dating

I

In geology and archaeology, the process of determining an object's or event's place within a chronological scheme.

Scientists may use either relative dating, in which items are sequenced on the basis of stratigraphic clues (see stratigraphy) or a presumed evolution in form or structure, or absolute dating, in which items are assigned a date independent of context. The latter type includes potassium-argon and carbon-14 dating; both are based on the measurement of radioactive decay. The record of changes in polarity of the Earth's magnetic field has provided a timescale for seafloor spreading and long-term marine sedimentation. Dendrochronology has proved useful in archaeology and climatology. See also fission-track dating; helium dating; lead-210 dating; rubidium-strontium dating; uranium-234–uranium-238 dating; uranium-thorium-lead dating.

II

(as used in expressions)

carbon 14 dating

radiocarbon dating

fission track dating

helium dating

lead 210 dating

potassium argon dating

rubidium strontium dating

uranium 234 uranium–238 dating

uranium thorium lead dating

common lead dating

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▪ geochronology

Introduction

      in geology, determining a chronology or calendar of events in the history of the Earth, using to a large degree the evidence of organic evolution in the sedimentary rocks accumulated through geologic time in marine and continental environments. To date past events, processes, formations, and fossil organisms, geologists employ a variety of techniques. These include some that establish a relative chronology in which occurrences can be placed in the correct sequence relative to one another or to some known succession of events. Radiometric dating and certain other approaches are used to provide absolute chronologies in terms of years before the present. The two approaches are often complementary, as when a sequence of occurrences in one context can be correlated with an absolute chronlogy elsewhere.

General considerations

Distinctions between relative-age and absolute-age measurements

      Local relationships on a single outcrop or archaeological site can often be interpreted to deduce the sequence in which the materials were assembled. This then can be used to deduce the sequence of events and processes that took place or the history of that brief period of time as recorded in the rocks or soil. For example, the presence of recycled bricks at an archaeological site indicates the sequence in which the structures were built. Similarly, in geology, if distinctive granitic pebbles can be found in the sediment beside a similar granitic body, it can be inferred that the granite, after cooling, had been uplifted and eroded and therefore was not injected into the adjacent rock sequence. Although with clever detective work many complex time sequences or relative ages can be deduced, the ability to show that objects at two separated sites were formed at the same time requires additional information. A coin, vessel, or other common artifact could link two archaeological sites, but the possibility of recycling would have to be considered. It should be emphasized that linking sites together is essential if the nature of an ancient society is to be understood, as the information at a single location may be relatively insignificant by itself. Similarly, in geologic studies, vast quantities of information from widely spaced outcrops have to be integrated. Some method of correlating rock units must be found. In the ideal case, the geologist will discover a single rock unit with a unique collection of easily observed attributes called a marker horizon that can be found at widely spaced localities. Any feature, including colour variations, textures, fossil content, mineralogy, or any unusual combinations of these can be used. It is only by correlations that the conditions on different parts of the Earth at any particular stage in its history can be deduced. In addition, because sediment deposition is not continuous and much rock material has been removed by erosion, the fossil record from many localities has to be integrated before a complete picture of the evolution of life on Earth can be assembled. Using this established record, geologists have been able to piece together events over the past 600 million years, or about one-eighth of Earth history, during which time useful fossils have been abundant. The need to correlate over the rest of geologic time, to correlate nonfossiliferous units, and to calibrate the fossil time scale has led to the development of a specialized field that makes use of natural radioactive isotopes in order to calculate absolute ages.

      The precise measure of geologic time has proven to be the essential tool for correlating the global tectonic processes (see below) that have taken place in the past. Precise isotopic ages are called absolute ages, since they date the timing of events not relative to each other but as the time elapsed between a rock-forming event and the present. Absolute dating by means of uranium and lead isotopes has been improved to the point that for rocks 3 billion years old geologically meaningful errors of ± 1 or 2 million years can be obtained. The same margin of error applies for younger fossiliferous rocks, making absolute dating comparable in precision to that attained using fossils. To achieve this precision, geochronologists have had to develop the ability to isolate certain high-quality minerals that can be shown to have remained closed to migration of the radioactive parent atoms they contain and the daughter atoms formed by radioactive decay over billions of years of geologic time. In addition, they have had to develop special techniques with which to dissolve these highly refractory minerals without contaminating the small amount (about one-billionth of a gram) of contained lead and uranium on which the age must be calculated. Since parent uranium atoms change into daughter atoms with time at a known rate, their relative abundance leads directly to the absolute age of the host mineral. Just as the use of the fossil record has allowed a precise definition of geologic processes in approximately the past 600 million years, absolute ages allow correlations back to the Earth's oldest known rocks formed almost 4 billion years ago. In fact, even in younger rocks, absolute dating is the only way that the fossil record can be calibrated. Without absolute ages, investigators could only determine which fossil organisms lived at the same time and the relative order of their appearance in the correlated sedimentary rock record.

      Unlike ages derived from fossils, which occur only in sedimentary rocks, absolute ages are obtained from minerals that grow as liquid rock bodies cool at or below the surface. When rocks are subjected to high temperatures and pressures in mountain roots formed where continents collide, certain datable minerals grow and even regrow to record the timing of such geologic events. When these regions are later exposed in uptilted portions of ancient continents, a history of terrestrial rock-forming events can be deduced. Episodes of global volcanic activity, rifting of continents, folding, and metamorphism are defined by absolute ages. The results suggest that the present-day global tectonic scheme was operative in the distant past as well.

The global tectonic rock cycle

      Bringing together virtually all geologic aspects of the Earth's outer rock shell (the lithosphere) into a unifying theory called plate tectonics has had a profound impact on the scientific understanding of our dynamic planet. Continents move, carried on huge slabs, or plates, of dense rock about 100 kilometres thick over a low-friction, partially melted zone (the asthenosphere) below. In the oceans, new seafloor, created at the globe-circling oceanic ridges, moves away, cools, and sinks back into the mantle in what are known as subduction zones (subduction zone) (i.e., long, narrow belts at which one plate descends beneath another). Where this occurs at the edge of a continent, as along the west coast of North and South America, large mountain chains develop with abundant volcanoes and their subvolcanic equivalents. These units, called igneous rock, or magma in their molten form, constitute major crustal additions. By contrast, crustal destruction occurs at the margins of two colliding continents, as, for example, where the subcontinent of India is moving north over Asia. Great uplift, accompanied by rapid erosion, is taking place and large sediment fans are being deposited in the Indian Ocean to the south. With time, water-soluble “cement” will cause the sandy units to become sandstone. Rocks of this kind in the ancient record may very well have resulted from rapid uplift and continent collision.

      When continental plates collide, the edge of one plate is thrust onto that of the other. The rocks in the lower slab undergo changes in their mineral content in response to heat and pressure and will probably become exposed at the surface again some time later. Rocks converted to new mineral assemblages because of changing temperatures and pressures are called metamorphic. Virtually any rock now seen forming at the surface can be found in exposed deep crustal sections in a form that reveals through its mineral content the temperature and pressure of burial. Such regions of the crust may even undergo melting and subsequent extrusion of melt magma, which may appear at the surface as volcanic rocks or may solidify as it rises to form granites at high crustal levels. Magmas produced in this way are regarded as recycled crust, whereas others extracted by partial melting of the mantle below are considered primary.

      Even the oceans and atmosphere are involved in this great cycle because minerals formed at high temperatures are unstable at surface conditions and eventually break down or weather, in many cases taking up water and carbon dioxide to make new minerals. If such minerals were deposited on a downgoing (i.e., subducted) oceanic slab, they would eventually be heated and changed back into high-temperature minerals, with their volatile components being released. These components would then rise and be fixed in the upper crust or perhaps reemerge at the surface. Such hot circulating fluids can dissolve metals and eventually deposit them as economic mineral deposits on their way to the surface.

      Geochronological studies have provided documentary evidence that these rock-forming and rock-re-forming processes were active in the past. Seafloor spreading (seafloor spreading hypothesis) has been traced, by dating minerals found in a unique grouping of rock units thought to have been formed at the oceanic ridges, to 500 million years ago, with rare occurrences as early as 2 billion years ago. Volcanic units resembling those formed over oceanic subduction zones can be dated worldwide to show that the Earth's most prolific volcanic event occurred about 2.7 billion years ago. Other ancient volcanic units document various cycles of mountain building. The source of ancient sediment packages like those presently forming off India can be identified by dating single detrital grains of zircon found in sandstone. Magmas produced by the melting of older crust can be identified because their zircons commonly contain inherited older cores. Episodes of continental collision can be dated by isolating new zircons formed as the buried rocks underwent local melting. Periods of deformation (deformation and flow) associated with major collisions cannot be directly dated if no new minerals have formed. The time of deformation can be bracketed, however, if datable units, which both predate and postdate it, can be identified. The timing of cycles involving the expulsion of fluids from deep within the crust can be ascertained by dating new minerals formed at high pressures in exposed deep crustal sections. In some cases, it is possible to prove that gold deposits may have come from specific fluids if the deposition time of the deposits can be determined and the time of fluid expulsion is known.

      Where the crust is under tension, as in Iceland, great fissures develop. These fissures serve as conduits that allow black lava, called basalt, to reach the surface. The portion that remains in a fissure below the surface usually forms a vertical black tubular body known as a dike (or dyke). Precise dating of such dikes can reveal times of crustal rifting in the past. Dikes and lava, now exposed on either side of Baffin Bay, have been dated to determine the time when Greenland separated from North America—namely, about 60 million years ago.

      Combining knowledge of the Earth processes observed today with absolute ages of ancient geologic analogues seems to indicate that the oceans and atmosphere were present by at least 3.5 billion years ago and that they were probably released by early heating of the planet. The continents were produced over time; the earliest portions were formed nearly 4 billion years ago, and the process still continues today. Absolute dating allows rock units formed at the same time to be identified and reassembled into ancient mountain belts, which in many cases have been disassociated by subsequent tectonic processes. The most obvious of these is the Appalachian (Appalachian Mountains) chain that occupies the east coast of North America and extends to parts of Newfoundland as well as parts of Ireland, England, and Norway. Relic oceanic crust, formed between 480 and 500 million years ago, was identified on both sides of the Atlantic in this chain, as were numerous correlative volcanic and sedimentary units. Evidence based on geologic description, fossil content, and absolute and relative ages leave no doubt that these rocks were all part of a single mountain belt before the Atlantic Ocean opened in stages from about 200 million years ago.

Determination of sequence

      Relative geologic ages can be deduced in rock sequences consisting of sedimentary, metamorphic, or igneous rock units. In fact, they constitute an essential part in any precise isotopic, or absolute, dating program. Such is the case because most rocks simply cannot be isotopically dated. Therefore, a geologist must first determine relative ages and then locate the most favourable units for absolute dating. It is also important to note that relative ages are inherently more precise, since two or more units deposited minutes or years apart would have identical absolute ages but precisely defined relative ages. While absolute ages require expensive, complex analytical equipment, relative ages can be deduced from simple visual observations.

      Most methods for determining relative geologic ages are well illustrated in sedimentary rocks (sedimentary rock). These rocks cover roughly 75 percent of the surface area of the continents, and unconsolidated sediments blanket most of the ocean floor. They provide evidence of former surface conditions and the life-forms that existed under those conditions. The sequence of a layered sedimentary series is easily defined because deposition always proceeds from the bottom to the top. This principle would seem self-evident, but its first enunciation more than 300 years ago by Nicolaus Steno (Steno, Nicolaus) represented an enormous advance in understanding. Known as the principle of superposition, it holds that in a series of sedimentary layers or superposed lava flows the oldest layer is at the bottom, and layers from there upward become progressively younger. On occasion, however, deformation may have caused the rocks of the crust to tilt, perhaps to the point of overturning them. Moreover, if erosion has blurred the record by removing substantial portions of the deformed sedimentary rock, it may not be at all clear which edge of a given layer is the original top and which is the original bottom.

      Identifying top and bottom is clearly important in sequence determination, so important in fact that a considerable literature has been devoted to this question alone. Many of the criteria of top–bottom determination are based on asymmetry in depositional features. Oscillation ripple marks, for example, are produced in sediments by water sloshing back and forth. When such marks are preserved in sedimentary rocks, they define the original top and bottom by their asymmetric pattern. Certain fossils also accumulate in a distinctive pattern or position that serves to define the top side.

      In wind-blown or water-lain sandstone, a form of erosion during deposition of shifting sand removes the tops of mounds to produce what are called cross-beds. The truncated layers provide an easily determined depositional top direction. The direction of the opening of mud cracks or rain prints can indicate the uppermost surface of mudstones formed in tidal areas. When a section of rock is uplifted and eroded, as during mountain-building episodes, great volumes of rock are removed, exposing a variety of differently folded and deformed rock units. The new erosion surface must postdate all units, dikes, veins, and deformation features that it crosses. Even the shapes formed on the erosional or depositional surfaces of the ancient seafloor can be used to tell which way was up. A fragment broken from one bed can only be located in a younger unit, and a pebble or animal track can only deform a preexisting unit—i.e., one below. In fact, the number of ways in which one can determine the tops of well-preserved sediments is limited only by the imagination, and visual criteria can be deduced by amateurs and professionals alike.

      One factor that can upset the law of superposition in major sediment packages in mountain belts is the presence of thrust faults. Such faults, which are common in compression zones along continental edges, may follow bedding planes and then cross the strata at a steep angle, placing older units on top of younger ones. In certain places, the fault planes are only a few centimetres thick and are almost impossible to detect.

      Relative ages also can be deduced in metamorphic rocks (metamorphic rock) as new minerals form at the expense of older ones in response to changing temperatures and pressures. In deep mountain roots, rocks can even flow like toothpaste in their red-hot state. Local melting may occur, and certain minerals suitable for precise isotopic dating may form both in the melt and in the host rock. In the latter case, refractory grains in particular may record the original age of the rock in their cores and the time of melting in their newly grown tips. Analytical methods are now available to date both growth stages, even though each part may weigh only a few millionths of a gram (see below Correlation (dating)). Rocks that flow in a plastic state record their deformation in the alignment of their constituent minerals. Such rocks then predate the deformation. If other rocks that are clearly not deformed can be found at the same site, the time of deformation can be inferred to lie between the absolute isotopic ages of the two units.

      Igneous rocks (igneous rock) provide perhaps the most striking examples of relative ages. magma, formed by melting deep within the Earth, cuts across and hence postdates all units as it rises through the crust, perhaps even to emerge at the surface as lava. Black lava, or basalt, the most common volcanic rock on Earth, provides a simple means for determining the depositional tops of rock sequences as well as proof of the antiquity of the bgeans. Pillow shapes are formed as basaltic lava is extruded (i.e., erupted) under water; these are convex upward with a lower tip that projects down between two convex tops below. The shapes of pillows in ancient basalts provide both a direct indication of depositional top and proof of underwater eruption. They are widespread in rocks as old as 3.5 billion years, implying that the oceans were already present.

      Basaltic lava rocks that are common where ancient continents have been rifted apart are fed from below by near vertical fractures penetrating the crust. Material that solidifies in such cracks remains behind as dikes (dike). Here the dikes must be younger than all other units. A more interesting case develops when a cooled older crust is fractured, invaded by a swarm of dikes, and subsequently subjected to a major episode of heating with deformation and intrusion of new magma. In this instance, even though the resulting outcrop pattern is extremely complex, all of the predike units can be distinguished by the relic dikes present. The dikes also record in their newly formed minerals components that can be analyzed to give both the absolute age and the temperature and pressure of the second event. Because dike swarms are commonly widespread, the conditions determined can often be extrapolated over a broad region. Dikes do not always continue upward in a simple fashion. In some cases, they spread between the layers of near-horizontal sedimentary or volcanic units to form bodies called sills (sill). In this situation, fragments of the host rock must be found within the intrusive body to establish its relatively younger age.

      Once most or all of the relative ages of various strata have been determined in a region, it may be possible to deduce that certain units have been offset by movement along fractures or faults while others have not. Dikes that cross fault boundaries may even be found. Application of the simple principle of crosscutting relationships can allow the relative ages of all units to be deduced.

      The principles for relative age dating described above require no special equipment and can be applied by anyone on a local or regional scale. They are based on visual observations and simple logical deductions and rely on a correlation and integration of data that occurs in fragmentary form at many outcrop locations.

Correlation

Principles and techniques

      Correlation is, as mentioned earlier, the technique of piecing together the informational content of separated outcrops. When information derived from two outcrops is integrated, the time interval they represent is probably greater than that of each alone. Presumably if all the world's outcrops were integrated, sediments representing all of geologic time would be available for examination. This optimistic hope, however, must be tempered by the realization that much of the Precambrian record—older than 570 million years—is missing. Correlating two separated outcrops means establishing that they share certain characteristics indicative of contemporary formation. The most useful indication of time equivalence is similar fossil content, provided of course that such remains are present. The basis for assuming that like fossils indicate contemporary formation is faunal succession. However, as previously noted, times of volcanism and metamorphism, which are both critical parts of global processes, cannot be correlated by fossil content. Furthermore, useful fossils are either rare or totally absent in rocks from Precambrian time, which constitutes more than 87 percent of Earth history. Precambrian rocks must therefore be correlated by means of precise isotopic dating.

      Unlike the principles of superposition and crosscutting, faunal succession (faunal succession, law of) is a secondary principle. That is to say, it depends on other sequence-determining principles for establishing its validity. Suppose there exist a number of fossil-bearing outcrops each composed of sedimentary layers that can be arranged in relative order, primarily based on superposition. Suppose, too, that all the layers contain a good representation of the animal life existing at the time of deposition. From an examination of such outcrops with special focus on the sequence of animal forms comes the empirical generalization that the faunas of the past have followed a specific order of succession, and so the relative age of a fossiliferous rock is indicated by the types of fossils it contains.

      As was mentioned at the outset of this article, William Smith (Smith, William) first noticed around 1800 that the different rock layers he encountered in his work were characterized by different fossil assemblages. Using fossils simply for identification purposes, Smith constructed a map of the various surface rocks outcropping throughout England, Wales, and southern Scotland. Smith's geologic map was extremely crude, but in its effect on Earth study it was a milestone.

      Following Smith's pioneering work, generations of geologists have confirmed that similar and even more extensive fossil sequences exist elsewhere. To this day, fossils are useful as correlation tools to geologists specializing in stratigraphy. In dating the past, the primary value of fossils lies within the principle of faunal succession: each interval of geologic history had a unique fauna that associates a given fossiliferous rock with that particular interval.

      The basic conceptual tool for correlation by fossils is the index, or guide, fossil. Ideally, an index fossil should be such as to guarantee that its presence in two separated rocks indicates their synchroneity. This requires that the lifespan of the fossil species be but a moment of time relative to the immensity of geologic history. In other words, the fossil species must have had a short temporal range. On the practical side, an index fossil should be distinctive in appearance so as to prevent misidentification, and it should be cosmopolitan both as to geography and as to rock type. In addition, its fossilized population should be sufficiently abundant for discovery to be highly probable. Such an array of attributes represents an ideal, and much stratigraphic geology is rendered difficult because of departure of the natural fossil assemblage from this ideal. Nevertheless, there is no greater testimony to the validity of fossil-based stratigraphic geology than the absolute dates made possible through radioactive measurements. Almost without exception, the relative order of strata defined by fossils has been confirmed by radiometric ages.

      Correlation based on the physical features of the rock record also has been used with some success, but it is restricted to small areas that generally extend no more than several hundred kilometres. The first step is determining whether similar beds in separated outcrops can actually be traced laterally until they are seen to be part of the same original layer. Failing that, the repetition of a certain layered sequence (e.g., a black shale sandwiched between a red sandstone and a white limestone) lends confidence to physical correlation. Finally, the measurement of a host of rock properties may well be the ultimate key to correlation of separated outcrops. The more ways in which two rocks are physically alike, the more likely it is that the two formed at the same time.

      Only a partial listing of physical characteristics is necessary to indicate the breadth of approach in this area. Such features as colour, ripple marks, mud cracks, raindrop imprints, and slump structures are directly observable in the field. Properties derived from laboratory study include (1) size, shape, surface appearance, and degree of sorting of mineral grains, (2) specific mineral types present and their abundances, (3) elemental composition of the rock as a whole and of individual mineral components, (4) type and abundance of cementing agent, and (5) density, radioactivity, and electrical-magnetic-optical properties of the rock as a whole.

      With the development of miniaturized analytical equipment, evaluation of rock properties down a small drill hole has become possible. The technique, called well logging, involves lowering a small instrument down a drill hole on the end of a wire and making measurements continuously as the wire is played out in measured lengths. By this technique it is possible to detect depth variations in electrical resistivity, self-potential, and gamma-ray emission rate and to interpret such data in terms of continuity of the layering between holes. Subsurface structures can thus be defined by the correlation of such properties.

      Field geologists always prize a layer that is so distinctive in appearance that a series of tests need not be made to establish its identity. Such a layer is called a key bed (marker bed). In a large number of cases, key beds originated as volcanic ash. Besides being distinctive, a volcanic-ash layer (tephrochronology) has four other advantages for purposes of correlation: it was laid down in an instant of geologic time; it settles out over tremendous areas; it permits physical correlation between contrasting sedimentary environments; and unaltered mineral crystals that permit radiometric measurements of absolute age often are present.

      Correlation may be difficult or erroneous if several different ash eruptions occurred, and a layer deposited in one is correlated with that from another. Even then, the correlation may be justified if the two ash deposits represent the same volcanic episode. Much work has been undertaken to characterize ash layers both physically and chemically and so avoid incorrect correlations. Moreover, single or multigrain zircon fractions from the volcanic source are now being analyzed to provide precise absolute ages for the volcanic ash and the fossils in the adjacent units.

Geologic column and its associated time scale

 The end product of correlation is a mental abstraction called the geologic column. It is the result of integrating all the world's individual rock sequences into a single sequence. In order to communicate the fine structure of this so-called column, it has been subdivided into smaller units. Lines are drawn on the basis of either significant changes in fossil forms or discontinuities in the rock record (i.e., unconformities, or large gaps in the sedimentary sequence); the basic subdivisions of rock are called systems, and the corresponding time intervals are termed periods. In the upper part of the geologic column, where fossils abound, these rock systems and geologic periods are the basic units of rock and time. Lumping of periods results in eras, and splitting gives rise to epochs. In both cases, a threefold division into early–middle–late is often used, although those specific words are not always applied. Similarly, many periods are split into three epochs. Names assigned to individual epochs follow no single worldwide standard except for the seven epochs making up the last two periods (see table—>).

      Over the interval from the Paleozoic to the present, about 38 epochs are recognized. This interval is represented by approximately 250 formations, discrete layers thick enough and distinctive enough in lithology to merit delineation as units of the geologic column. Also employed in subdivision is the zone (biozone) concept, in which it is the fossils in the rocks rather than the lithologic character that defines minor stratigraphic boundaries. The basis of zone definition varies among geologists, some considering a zone to be all rocks containing a certain species (usually an invertebrate), whereas others focus on special fossil assemblages.

      The lower part of the geologic column, where fossils are very scarce, was at one time viewed in the context of two eras of time, but subsequent mapping has shown the provincial bias in such a scheme. Consequently, the entire lower column is now considered a single unit, the Precambrian. The results of isotopic dating are now providing finer Precambrian subdivisions that have worldwide applicability.

      The geologic column and the relative geologic time scale are sufficiently defined to fulfill the use originally envisioned for them—providing a framework within which to tell the story of Earth history. Just as human history has its interweaving plots of warfare, cultural development, and technological advance, so the Earth's rocks tell another story of intertwined sequences of events. Mountains have been built and eroded away, seas have advanced and retreated, a myriad of life-forms has inhabited land and sea. In all these happenings the geologic column and its associated time scale spell the difference between an unordered series of isolated events and the unfolding story of a changing Earth.

Absolute dating

      Although relative ages can generally be established on a local scale, the events recorded in rocks from different locations can be integrated into a picture of regional or global scale only if their sequence in time is firmly established. The time that has elapsed since certain minerals formed can now be determined because of the presence of a small amount of natural radioactive atoms in their structures. Whereas studies using fossil dating began almost 300 years ago, radioactivity itself was not discovered until roughly a century ago, and it has only been from about 1950 that extensive efforts to date geologic materials have become common. Methods of isotopic measurement continue to be refined today, and absolute dating has become an essential component of virtually all field-oriented geologic investigations. In the process of refining isotopic measurements, methods for low-contamination chemistry had to be developed, and it is significant that many such methods now in worldwide use resulted directly from work in geochronology.

      It has already been explained how different Earth processes create different rocks as part of what can be considered a giant rock-forming and -reforming cycle. Attention has been called wherever possible to those rocks that contain minerals suitable for precise isotopic dating. It is important to remember that precise ages cannot be obtained for just any rock unit but that any unit can be dated relative to a datable unit. The following discussion will show why this is so, treating in some detail the analytic and geologic problems that have to be overcome if precise ages are to be determined. It will become apparent, for example, that isotopic ages can be reset by high temperatures; however, this seeming disadvantage can be turned to one's favour in determining the cooling history of a rock. As various dating methods are discussed, the great interdependence of the geologic and analytic components essential to geochronology should become evident.

      The field of isotope geology complements geochronology. Workers in isotope geology follow the migration of isotopes produced by radioactive decay through large- and small-scale geologic processes. Isotopic tracers of this kind can be thought of as an invisible dye injected by nature into Earth systems that can be observed only with sophisticated instruments. Studying the movement or distribution of these isotopes can provide insights into the nature of geologic processes.

Principles of isotopic dating

      All absolute isotopic ages are based on radioactive decay (radioactivity), a process whereby a specific atom or isotope is converted into another specific atom or isotope at a constant and known rate. Most elements exist in different atomic forms that are identical in their chemical properties but differ in the number of neutral particles—i.e., neutrons—in the nucleus. For a single element, these atoms are called isotopes. Because isotopes differ in mass, their relative abundance can be determined if the masses are separated in a mass spectrometer (see below Use of mass spectrometers (dating)).

      Radioactive decay can be observed in the laboratory by either of two means: (1) a radiation counter (e.g., a Geiger counter), which detects the number of high-energy particles emitted by the disintegration of radioactive atoms in a sample of geologic material, or (2) a mass spectrometer, which permits the identification of daughter atoms formed by the decay process in a sample containing radioactive parent atoms. The particles given off during the decay process are part of a profound fundamental change in the nucleus. To compensate for the loss of mass (and energy), the radioactive atom undergoes internal transformation and in most cases simply becomes an atom of a different chemical element. In terms of the numbers of atoms present, it is as if apples changed spontaneously into oranges at a fixed and known rate. In this analogy, the apples would represent radioactive, or parent, atoms, while the oranges would represent the atoms formed, the so-called daughters. Pursuing this analogy further, one would expect that a new basket of apples would have no oranges but that an older one would have many. In fact, one would expect that the ratio of oranges to apples would change in a very specific way over the time elapsed, since the process continues until all the apples are converted. In geochronology the situation is identical. A particular rock or mineral that contains a radioactive isotope (or radio-isotope) is analyzed to determine the number of parent and daughter isotopes present, whereby the time since that mineral or rock formed is calculated. Of course, one must select geologic materials that contain elements with long half-lives—i.e., those for which some parent atoms would remain.

      Given below is the simple mathematical relationship that allows the time elapsed to be calculated from the measured parent/daughter ratio. The age calculated is only as good as the existing knowledge of the decay rate and is valid only if this rate is constant over the time that elapsed.

      Fortunately for geochronology the study of radioactivity has been the subject of extensive theoretical and laboratory investigation by physicists for almost a century. The results show that there is no known process that can alter the rate of radioactive decay. By way of explanation it can be noted that since the cause of the process lies deep within the atomic nucleus, external forces such as extreme heat and pressure have no effect. The same is true regarding gravitational, magnetic, and electric fields, as well as the chemical state in which the atom resides. In short, the process of radioactive decay is immutable under all known conditions. Although it is impossible to predict when a particular atom will change, given a sufficient number of atoms, the rate of their decay is found to be constant. The situation is analogous to the death rate among human populations insured by an insurance company. Even though it is impossible to predict when a given policyholder will die, the company can count on paying off a certain number of beneficiaries every month. The recognition that the rate of decay of any radioactive parent atom is proportional to the number of atoms (N) of the parent remaining at any time gives rise to the following expression:

      Converting this proportion to an equation incorporates the additional observation that different radioisotopes have different disintegration rates even when the same number of atoms are observed undergoing decay. In other words, each radioisotope has its own decay constant, abbreviated λ, which provides a measure of its intrinsic rapidity of decay. Proportion 1 becomes:

      Stated in words, this equation says that the rate at which a certain radioisotope disintegrates depends not only on how many atoms of that isotope are present but also on an intrinsic property of that isotope represented by λ, the so-called decay constant. Values of λ vary widely—from 10²⁰ reciprocal seconds (i.e., the unit of 1 second) for a rapidly disintegrating isotope such as helium-5 to less than 10⁻²⁵ reciprocal seconds for slowly decaying cerium-142.

      In the calculus, the rate of decay R in equation 2 is written as the derivative dN/dt, in which dN represents the small number of atoms that decay in an infinitesimally short time interval dt. Replacing R by its equivalent dN/dt results in the differential equation

      Solution of this equation by techniques of the calculus yields one form of the fundamental equation for radiometric age determination,

      in which N₀ is the number of radioactive atoms present in a sample at time zero, N is the number of radioactive atoms present in the sample today, e is the base of natural logarithms (equal to about 2.72), λ is the decay constant of the radioisotope being considered, and t is the time elapsed since time zero.

      Two alterations are generally made to equation 4 in order to obtain the form most useful for radiometric dating. In the first place, since the unknown term in radiometric dating is obviously t, it is desirable to rearrange equation 4 so that it is explicitly solved for t. Second, the more common way to express the intrinsic decay rate of a radioisotope is through its half-life (abbreviated t_1/2) rather than through the decay constant λ. Half-life is defined as the time period that must elapse in order to halve the initial number of radioactive atoms. The half-life and the decay constant are inversely proportional because rapidly decaying radioisotopes have a high decay constant but a short half-life. With t made explicit and half-life introduced, equation 4 is converted to the following form, in which the symbols have the same meaning:

      Alternatively, because the number of daughter atoms is directly observed rather than N, which is the initial number of parent atoms present, another formulation may be more convenient. Since the initial number of parent atoms present at time zero N₀ must be the sum of the parent atoms remaining N and the daughter atoms present D, one can write:

      From equation 4 above, it follows that N₀ = N(e^λt). Substituting this in equation 6 gives

      If one chooses to use P to designate the parent atom, the expression assumes its familiar form:

      and

      This pair of equations states rigorously what might be assumed from intuition, that minerals formed at successively longer times in the past would have progressively higher daughter-to-parent ratios. This follows because, as each parent atom loses its identity with time, it reappears as a daughter atom. The increase in D/P with time is evident in equation (7—>) because larger values of time will increase the value of e^λt, where λ is constant. Equation (8—>) documents the simplicity of direct isotopic dating. The time of decay is proportional to the natural logarithm (represented by ln) of the ratio of D to P. In short, one need only measure the ratio of the number of radioactive parent and daughter atoms present, and the time elapsed since the mineral or rock formed can be calculated, provided of course that the decay rate is known. Likewise, the conditions that must be met to make the calculated age precise and meaningful are in themselves simple:

      1. The rock or mineral must have remained closed to the addition or escape of parent and daughter atoms since the time that the rock or mineral (system) formed.

      2. It must be possible to correct for other atoms identical to daughter atoms already present when the rock or mineral formed.

      3. The decay constant must be known.

      4. The measurement of the daughter-to-parent ratio must be accurate because uncertainty in this ratio contributes directly to uncertainty in the age.

      Different schemes have been developed to deal with the critical assumptions stated above. In uranium–lead dating, minerals virtually free of initial lead can be isolated and corrections made for the trivial amounts present. In whole rock isochron methods that make use of the rubidium–strontium or samarium–neodymium decay schemes (see below), a series of rocks or minerals are chosen that can be assumed to have the same age and identical abundances of their initial isotopic ratios. The results are then tested for the internal consistency that can validate the assumptions. In all cases, it is the obligation of the investigator making the determinations to include enough tests to indicate that the absolute age quoted is valid within the limits stated. In other words, it is the obligation of geochronologists to try to prove themselves wrong by including a series of cross-checks in their measurements before they publish a result. Such checks include dating a series of ancient units with closely spaced but known relative ages and replicate analysis of different parts of the same rock body with samples collected at widely spaced localities.

      The importance of internal checks as well as interlaboratory comparisons becomes all the more apparent when one realizes that geochronology laboratories are limited in number. Because of the expensive equipment necessary and the combination of geologic, chemical, and laboratory skills required, geochronology is usually carried out by teams of experts. Most geologists must rely on geochronologists for their results. In turn, the geochronologist relies on the geologist for relative ages.

Edwin A. Olson Thomas Edvard Krogh

Evaluation and presentation schemes in dating

Origin of radioactive elements used

      In order for a radioactive parent–daughter pair to be useful for dating, many criteria must be met. This section examines these criteria and explores the ways in which the reliability of the ages measured can be assessed. Because geologic materials are diverse in their origin and chemical content and datable elements (chemical element) are unequally distributed, each method has its strengths and weaknesses.

  Principal cosmogenic and uranium-thorium series radioisotopesWhen the elements in the Earth were first created, many radioactive isotopes were present. Of these, only the radioisotopes with extremely long half-lives remain. The table (Principal cosmogenic and uranium-thorium series radioisotopes) lists a number of such isotopes and their respective daughter products that are used in various forms of rock dating. It should be mentioned in passing that some of the radioisotopes present early in the history of the solar system and now completely extinct have been recorded in meteorites (meteorite) in the form of the elevated abundances of their daughter isotopes. Analysis of such meteorites makes it possible to estimate the time that elapsed between element creation and meteorite formation. Natural elements that are still radioactive today produce daughter products at a very slow rate; hence, it is easy to date very old minerals but difficult to obtain the age of those formed in the recent geologic past. This follows from the fact that the amount of daughter isotopes present is so small that it is difficult to measure. The difficulty can be overcome to some degree by achieving lower background contamination, by improving instrument sensitivity, and by finding minerals with abundant parent isotopes. Geologic events of the not-too-distant past are more easily dated by using recently formed radioisotopes with short half-lives that produce more daughter products per unit time. Two sources of such isotopes exist. In one case, intermediate isotopes in the uranium or thorium decay chain can become isolated in certain minerals due to differences in chemical properties and, once fixed, can decay to new isotopes, providing a measure of the time elapsed since they were isolated. To understand this, one needs to know that though uranium-238 (²³⁸U) does indeed decay to lead-206 (²⁰⁶Pb), as indicated in Table 2—>, it is not a one-step process. In fact, this is a multistep process involving the expulsion of eight alpha particles and six beta particles, along with a considerable amount of energy. There exists a series of different elements, each of them in a steady state where they form at the same rate as they disintegrate. The number present is proportional to their decay rate, with long-lived members being more abundant. Because all of these isotopes have relatively short half-lives, none remains since the creation of the elements, but instead they are continuously provided by the decay of the long-lived parent. This type of dating, known as disequilibrium dating, will be explored below in the section Uranium-series disequilibrium dating (dating).

       Principal cosmogenic and uranium-thorium series radioisotopesAnother special type of dating employs recently formed radioisotopes produced by cosmic-ray bombardment of target atoms at the Earth's surface or in the atmosphere. The amounts produced, although small, provide insight into many near-surface processes in the geologic past. This aspect of geology is becoming increasingly important as researchers try to read the global changes that took place during the Earth's recent past in an effort to understand or predict the future. The most widely used radioactive cosmogenic isotope is carbon of mass 14 (¹⁴C), which provides a method of dating events that have occurred over roughly the past 50,000 years. This time spans much of the historic and prehistoric record of mankind. Cosmogenic isotopes and those used for disequilibrium dating are listed in the table (Principal cosmogenic and uranium-thorium series radioisotopes).

The isochron method

      Many radioactive dating methods are based on minute additions of daughter products to a rock or mineral in which a considerable amount of daughter-type isotopes already exists. These isotopes did not come from radioactive decay in the system but rather formed during the original creation of the elements. In this case, it is a big advantage to present the data in a form in which the abundance of both the parent and daughter isotopes are given with respect to the abundance of the initial background daughter. The incremental additions of the daughter type can then be viewed in proportion to the abundance of parent atoms. In mathematical terms this is achieved as follows. It has already been shown—equation 7—>—that the number of daughter atoms present from radioactive decay D* can be related to the number of parent atoms remaining P by the simple expression:

      When some daughter atoms are initially present (designated D₀), the total number D is the sum of radiogenic and initial atoms, so that

      To establish the condition that both parent and daughter abundances should be relative to the initial background, a stable isotope S of the daughter element can be chosen and divided into all portions of this equation; thus,

 This equation has the form; y = b + xm, which is that of a straight line on x–y coordinates. The slope m is equal to (e^λt − 1) and the intercept is equal to (D/S)₀. This term, shown in Figure 1—>, is called the initial ratio. The slope is proportional to the geologic age of the system.

 In practice, the isochron approach has many inherent advantages. When a single body of liquid rock crystallizes, parent and daughter elements may separate so that, once solid, the isotopic data would define a series of points, such as those shown as open circles designated R₁, R₂, R₃ in Figure 1—>. They plot along a horizontal line reflecting a common value for the initial daughter isotope ratio (D/S)₀. With time each would then develop additional daughter abundances in proportion to the amount of parent present. If a number of samples are analyzed and the results are shown to define a straight line within error, then a precise age is defined because this is only possible if each is a closed system and each has the same initial ratio and age. The uncertainty in determining the slope is reduced because it is defined by many points. A second advantage of the method relates to the fact that under high-temperature conditions the daughter isotopes may escape from the host minerals. In this case, a valid age can still be obtained, provided that they remain within the rock. Should a point plot below the line, it could indicate that a particular sample was open to migration of the dating elements or that the sample was contaminated and lay below the isochron when the rock solidified.

      Rubidium–strontium (Rb–Sr) dating (rubidium-strontium dating) was the first technique in which the whole rock isochron method was extensively employed. Certain rocks that cooled quickly at the surface were found to give precisely defined linear isochrons, but many others did not. Some studies have shown that rubidium is very mobile both in fluids that migrate through the rock as it cools and in fluids that are present as the rock undergoes chemical weathering. Similar studies have shown that the samarium–neodymium (Sm–Nd) parent–daughter pair is more resistant to secondary migration but that, in this instance, sufficient initial spread in the abundance of the parent isotope is difficult to achieve.

Analysis of separated minerals (mineral)

 When an igneous rock crystallizes, a wide variety of major and trace (isotopic tracer) minerals may form, each concentrating certain elements and radioactive trace elements within the rock. By careful selection, certain minerals that contain little or no daughter element but abundant parent element can be analyzed. In this case, the slope of the line in Figure 1—> is computed from an assumed value for the initial ratio, and it is usually possible to show that uncertainties related to this assumption are negligible. This is possible in potassium–argon (K–Ar) dating (potassium-argon dating), for example, because most minerals do not take argon into their structures initially. In rubidium–strontium dating, micas exclude strontium when they form, but accept much rubidium. In uranium–lead (U–Pb) dating of zircon, the zircon is found to exclude initial lead almost completely. Minerals, too, are predictable chemical compounds that can be shown to form at specific temperatures and remain closed up to certain temperatures if a rock has been reheated or altered. A rock, on the other hand, may contain minerals formed at more than one time under a variety of conditions. Under such circumstances the isolation and analysis of certain minerals can indicate at what time these conditions prevailed. If a simple mineral is widespread in the geologic record, it is more valuable for dating as more units can be measured for age and compared by the same method. However, if a single parent–daughter pair that is amenable to precise analysis can be measured in a variety of minerals, the ages of a wide variety of rock types can be determined by a single method without the need for intercalibration. In some cases the discovery of a rare trace mineral results in a major breakthrough as it allows precise ages to be determined in formerly undatable units. For example, the mineral baddeleyite, an oxide of zirconium (ZrO₂), has been shown to be widespread in small amounts in mafic igneous rocks (i.e., those composed primarily of one or more ferromagnesian, dark-coloured minerals). Here, a single uranium–lead isotopic analysis can provide an age more precise than can be obtained by the whole rock isochron method involving many analyses. When single minerals are analyzed, each grain can be studied under a microscope under intense side light so that alterations or imperfections can be revealed and excluded. If minerals are used for dating, the necessary checks on the ages are achieved by analyzing samples from more than one location and by analyzing different grain sizes or mineral types that respond differently to disturbing events. It can be said that minerals provide a high degree of sample integrity that can be predicted on the basis of experience gained through numerous investigations under a variety of geologic conditions. An ideal mineral is one that has sufficient parent and daughter isotopes to measure precisely, is chemically inert, contains little or no significant initial daughter isotopes, and retains daughter products at the highest possible temperatures. A specific datable mineral like rutile, which can be linked to a specific event such as the formation of a mineral deposit, is especially important.

Model ages

 Since the Earth was formed, the abundance of daughter product isotopes, such as those listed in Table 2—>, has increased through time. For example, the ratio of lead of mass 206 relative to that of mass 204 has changed from an initial value of about 10 present when the Earth was formed to an average value of about 19 in rocks at the terrestrial surface today. This is true because uranium is continuously creating more lead. A lead-rich mineral formed and isolated early in Earth history would have a low lead-206 to lead-204 ratio because it did not receive subsequent additions by the radioactive decay of uranium. If the Earth's interior were a simple and homogeneous reservoir with respect to the ratio of uranium to lead, a single sample extracted by a volcano would provide the time of extraction. This would be called a model age. No parent–daughter value for a closed system is involved, rather just a single isotopic measurement of lead viewed with respect to the expected evolution of lead in the Earth. Unfortunately the simplifying assumption in this case is not true, and lead model ages are approximate at best. Other model ages can be calculated using neodymium isotopes by extrapolating present values back to a proposed mantle-evolution line. In both cases, approximate ages that have a degree of validity with respect to one another result, but they are progressively less reliable as the assumptions on which the model is calculated are violated.

      The progressive increase in the abundance of daughter isotopes over time gains a special significance where the parent element is preferentially enriched in either the mantle or the crust. For example, rubidium is concentrated in the crust, and as a result the present-day continents, subjected to weathering, have an elevated radiogenic to stable isotope ratio (⁸⁷Sr/⁸⁶Sr) of 0.720. In contrast, modern volcanic rocks in the oceans imply that much of the mantle has a value between about 0.703 and 0.705. Should crustal material be recycled, the strontium isotopic signature of the melt would be diagnostic.

Multiple ages for a single rock; the thermal effect

      Fossils record the initial, or primary, age of a rock unit. Isotopic systems, on the other hand, can yield either the primary age or the time of a later event, because crystalline materials are very specific in the types of atoms they incorporate, in terms of both the atomic size and charge. An element formed by radioactive decay is quite different from its parent atom and thus is out of place with respect to the host mineral. All it takes for such an element to be purged from the mineral is sufficient heat to allow solid diffusion to occur. Each mineral has a temperature at which rapid diffusion sets in, so that, as a region is slowly heated, first one mineral and then another loses its daughter isotopes. When this happens, the isotopic “clock” is reset to zero, where it remains until the mineral cools below the blocking temperature. (This is the temperature below which a mineral becomes a closed chemical system for a specific radioactive decay series. Accordingly, the parent–daughter isotope ratio indicates the time elapsed since that critical threshold was reached.) In this case, the host mineral could have an absolute age very much older than is recorded in the isotopic record. The isotopic age then is called a cooling age. It is even possible by using a series of minerals with different blocking temperatures to establish a cooling history of a rock body—i.e., the times since the rock body cooled below successively lower temperatures. Such attempts can be complicated by the fact that a mineral may “grow” below the blocking temperature rather than simply become closed to isotopic migration. When this happens, the age has little to do with the cooling time. Another problem arises if a region undergoes a second reheating event. Certain minerals may record the first event, whereas others may record the second, and any suggestion of progressive cooling between the two is invalid. This complication does not arise when rapid cooling has occurred. Identical ages for a variety of minerals with widely different blocking temperatures is unequivocal proof of rapid cooling.

      Fortunately for geologists the rock itself records in its texture and mineral content the conditions of its formation. A rock formed at the surface with no indication of deep burial or new mineral growth can be expected to give a valid primary age by virtue of minerals with low blocking temperatures. On the other hand, low-blocking-point minerals from a rock containing minerals indicative of high temperatures and pressures cannot give a valid primary age. Such minerals would be expected to remain open until deep-level rocks of this sort were uplifted and cooled.

      Given these complicating factors, one can readily understand why geochronologists spend a great deal of their time and effort trying to see through thermal events that occurred after a rock formed. The importance of identifying and analyzing minerals with high blocking temperatures also cannot be overstated. Minerals with high blocking temperatures that form only at high temperatures are especially valuable. Once formed, these minerals can resist daughter loss and record the primary age even though they remained hot (say, 700° C) for a long time. The mineral zircon datable by the uranium–lead method is one such mineral. The mica mineral biotite dated by either the potassium–argon or the rubidium–strontium method occupies the opposite end of the spectrum and does not retain daughter products until cooled below about 300° C. Successively higher blocking temperatures are recorded for another mica type known as muscovite and for amphibole, but the ages of both of these minerals can be completely reset at temperatures that have little or no effect on zircon.

      Taken in perspective, it is evident that many parts of the Earth's crust have experienced reheating temperatures above 300° C—i.e., reset mica ages are very common in rocks formed at deep crustal levels. Vast areas within the Precambrian shield, which have identical ages reflecting a common cooling history, have been identified. These are called geologic provinces. By contrast, rocks that have approached their melting point, say, 750° C, which can cause new zircon growth during a second thermal event, are rare, and those that have done this more than once are almost nonexistent.

Instruments and procedures

Use of mass spectrometers

      The age of a geologic sample is measured on as little as a billionth of a gram of daughter isotopes. Moreover, all the isotopes of a given chemical element are nearly identical except for a very small difference in mass. Such conditions necessitate instrumentation of high precision and sensitivity. Both these requirements are met by the modern mass spectrometer. A high-resolution mass spectrometer of the type used today was first described by the American physicist Alfred O. Nier in 1940, but it was not until about 1950 that such instruments became available for geochronological research.

      For isotopic dating with a mass spectrometer, a beam of charged atoms, or ions, of a single element from the sample is produced. This beam is passed through a strong magnetic field in a vacuum, where it is separated into a number of beams, each containing atoms of only the same mass. Because of the unit electric charge on every atom, the number of atoms in each beam can be evaluated by collecting individual beams sequentially in a device called a Faraday cup. Once in this collector, the current carried by the atoms is measured as it leaks across a resistor to ground. Currents measured are small, only from 10⁻¹¹ to 10⁻¹⁵ ampere, so that shielding and preamplification are required as close to the Faraday cup as possible. It is not possible simply to count the atoms, because all atoms loaded into the source do not form ions and some ions are lost in transmission down the flight tube. Precise and accurate information as to the number of atoms in the sample can, however, be obtained by measuring the ratio of the number of atoms in the various separated beams. By adding a special artificially enriched isotope during sample dissolution and by measuring the ratio of natural to enriched isotopes in adjacent beams, the number of daughter isotopes can be readily determined. The artificially enriched isotope is called a “spike.” It is usually a highly purified form of a low-abundance natural isotope, but an even better spike is an isotope with a mass not found in nature at all. Lead-205 produced in a type of particle accelerator called a cyclotron constitutes such an ideal spike.

      As the sample is heated and vaporizes under the vacuum in the source area of the mass spectrometer, it is commonly observed that the lighter isotopes come off first, causing a bias in the measured values that changes during the analysis. In most cases this bias, or fractionation, can be corrected if the precise ratio of two of the stable isotopes present is known. Today's state-of-the-art instruments produce values for strontium and neodymium isotopic abundances that are reproducible at a level of about 1 in 20,000. Such precision is often essential in the isochron method (see above) because of the small changes in relative daughter abundance that occur over geologic time.

Technical advances

      The ability to add a single artificial mass to the spectrum in a known amount and to determine the abundances of other isotopes with respect to this provides a powerful analytical tool. By means of this process known as isotope dilution, invisibly small amounts of material can be analyzed, and because only ratios are involved, a loss of part of the sample during preparation has no effect on the result. Spike solutions can be calibrated simply by obtaining a highly purified form of the element being calibrated. After carefully removing surface contamination, a precisely weighted portion of the element is dissolved in highly purified acid and diluted to the desired level in a weighed quantity of water. What is required is dilution of one cubic centimetre to a litre from which a second cubic centimetre is again diluted to a litre to approach the range of parts per million or parts per billion typically encountered in samples. In this way, a known number of natural isotopes can be mixed with a known amount of spike and the concentration in the spike solution determined from the ratio of the masses. Once the calibration has been completed, the process is reversed and a weighed amount of spike is mixed with the parent and daughter elements from a mineral or rock. The ratio of the masses then gives the number of naturally produced atoms in the sample. The use of calibrated enriched isotopic tracers facilitates checks for contamination, even though the process is time-consuming. A small but known amount of tracer added to a beaker of water can be evaporated under clean-room conditions. Once loaded in a mass spectrometer, the contamination from the beaker and the water is easily assessed with respect to the amount of spike added. Contamination as small as 10⁻¹² gram can be detected by this method.

      The materials analyzed during isotopic investigations vary from microgram quantities of highly purified mineral grains to gram-sized quantities of rock powders. In all cases, the material must be dissolved without significant contamination. The spike should be added before dissolution. Most of the minerals in rocks can be dissolved in a day or so at a temperature near 100° C. Certain minerals that are highly refractory both in nature and in the laboratory (e.g., zircon) may require five days or more at temperatures near 220° C. In this case, the sample is confined in a solid Teflon (trade name for a synthetic resin composed of polytetrafluoroethylene), metal-clad pressure vessel, introduced by the Canadian geochronologist Thomas E. Krogh in 1973.

      The method just described proved to be a major technical breakthrough as it resulted in a reduction in lead-background contamination by a factor of between 10,000 and nearly 1,000,000. This means that a single grain can now be analyzed with a lower contamination level (or background correction) than was possible before with 100,000 similar grains. Advances in high-sensitivity mass spectrometry of course were essential to this development.

      Once dissolved, the sample is ready for the chemical separation of the dating elements. This is generally achieved by using the methods of ion-exchange chromatography. In this process, ions are variously adsorbed from solution onto materials with ionic charges on their surface and separated from the rest of the sample. After the dating elements have been isolated, they are loaded into a mass spectrometer and their relative isotopic abundances determined.

      The abundance of certain isotopes used for dating is determined by counting the number of disintegrations per minute (i.e., emission activity). The rate is related to the number of such atoms present through the half-life. For example, a certain amount of carbon-14 (¹⁴C) is present in all biological components at the Earth's surface. This radioactive carbon is continually formed when nitrogen atoms of the upper atmosphere collide with neutrons produced by the interaction of high-energy cosmic rays with the atmosphere. An organism takes in small amounts of carbon-14, together with the stable (nonradioactive) isotopes carbon-12 (¹²C) and carbon-13 (¹³C), as long as it is alive. Once it dies, however, no additional carbon-14 is acquired and the level of radiocarbon in the organism's tissue decreases progressively as a function of half-life. The time that has passed since the organism was alive can be determined by counting the beta emissions from a tissue sample. The number of emissions in a given time period is proportional to the amount of residual carbon-14.

      The introduction of an instrument called an accelerator mass spectrometer has brought about a major advance in radiocarbon dating. Unlike the old detector (e.g., the Geiger counter) that counts the few decay particles emitted from a large amount of carbon, the new instrument counts directly all of the carbon-14 atoms in a sample. This increase in instrument sensitivity has made it possible to reduce the sample size by as much as 10,000 times and at the same time improve the precision of ages measured. (For a detailed discussion of radiocarbon age determination, see below Carbon-14 dating and other cosmogenic methods. (dating))

      In a similar development, the use of highly sensitive thermal ionization mass spectrometers is replacing the counting techniques employed in some disequilibrium dating (see below). Not only has this led to a reduction in sample size and measurement errors but it also has permitted a whole new range of problems to be investigated. Certain parent–daughter isotopes are extremely refractory and do not ionize in a conventional mass spectrometer. To solve this problem, researchers are developing new instruments in which a small amount of material can be evaporated from the surface with a pulse of energy and ionized with a pulse of laser light. A major trend anticipated in geochronology and isotope geochemistry involves the analysis of mineral grains in place without chemical dissolution and mass spectrometry. This type of analysis requires expensive equipment in which a focused beam of ions is directed at a spot on a mineral sample. This causes atoms to evaporate from the surface, and the ions produced are extracted and measured in a mass spectrometer. Uranium–lead dating of zircon by this method has been pioneered by William Compston at the Australian National University.

Major methods of isotopic dating

      Isotopic dating relative to fossil dating requires a great deal of effort and depends on the integrated specialized skills of geologists, chemists, and physicists. It is, nevertheless, a valuable resource that allows correlations to be made over virtually all of Earth history with a precision once only possible with fossiliferous units that are restricted to the most recent 12 percent or so of geologic time. Although any method may be attempted on any unit, the best use of this resource requires that every effort be made to tackle each problem with the most efficient technique. Because of the long half-life of some isotopic systems or the high background or restricted range of parent abundances, some methods are inherently more precise. The skill of a geochronologist is demonstrated by the ability to attain the knowledge required and the precision necessary with the least number of analyses. The factors considered in selecting a particular approach are explored here.

Uranium–lead method

 As each dating method was developed, tested, and improved, mainly since 1950, a vast body of knowledge about the behaviour of different isotopic systems under different geologic conditions has evolved. It is now clear that with recent advances the uranium–lead method is superior in providing precise age information with the least number of assumptions. The method has evolved mainly around the mineral zircon (ZrSiO₄). Because of the limited occurrence of this mineral, it was once true that only certain felsic igneous rocks (those consisting largely of the light-coloured, silicon and aluminum-rich minerals feldspar and quartz) could be dated. Today, however, baddeleyite (ZrO₂) has been found to be widespread in the silica-poor mafic igneous rocks. In addition, perovskite (CaTiO₃), a common constituent of some ultramafic igneous rocks, has been shown to be amenable to precise uranium–lead dating. As a result of these developments, virtually all igneous rocks can now be dated. This capability, moreover, has been enhanced because the most advanced geochronological laboratories are able to analyze samples that weigh only a few millionths of a gram. This amount can be found in a comparatively large number of rocks, whereas the amount previously required (about 0.1 gram) cannot. Age determinations also can now be made of low-uranium trace minerals such as rutile (TiO₂), a common constituent found in mineral deposits, adding still further to the number of entities that are datable by the uranium–lead method. Other minerals commonly employed to date igneous and metamorphic rocks include titanite, monazite, and even garnet in certain favourable cases. Additional minerals listed in Table 2—> have been tried with varying success.

Double uranium-lead chronometers

      The reason why uranium–lead dating is superior to other methods is simple: there are two uranium–lead chronometers. Because there exist two radioactive uranium atoms (those of mass 235 and 238), two uranium–lead ages can be calculated for every analysis. The age results or equivalent daughter–parent ratio can then be plotted one against the other on a concordia diagram, as shown in Figure 2. If the point falls on the upper curve shown, the locus of identical ages, the result is said to be concordant, and a closed-system unequivocal age has been established. Any leakage of daughter isotopes from the system will cause the two ages calculated to differ, and data will plot below the curve. Because each of the daughters has a different half-life, early leakage will affect one system more than the other. Thus there is a built-in mechanism that can prove or disprove whether a valid age has been measured. Historically it had been observed that the uranium–lead systems in the mineral zircon from unmetamorphosed rocks were almost invariably disturbed or discordant but yielded a linear array on the concordia diagram. Given a set of variably disturbed samples, an extrapolation to zero disturbance was possible (see Figure 2). More recently, it has been found that of all the grains present in a rock a very few still retain closed isotopic systems but only in their interior parts. Thus grains with a diameter comparable to that of a human hair, selected under a microscope to be crack-free and of the highest possible quality, have been found to be more concordant than cracked grains. In addition, it has been shown that most such grains can be made much more concordant by mechanically removing their outer parts using an air-abrasion technique (upper points in Figure 2). Of course, the ability to analyze samples weighing only a few millionths of a gram was essential to this development. As noted earlier, this in turn was possible solely because the lead background contamination had been reduced from 1 × 10⁻⁶ grams to almost 1 × 10⁻¹² grams per analysis. The methods of selection and abrasion used to locate grains with closed isotopic systems could be worked out only because the uranium–lead method has the inherent ability to assess with a single analysis whether or not a closed isotopic system has prevailed.

      The presence of two radioactive parents provides a second major advantage because, as daughter products, lead atoms are formed at different rates and their relative abundance undergoes large changes as a function of time. Thus the ratio of lead-207 to lead-206 changes by about 0.1 percent every two million years. Since this ratio is easily calibrated and reproduced at such a level of precision, errors as low as ±2 million years at a confidence level of 95 percent are routinely obtained on lead-207–lead-206 ages. By contrast, errors as high as ±30 to 50 million years are usually quoted for the rubidium–strontium and samarium–neodymium isochron methods (see below).

Importance of zircon in uranium-lead dating

      The mineral zircon adds three more fundamental advantages to uranium–lead dating. First, its crystal structure allows a small amount of tetravalent uranium to substitute for zirconium, but excludes with great efficiency the incorporation of lead. (It might be said that one begins with an empty box.) Second, zircon, once formed, is highly resistant to change and has the highest blocking temperature ever observed. Finally, with few predictable exceptions, zircon grows or regrows only in liquid rock or in solid rock reheated to approach its melting point. Combining all of these attributes, it is often possible to measure both the time of crystallization and the time of second melting in different parts of the same grain or in different selected grains from the same rock. Of course, such a high blocking temperature can have its disadvantages. Inherited cores may give a mixed false age when the age of crystallization is sought. For this reason, three or more grain types or parts of a grain are analyzed to establish that material of only one age is present.

      Experience with the results of the uranium–lead method for zircons has demonstrated an interesting paradox. If left at low surface temperatures for a geologically long time, the radioactivity within the crystal can destroy the crystal lattice structure, whereas at higher temperatures this process is self-annealing. In fact, when examined by X-ray methods, some zircons have no detectable structure, indicating that at least 25 percent of the initial atoms have been displaced by radiation damage (radiation-damage dating). Under these conditions a low-temperature event insufficient to even reset the potassium–argon system (see below) in biotite can cause lead to be lost in some grains. It is no coincidence that, when criteria were finally found to locate concordant grains, these grains were also found to be those with the lowest uranium content and the lowest related radiation damage.

 Given the two related uranium–lead parent–daughter systems, it is possible to determine both the time of the initial, or primary, rock-forming event and the time of a major reheating, or secondary, event. This is illustrated in Figure 3—>. Here, the uranium–lead isotopes in the mineral titanite (CaTiSiO₅) from a series of rocks that have a common geologic history plot on a straight line. The minerals first formed 1,651 million years ago but were later heated and lost varying amounts of lead 986 million years ago. In many cases, new titanite, distinguishable on the basis of colour, has formed in the same rock, while older, partly reset titanite is still present. Data points 14 and 7 in the figure represent such a pair. On this diagram, the presence of surface-correlated lead loss will displace data from the titanite line toward the time of loss close to zero age on the concordia curve. The uranium–lead data then would plot below the line shown, and neither the primary nor secondary age would be defined. The importance of eliminating recent loss, as discussed above, is clearly evident. It should be noted that, if these ages had been measured by any of the other schemes that have only a single parent–daughter pair, a whole series of different numbers spanning the time from 1.65 billion to 988 million years ago would be observed. There would be no way of telling which of the measured ages, if any, was valid.

      Uranium–lead dating relies on the isolation of very high-quality grains or parts of mineral grains that are extremely rare but nevertheless present in most igneous, metamorphic, and sedimentary rock units. Samples weighing 10 to 50 kilograms are collected, crushed, and ground into a fine sand, and the various minerals are isolated on the basis of specific gravity, grain size, and magnetic properties. The minerals used are not visible in the field, but their presence can be inferred from the easily identified major minerals present.

      One of the most interesting applications of the improved uranium–lead zircon technique has to do with its ability to achieve nearly concordant results from single grains extracted from sandstone. This is possible because zircon is chemically inert and is not disturbed during weathering and because single grains with a diameter about the thickness of a human hair contain sufficient uranium and lead for analysis in the most advanced laboratories. In one sample it was determined that a sandstone that underlies most of the province of Nova Scotia in Canada was probably originally deposited off the coast of North Africa and thrust over the continent before the opening of the Atlantic Ocean. This follows because the ages observed occur in North Africa, whereas those common in North America are absent.

      Another sample, this one from sandstone deposited by a large river in northern Scotland, must have been derived from continental rocks whose ages are represented by those determined for the individually dated sand grains. In this case, the continent from which the sand was derived has moved away as a result of continental drift, but it can be identified by the ages measured.

Rubidium–strontium method (rubidium-strontium dating)

      The radioactive decay of rubidium-87 (⁸⁷Rb) to strontium-87 (⁸⁷Sr) was the first widely used dating system that utilized the isochron method. rubidium is a relatively abundant trace element in the Earth's crust and can be found in many common rock-forming minerals in which it substitutes for the major element potassium. Because rubidium is concentrated in crustal rocks, the continents have a much higher abundance of the daughter isotope strontium-87 compared with the stable isotopes. This relative abundance is expressed as the ⁸⁷Sr/⁸⁶Sr ratio, where strontium-86 is chosen to represent the stable isotopes strontium-88, strontium-86, and strontium-84, which occur in constant proportions in natural materials. Thus a precise measurement of the ⁸⁷Sr/⁸⁶Sr ratio in a modern volcano can be used to determine age if recycled older crust is present. A ratio for average continental crust of about 0.72 has been determined by measuring strontium from clamshells from the major river systems. In contrast, the Earth's most abundant lava rocks, which represent the mantle and make up the major oceanic ridges, have values between 0.703 and 0.705. This difference may appear small, but considering that modern instruments can make the determination to a few parts in 70,000, it is quite significant. Dissolved strontium in the oceans today has a value of 0.709 that is dependent on the relative input from the continents and the ridges. In the geologic past changes in the activity of these two sources has produced varying ⁸⁷Sr/⁸⁶Sr ratios over time. Thus if well-dated, unaltered fossil shells containing strontium from ancient seawater are analyzed, changes in this ratio with time can be observed and applied in reverse to estimate the time when fossils of unknown age were deposited.

Dating simple igneous rocks (igneous rock)

 The rubidium–strontium pair is ideally suited for the isochron dating of igneous rocks. As a liquid rock cools, first one mineral and then another achieves saturation and precipitates, each extracting specific elements in the process. Strontium is extracted in many minerals that are formed early, whereas rubidium is gradually concentrated in the final liquid phase. At the time of crystallization, this produces a wide range in the Rb/Sr ratio in rocks that have identical ⁸⁷Sr/⁸⁶Sr ratios. On the isochron diagram shown in Figure 1—> above, the samples would plot initially at points R₁ to R₃ along a line representing the initial ratio designated (⁸⁷Sr/⁸⁶Sr)₀. Over geologic time, this ratio is increased in proportion to the ⁸⁷Rb/⁸⁶Sr ratio, as discussed earlier, and the line rotates with a slope equal to (e^λt − 1) that represents the time elapsed; thus, the present-day ratio (⁸⁷Sr/⁸⁶Sr)_p equals the initial ratio (⁸⁷Sr/⁸⁶Sr)₀ plus radiogenic additions, or (⁸⁷Sr/⁸⁶Sr)_p = (⁸⁷Sr/⁸⁶Sr)₀ + ⁸⁷Rb/⁸⁶Sr (e^λt − 1). This equation is that of a straight line of the form y = b + xm, where y = (⁸⁷Sr/⁸⁶Sr)_p, the value measured today; b represents (⁸⁷Sr/⁸⁶Sr)₀, the value initially present; x stands for the ⁸⁷Rb/⁸⁶Sr ratio; and m is the slope of the line (e^λt − 1).

      In practice, rock samples weighing several kilograms each are collected from a suite of rocks that are believed to have been part of a single homogeneous liquid prior to solidification. The samples are crushed and homogenized to produce a fine representative rock powder from which a fraction of a gram is withdrawn and dissolved in the presence of appropriate isotopic traces, or spikes. Strontium and rubidium are extracted and loaded into the mass spectrometer, and the values appropriate to the x and y coordinates are calculated from the isotopic ratios measured. Once plotted as R1_p (i.e., rock 1 present values), R2_p, and R3_p, the data are examined to assess how well they fit the required straight line. Using estimates of measurement precision, the crucial question of whether or not scatter outside of measurement error exists is addressed. Such scatter would constitute a geologic component, indicating that one or more of the underlying assumptions has been violated and that the age indicated is probably not valid. For an isochron to be valid, each sample tested must (1) have had the same initial ratio, (2) have been a closed system over geologic time, and (3) have the same age.

      Well-preserved, unweathered rocks that crystallized rapidly and have not been subjected to major reheating events are most likely to give valid isochrons. Weathering is a disturbing influence, as is leaching or exchange by hot crustal fluids, since many secondary minerals contain rubidium. Volcanic rocks are most susceptible to such changes because their minerals are fine-grained and unstable glass may be present. On the other hand, meteorites that have spent most of their time in the deep freeze of outer space can provide ideal samples.

Dating minerals

       potassium-bearing minerals including several varieties of mica, are ideal for rubidium–strontium dating as they have abundant parent rubidium and a low abundance of initial strontium. In most cases, the changes in the ⁸⁷Sr/⁸⁶Sr ratio are so large that an initial value can be assumed without jeopardizing the accuracy of the results. When minerals with a low-rubidium or a high-strontium content are analyzed, the isochron-diagram approach can be used to provide an evaluation of the data. As discussed above, rubidium–strontium mineral ages need not be identical in a rock with a complex thermal history, so that results may be meaningful in terms of dating the last heating event but not in terms of the actual age of a rock.

Dating metamorphic rocks (metamorphic rock)

      Should a simple igneous body be subjected to an episode of heating or of deformation or of a combination of both, a well-documented special data pattern develops. With heat, daughter isotopes diffuse out of their host minerals but are incorporated into other minerals in the rock. Eventually the ⁸⁷Sr/⁸⁶Sr ratio in the minerals becomes identical. When the rock again cools, the minerals close and again accumulate daughter products to record the time since the second event. Remarkably, the isotopes remain within the rock sample analyzed, and so a suite of whole rocks can still provide a valid primary age. This situation is easily visualized on an isochron diagram, where a series of rocks plots on a steep line showing the primary age, but the minerals in each rock plot on a series of parallel lines that indicate the time since the heating event. If cooling is very slow, the minerals with the lowest blocking temperature, such as biotite mica, will fall below the upper end of the line.

      A more dramatic presentation of this phenomenon is found when the changes in the ⁸⁷Sr/⁸⁶Sr ratios in a variety of minerals in a single rock are depicted as a function of geologic time. Here, an essentially rubidium-free, strontium-rich phase like apatite retains its initial ⁸⁷Sr/⁸⁶Sr ratio over time, whereas the value in such rubidium-rich, strontium-poor minerals as biotite increases rapidly with time. The rock itself gives the integrated, more gradual increase. At the time of heating, identical ⁸⁷Sr/⁸⁶Sr ratios are again achieved as described above, only to be followed by a second episode of isotopic divergence.

      Approaches to this ideal case are commonly observed, but peculiar results are found in situations where the heating is minimal. If one assumes for a moment that only the mineral with the lowest blocking temperature loses its daughter isotope, it is easy to imagine that other low-temperature minerals formed at this time may acquire extremely high ⁸⁷Sr/⁸⁶Sr ratios. Epidote, a low-temperature alteration mineral with a very high concentration of radiogenic strontium, has been found in rocks wherein biotite has lost strontium by diffusion. The rock itself has a much lower ratio, so that it did not take part in this exchange.

      Although rubidium–strontium dating is not as precise as the uranium–lead method, it was the first to be exploited and has provided much of the prevailing knowledge of Earth history. The procedures of sample preparation, chemical separation, and mass spectrometry are relatively easy to carry out, and datable minerals occur in most rocks. Precise ages can be obtained on high-level rocks (i.e., those closer to the surface) and meteorites, and imprecise but nevertheless valuable ages can be determined for rocks that have been strongly heated. The mobility of rubidium in deep-level crustal fluids and melts that can infiltrate other rocks during metamorphism as well as in fluids involved in weathering can complicate the results.

Samarium–neodymium method

      The radioactive decay of samarium of mass 147 (¹⁴⁷Sm) to neodymium of mass 143 (¹⁴³Nd) has been shown to be capable of providing useful isochron ages for certain geologic materials. Both parent and daughter belong to the rare earth element group, which is itself the subject of numerous geologic investigations. All members of this group have similar chemical properties and charge, but differ significantly in size. Because of this, they are selectively removed as different minerals are precipitated from a melt. In the opposite sense, their relative abundance in a melt can indicate the presence of certain residual minerals during partial melting. Unlike rubidium, which is enriched over strontium in the crust, samarium is relatively enriched with respect to neodymium in the mantle. Consequently, a volcanic rock composed of melted crust would have elevated radiogenic strontium values and depressed radiogenic neodymium values with respect to the mantle. As a parent–daughter pair, samarium-147 and neodymium-143 are unique in that both have very similar chemical properties, and so loss by diffusion may be reduced. Their low concentrations in surface waters indicates that changes during low-temperature alteration and weathering are less likely. Their presence in certain minerals in water-deposited gold veins, however, does suggest mobility under certain conditions. In addition, their behaviour under high-temperature metamorphic conditions is as yet poorly documented.

      The exploitation of the samarium–neodymium pair for dating only became possible when several technical difficulties were overcome. Procedures to separate these very similar elements and methods of measuring neodymium isotope ratios with uncertainties of only a few parts in 100,000 had to be developed.

      In theory, the samarium–neodymium method is identical to the rubidium–strontium approach (see above). Both use the isochron method to display and evaluate data. In the case of samarium–neodymium dating, however, the chemical similarity of parent and daughter adds another complication because fractionation during crystallization is extremely limited. This makes the isochrons short and adds further to the necessity for high precision. The result is that, with few exceptions, uncertainties in measured ages are as large as 30 to 100 million years, even for the oldest rocks and meteorites. Mineral isochrons provide the best results.

      The equation relating present-day neodymium isotopic abundance as the sum of the initial ratios and radiogenic additions is that of a straight line, as discussed earlier for rubidium–strontium.

      In a successful application of the samarium–neodymium method to a sample of basalt from the Moon, the constituent minerals plagioclase, ilmenite, and pyroxene provide enough spread in the ¹⁴⁷Sm/¹⁴³Nd ratio to allow an age of 3,700 ± 70 million years to be calculated. Other successful examples have been reported where rocks with open rubidium–strontium systems have been shown to have closed samarium–neodymium systems. In other examples, the ages of rocks with insufficient rubidium for dating have been successfully determined. There is considerable promise for dating garnet, a common metamorphic mineral, because it is known to concentrate the parent isotope.

      In general, the use of the samarium–neodymium method as a dating tool is limited by the fact that other methods (mainly the uranium–lead approach) are more precise and require fewer analyses. In the case of meteorites and lunar rocks where samples are limited and minerals for other dating methods are not available, the samarium–neodymium method can provide the best ages possible.

Rhenium–osmium method

      The decay scheme in which rhenium-187 is transformed to osmium-187 shows promise as a means of studying mantle–crust evolution but has displayed only limited potential for isotopic dating. Technical difficulties have yet to be overcome. osmium is strongly concentrated in the mantle and extremely depleted in the crust, so that crustal osmium must have exceedingly high radiogenic-to-stable ratios while the mantle values are low. In fact, crustal levels are so low that they are extremely difficult to measure with current technology. Most work to date has centred around rhenium- or osmium-enriched minerals. Another problem that is still under investigation involves the difficulty of ionizing osmium in a mass spectrometer. A number of new approaches are being studied. In one method, success has been demonstrated in ionizing osmium in an instrument called an ion microprobe. This instrument bombards the sample target with a beam of ions of such high energy that atoms in the sample evaporate into a vacuum and a relatively small number becomes ionized. The ions are then extracted into a mass spectrometer, and the desired isotopic abundances are determined. Another related approach being tested involves the evaporation of the sample by a short pulse of ions, with a subsequent pulse of laser light tuned to ionize the desired element. Once the technical difficulties are surmounted, the distribution of rhenium and radiogenic and stable osmium isotopes will be explored. The greatest potential for this method might be in studies concerning the origin and age of mineral deposits since rhenium and osmium are known to occur in such materials.

Potassium–argon methods (potassium-argon dating)

      The radioactive decay scheme involving the breakdown of potassium of mass 40 (⁴⁰K) to argon gas of mass 40 (⁴⁰Ar) formed the basis of the first widely used isotopic dating method. Since radiogenic argon-40 was first detected in 1938 by the American geophysicist Lyman T. Aldrich and A.O. Nier, the method has evolved into one of the most versatile and widely employed methods available. potassium is one of the 10 most abundant elements that together make up 99 percent of the Earth's crust and is therefore a major constituent of many rock-forming minerals. In fact, potassium-40 decays to both argon-40 and calcium-40, but because argon is absent in most minerals while calcium is present, the argon produced is easier to detect and measure. Most of the argon in the Earth's atmosphere has been created by the decay of potassium-40 as the argon-40 abundance is about 1,000 times higher than expected from cosmic abundances. Argon dating involves a different technology from all the other methods so far described because argon exists as a gas at room temperature. Thus it can be purified as it passes down a vacuum line by freezing out or reacting out certain contaminants. It is then introduced into a mass spectrometer through a series of manual or computer-controlled valves. Technical advances, including the introduction of the argon-40–argon-39 method and laser heating, that have improved the versatility of the method, are described below.

      In conventional potassium–argon dating, a potassium-bearing sample is split into two fractions: one is analyzed for its potassium content, while the other is fused in a vacuum to release the argon gas. After purification has been completed, a spike enriched in argon-38 is mixed in and the atomic abundance of the daughter product argon-40 is measured relative to the argon-38 added. The amount of the argon-36 present is then determined relative to argon-38 to provide an estimate of the background atmospheric correction. In this case, relatively large samples, which may include significant amounts of alteration, are analyzed. Since potassium is usually added by alteration, the daughter–parent ratio and the age might be too low.

      A method designed to avoid such complexities was introduced by the geochronologists Craig M. Merrihue and Grenville Turner in 1966. In this technique, known as the argon-40–argon-39 method, both parent and daughter can be determined in the mass spectrometer as some of the potassium atoms in the sample are first converted to argon-39 in a nuclear reactor. In this way, the problem of measuring the potassium in inhomogeneous samples is eliminated and smaller amounts of material can be analyzed. An additional advantage then becomes possible. The sample can be heated in stages at different temperatures and the age calculated at each step. If alteration is evident, the invalid low-temperature age can be eliminated and a valid high-temperature age determined. In some cases, partly reset systems also may be detected.

      As in all dating systems, the ages calculated can be affected by the presence of inherited daughter products. In a few cases, argon ages older than that of the Earth which violate local relative age patterns have even been determined for the mineral biotite. Such situations occur mainly where old rocks have been locally heated, which released argon-40 into pore spaces at the same time that new minerals grew. Under favourable circumstances the isochron method may be helpful, but tests by other techniques may be required. For example, the rubidium–strontium method would give a valid isotopic age of the biotite sample with inherited argon.

      As techniques evolved, argon background levels have been reduced and the method has become more and more sensitive. Capitalizing on this, it is now possible to measure the minute amount of argon released when a single spot on a crystal is heated by an intense laser beam. For geologically old potassium-rich materials, a single spot may produce sufficient gas for analysis, whereas single millimetre-sized grains may be required in very young materials. Progressive refinement of the method has made new areas of research possible, and the ability to understand complexities encountered in earlier investigations has increased. In one study the age of volcanic ash as young as 215,000 ± 4,000 years and the presence of inherited older grains in another ash sample were thoroughly documented. This was done by melting single millimetre-sized grains with a laser and measuring individual argon-40–argon-39 ages with a highly sensitive gas mass spectrometer.

      The potassium–argon method has provided a great deal of information about the Earth's recent and ancient past. It has been instrumental, for example, in determining the ages of the stripes of alternating normally and reversely magnetized volcanic rocks that parallel the axis of the mid-oceanic ridges. In ancient shield areas large segments of crust that were uplifted and cooled at the same time—i.e., geologic provinces—have been identified by the potassium–argon method. The technique is highly responsive to thermal events in a relatively predictable fashion, so the cooling history of a region may be established.

Thomas Edvard Krogh

fission-track dating

      This is a special type of dating method that makes use of a microscope rather than a mass spectrometer, and capitalizes on damaged zones, or tracks, created in crystals during the spontaneous fission of uranium-238. In this unique type of radioactive decay, the nucleus of a single parent uranium atom splits into two fragments of similar mass with such force that a trail of crystal damage is left in the mineral. Immersing the sample in an etching solution of strong acid or base enlarges the fission tracks into tube-shaped holes large enough to be seen under a high-powered microscope. The number of tracks present can be used to calculate the age of the sample if the uranium content is known. Fortunately the uranium content of precisely the spot under scrutiny can be obtained by a similar process when working with a polished crystal surface. The sample is bombarded with slow (thermal) neutrons in a nuclear reactor, resulting in induced fission of uranium-235 (as opposed to spontaneous fission of uranium-238). The fission tracks produced by this process are recorded by a thin plastic film placed against the surface of the sample. The uranium content of the material can then be calculated so long as the neutron dose is known. The age of the sample is obtained using the equation, age = N × Ds/Di × 6 × 10⁻⁸, in which N is the total neutron dose expressed as neutrons per square centimetre and Ds is the observed track density for spontaneous fission while Di is that for induced fission.

      The preservation of crystal damage (radiation-damage dating) (i.e., the retention of fission tracks) is highly sensitive to temperature and varies from mineral to mineral. The technique can be used to determine mild thermal events as low as 100° C. Alternately, primary ages can be calculated if the rock was formed at the surface and cooled quickly. Under these conditions the calculated fission-track ages of two minerals with widely different annealing temperatures would be identical. The accuracy achieved depends on the number of tracks counted, so that artificial glass coloured with 10 percent uranium can be dated as soon as 30 years after manufacture. With uranium levels of a few parts per million, samples as young as 300,000 years can be dated by counting tracks for one hour. When dealing with very old materials, high-uranium samples must be avoided because there are so many interlocking tracks that they can no longer be counted.

      A special feature of fission-track dating lies in its ability to map the uranium distribution within mineral grains. In a uranium map for single zircon grains, the outer zones that grew during a major melting event contained much more uranium than the grains originally present. The uranium–lead age was highly biased toward the younger event and the primary age could be determined only after the outer zones were removed. In practice, fission-track dates are regarded as cooling ages unless proved otherwise. It might also be noted that uncertainties in results may arise from an uneven distribution of uranium, statistical errors in counting, and inaccurate estimates of neutron flux (dose of neutrons).

      Fission-track dating can be used on a wide variety of minerals found in most geologic materials, and it is relatively inexpensive to apply. Because closure temperatures vary widely from, say, 300° C for titanite and zircon to less than 100° C for biotite and apatite, valuable information can be obtained regarding the uplift and cooling rates of crustal rocks.

carbon-14 dating and other cosmogenic methods

      The occurrence of natural radioactive carbon in the atmosphere provides a unique opportunity to date organic materials as old as 50,000 years. Unlike most isotopic dating methods, the conventional carbon-14 dating technique is not based on counting daughter isotopes. It relies instead on the progressive decay or disappearance of the radioactive parent with time.

      The discovery of natural carbon-14 by Willard Libby (Libby, Willard Frank) of the United States began with his recognition that a process that had produced radiocarbon in the laboratory was also going on in the Earth's upper atmosphere—namely, the bombardment of nitrogen by free neutrons. Newly created carbon-14 atoms were presumed to react with atmospheric oxygen to form carbon dioxide (CO₂) molecules. Radioactive carbon thus was visualized as gaining entrance wherever atmospheric carbon dioxide enters—into land plants by photosynthesis, into animals that feed on the plants, into marine waters and freshwaters as a dissolved component, and from there into aquatic plants and animals. In short, all parts of the carbon cycle were seen to be invaded by the isotope carbon-14.

      Invasion is probably not the proper word for a component that Libby calculated should be present only to the extent of about one atom in a trillion stable carbon atoms. So low is such a carbon-14 level that no one had detected natural carbon-14 until Libby, guided by his own predictions, set out specifically to measure it. His success initiated a series of measurements designed to answer two questions: Is the concentration of carbon-14 uniform throughout the plant and animal kingdoms? And, if so, has today's uniform level prevailed throughout the recent past?

      After showing the essential uniformity of carbon-14 in living material, Libby sought to answer the second question by measuring the radiocarbon level in organic samples dated historically—materials as old as 5,000 years from sources such as Egyptian tombs. With correction for radioactive decay during the intervening years, such old samples hopefully would show the same starting carbon-14 level as exists today. This was just what Libby's measurements indicated. His conclusion was that over the past 5,000 years the carbon-14 level in living materials has remained constant within the 5 percent precision of measurement. A dating method was thus available, subject only to confirmation by actual application to specific chronologic problems.

      Since Libby's foundational studies, tens of thousands of carbon-14 measurements of natural materials have been made. Expressed as a fraction of the contemporary level, they have been mathematically converted to ages through equation 5—> above. Archaeology has been the chief beneficiary of radioactive-carbon dating, but late glacial and postglacial chronological studies in geology have also been aided greatly.

      Improvements in measurement accuracy and the ever-mounting experience in applying carbon-14 dating have provided superior and more voluminous data with which to better answer Libby's original questions. It is now clear that carbon-14 is not homogeneously distributed among today's plants and animals. The occasional exceptions all involve nonatmospheric contributions of carbon-14-depleted carbon dioxide to organic synthesis. Specifically, volcanic carbon dioxide is known to depress the carbon-14 level of nearby vegetation and dissolved limestone carbonate occasionally has a similar effect on freshwater mollusks, as does upwelling of deep ocean water on marine mollusks. In every case, the living material affected gives the appearance of built-in age.

      In addition to spatial variations of the carbon-14 level, the question of temporal variation has received much study. A 2 to 3 percent depression of the atmospheric radioactive-carbon level since 1900 was noted soon after Libby's pioneering work, almost certainly the result of the dumping of huge volumes of carbon-14-free carbon dioxide into the air through smokestacks. Of more recent date was the overcompensating effect of man-made carbon-14 injected into the atmosphere during nuclear-bomb (nuclear weapon) testing. The result was a rise in the atmospheric carbon-14 level by more than 50 percent. Fortunately, neither effect has been significant in the case of older samples submitted for carbon-14 dating. The ultimate cause of carbon-14 variations with time is generally attributed to temporal fluctuations in the cosmic rays that bombard the upper atmosphere and create terrestrial carbon-14. Whenever the number of cosmic rays in the atmosphere is low, the rate of carbon-14 production is correspondingly low, resulting in a decrease of the radioisotope in the carbon-exchange reservoir described above. Studies have revealed that the atmospheric radiocarbon level prior to 1000 BC deviates measurably from the contemporary level. In the year 6200 BC it was about 8 percent above what it is today. In the context of carbon-14 dating, this departure from the present-day level means that samples with a true age of 8,200 years would be dated by radiocarbon as 7,500 years old.

      The problems stemming from temporal variations can be overcome to a large degree by the use of calibration curves in which the carbon-14 content of the sample being dated is plotted against that of objects of known age. In this way, the deviations can be compensated for and the carbon-14 age of the sample converted to a much more precise date. Calibration curves have been constructed using dendrochronological data (tree-ring measurements of bristlecone pines as old as 8,200 years); periglacial varve, or lake sediment, data (see above); and, in archaeological research, certain materials of historically established ages. It is clear that carbon-14 dates lack the accuracy that traditional historians would like to have. There may come a time when all radiocarbon ages rest on firmer knowledge of the sample's original carbon-14 level than is now available. Until then, the inherent error from this uncertainty must be recognized.

      A final problem of importance in carbon-14 dating is the matter of sample contamination. If a sample of buried wood is impregnated with modern rootlets or a piece of porous bone has recent calcium carbonate precipitated in its pores, failure to remove the contamination will result in a carbon-14 age between that of the sample and that of its contaminant. Consequently, numerous techniques for contaminant removal have been developed. Among them are the removal of humic acids from charcoal and the isolation of cellulose from wood and collagen from bone. Today, contamination as a source of error in samples younger than 25,000 years is relatively rare. Beyond that age, however, the fraction of contaminant needed to have measurable effect is quite small, and, therefore, undetected or unremoved contamination may occasionally be of significance.

      A major breakthrough in carbon-14 dating occurred with the introduction of the accelerator mass spectrometer. This instrument is highly sensitive and allows precise ages on as little as one milligram of carbon, where the older method might require as much as 25 grams for ancient material. The increased sensitivity results from the fact that all of the carbon atoms of mass 14 can be counted in a mass spectrometer. By contrast, if carbon-14 is to be measured by its radioactivity, only those few atoms decaying during the measurement period are recorded. By using the accelerator mass spectrometer possible interference from nitrogen-14 is avoided since it does not form negative ion beams, and interfering molecules are destroyed by stripping electrons away by operating at several million volts.

      The development of the accelerator mass spectrometer has provided new opportunities to explore other rare isotopes produced by the bombardment of the Earth and meteorites by high-energy cosmic rays. Many of these isotopes have short half-lives and hence can be used to date events that happened in the past few thousand to a few million years. In one case, the time of exposure, like the removal of rock by a landslide, can be dated by the presence of the rare beryllium-10 (¹⁰Be) isotope formed in the newly exposed surface of a terrestrial object or meteoroidal fragment by cosmic-ray bombardment. Other applications include dating groundwater with chlorine-36 (³⁶Cl), dating marine sediments with beryllium-11 (¹¹Be) and aluminum-26 (²⁶Al), and dating glacial ice with krypton-81 (⁸¹Kr). In general, the application of such techniques is limited by the enormous cost of the equipment required.

Uranium-series disequilibrium dating

       Principal cosmogenic and uranium-thorium series radioisotopesThe isotopic dating methods discussed so far are all based on long-lived radioactive isotopes that have survived since the elements were created or on short-lived isotopes that were recently produced by cosmic-ray bombardment. The long-lived isotopes are difficult to use on young rocks because the extremely small amounts of daughter isotopes present are difficult to measure. A third source of radioactive isotopes is provided by the uranium (uranium series)- and thorium (thorium series)-decay chains. As noted in the table (Principal cosmogenic and uranium-thorium series radioisotopes), these uranium–thorium series radioisotopes, like the cosmogenic isotopes, have short half-lives and are thus suitable for dating geologically young materials. The decay of uranium to lead is not achieved by a single step but rather involves a whole series of different elements, each with its own unique set of chemical properties.

      In closed-system natural materials, all of these intermediate daughter elements exist in equilibrium amounts. That is to say, the amount of each such element present is constant and the number that form per unit time is identical to the number that decay per unit time. Accordingly, those with long half-lives are more abundant than those with short half-lives. Once a uranium-bearing mineral breaks down and dissolves, the elements present may behave differently and equilibrium is disrupted. For example, an isotope of thorium is normally in equilibrium with uranium-234 but is found to be virtually absent in modern corals even though uranium-234 is present. Over a long period of time uranium-234, however, decays to thorium-230, which results in a build-up of the latter in old corals and thereby provides a precise measure of time.

      Most of the studies using the intermediate daughter elements were for years carried out by means of radioactive counting techniques—i.e., the number of atoms present was estimated by the radioactivity of the sample. The introduction of highly sensitive mass spectrometers that allow the total number of atoms to be measured rather than the much smaller number that decay has resulted in a revolutionary change in the family of methods based on uranium and thorium disequilibrium.

Thorium-230 dating (ionium-thorium dating)

      The insoluble nature of thorium provides for an additional disequilibrium situation that allows sedimentation rates in the modern oceans to be determined. In this case, thorium-230 in seawater, produced principally by the decay of uranium-234, is deposited preferentially in the sediment without the uranium-234 parent. This is defined as excess thorium-230 because its abundance exceeds the equilibrium amount that should be present. With time, the excess decays away and the age of any horizon in a core sample can be estimated from the observed thorium-230-to-thorium-232 ratio in the seawater-derived component of the core. Sedimentation rates between 1 and 20 millimetres per 1,000 years are commonly found with slight variations between the major ocean basins.

lead-210 dating

      The presence of radon gas as a member of the uranium-decay scheme provides a unique method for creating disequilibrium. The gas radon-222 (²²²Rn) escapes from the ground and decays rapidly in the atmosphere to lead-210 (²¹⁰Pb), which falls quickly to the surface where it is incorporated in glacial ice and sedimentary materials. By assuming that the present deposition rate also prevailed in the past, the age of a given sample at depth can be estimated by the residual amount of lead-210.

Edwin A. Olson Thomas Edvard Krogh

Additional Reading

Surveys of methodologies of ascertaining geologic time include Frederick E. Zeuner, Dating the Past: An Introduction to Geochronology, 4th rev. ed. (1958, reissued 1972); Patrick M. Hurley, How Old Is the Earth? (1959, reprinted 1979); E.I. Hamilton, Applied Geochronology (1965); G. Brent Dalrymple and Marvin A. Lanphere, Potassium-Argon Dating: Principles, Techniques, and Applications to Geochronology (1969); and Henry N. Michael and Elizabeth K. Ralph (eds.), Dating Techniques for the Archaeologist (1971). Stratigraphic geology as the basis of relative age measurement is discussed in W.B. Harland, A. Gilbert Smith, and B. Wilcock (eds.), The Phanerozoic Time-Scale (1964); John W. Harbaugh, Stratigraphy and the Geologic Time Scale, 2nd ed. (1974); Arthur Holmes, Holmes Principles of Physical Geology, 3rd ed. rev. by Doris L. Holmes (1978); N.J. Snelling (ed.), The Chronology of the Geological Record (1985); Derek V. Ager, The Nature of the Stratigraphical Record, 2nd ed. (1981); and Gilles S. Odin (ed.), Numerical Dating in Stratigraphy, 2 vol. (1982). The development of methods of absolute age measurement is examined in Henry Faul (ed.), Nuclear Geology (1954); Henry Faul, Ages of Rocks, Planets, and Stars (1966); the collected symposium papers published as Radioactive Dating (1963); Robert L. Fleischer, P. Buford Price, and Robert M. Walker, Nuclear Tracks in Solids: Principles and Applications (1975); E. Jäger and J.C. Hunziker (eds.), Lectures in Isotope Geology (1979); Gunter Faure, Principles of Isotope Geology, 2nd ed. (1986); and Robert Bowen, Isotopes in Earth Sciences (1988). Thomas Edvard Krogh

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