K/Ar AND Ar/Ar DATING

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1 K K/Ar AND Ar/Ar DATING R M Twyman, University of York, York, UK ª 2007 Elsevier B.V. All rights reserved. Introduction Radiometric dating methods measure the decay of naturally occurring radioactive isotopes, and are used to determine the ages of rocks, minerals, and archaeological artifacts. Of the 84 elements found in nature, there are 70 naturally occurring radioactive isotopes whose half-lives vary from a few thousand years (e.g., carbon-14 ( 14 C) 5,730 years) to billions of years (e.g., samarium-147 ( 147 Sm), years). Potassium argon dating is based on measuring the decay of potassium-40 ( 40 K) to argon-40 ( 40 Ar), a process with a half-life of years. This makes the process suitable for dating rocks and minerals ranging from a few tens of thousands to more than 1 billion years in age, spanning most geologically relevant time periods is Earth s history. Radioactive decay is a nuclear process and is independent of chemical and physical conditions found in geological processes. It has been shown that radioactive decay is constant over the wide range of temperatures and pressures encountered in geological events. Consequently, potassium argon dating is one of the most widely used geological dating methods. Argon argon dating is a derivative method in which samples are bombarded in a fast neutron reactor, converting a proportion of the abundant and stable isotope 39 K into 39 Ar. This article describes the principles and practical aspects of these two forms of radiometric dating. Principles of Radiometric Dating Atomic nuclei are composed of protons and neutrons, only certain combinations of which are inherently stable. Radioactive decay is a property of unstable nuclei, involving either the ejection or capture of subatomic particles, and resulting ultimately in the formation of a stable nucleus. The daughter nucleus formed by radioactive decay may be a different isotope of the same element as the parental nucleus if the number of protons remains the same, or a different element may be formed as is the case in 39 Kto 39 Ar decay. In some cases, radioactive nuclei decay directly into stable nuclei, whereas in others the daughter nucleus may itself be unstable, and may decay further. Radioactive decay may proceed through several steps until a stable nucleus is formed. Radiometric dating relies on one of three types of radioactive decay. The first and most dramatic occurs predominantly among heavier isotopes and is known as -decay. During this process, the unstable nucleus ejects an -particle, which comprises two protons and two neutrons. The atomic mass of the daughter nucleus is four units lower than that of the parent nucleus. More common among lighter isotopes is - decay, in which a high-energy electron (-particle) is ejected from the nucleus, converting a neutron into a proton, and releasing an antineutrino. Although the number of protons in the nucleus is increased by one, the number of neutrons decreases by one and the atomic mass therefore remains unchanged. The third form of radioactive decay is known as electron capture, and is essentially the reverse of -decay. During this process, an electron from the innermost electron shell is captured in the nucleus and converts a proton into a neutron. The atomic number of the nucleus decreases by one, but because a neutron is gained there is, again, no overall change in atomic mass. Electron capture occurs in 39 Kto 39 Ar decay. The half-life of a radioactive isotope is a measure of nuclear stability, and reflects the statistical likelihood that a given nucleus will decay in a given time (see Dating Techniques). This likelihood is expressed in the form of a decay constant, as shown in the following equation: N ¼ N 0 e lt where N is the number of radioactive parent nuclei present at any particular time t, and N 0 is the number of such nuclei initially present in the sample. The

2 1314 K/Ar AND Ar/Ar DATING half-life (t 1=2 ) is the value of t when N ¼ N 0 /2, i.e., the time taken for half the atomic nuclei in a given sample to decay. From a practical standpoint, the above equation is of little use in radiometric dating because N 0 is never known. However, it can be assumed for any time point t that N 0 is the sum of the parental nuclei (P) remaining in the sample and the daughter nuclei (D) formed by radioactive decay. This can be expressed formally as: N 0 ¼ N P þ N D We can therefore substitute N P þ N D for N 0 in the original equation to yield: N ¼ðN P þ N D Þ e lt This can be rearranged to give: N D ¼ N P ðe lt þ 1Þ If this equation is solved for t, it allows the age of a rock or mineral to be determined by measuring the relative abundances of the parent and daughter nuclei in the sample, which is the underlying principle of radiometric dating: t ¼ 1=l log e ðn D =N P þ 1Þ More specifically for the subject of this article, the age of a sample can be described in the simplest terms by the following equation: t ¼ 1=l log e ð 40 Ar= 40 K þ 1Þ It should be emphasized, however, that the above holds true only if the sample contained no 40 Ar at the time of formation, i.e., if at time t ¼ 0 there was 100% 40 K (the parent radioactive nucleus) and 0% 40 Ar (the stable daughter nucleus). The potassium argon method is the only radiometric dating method where this assumption can generally be made, since any argon formed by decay prior to the formation of solid rock will diffuse away, while argon produced after solidification will accumulate within the rock. Even so, this requires that the rock cools rapidly. It is necessary to take into account the possibility of argon from other sources being present in the rock, for example, diffusing in from the atmosphere or being formed through the decay of other isotopes. If we call the number of daughter nuclei present at time zero N D0, the generic equation can be modified as follows to correct for the incorporation of argon at formation: t ¼ 1=l log e ½ðN D N D0 Þ=N P þ 1Š Replacing the generic terms with specific isotopes, we get the following simplified equation which can be used to calculate the age of material using the potassium argon method: t ¼ 1=l log e ½ð 40 Ar t 40 Ar t ¼ 0 Þ= 40 K þ 1Š Thisholdstrueaslongasthesampleisaclosed system, i.e., there is no change in the abundance ratio between the parent and daughter isotopes other than that caused by radioactive decay. If this condition is not met, or if external factors influencing the ratio are not accounted for, then dating using the potassium argon method will be inaccurate. Relevant examples may include the creation of more parental isotope through the radioactive decay of larger nuclei, the mixing of samples of different ages over geological timescales, or the loss of daughter isotope through the leaching of gaseous argon after the rock has formed. This depends on the type of sample and the geological conditions under which it was formed and preserved, and may need to be evaluated on a case-by-case basis. Potassium Argon Dating The potassium argon method is based on the decay of 40 K to 40 Ar. It is a widely used method not only because the half-life of the reaction makes it suitable for the dating of rocks ranging in age from thousands to billions of years, but also because potassium is very abundant in rocks and minerals, and is overall the eighth most common element in the Earth s crust. Potassium has one radioactive isotope ( 40 K) and two stable isotopes ( 39 Kand 41 K). The relative abundances are 39 K, 92.23%; 40 K, 6.73%; and 41 K, %. The 40 K isotope undergoes two forms of decay with different likelihoods (Fig. 1). About 11.7% of decay events involve electron capture and result in the formation of 40 Ar, whereas 88.3% of events occur through -emission and result in the formation of calcium-40 ( 40 Ca). The ratio of these events is known as the branching ratio, and must be taken into account in potassium argon dating calculations. Since 40 Ca is formed more frequently than 40 Ar, in might seem logical to measure the calcium daughter rather than argon. However, this is impractical for two reasons, first because 40 Ca is the most abundant calcium isotope in rocks making it more difficult to measure small increments resulting from decay of 40 K, and second because calcium does not diffuse out of molten rock like argon, so the amount of the isotope initially present in the rock needs to be known. Since argon is trapped only when the rock solidifies, the formation of solid rock fixes the point at which argon begins to accumulate through 40 K

3 K/Ar AND Ar/Ar DATING 1315 β-emission neutron becomes proton % 11.7% 4 0K 19 protons, 21 neutrons unstable electron capture proton becomes neutron + 40Ca 20 protons, 20 neutrons stable 40Ar 18 protons, 22 neutrons stable Figure 1 The decay of 40 Kto 40 Ca by -emission (88.3% of events) and to 40 Ar by electron capture (11.7% of events). decay, starting the radiometric clock when the rock first forms. However, argon is an inert gas and will not combine with other elements. Therefore, if the rock is heated at some time after formation, argon gas can escape from the crystal lattices and the radiometric clock can be reset, making the sample appear younger than it actually is. The method, therefore, works best with intrusive igneous and extrusive volcanic rocks that have crystallized from melts and have not been reheated. The method does not work well on metamorphic rocks because these rocks have been produced from other rocks by heat and pressure without being completely melted, and have probably lost some or all of the argon that has accumulated since formation. The simplified equation shown above can be modified to take into account the branching ratio of 40 K decay, which gives the following: t ¼ 1=ðl 40 K! 40 Ar þ l 40 K! 40 CaÞ log e ð 40 Ar= 40 K½l 40 K! 40 Ar þ l 40 K! 40 Ca=l 40 K! 40 ArŠþ1Þ If values for the decay constants 40 K! 40 Ar and 40 K! 40 Ca for are substituted in this equation, we arrive at: t ¼ 1: log e ð9: Ar= 40 K þ 1Þ The distribution of argon isotopes must also be taken into account. The potassium argon method uses a spike of 38 Ar mixed with the argon extracted from the rock/mineral to determine the amount of 40 Ar. Like potassium, argon has three isotopes with the following abundances in air: 40 Ar, 99.60%; 38 Ar, 0.063%; and 36 Ar, 0.337%. Since this argon can diffuse into rocks (especially volcanic rocks) when they form, corrections to dating calculations must be made for the amount of atmospheric argon in a sample at the time of formation, and must also take into account any argon in the apparatus used to process the sample otherwise the excess argon makes the sample appear older than its true age. This correction involves measuring the amount of 36 Ar in the experimental apparatus and multiplying this by which is the 40 Ar/ 36 Ar ratio in the atmosphere, and subtracting this result from the total amount of 40 Ar. What remains is the quantity we wish to measure, i.e., the amount of radiogenic 40 Ar produced the radioactive decay of 40 K. However, as stated above, excess argon can also originate from other sources such as the mantle, as bubbles trapped in a melt, or a xenocryst or xenolith trapped during emplacement. Argon Argon Dating The 40 Ar/ 39 Ar dating method is a derivative of potassium argon dating in which the sample is irradiated in a nuclear reactor with fast neutrons to convert a fraction of the 39 Kto 39 Ar. Like the conventional method, argon argon dating relies on the measurement of 40 Ar produced by the radioactive decay of 40 K, but unlike conventional potassium argon dating, it is unnecessary also to measure the amount of 40 K in the sample. Instead, the 39 Ar produced in the nuclear reactor is used as a substitute for 40 K, and the age is calculated from the ratio or argon isotopes. This can be determined in a single experiment, rather

4 1316 K/Ar AND Ar/Ar DATING than the two separate measurements required for conventional potassium argon dating. As is the case in the conventional method, certain assumptions need to be made and correction factors need to be calculated to ensure accurate results. For argon argon dating, an important factor is the conversion of 39 Kto 39 Ar. The amount of 39 Ar produced in any given irradiation will not only depend on the amount of 39 K in the sample, but also the duration and intensity of irradiation, the latter expressed as the neutron flux density. It is virtually impossible to calculate these factors from first principles so the approach used is to simultaneously irradiate a control sample known as the flux monitor, whose age has already been determined. The argon ratios from the flux monitor are used to calculate afluxconstant,j, which is applied to the age calculation for the experimental sample as follows: t ¼ 1: log e ð J 40 Ar= 39 Ar þ 1Þ Corrections must be made for atmospheric argon and for interfering argon isotopes produced by neutron reactions with calcium and other potassium isotopes. These reactions are shown in Table 1. If an irradiated sample is completely melted, the argon in the sample is released in a single stage and provides an age comparable to that derived from conventional potassium argon dating, at least when correction factors have been taken into account. However, the main advantage of the 40 Ar/ 39 Ar method is that multiple aliquots can be tested from the same sample, usually using either a laser probe or by step heating in a furnace to release argon samples at progressively higher temperatures that can be collected and analyzed separately. Ages calculated for each temperature increment can be plotted on an agespectrum diagram, which for an undisturbed sample will yield a horizontal line (i.e., all ages are the same). For other samples, there is some variation in the calculated age at different temperatures and the data can be plotted on an 40 Ar/ 39 Ar isochron or isotope-correlation diagram. The data should fall on or near a straight line whose slope is equal to the ratio 40 Ar/ 39 Ar and whose intercept is the 40 Ar/ 36 Ar ratio of nonradiogenic argon. Although potentially more accurate than potassium argon dating and more applicable to smaller samples, the method does have some drawbacks. One is the reliance on an age standard which must be dated by an alternative method (usually the potassium argon method) in order to derive the neutron flux (J) constant. Another is the inherent error in extrapolating the J constant between samples differing in structure and homogeneity. This error can be minimized as much as possible by closely matching the irradiation conditions of the sample and control, and by using a series of control samples. Some materials are also subject to a phenomenon known as argon recoil, in which the kinetic energy gained by 39 Ar during the neutron bombardment is sufficient to eject it from the sample. This is a significant problem in grained materials like clay, and may also result in the redistribution of argon in inhomogeneous samples. Applications of K-Ar and Ar-Ar dating in Quaternary Science Because 40 K has a long half-life, K-Ar dating is most applicable for determining the age of minerals and rocks from hundreds of thousands to tens of millions of years old. However, the technique is also useful for archaeological applications, e.g., assigning approximate ages to archaeological artifacts at sites rich in volcanic rock. K-Ar dating has been particularly useful, for example, for dating artifacts at Olduvai Gorge, a steep ravine approximately 45 km in length located in the eastern Serengeti Plains in northern Tanzania, Africa. Olduvai Gorge is one of the most important sites of prehistoric archaeology in the world and has contributed much to our understanding of early human development. The deep stratigraphy reveals several layers, or beds, of volcanic material Table 1 The principle of argon-argon dating is to measure the amount of 39 Ar produced from 39 K as a proportion of the amount of 40 Ar. However, 39 Ar and 40 Ar can both be produced in competing reactions involving various isotopes of calcium, chlorine, potassium and argon present in the same sample. The reactions causing the most interference are identified by sad faces in the table, and correction factors must be introduced to account for them. Such interfering reactions are monitored using laboratory salts and glasses which are irradiated along with the sample. Other reactions identified by happy faces are beneficial, because they provide a means to calculate correction factors. For example, the production of 38 Ar from 37 Cl allows the amount of chlorine in a sample to be determined. Argon isotopes Produced by the irradiation of: Ca K Ar Cl 36 Ar 40 Ca 37 Ar 40 Ca 39 K 36 Ar 38 Ar 42 Ca 39 K, 41 K 40 Ar 37 Cl 39 Ar 42 Ca, 43 Ca 39 K, 40 K 38 Ar, 40 Ar 40 Ar 43 Ca, 44 Ca 40 K, 41 K

5 K/Ar AND Ar/Ar DATING 1317 which allow K-Ar dating of the embedded archaeological deposits. This has revealed that tools made from rocks and pebbles were made by the inhabitants of Olduvai more than 2 million years ago, while fossils have been found in rocks which have been dated at 2.5 million years old. Bones discovered in the various beds of Olduvai rock include modern humans from as recently as 15 20,000 years ago, back to primitive homonids such as Australopithecus boisei and Homo habilis. K-Ar dating has also been used at other prehistoric African sites with a history of volcanic activity including Hadar, on the Awash River in Ethiopia, where the 3-million-year-old fossil of Australopithecus afarensis, named Lucy, was discovered. See also: Dating Techniques. Fission-Track Dating. Radiocarbon Dating: Conventional Method. U-Series Dating. References Dalrymple, G. B., and Lanphere, M. A. (1969). Potassium Argon Dating. W. H. Freeman and Company, San Francisco. Faure, G. (1986). Principles of Isotope Geology, Second edition. Wiley, New York. McDougall, I., and Harrison, T. M. (1999). Geochronology and Thermochronology by the 40 Ar/ 39 Ar Method, Second edition. Oxford University Press, New York. Wintle, A. G. (1996). Archaeologically-relevant dating techniques for the next century: small, hot and identified by acronyms. Journal of Archaeological Science 23,

Diffusion in minerals and melts

Diffusion in minerals and melts There are three types of diffusion in a rock Surface diffusion essentially over a 2 dimensional area Grain-boundary diffusion along grain boundaries, slower than surface