Isochron dating
Encyclopedia
Isochron dating is a common technique of radiometric dating
Radiometric dating
Radiometric dating is a technique used to date materials such as rocks, usually based on a comparison between the observed abundance of a naturally occurring radioactive isotope and its decay products, using known decay rates...

 and is applied to date certain events, such as crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

lization, metamorphism
Metamorphism
Metamorphism is the solid-state recrystallization of pre-existing rocks due to changes in physical and chemical conditions, primarily heat, pressure, and the introduction of chemically active fluids. Mineralogical, chemical and crystallographic changes can occur during this process...

, shock events, and differentiation of precursor melts, in the history of rocks
Rock (geology)
In geology, rock or stone is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic...

. Isochron dating can be further separated into mineral isochron dating and whole rock isochron dating; both techniques are applied frequently to date terrestrial and also extraterrestrial rocks (meteorite
Meteorite
A meteorite is a natural object originating in outer space that survives impact with the Earth's surface. Meteorites can be big or small. Most meteorites derive from small astronomical objects called meteoroids, but they are also sometimes produced by impacts of asteroids...

s). The advantage of isochron dating as compared to simple radiometric dating techniques is that no assumptions are needed about the initial amount of the daughter nuclide
Nuclide
A nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of protons Z, its number of neutrons N, and its nuclear energy state....

 in the radioactive decay
Radioactive decay
Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...

 sequence. Indeed the initial amount of the daughter product can be determined using isochron dating. This technique can be applied if the daughter element has at least one stable isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 other than the daughter isotope into which the parent nuclide decays.

Basis for method

All forms of isochron dating assume that the source of the rock or rocks contained unknown amounts of both radiogenic and non-radiogenic isotopes of the daughter element, along with some amount of the parent nuclide. Thus, at the moment of crystallization, the ratio of the concentration of the radiogenic isotope of the daughter element to that of the non-radiogenic isotope is some value independent of the concentration of the parent. As time goes on, some amount of the parent decays into the radiogenic isotope of the daughter, increasing the ratio of the concentration of the radiogenic isotope to that of the daughter. The greater the initial concentration of the parent, the greater the concentration of the radiogenic daughter isotope will be at some particular time. Thus, the ratio of the daughter to non-radiogenic isotope will become larger with time, while the ratio of parent to daughter will become smaller. For rocks that start out with a small concentration of the parent, the daughter/non-radiogenic ratio will not change quickly as compared to rocks starting with a large concentration of the parent.

Isochron plots

To perform dating, a rock is crushed to a fine powder and minerals are separated by various physical and magnetic means. Each mineral has different ratios between parent and daughter concentrations. For each mineral, the ratios are related by the following equation:
         (1)

where
is the initial concentration of the daughter isotope,
is the concentration of the non-radiogenic isotope of the daughter element (assumed constant),
is the initial concentration of the parent isotope, and
is the total amount of the parent isotope which has decayed by time .

The proof of (1) amounts to simple algebraic manipulation. It is useful in this form because it exhibits the relationship between quantities that actually exist at present. To wit, , and respectively correspond to the concentrations of parent, daughter and non-radiogenic isotopes found in the rock at the time of measurement.

The ratios (relative concentration of daughter and non-radiogenic isotopes) and (relative concentration of parent and non-radiogenic isotope) are measured by mass spectrometry
Mass spectrometry
Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...

 and plotted against each other in a three-isotope plot known as an isochron plot. Ratios are used instead of absolute concentrations because mass spectrometers usually measure the former rather than the latter. (See particularly the section on isotope ratio mass spectrometry.)

If all data points lie on a straight line, this line is called an isochron. The better the fit of the data points to a line, the more reliable the resulting age estimate. Since the ratio of the daughter and non-radiogenic isotopes is proportional to the ratio of the parent and non-radiogenic isotopes, the slope of the isochron gets steeper with time. The change in slope from initial conditions--assuming an initial isochron slope of zero (a horizontal isochron) at the point of intersection (intercept) of the isochron with the y-axis--to the current computed slope gives the age of the rock. The slope of the isochron, , represents the ratio of daughter to parent as used in standard radiometric dating
Radiometric dating
Radiometric dating is a technique used to date materials such as rocks, usually based on a comparison between the observed abundance of a naturally occurring radioactive isotope and its decay products, using known decay rates...

.

Whole rock isochron dating uses the same ideas but instead of different minerals obtained from one rock uses different types of rocks that are derived from a common reservoir; e.g. the same precursor melt. It is possible to date the differentiation of the precursor melt which then cooled and crystallized into the different types of rocks.

One of the best known isotopic systems for isochron dating is the rubidium-strontium
Rubidium-strontium dating
The rubidium-strontium dating method is a radiometric dating technique that geologists use to determine the age of rocks.Development of this process was aided by Fritz Strassmann, who later went on to discover nuclear fission with Otto Hahn and Lise Meitner....

 system. Other systems that are used for isochron dating include samarium-neodymium
Samarium-neodymium dating
Samarium-neodymium dating is useful for determining the age relationships of rocks and meteorites, based on decay of a long-lived samarium isotope to a radiogenic neodymium isotope. Nd isotope ratios are used to provide information on the source of igneous melts as well as to provide age data...

, and uranium-lead
Uranium-lead dating
Uranium-lead is one of the oldest and most refined of the radiometric dating schemes, with a routine age range of about 1 million years to over 4.5 billion years, and with routine precisions in the 0.1-1 percent range...

. Some isotopic systems based on short living extinct radionuclides such as 53Mn
Manganese
Manganese is a chemical element, designated by the symbol Mn. It has the atomic number 25. It is found as a free element in nature , and in many minerals...

, 26Al, 129I
Iodine
Iodine is a chemical element with the symbol I and atomic number 53. The name is pronounced , , or . The name is from the , meaning violet or purple, due to the color of elemental iodine vapor....

, 60Fe
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

 and others are used for isochron dating of events in the early history of the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

. However, methods using extinct radionuclides give only relative ages and have to be calibrated with radiometric dating techniques based on long living radionuclides like Pb-Pb-dating to give absolute ages.

Application

Isochron dating is useful in the determination of the age of igneous rock
Igneous rock
Igneous rock is one of the three main rock types, the others being sedimentary and metamorphic rock. Igneous rock is formed through the cooling and solidification of magma or lava...

s, which have their initial origin in the cooling of liquid magma
Magma
Magma is a mixture of molten rock, volatiles and solids that is found beneath the surface of the Earth, and is expected to exist on other terrestrial planets. Besides molten rock, magma may also contain suspended crystals and dissolved gas and sometimes also gas bubbles. Magma often collects in...

. It is also useful to determine the time of metamorphism, shock events (such as the consequence of an asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...

 impact) and other events depending of the behaviour of the particular isotopic systems under such events.

External links

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