K–Ar dating
Potassium–argon dating, abbreviated K–Ar dating, is a radiometric dating method used in geochronology and archaeology. It is based on measurement of the product of the radioactive decay of an isotope of potassium (K) into argon (Ar). Potassium is a common element found in many materials, such as micas, clay minerals, tephra, and evaporites. In these materials, the decay product ^{40}Ar is able to escape the liquid (molten) rock, but starts to accumulate when the rock solidifies (recrystallizes). The amount of Argon sublimation that occurs is a function of the purity of the sample, the composition of the mother material, and a number of other factors. These factors introduce error limits on the upper and lower bounds of dating, so that final determination of age is reliant on the environmental factors during formation, melting, and exposure to decreased pressure and/or openair. Time since recrystallization is calculated by measuring the ratio of the amount of ^{40}Ar accumulated to the amount of ^{40}K remaining. The long halflife of ^{40}K allows the method to be used to calculate the absolute age of samples older than a few thousand years.^{[1]}
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 geomagnetic polarity time scale was calibrated largely using K–Ar dating.^{[2]}
Contents
Decay series
Potassium naturally occurs in 3 isotopes: ^{39}K (93.2581%), ^{40}K (0.0117%), ^{41}K (6.7302%). Two are stable, while the radioactive isotope ^{40}K decays with a halflife of ×10^{9} years to 1.248^{40}Ca and ^{40}Ar. Conversion to stable ^{40}Ca occurs via electron emission (beta decay) in 89.1% of decay events. Conversion to stable ^{40}Ar occurs via electron capture in the remaining 10.9% of decay events.^{[3]}
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 ^{40}K decays to ^{40}Ar (argon), the atom typically remains trapped within the lattice because it is larger than the spaces between the other atoms in a mineral crystal. But it can escape into the surrounding region when the right conditions are met, such as change in pressure and/or temperature. ^{40}Ar atoms are able to 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 ^{40}K will decay and ^{40}Ar will again accumulate, along with the entrained argon atoms, trapped in the mineral crystals. Measurement of the quantity of ^{40}Ar atoms is used to compute the amount of time that has passed since a rock sample has solidified.
Despite ^{40}Ca being the favored daughter nuclide, it is rarely useful dating as calcium is common in the crust, with ^{40}Ca being the most abundant isotope. Thus, the amount of calcium originally present is not known with enough accuracy to be able to measure the small increase produced by radioactive decay.
Formula
The ratio of the amount of ^{40}Ar to that of ^{40}K is directly related to the time elapsed since the rock was cool enough to trap the Ar by the following equation:
 t is time elapsed
 t_{1/2} is the halflife of ^{40}K
 K_{f} is the amount of ^{40}K remaining in the sample
 Ar_{f} is the amount of ^{40}Ar found in the sample.
The scale factor 0.109 corrects for the unmeasured fraction of ^{40}K which decayed into ^{40}Ca; the sum of the measured ^{40}K and the scaled amount of ^{40}Ar gives the amount of ^{40}K which was present at the beginning of the elapsed time 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 ^{40}Ar to ^{40}K in a rock or mineral, the amount of Ar is measured by mass spectrometry of the gases released when a rock sample is melted in vacuum. The potassium is quantified by flame photometry or atomic absorption spectroscopy.
The amount of ^{40}K is rarely measured directly. Rather, the more common ^{39}K is measured and that quantity is then multiplied by the accepted ratio of ^{40}K/^{39}K (i.e., 0.0117%/93.2581%, see above).
The amount of ^{36}Ar is also measured to assess how much of the total argon is atmospheric in origin.
Assumptions
According to McDougall & Harrison (1999, p. 11) the following assumptions must be true for computed dates to be accepted as representing the true age of the rock:^{[4]}
 The parent nuclide, 40
K
, 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 40
K
possibly may occur at high pressures, theoretical calculations indicate that for pressures experienced within a body of the size of the Earth the effects are negligibly small.^{[1]}  The 40
K
/39
K
ratio in nature is constant so the 40
K
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.^{[5]}  The radiogenic argon measured in a sample was produced by in situ decay of 40
K
in the interval since the rock crystallized or was recrystallized. Violations of this assumption are not uncommon. Wellknown examples of incorporation of extraneous 40
Ar
include chilled glassy deepsea basalts that have not completely outgassed preexisting 40
Ar
*,^{[6]} and the physical contamination of a magma by 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 nonradiogenic 40
Ar
from the atmosphere. The equation may be corrected by subtracting from the 40
Ar
_{measured} value the amount present in the air where 40
Ar
is 295.5 times more plentiful than 36
Ar
. 40
Ar
_{decayed} = 40
Ar
_{measured} − 295.5 × 36
Ar
_{measured}.  The sample must have remained a closed system since the event being dated. Thus, there should have been no loss or gain of 40
K
or 40
Ar
*, other than by radioactive decay of 40
K
. 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 40
Ar
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.^{[7]}
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 which compares isotopic ratios from the same portion of the sample to avoid this problem.
Applications
Due to the long halflife, the technique is most applicable for dating minerals and rocks more than 100,000 years old. For shorter timescales, it is unlikely that enough argon40 will have had time to accumulate in order to be accurately measurable. K–Ar dating was instrumental in the development of the geomagnetic polarity time scale.^{[2]} 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.^{[8]} It has also been indispensable in other early east African sites with a history of volcanic activity such as Hadar, Ethiopia.^{[8]} The K–Ar method continues to have utility in dating clay mineral diagenesis.^{[9]} Clay minerals are less than 2 micrometres 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 Mars Curiosity 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.^{[10]}^{[11]}
Notes
 ^ ^{a} ^{b} McDougall & Harrison 1999, p. 10
 ^ ^{a} ^{b} McDougall & Harrison 1999, p. 9
 ^ "ENSDF Decay Data in the MIRD Format for 40K". National Nuclear Data Center. June 1993. Retrieved 20 September 2013.
 ^ McDougall & Harrison 1999, p. 11: "As with all isotopic dating methods, there are a number of assumptions that must be fulfilled for a K–Ar age to relate to events in the geological history of the region being studied."
 ^ McDougall & Harrison 1999, p. 14

^ 40
Ar
* means radiogenic argon  ^ McDougall & Harrison 1999, pp. 9–12
 ^ ^{a} ^{b} Tattersall 1995
 ^ Aronson & Lee 1986
 ^ NASA Curiosity: First Mars Age Measurement and Human Exploration Help, Jet Propulsion Laboratory, 20131209
 ^ Martian rockdating technique could point to signs of life in space, University of Queensland, 20131213
References
 McDougall, I.; Harrison, T. M. (1999). Geochronology and thermochronology by the ^{40}Ar/^{39}Ar method. Oxford University Press. ISBN 0195109201.
 Tattersall, I. (1995). The Fossil Trail: How We Know What We Think We Know About Human Evolution. Oxford University Press. ISBN 0195061012.
Further reading
The Wikibook Historical Geology has a page on the topic of: KAr dating 
 "K/Ar and 40K/39K methodology". New Mexico Geochronology Research Laboratory. Archived from the original on 20060417.
 Michaels, G. H.; Fagan, B. M. (15 December 2005). "Chronological Methods 9: Potassium–Argon Dating". University of California. Archived from the original on 20100810.
 Aronson, J. L.; Lee, M. (1986). "K/Ar systematics of bentonite and shale in a contact metamorphic zone". Clays and Clay Minerals. 34 (4): 483–487. Bibcode:1986CCM....34..483A. doi:10.1346/CCMN.1986.0340415 .
 Moran, T. J. (2009). "Teaching Radioisotope Dating Using the Geology of the Hawaiian Islands" (PDF). Journal of Geoscience Education. 57 (2): 101–105. Bibcode:2009JGeEd..57..101M. doi:10.5408/1.3544237 .