isotopic dating The possibility of determining the ages of rocks and minerals by using radioactive isotopes was recognized early in the twentieth century by scientists such as Arthur Holmes in the UK and B. B. Boltwood in the United States, but the widespread application of these methods was not possible until the 1950s, when precise analytical methods became available. The special merit of radiometric dating is that it provides ages in years (usually in millions of years), as compared with most of the other methods available to the geologist, which yield only relative ages.

Isotopic dating depends on measuring variations in the abundance of naturally occurring isotopes. Each chemical element is characterized by its number of protons, but also has isotopes which differ in the number of neutrons in the atomic nucleus. An isotope can be stable or unstable (radioactive). An unstable isotope (a parent or radioactive isotope) decays into an isotope of another element (a daughter or radiogenic isotope), which itself may be stable or unstable. In the process of decay, a radioactive element emits various forms of energy (α, β, or γ radiation or spontaneous fission). A decay series of unstable isotopes ends when a stable isotope is reached: for example, the stable lead isotope ²⁰⁶Pb (lead-206) ends the decay series that starts with ²³⁸U (uranium-238). The rates of decay and the half-lives of unstable isotopes vary greatly but they are accurately known. This makes it possible to date rocks and minerals over a wide range of geological ages.

A simple equation describes the exponential decay of a radioactive parent isotope and is the basis for every kind of dating involving radioactive and radiogenic isotopes:N = N₀e^−λt,

where N is the number of atoms of a radioactive parent isotope present at any time t, N₀ is the number of parent atoms that were present when the number of daughter atoms was 0 (t = 0), and λ is the decay constant, which is specific for any particular isotope. Solving this equation for t givest = (1/λ)ln(N/N₀),

or expressing t as a function of the number of atoms of the radiogenic daughter isotope D produced,t = (1/λ)ln( (D + N)/N)

with D = N₀−N. In dating, concentrations of isotopes and isotopic ratios are measured to determine the time that has elapsed since the rock or mineral was formed. Many different techniques are employed to determine the concentrations of isotopes or their respective ratios. Concentrations of isotopes with short half-lives can be accurately measured by the radiation they emit, even when their concentrations are relatively low. The development of mass spectrometers that can also be coupled to particle accelerators has brought particularly significant gains in precision.

The radiometric age obtained by isotopic dating of a rock or a specific mineral within a rock may date various geological processes, such as the formation of magmatic and volcanic rocks, metamorphic alterations, and sedimentary or diagenetic events. Most ages are closure ages, which correspond to the time when diffusion of the radiogenic isotope out of a mineral ceased. This would have occurred at a given ‘blocking temperature’, when the mineral became closed to exchange with the surrounding material. This point ‘sets the clock’ for isotope dating and corresponds to the age determined. A basic requirement for successful isotopic dating is that the rock or mineral has been a closed system since its formation. If at some point in the history of a rock or mineral the system had become open again (for example, because of metamorphic processes) the clock would be disturbed or reset. This means that the date obtained always corresponds to the last resetting of the clock. Different minerals within the same rock sample can thus give different ages if, for example, one of the minerals was thermally less stable and became open as a consequence of reheating.

If a mineral has been a closed system since the point of its formation, the simplest case for dating is a parent–daughter isotope system in which the content of the daughter isotope was zero when the system became closed. In such favourable cases as U/Pb (uranium–lead) dating of zircons, which do not initially contain lead, or ⁸⁷Rb/⁸⁷Sr (rubidium–strontium) dating of muscovite micas without initial common strontium, ages may be calculated from the determination of parent and daughter isotope abundances alone. This approach is also valid for fossil Pleistocene corals because the calcium carbonate of the corals contains relatively high concentrations of uranium but virtually no thorium when it is precipitated by corals. The uranium starts to decay and the radioactive disequilibrium between the parent ²³⁸U (uranium-238) and the daughter ²³⁰Th (thorium-230) can be used to derive very precise datings for events that took place during the past 500 000 years. (In radioactive equilibrium the amounts of decaying parent and shorter-lived daughter isotopes are the same; see Fig. 1.) Estimates of the extent and timing of past sea-level changes can, for example, be inferred from datings of corals that grew on fossil beach terraces during periods of maximum of sea-level. Speleothems (stalactites, stalagmites, and other chemical deposits in caves and veins calcites from caves can also be dated by this method. To achieve the required precision, the minerals used for dating generally have to be separated and the elements of interest have to be chemically purified before measurement. Ion-probe techniques are an exception in that they allow direct measurement and dating of single specific mineral grains or even subzones of grains such as zircons or monazites.

In most other instances concentrations of the daughter isotopes are present when the system becomes closed; for example, ¹⁴³Nd (neodymium-143) initially present in a rock or mineral that is to be dated using the ¹⁴⁷Sm/¹⁴³Nd (samarium–neodymium) scheme. Age determinations from parent–daughter isotope systems therefore have to be corrected for the initial content of the daughter isotope. This is normally done by developing isochrons. The ratios of the respective parent and daughter isotopes to a stable isotope of the daughter element are determined in various minerals or in a suite of well-homogenized whole-rock samples and are plotted against each other. If the system has been closed and the initial ratio between daughter isotope and stable isotope was the same for all compounds, the data points form a straight line (the isochron); an example is shown in Fig. 2. The intercept of the isochron with the Y-axis gives the initial ratio between daughter and stable isotope in the homogeneous reservoir from which the minerals precipitated, while the slope of the isochron corresponds to the age. Suitable isotope systems are now available for almost every type of rock, ranging from magmatic and metamorphic rocks to sedimentary rocks. Parent–daughter isotope couples which can be applied for dating using the isochron technique include ¹⁴⁷Sm/¹⁴³Nd (samarium-147–neodymium-143), ²³⁸U/²⁰⁶Pb (uranium-238–lead-206), ⁸⁷Rb/⁸⁷Sr (rubidium-87–strontium-87), ¹⁸⁷Re/¹⁸⁷Os (rhenium-187–osmium-187), and ¹⁷⁶Lu/¹⁷⁶Hf (lutetium-176–hafnium-176). The long half-lives (low decay constants) of these isotope systems also make them suitable for dating meteorites, which are thought to represent undifferentiated material of the Solar System, by calculating isochrons of various minerals of the meteorites. Most meteorites are found to be 4.56 Ga (billion years old, and this age has been interpreted as corresponding to the age of the Solar System. The oldest rocks on Earth dated so far are gneisses from Greenland, which yield U/Pb (uranium/lead) ages of up to 3.8 Ga. Applying an ion-probe mass spectrometer, Compston and his colleagues at the Australian National University studied zircon grains in a quartzite from Western Australia which gave even higher U/Pb (uranium–lead) ages, between 4.1 and 4.2 Ga. These point to the existence of chemically evolved rocks of this age.

For the uranium–lead dating method, two radioactive uranium isotopes (²³⁸U and ²³⁵U) that decay into the stable isotopes ²⁰⁶Pb and ²⁰⁷Pb are available. When the daughter to parent ratios of these isotopes are plotted against each other on a graph, the result is not a straight line but a curve. Their combination offers the possibility of dating single minerals by two different isotope systems of the same elements. These are considered reliable when they both give the same ages (concordant ages), but it is also possible to take later losses or gains of uranium or lead into account when the ages are discordant.

Although no older rocks are at present known, isotopic dating methods exist that could be used to gain information on the timing of processes such as the formation of the Earth's atmosphere, which took place in the early Solar System prior to 4.2 Ga: that is, within a few tens or hundreds of millions of years after the accretion of the Earth. Daughter isotopes of extinct isotopes can be used for this purpose. Examples are the iodine isotope ¹²⁹I (iodine-129) which had a half-life of 17 Myr (17 million years) and decayed into ¹²⁹Xe (xenon-129), and the plutonium isotope ²⁴⁴Pu (plutonium-244), which had a half-life of 83 Myr and decayed into ¹³⁶Xe (xenon-136). The presence of radiogenic ¹²⁹Xe and ¹³⁶Xe in the atmosphere today shows that there must have been an atmosphere that was able to retain xenon at a time as early as 50 to 100 Myr after the formation of the Earth.

Another frequently used absolute isotope dating method that is suitable not only for magmatic or metamorphic rocks but also for certain sedimentary rocks is based on the isotope couple ⁴⁰K/⁴⁰Ar (potassium-40–argon-40), in which the daughter isotope ⁴⁰Ar is a gas. The argon present in the rock can be extracted and measured by a number of techniques. If the potassium-bearing mineral or rock has been a closed system for the noble gas argon, the amount ⁴⁰Ar is proportional to the amount of potassium and the time that has elapsed since closure of the system. The total half-life of ⁴⁰K amounts to 1.25 Ga. This makes possible a wide range of dating applications, from ages of a few million years back to the Precambrian, because potassium is present in most rock-forming minerals, some of which represent closed systems for argon. Not only basalts, granites, and volcanic tuffs, but also shales and glauconite-bearing sediments can be dated by this method.

Cosmogenic isotopes

Isotopes generated by the interaction of cosmic rays with gases or solid matter on the Earth can also be applied for dating purposes. The most widely used cosmogenic isotope for absolute dating is carbon-14 (¹⁴C), which is exchanged with living organisms as ¹⁴CO₂. The clock for dating is set when the organism dies and stops exchanging. The initial ¹⁴C/¹²C ratio is well known, and the age of an organism can thus be very precisely determined from its present ¹⁴C/¹²C ratio. Carbon-14 is used to date biogenic carbonate in such organisms as foraminifera (zooplankton) or corals, organic material in sediments, or fossil wood back to about 35 000 years bp (before the present). Dating with ¹⁴C is not reliable beyond that because after five to six half-lives (in this case one half-life is 5730 years) it cannot be measured accurately. Short-lived isotopes (with half-lives of several years) such as ⁷Be (beryllium-7) introduced from the atmosphere can be used to date mixing processes in the ocean. A different dating approach using cosmogenic isotopes such as ¹⁰Be (beryllium-10), ²⁶Al (aluminium-26), ³⁶Cl (chlorine-36), ³²Si (silicon-32), or ³⁹Ar (argon-39) is based on their specific production rates in situ in minerals which are exposed to cosmic radiation. The quantity of a cosmogenic isotope present, for example in a quartz sample found on top of a moraine, is ideally proportional to the duration of its exposure to cosmic radiation. The age of the retreat of the glacier that left the moraine can thus be determined, provided that the reaction cross-section of the corresponding mineral (i.e. how much of a cosmogenic isotope is produced per volume of mineral) is accurately known. Such exposure ages can also serve to estimate the erosion rates of landscapes or the rates of lateral movement along strike-slip faults by dating river terraces cut by faults and measuring the amount of their displacement. Exposure ages have further applications in cosmochemistry to date the exposure times of lunar rocks or the travel times of meteorites after their expulsion from larger parent bodies.

Relative isotopic dating methods

In addition to the ‘absolute’ dating methods considered above, there are also various indirect isotope dating methods, which are mainly used to date sedimentary sequences. These methods are based on a reference data set with a well-constrained age model, derived, for example, from absolute dating methods. The sample record to be dated is compared with the reference data set. On Phanerozoic timescales the best-documented indirect isotopic dating method uses variations of the ⁸⁷Sr/⁸⁶Sr ratio measured in biogenic carbonates, which are supposed to have recorded the strontium isotope ratio of ambient sea water. The strontium isotope record shows variations that have been mainly related to orogenic events and changes in weathering regimes.

On Tertiary and Pleistocene timescales, the ¹⁸O/¹⁶O ratio (both isotopes are stable) in carbonate shells of marine zooplankton is one of the most important relative dating methods for marine sediments. During the Tertiary sub-era, the oxygen isotope composition of deep water underwent drastic and well-dated changes caused by the onset of formation of cold deep-water masses and the build-up of the first ice sheets in Antarctica, which caused a global fractionation of oxygen isotopes. During the Pleistocene the oxygen isotope composition of the deep water changed on glacial–interglacial timescales when, in addition, huge amounts of isotopically light oxygen were stored in the ice sheets during glacial periods and related temperature fluctuations enhanced the difference between the glacial and interglacial oxygen-isotope signature of the ocean water. Profiles of relative oxygen-isotope variations measured on sediment cores with unknown sedimentation rates are compared to the reference data set and can then be translated into absolute ages using a model of well-constrained astronomical forcing of the reference data sets. Other examples of relative isotopic dating are the deuterium (²H) variations in ice cores and the osmium isotope record of marine sediments. These relative methods can be combined with dating methods based on the decay of radioactive isotopes such as ²³⁰Th (thorium-230) or cosmogenic ¹⁰Be (beryllium-10) and ²⁶Al (aluminium-26). These isotopes are introduced into the ocean at a nearly constant rate and are particle-reactive, which causes their rates of deposition in marine sediments to be constant to a first approximation. Concentration profiles of ²³⁰Th or ¹⁰Be in marine detrital or chemical sediments such as ferromanganese crusts show an exponential decrease in downcore profiles as a function of sedimentation rates or growth rates, and can therefore be used for dating.

Indirect isotopic dating techniques

Some dating techniques are not based on the isotopes themselves but on the traces their decay has left; for example, in a mineral. In the fission-track method for uranium the tracks of destruction caused by the spontaneous fission products of uranium in a mineral are counted. Knowing the rate of spontaneous fission, ages may be derived from a number of assumptions. Similar damage is caused by the alpha recoil, which is a trace of the energy released during the alpha decay of uranium and thorium isotopes.

Martin Frank

Bibliography

Faure, G. (1986) Principles of isotope geology. (2nd edn). John Wiley and Sons, New York.
Dickin, A. P. (1995) Radiogenic isotope geology. Cambridge University Press.

Isotopic Analysis

█ ALEXANDR IOFFE

Varieties of the same chemical element, but with different atomic weights, are called isotopes. Isotopic analysis (IA) is the analysis of the isotope composition of a sample. Samples in IA can contain almost anything: different objects of everyday life, pieces of rocks, pieces of wood, samples of tissue taken from a human body, chemical compounds, and so on. In general, and with some degree of simplification, isotopic analysis is used for identification of a sample and for the determination of its age. Isotopic analysis is based upon the use of mass spectrometers or radioactive radiation counters. A mass spectrometer is a device that determines the quantity and composition of different isotopes (of the same chemical element as well as various elements) in the sample.

The Oak Ridge National Laboratory in 2001 designed a portable mass spectrometer that is capable of detecting chemical and biological agents of war in the air, and can also detect chemical warfare agents on the ground. Called the chemical-biological mass spectrometer (CBMS), the device works by collecting an air sample or chemical sample via a chemical probe and classifying it first according to its size, then according to its unique ion products. The system can detect a wide range of chemical and biological weapons on the battlefield, such as anthrax spores, nerve gas, viruses, and toxins. The CMBS is scheduled to be manufactured in sufficient numbers to be operational in the field by 2004.

Another new mass spectrometry device, similar to the walk-through scanners used in airports, may soon be able to detect microscopic amounts of explosives or narcotic substances hidden in clothing or on a person. When passing through the scanner, a jet of air puffs clothing and air samples immediately surrounding the person are concentrated and analyzed using ion mobility spectrometry. Minute amounts of explosives, chemical weapons, and illegal drugs that cling to the skin or clothing can be easily found. The highly sensitive nature of the scanner can also be a drawback, as targeted substances may be found on persons unaware of their presence. For example, the scanner could detect a narcotic residue on coins randomly received at an airport vending machine by an unsuspecting person. The likelihood for false positive results, along with the high cost of the machine and the seven-second period necessary to scan each individual, may inhibit its widespread use in airports. Some airports do use similar technology to screen checked baggage.

The isotope composition of many objects is unique (relative to the composition itself as well as to the isotope concentrations), and because of this, isotopic analysis offers the possibility for identification of a sample. Isotopic analysis is also utilized in varying disciplines, including chemistry, medicine, biology, geology, archeology, and criminal forensics. Recently, isotopic analysis has seen use in the diagnosis of some diseases through analysis of air exhaled by the patient. Often, isotopic analysis permits the scientist to distinguish the genuine product from its imitation. For example, the technology is used to distinguish expensive types of wine and liquor from their imitations. When archaeologists investigate various fragments of ancient objects, they sometimes use isotopic analysis to determine where these objects were made, or to elucidate the source of the raw material for their production.

Isotopes can be both stable and radioactive. Isotopic analysis of radioactive isotopes permits scientists to determine the age of the investigated sample. Often the isotope C¹⁴ is used for this purpose. This isotope itself is unstable and decays with time, and in the decay process, other stable isotopes are created. In nature, the concentration of C¹⁴ is maintained because of cosmic radiation. While a tree lives, for example, the concentration of C¹⁴ in its wood is equal to the C¹⁴ concentration in the environment, because atoms of radioactive carbon penetrate the wood from the atmosphere with CO² molecules due to photosynthesis, and also through the tree root system. But when the tree dies, these exchange processes cease, and the C¹⁴ concentration in the tree begins to decrease. The law of radioactive carbon concentration alteration in the sample is known, hence if its concentration is measured in the sample and compared with the concentration of the isotope in nature, the age of the tree itself can be determined (or more precisely, the time since the tree died). When the decay period of the radioisotope is considered, the age of the sample can be determined within an accuracy of several decades. For this analysis, a sample weight of only several milligrams (mg) is often sufficient. For example, a mammoth calf whose body was recently found in Siberia in the frozen ground was determined to have lived about 27,000 years ago, and only 4 mg of the mammoth muscle tissue was needed for the analysis.

█ FURTHER READING:

ELECTRONIC:

Lawrence Livermore National Laboratory. "National Resource for Biomedical Accelerator Mass Spectrometry." <http://www.llnl.gov/bioams/index.html> (January, 4, 2003).

"New Airport Security Measures." I-mass.com. <http://imass.com/airp1100.html> (January, 4, 2003).

Oak Ridge National Laboratory. "Chemical Biological Mass Spectrometer." <http://infosrv1.ctd.ornl.gov/ORNLReview/measure/analy/direct/chem-bio.htm> (January, 4, 2003).

SEE ALSO

Air Plume and Chemical Analysis
Biological Warfare
Gas Chromatograph-Mass Spectrometer
Microbiology: Applications to Espionage, Intelligence, and Security

Isotopic Analysis

Varieties of the same chemical element, but with different atomic weights, are called isotopes. Isotopic analysis (IA) is the analysis of the isotope composition of a sample. Samples in IA can contain almost anything: different objects of everyday life, pieces of rocks, pieces of wood, samples of tissue taken from a human body, chemical compounds, and so on. In general, IA is used for identification of a sample and for the determination of its age. Determining the age of an object can be important in a forensic examination, especially when examining human remains from cold cases, ancient sites, or mass graves. IA is based upon the use of mass spectrometers or radioactive radiation counters. A mass spectrometer is a device that determines the quantity and composition of different isotopes (of the same chemical element as well as various elements) in the sample.

The isotope composition of many objects is unique (relative to the composition itself as well as to the isotope concentrations), and because of this, isotopic analysis offers the possibility for identification of a sample. Isotopic analysis is also utilized in varying disciplines, including chemistry, medicine , biology, geology , archeology, and criminal forensics. Recently, isotopic analysis has seen use in the diagnosis of some diseases through analysis of air exhaled by the patient. Often, isotopic analysis permits the scientist to distinguish the genuine product from its imitation. For example, the technology is used to distinguish expensive types of wine and liquor from their imitations.

Isotopes can be both stable and radioactive. IA of radioactive isotopes permits scientists to determine the age of the investigated sample. Often the isotope¹⁴C is used for this purpose. This isotope itself is unstable and decays with time, and in the decay process, other stable isotopes are created. In nature, the concentration of¹⁴C is maintained because of cosmic radiation. While a tree lives, for example, the concentration of¹⁴C in its wood is equal to the ¹⁴C concentration in the environment, because atoms of radioactive carbon penetrate the wood from the atmosphere with carbon dioxide (CO₂) molecules due to photosynthesis, and also through the tree root system. But when the tree dies, these exchange processes cease, and the ¹⁴C concentration in the tree begins to decrease. The law of radioactive carbon concentration alteration in the sample is known, hence if its concentration is measured in the sample and compared with the concentration of the isotope in nature, the age of the tree itself can be determined (or more precisely, the time since the tree died). When the decay period of the radioisotope is considered, the age of the sample can be determined within an accuracy of several decades.

see also Analytical instrumentation; Radiation damage to tissues.

isotopic dating Means of determining the age of certain materials by reference to the relative abundances of the parent isotope (which is radioactive) and the daughter isotope (which may or may not be radioactive). If the decay constant (the half-life or disintegration rate of the parent isotope) and the concentration of the daughter isotope are known, it is possible to calculate an age. See also DATING METHODS; RADIOACTIVE DECAY; RADIOCARBON DATING; and RADIOMETRIC DATING.

isotopic dating A means of determining the age of certain materials by reference to the relative abundance of the parent isotope (which is radioactive) and the daughter isotope (which may or may not be radioactive). If the decay constant (the ‘half-life’ or disintegration rate of the parent isotope) and the concentration of the daughter isotope are known, it is possible to calculate an age. See also dating methods; radiocarbon dating; and radiometric dating.

isotopic dating A means of determining the age of certain materials by reference to the relative abundances of the parent isotope (which is radioactive) and the daughter isotope (which may or may not be radioactive). If the decay constant (the ‘half-life’ or disintegration rate of the parent isotope) and the concentration of the daughter isotope are known, it is possible to calculate an age. See also RADIOCARBON DATING.