a zircon grain that formed 4.404 Ga and survived the Late Heavy Bombardment.

**Uranium ( ^{234}U) → Thorium (^{230}Th)** by α decay.

- t
_{1/2}= 250 kyr - Carbonates
- Benefits: Abundances can be used to measure sedimentation rates (U preferentially stays in solution)
- Limitations:
^{230}Th decays rapidly to^{232}Th. Because the decay pathway of U is so complex multiple isotopes have to be taken into account.

Several other systems are useful for dating igneous and metamorphic rocks, including:

^{87}Rb→^{87}Sr^{147}Sm→^{143}Nd^{176}Lu→^{176}Hf- various U/Pb/Th systems

^{14}C Dating

This method is **not** used on minerals. Rather, it exploits the fractionation of radioactive ^{14}C and stable ^{12}C by plants during photosynthesis. ^{14}C is produced in the upper atmosphere by bombardment of ^{14}N by cosmogenic neutrons and is fractionated by photosynthesis such that it is incorporated into plant tissue in a fixed ratio to ^{12}C. This fractionation is conserved across green plants and tells us the initial ratio of these isotopes when the plant was growing. Because of its short half-life (5,730 years), ^{14}C dating is useful only as far back as 40,000 yrs.

Note:

- Well calibrated samples show that the rate of
^{14}C generation has varied slightly over time. Thus,^{14}C dates must be adjusted to take these variations into account. (One of the first applications of the method was to wood used in the construction of the step pyramid at Saqqara (right) a structure whose age was known from ancient Egyptian historical records.) - The application to geochronology comes in when datable plant material is found in association with sediments.