K–Ar dating

Decay series

Potassium naturally occurs in 3 isotopes: (93.2581%), (0.0117%), (6.7302%). and are stable. The isotope is radioactive; it decays with a half-life of to and . Conversion to stable occurs via electron emission (beta decay) in 89.3% of decay events. Conversion to stable occurs via electron capture in the remaining 10.7% of decay events.{{cite report |access-date=29 December 2019}}

Argon, being a noble gas, is a minor component of most rock samples of geochronological interest: It does not bind with other atoms in a crystal lattice. When decays to ; the atom typically remains trapped within the lattice because it is larger than the spaces between the other atoms in a mineral crystal. However, it can escape into the surrounding region when the right conditions are met, such as changes in pressure or temperature. atoms can diffuse through and escape from molten magma because most crystals have melted, and the atoms are no longer trapped. Entrained argon – diffused argon that fails to escape from the magma – may again become trapped in crystals when magma cools to become solid rock again. After the recrystallization of magma, more will decay and will again accumulate, along with the entrained argon atoms, trapped in the mineral crystals. Measurement of the quantity of atoms are used to compute the amount of time that has passed since a rock sample has solidified.

Despite being the favored daughter nuclide, it is rarely useful in dating because calcium is so common in the crust, with being the most abundant isotope. Thus, the amount of calcium originally present is unknown and can vary enough to confound measurements of the small increases produced by radioactive decay.

Formula

The ratio of the amount of to that of is directly related to the time elapsed since the rock was cool enough to trap the Ar by the equation: : t = t_\frac{1}{2}\log_2\left(\frac{\ce{K}_f + \frac{\ce{Ar}_f}{0.109}}{\ce{K}_f}\right), Where:

• t is time elapsed
• t1/2 is the half-life of
• Kf is the amount of remaining in the sample
• Arf is the amount of found in the sample.

The scale factor 0.109 corrects for the unmeasured fraction of which decayed into ; the sum of the measured and the scaled amount of gives the amount of which was present at the beginning of the elapsed period. In practice, each of these values may be expressed as a proportion of the total potassium present, as only relative, not absolute, quantities are required.

Obtaining the data

To obtain the content ratio of isotopes to in a rock or mineral, the amount of Ar is measured by mass spectrometry of the gases released when a rock sample is volatilized in a vacuum. The potassium is quantified by flame photometry or atomic absorption spectroscopy.

The amount of is rarely measured directly. Rather, the more common is measured and that quantity is then multiplied by the accepted ratio of / (i.e., 0.0117%/93.2581%, see above).

The amount of is also measured to assess how much of the total argon is atmospheric in origin.

Assumptions

According to , the following assumptions must be true for computed dates to be accepted as representing the true age of the rock:

• The parent nuclide, , decays at a rate independent of its physical state and is not affected by differences in pressure or temperature. This is a well-founded major assumption, common to all dating methods based on radioactive decay. Although changes in the electron capture partial decay constant for possibly may occur at high pressures, theoretical calculations indicate that for pressures experienced within a body the size of the Earth, the effects are negligibly small.
• The / ratio in nature is constant so the is rarely measured directly, but is assumed to be 0.0117% of the total potassium. Unless some other process is active at the time of cooling, this is a very good assumption for terrestrial samples.
• The radiogenic argon measured in a sample was produced by in situ decay of in the interval since the rock crystallized or was recrystallized. Violations of this assumption are not uncommon. Well-known examples of incorporation of extraneous include chilled glassy deep-sea basalts that have not completely outgassed preexisting *, and the physical contamination of magma by the inclusion of older xenolitic material. The Ar–Ar dating method was developed to measure the presence of extraneous argon.
• Great care is needed to avoid contamination of samples by absorption of non-radiogenic from the atmosphere. The equation may be corrected by subtracting from the measured value of the amount present in the air where is 295.5 times more plentiful than . decayed = measured − 295.5 × measured.
• The sample must have remained a closed system since the event was dated. Thus, there should have been no loss or gain of or *, other than by radioactive decay of . Departures from this assumption are quite common, particularly in areas of complex geological history, but such departures can provide useful information that is of value in elucidating thermal histories. A deficiency of in a sample of a known age can indicate a full or partial melt in the thermal history of the area. Reliability in the dating of a geological feature is increased by sampling disparate areas which have been subjected to slightly different thermal histories.

Both flame photometry and mass spectrometry are destructive tests, so particular care is needed to ensure that the aliquots used are truly representative of the sample. Ar–Ar dating is a similar technique that compares isotopic ratios from the same portion of the sample to avoid this problem.

Applications

Due to the long half-life of , the technique is most applicable for dating minerals and rocks over 100,000 years old. For shorter timescales, it is unlikely that enough will have had time to accumulate to be accurately measurable. K–Ar dating was instrumental in developing the geomagnetic polarity time scale. It has also been indispensable in other early East African sites with a history of volcanic activity such as Hadar, Ethiopia. The K–Ar method continues to have utility in dating clay mineral diagenesis. In 2017, the successful dating of illite formed by weathering was reported. This finding indirectly led to the dating of the strandflat of Western Norway from where the illite was sampled. Clay minerals are less than 2 μm thick and cannot easily be irradiated for Ar–Ar analysis because Ar recoils from the crystal lattice.

In 2013, the K–Ar method was used by the Curiosity Mars rover to date a rock on the Martian surface, the first time a rock has been dated from its mineral ingredients while situated on another planet.

Notes

References

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References

1. {{harvnb. McDougall. Harrison. 1999
2. {{harvnb. McDougall. Harrison. 1999
3. {{harvnb. McDougall. Harrison. 1999
4. {{harvnb. McDougall. Harrison. 1999
5. {{SimpleNuclide. Argon. 40* means radiogenic argon
6. {{harvnb. McDougall. Harrison. 1999
7. Although it finds the most utility in [[geology. Tattersall. 1995
8. {{harvnb. Aronson. Lee. 1986
9. (2017). "The inheritance of a Mesozoic landscape in western Scandinavia". Nature.
10. (9 December 2013). "NASA Curiosity: First Mars Age Measurement and Human Exploration Help". [[Jet Propulsion Laboratory]].
11. (13 December 2013). "Martian rock-dating technique could point to signs of life in space". University of Queensland.