Potassium-argon dating

Potassium-argon dating or K-Ar dating is a radiometric dating method used in geochronology and archeology. It is based on measuring the products of the radioactive decay of potassium (K), which is a common element found in materials such as micas, clay minerals, tephra, and evaporites. The long half-life of ⁴⁰K allows the method to be used on all samples older than a few thousand years.harvnb|McDougal and Harrison|1999|Ref=McDougall_1999|p=10.] The quickly cooled lavas that make nearly ideal samples for K-Ar dating also preserve a record of the direction and intensity of the local magnetic field as the sample cooled past the Curie temperature of iron. The development of the geomagnetic polarity time scale depended largely on K-Ar dating.harvnb|McDougal and Harrison|1999|Ref=McDougall_1999|p=9]

Decay series

Potassium naturally occurs in 3 isotopes - ³⁹K (93.2581%), ⁴⁰K (0.0117%), ⁴¹K (6.7302%). The radioactive isotope ⁴⁰K decays with a half-life of 1.248x10⁹ (1.248 billion) years. Conversion to stable ⁴⁰Ca occurs via electron emission beta decay occurs in 89.1% of decay events. Conversion to stable ⁴⁰Ar occurs via positron emission beta decay or electron capture in 10.9% of decay events. [http://www.nndc.bnl.gov/useroutput/40k_mird.html]

Method

Argon, being a noble gas, is not a major component of most samples of geochronological or archeological interest. When ⁴⁰K decays to ⁴⁰Ar, the gas may be unable to diffuse out of the host rock. Because argon is able to escape from molten rock, this accumulation provides a record of how much of the original ⁴⁰K has decayed, and hence the amount of time that has passed since the sample solidified.

Calcium is common in the crust, with ⁴⁰Ca being the most common isotope. Despite ⁴⁰Ca being the favored daughter nuclide, its usefulness in dating is limited since a great many decay events are required for a small change in relative abundance.

The ⁴⁰Ar content of a rock is determined by mass spectrometry of the gasses released when a sample is melted. The amount of ⁴⁰K is determined using flame photometry or atomic absorption spectroscopy. The ratio of the amount of ⁴⁰Ar to ⁴⁰K is related to the time elapsed since the rock was cool enough to trap the Ar by:

$t\; =\; frac\{t\_frac\{1\}\{2\{ln(2)\}\; ln(frac\{K\_f\; +\; frac\{Ar\_f\}\{0.109\{K\_f\})$

In the foregoing, "t" is time elapsed, "t_1/2" is the half life of ⁴⁰K, K_f is the amount of ⁴⁰K remaining in the sample, and Ar_f is the amount of ⁴⁰Ar found in the sample. The scale factor 0.109 corrects for the unmeasured fraction of ⁴⁰K which decayed into ⁴⁰Ca; the sum of the measured ⁴⁰K and the scaled amount of ⁴⁰Ar gives the amount of ⁴⁰K in the original unaged sample. In practice, each of these values is scaled to the total potassium fraction as only relative, not absolute, quantities are required.

Extraneous argon is commonly incorporated into the cooling sample. The above equation may be corrected for the presence of non-radiogenic SimpleNuclide|Argon|40 by subtracting from the measured ⁴⁰Ar value the amount originally present as determined by the ⁴⁰Ar/³⁶Ar ratio. Ordinarily, ⁴⁰Ar is 295.5 times more plentiful than ³⁶Ar, though this may need to be adjusted if the sample cooled in an isotopically enriched or depleted region. The amount of the measured ⁴⁰Ar that resulted from ⁴⁰K decay is then: SimpleNuclide|Argon|40_decayed = SimpleNuclide|Argon|40_measured - 295.5 * SimpleNuclide|Argon|36_measured.

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. Argon-argon dating is a similar technique which compares isotopic ratios from the same portion of the sample to avoid this problem.

Some additional information about the history and composition of a sample is required before K-Ar isotopic comparison may be used to produce accurate dates. [harvnb|McDougal and Harrison|1999|Ref=McDougall_1999|p=9-12.] Great care is needed in selecting a sample for dating, as many potential samples have been contaminated by various means. The sample must have remained a closed system since it cooled enough to retain argon, neither admitting nor emitting either of the isotopes of interest. A deficiency of 40Ar in a sample of a known age can indicate a full or partial melt in the thermal history of the area. Molten magma can be contaminated by inclusion of older xenolithic material such as chilled deep sea basalts that may not completely outgas preexisting 40Ar before cooling. Reliability in the dating of a geological feature is increased by sampling disparate areas which have been subjected to slightly different thermal histories. [harvnb|McDougal and Harrison|1999|Ref=McDougall_1999|p=11-12.]

Accuracy relies on the isotopic ratios included in the sample being representative since ⁴⁰K is usually not 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. [harvnb|McDougal and Harrison|1999|Ref=McDougall_1999|p=14.] Accuracy also requires that the nuclear decay rate be unaffected by external conditions such as temperature and pressure. Because of the energy scales involved, this is a very good assumption, though the ⁴⁰K electron capture partial decay constant may be enhanced at ultrahigh pressure.

Applications

Due to the long half-life, the technique is most applicable for dating minerals and rocks more than 100,000 years old. K-Ar dating was instrumental in the development of the geomagnetic polarity time scale. Although it finds the most utility in geological applications, it plays an important role in archaeology. One archeological application has been in bracketing the age of archeological deposits at Olduvai Gorge by dating lava flows above and below the deposits.Fact|date=September 2008 It has also been indispensable in other early east African sites with a history of volcanic activity such as Hadar, Ethiopia.Fact|date=September 2008 The K-Ar method continues to have utility in dating clay mineral diagenesis [Aronson and Lee, (1986)] . Clay minerals are less than 2 microns thick and cannot easily be irradiated for Ar-Ar analysis because Ar recoils from the crystal lattice.

Notes

References

*.

Further reading

* [http://www.ees.nmt.edu/Geol/labs/Argon_Lab/Methods/Methods.html K-Ar N. Mex. Geochron. Lab]
* [http://id-archserve.ucsb.edu/Anth3/Courseware/Chronology/09_Potassium_Argon_Dating.html Potassium-Argon Dating Univ. Cal.]
*J. L. Aronson and Mingchou Lee "K/Ar systematics of bentonite and shale in a contact metamorphic zone, Cerrillos, New Mexico" Clays and Clay Minerals, Aug 1986; 34: 483 - 487.