Dating Rocks

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As far as we know, the first person to wonder "how old is this rock?" was William Smith (1769–1834), an engineer and surveyor working in the Bath district of western England. He recognized that the earth was being laid down in layers like pages in a book, with the oldest pages at the bottom.

Different methods of radiometric dating vary in the timescale over which they are accurate and the materials to which they can be applied.

Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) changed all that. It is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon.



No other element has played a larger role than carbon on our planet. Without carbon there would be NO LIFE!

Carbon has as many as 15 isotopes (an uneven number of protons and neutrons), but most are ephemeral, only lasting from a few nanoseconds to a few minutes. Electrons, especially Valence Electrons come and go, but an imbalance of protons and neutrons is serious stuff. The three that are "naturally occurring" are ¹²C, ¹³C, and ¹⁴C.
¹²C is the normal carbon atom with 12 protons, 12 neutrons, and 12 electrons. BUT ¹³C has an extra neutron, and ¹⁴C has two!



Although we can't predict when an individual radioactive atom will decay, the rate at which a large collection of radioactive material decays is predictable and measured according to the isotope's half-life.

A half-life is the length of time it takes for half of the material to decay. Carbon-14 has a half-life of 5,730 years, so if you had a big block of carbon-14, in 5,730 years, half of the atoms in your block will have decayed back into the original nitrogen-14. After another 5,730 years, a total of 75% will have decayed, and after another 5,730 years, 87.5% will have decayed, and so on.



The Earth's air contains carbon dioxide, and some of the carbon in the CO₂ molecules is carbon-14. When plants take in carbon dioxide to grow, the carbon-14 becomes trapped in their cells, and anything that eats the plants, also eats the carbon-14. Because of this, radioactive carbon-14 is in every single organism on the planet, including you, but mercifully at such small levels it doesn't harm you; in fact, in some ways, it's extremely convenient.

All living things consume carbon-14 their whole lives, but, when they die, no new carbon-14 enters the body, and the stockpile begins to slowly decay into nitrogen-14 which is trapped in solid parts of the organism. By using extremely sensitive equipment, scientists can determine the ratio between carbon-14 and nitrogen-14 in the remains and figure out how long ago the organism died. With a 75% carbon-14 to 25% nitrogen-14 ratio, we know about 2,850 years have passed, at 50%/50%, about 5,700 years have passed, and at 25%/75%, 11,400 years have passed, and so on. This is called radiocarbon dating, and you can use the same principle on numerous other radioactive elements, each with different half-lifes, a process called radiometric dating.

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en.wikipedia.org/wiki/Radiocarbon_dating

The method was developed in the late 1940s at the University of Chicago by Willard Libby. It is based on the fact that radiocarbon (¹⁴C) is constantly being created in the Earth's atmosphere by the interaction of cosmic rays with atmospheric nitrogen. The resulting ¹⁴C combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire ¹⁴C by eating the plants. When the animal or plant dies, it stops exchanging carbon with its environment, and thereafter the amount of ¹⁴C it contains begins to decrease as the ¹⁴C undergoes radioactive decay. Measuring the amount of ¹⁴C in a sample from a dead plant or animal, such as a piece of wood or a fragment of bone, provides information that can be used to calculate when the animal or plant died. The older a sample is, the less ¹⁴C there is to be detected, and because the half-life of 14C (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to approximately 50,000 years ago, although special preparation methods occasionally make accurate analysis of older samples possible.

Libby received the Nobel Prize in Chemistry for his work in 1960.

Research has been ongoing since the 1960s to determine what the proportion of ¹⁴C in the atmosphere has been over the past fifty thousand years.

The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age. Other corrections must be made to account for the proportion of 14C in different types of organisms (fractionation), and the varying levels of ¹⁴C throughout the biosphere (reservoir effects). Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the 1950s and 1960s. Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its ¹⁴C to decay below detectable levels, fossil fuels contain almost no ¹⁴C. As a result, beginning in the late 19th century, there was a noticeable drop in the proportion of ¹⁴C as the carbon dioxide generated from burning fossil fuels began to accumulate in the atmosphere. Conversely, nuclear testing increased the amount of ¹⁴C in the atmosphere, which reached a maximum in about 1965 of almost double the amount present in the atmosphere prior to nuclear testing.

Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying ¹⁴C atoms in a sample. More recently, accelerator mass spectrometry has become the method of choice; it counts all the ¹⁴C atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples (as small as individual plant seeds), and gives results much more quickly. The development of radiocarbon dating has had a profound impact on archaeology. In addition to permitting more accurate dating within archaeological sites than previous methods, it allows comparison of dates of events across great distances. Histories of archaeology often refer to its impact as the "radiocarbon revolution". Radiocarbon dating has allowed key transitions in prehistory to be dated, such as the end of the last ice age, and the beginning of the Neolithic and Bronze Age in different regions.

Now many more are available for cross-checking.

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en.wikipedia.org/wiki/Dendrochronology

Tree Ring Chronology

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Mike Baillie wrote Exodus to Arthur in 1999.I highly recommend it!

In the Introduction he wrote: - - - - - - -

"A tree-ring chronology is a year»by-year record of what trees thought of their growth conditions in the past. The lengths of the records are not restricted to the lifespans of the oldest trees. By overlapping the patterns of wide and narrow growth rings from living trees with the patterns of successively older and older timbers from historic buildings, archaeological sins and natural sources. really long tree-ring records can be produced.
The international tree-ring community now have such annual tree-ring records running back for thousands of years, from areas as diverse as Ireland, Germany. Fennoscandia, northern Russia, North and South America and Tasmania. Thus we can look at any year in the past several thousand years and see what trees, widely dispersed around the globe, thought of conditions.

It turns out that when we interrogate some of these records in this way we find some positively alarming evidence of extreme environmental events in the past which also 'seem' to he recorded in human history.

I use the word seem because much of human history is nor very well dated in comparison to the tree-ring records which are precisely dated to exact calendar years. So we know the exact dates of the environmental downturns and these fall close to the dating estimates cf human trauma deduced by ancient historians and archaeologists, Because of the way these extreme events showed up, with tentative links to volcanic acid in Greenland, the initial hypothesis about their cause was that they were related to the environmental effects of large explosive volcanic eruptions."

(I'm sneaking in a plug from Good Reads)
Brian Kitchen - Feb 07, 2018 - Brian Kitchen rated *****

A very interesting book which I found fascinating. Written by Professor Mike Baillie nearly 20 years ago, it still has relevance today, putting forward the plausible theory that Earth has had many near misses with Comets over the centuries.
He expands on his theory to suggest that some of the catastrophes that happened in ancient and not so ancient times, may have been caused by cometary debris striking the Earth, the Tunguska event being one of many.
Having an interest in the history of Roman Britain, the theory he puts forward that there was a catastrophic event in 540AD which plunged Britain into the Dark Ages, gave me a more plausible explanation for how this occurred, than the more normally accepted ones. I had always wondered why there are very few remains of Roman buildings in Britain, compared say to continental Europe. A near miss with a comet, resulting in a bombardment of fiery debris which would potentially cause fire damage, especially when one considers that Britain was still heavily wooded at the time, gave me an answer I'd long sought.
Well worth reading and one that I can recommend to anyone seeking answers to some of the mysteries of ancient times.

First a little about trees. Knowing about what happens to trees now can provide insight to what happened to trees back then.
In general tree trunks and limbs consist of:



pith: the central spongy tissue of the stem of a vascular plant.
medullary ray: vertical band or plate of unspecialized tissue that radiate between the pith at the core of the trunk through the heartwood and sapwood to the bark. Rays are present in all woods and are used for transferring sap from the cambium to the center of the tree.
Depending on the species of wood, some rays may be a single cell wide and 6 to 8 cells high; while others may be 6 to 8 cells wide and 20 to 30 cells high, seldom in a straight line.
heartwood: The older central wood of trees and woody plants. After some period of time the cells in the center of the tree cease to function (other than to provide mechanical support to the tree) and die. When this happens alien materials are often trapped in the cell cavities and plug passages. Heartwood usually becomes much dryer, darker, and harder than the younger sapwood.
vessels: specialized conducting cells much larger in diameter than other wood cell types.
sapwood: the living outer portion of the tree. The newly formed outer wood layers located just inside the vascular cambium of a tree trunk that is active in the conduction of water and nutrients. Each annual layer produces a two part series:
early wood: The light colored part of the wood in a growth ring of a tree that is produced earlier in the growing season. The cells of early wood are larger and have thinner walls than those produced later in the growing season.
late wood: The dark colored part of the wood in a growth ring of a tree that is produced later in the growing season. The cells of late wood are smaller and have darker thicker cell walls than those produced earlier in the season.
Within an annual growth ring the change of early wood to late wood is gradual, but each new layer of early wood from the next growing season makes an obvious contrast with the late wood from the year before it.
cambium: the layer of actively dividing cells between xylem (fluid-conducting) and phloem (food-conducting) tissues that are responsible for the secondary growth resulting in an increase in thickness. As the cambium grows, it generates two types of wood cells:
1.Wood is mostly longitudinal cells rectangular in cross section, each about a hundred times longer than its width. In softwoods they may exceed 7mm. In hardwoods they seldom exceed 1.5mm. These long narrow cells align themselves with the axis of the trunk, limb, or root and give wood its grain. Some spiral around the tree as they grow, others remain fairly straight.
2. The cambium also produces a smaller number of ray cells that line up in rays extending out from the pith, perpendicular to the axis.
bark: a combination of cork (cambium) and old dead phloem.

Softwoods have the same rectangular cross-sectioned water bearing cell type throughout, but different cell sizes.
A good growing season results in an increase in the percent of early wood.
Examples: Cedar, Fir, Larch, Pine, Redwood, Yew.

Hardwoods contain vessels, softwoods do not. There are two types of hardwood vessels:
1. Diffuse-porous Hardwoods produce medium to small vessels throughout the year, but late wood is mostly fibers:
Examples: Alder, Basswood, Beech, Sugar Maple, Poplar, and Sycamore.

2. Ring-porous Hardwoods produce large thin wall vessels that permit more-rapid water conduction in early wood, that transitions to smaller vessels and fibers in late wood as the year progresses. A good growing season results in the same amount of early wood vessels but an increase in the amount of late wood fibers.
Examples: Ash, Elm, Hackberry, Hickory, Oak, and Sassafras.



Many of these features can be observed in petrified wood, as can the following mishaps.

Dead wood in WET conditions deteriorate by acid, bacteria, fungi and insect action.

In DRY conditions they lose water, shrink, twist, and crack in interesting ways.
It can be abraded, splintered or shattered by tumbling, burnt by fire, or struck by lightning.

The rate at which moisture moves in drying wood depends on the relative humidity of the surrounding air, the steepness of the moisture gradient, and the temperature of the wood.

The lower the relative humidity, the greater the capillary flow.

Low relative humidity also stimulates diffusion by lowering the moisture content at the surface, steepening the moisture gradient and increasing the diffusion rate.

If the humidity is very low excessive shrinkage occurs resulting in end and surface checking.

The greater the temperature of the wood, the faster moisture will move from the wetter interior to the drier surface.

If the temperature is too high cells rip apart and internal honeycomb breakage occurs.


In General, drying induces shrinkage stresses because of differences in internal, external, upper, lower, radial, tangential, and longitudinal shrinkage rates. Stresses in the differential shrinkage between the outer part of a tree (the shell) and the interior part (the core) produces many structural defects. Air and sunshine causes the fibers in the shell to dry first and begin shrinking, but the core has not yet begun to shrink. The damp core prevents the shell from total shrinking, holding the shell cells into radial, longitudinal, and tangential tension and the core cells into compression.

If the shell dries too rapidly, it is stressed beyond its elastic limit and dries in a stretched condition without attaining full shrinkage, forcing surface cracks or checks.
As drying continues the core begins to dry and attempts to shrink. However, the shell is now held in an expanded condition that prevents normal core shrinkage. The stresses reverse as the core goes into tension and the shell into compression. These internal tension stresses cause internal ruptures called honeycomb.

Specifically, heartwood has plugged up passageways and the least moisture, so it shrinks and cracks the least. Sapwood has more open passageways and moisture content, so it generally dries faster, shrinks and twists the most, checks and cracks on the surface, and honeycombs internally. Early wood has the most moisture and suffers the most destruction and separation. As tangential stresses develop long splits usually develop along the rays.

Petrifying:

phys.org/news2801.html
Artificial petrified wood has been produced in a Washington laboratory. In the process small cubes of pine are soaked in an acid bath for two days, then in a silica solution for another two. The product is then cooked at 1400 ̊C in an argon atmosphere for two hours. The result was silicon carbide ceramic which preserved the intricate cell structure of the wood.

www.sciencedirect.com/science/article/pii/S0037073804001940
Experimental results in a hot spring in Japan show that samples of alder wood were silicified to about 40% by weight over a period of 7 years. They concluded that silicification under suitable temperature and water saturation conditions might take place over periods of tens to hundreds of years. Here is the abstract of the article, published in "Sedimentary Geology", a peer-reviewed scientific journal.

science.howstuffworks.com/environmental/earth/geology/petrified-wood-info.htm
Petrified Wood, wood that has been fossilized by being turned into stone. Petrifaction is a natural process that may form fossils from the solid remains of any plant or animal. However, it more commonly happens to wood than to animals and non-woody plants. The process occurs when the substance soaks, over a long period of time, in water containing a mineral (or minerals). Gradually, the mineral either fills every pore and cavity of the organic matter, or the mineral-containing water dissolves the original organic material and replaces it with mineral matter. Eventually, the mineral forms a perfect copy of the original substance, including cell structure and fibers. The replacement mineral is usually a variety of quartz, ordinarily of the chalcedony type. Sometimes it is opal, calcite (calcium carbonate), or carnotite, a source of uranium.

Petrified wood usually is very hard. It may be beautifully colored by chemical impurities such as iron and copper. Cut and polished petrified wood is used for jewelry, paperweights, and lamp bases.

The rate of petrifaction is not exactly known. In some cases it may be fairly rapid. For example, mine timbers have been partly petrified after a few years' exposure to mineral-laden water. Most petrified wood was formed long ago. For instance, stone logs in Petrified Forest National Park, Arizona, are of the Triassic Period and more than 160,000,000 years old.

Diagenesis is dependent on the environment. Trees buried in limestone or dolomite turn to coal. Siliceous soils produce agate.

Volcanic ash contains many minerals. The colors observed in petrified wood may be caused by the following elements:

Carbon - black
Cobalt - green/blue
Chromium - green/blue
Copper - green/blue
Iron oxides - red, brown, and yellow
Manganese - pink/orange
Manganese oxides - blackish/yellow
Vanadium - green
Uranium - yellow

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Back to Mike - >Tree Ting Tool >

This intriguing challenge to traditional views of history, provides explanations for many of the myths and legends that continue to haunt humankind. In particular, it argues that, in the last five millennia, the Earth has undergone several catastrophic encounters with comets and their debris - and that mythology has preserved these events better than so-called "factual" records.

How do we know? The TREES TOLD US SO!

Did you know when a comet pelted Rome with hot rocks in 207 BC the Romans sent for the goddess Cybele to protect them? Who was Cybele? She was a meteorite from a previous fall! The trees recorded it all.

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The Uranium-Lead (U-Pb) System



Radioactive uranium decays to stable lead. The U-Pb system is the most common method of geochronology for one reason:



zircons. These common igneous minerals nearly always contain enough U to be dated, and their extreme durability allows them to survive metamorphism and erosion, so they are often found in metamorphic and sedimentary rocks as well. It’s no exaggeration to say we’d know far less about geology as a whole it wasn’t for these little heroes of geochronology. Many other minerals, notably uraninite and monazite, may also be dated with the U-Pb method. Thorium, a radioactive element common in many rare Earth element deposits, also decays to lead, enabling thorium minerals to be dated via similar methods.

Uranium–lead dating, abbreviated U–Pb dating, is one of the oldest and most refined of the radiometric dating schemes. It can be used to date rocks that formed and crystallised from about 1 million years to over 4.5 billion years ago with routine precisions in the 0.1–1 percent range.

The method is usually applied to zircon. This mineral incorporates uranium and thorium atoms into its crystal structure, but strongly rejects lead when forming. As a result, newly-formed zircon deposits will contain no lead, meaning that any lead found in the mineral is radiogenic. Since the exact rate at which uranium decays into lead is known, the current ratio of lead to uranium in a sample of the mineral can be used to reliably determine its age.

The method relies on two separate decay chains:
1. the uranium series from 238U to 206Pb, with a half-life of 4.47 billion years, and . . .
2. the actinium series from 235U to 207Pb, with a half-life of 710 million years.

en.wikipedia.org/wiki/Hadean_zircon
en.wikipedia.org/wiki/Zircon

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en.wikipedia.org/wiki/Rhenium%E2%80%93osmium_dating

The Rhenium-Osmium (Re-Os) System

Although Re is one of the rarest elements on Earth, its decay to Os makes it particularly useful for dating ore deposits such as GOLD and sulfides. Extremely trace amounts of Re are often present in sulfide minerals, such as pyrite and molybdenite, allowing these minerals to be directly dated. Since sulfides are the main ore minerals in most base metal deposits, this technique has found wide application, particularly to porphyry deposits.

en.wikipedia.org/wiki/Isochron_dating


An isochron plot of the radiogenic daughter isotope (D*) against the parent isotope (P), all normalized to a stable isotope of the daughter element (Dref). It demonstrates the isotopic evolution as the sample ages from t0 to t1 to t2.
Isochron dating is a common technique of radiometric dating and is applied to date certain events, such as crystallization, metamorphism, shock events, and differentiation of precursor melts, in the history of rocks. 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 (meteorites). 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 in the radioactive decay 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 other than the daughter isotope into which the parent nuclide decays.[1][2][3]

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en.wikipedia.org/wiki/K%E2%80%93Ar_dating

The Potassium-Argon/Argon-Argon (K-Ar/Ar-Ar) System

While K is an extremely common element in rock-forming minerals, it is also weakly radioactive, and its decay to Ar allows minerals such as potassium feldspar and sericite to be dated. These common gangue minerals are formed by potassic and/or phyllic alteration in many deposits, and their ages should, in theory, reflect the age of the deposit. Argon, however, being a gas, may escape after its formation, and thus Ar dates may reflect geological events long after ore deposition. Great care must be taken when interpreting K-Ar and Ar-Ar data.

Half life of potassium-40,is approximately 1.25 billion years.

what will be the fraction of radioactivity left after 5 billion years?

Chemistry Nuclear Chemistry Nuclear Half-Life Calculations

Answer - There are 4 half-lives, so after five billion years, there will be 1/16th P0. left.

The long half-life of ⁴⁰K allows the method to be used to calculate the absolute age of samples older than a few thousand years.
The quickly cooled lavas that make nearly ideal samples for K–Ar dating also preserve a record of the direction and intensity of the local magnetic field as the sample cooled past the Curie temperature of iron.

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en.wikipedia.org/wiki/Rubidium%E2%80%93strontium_dating

The rubidium-strontium dating method is a radiometric dating technique used by scientists to determine the age of rocks and minerals from the quantities they contain of specific isotopes of rubidium (87Rb) and strontium (87Sr, 86Sr).

Development of this process was aided by German chemists Otto Hahn and Fritz Strassmann, who later went on to discover nuclear fission in December 1938.

The utility of the rubidium–strontium isotope system results from the fact that 87Rb (one of two naturally occurring isotopes of rubidium) decays to 87Sr with a half-life of 49.23 billion years. In addition, Rb is a highly incompatible element that, during partial melting of the mantle, prefers to join the magmatic melt rather than remain in mantle minerals. As a result, Rb is enriched in crustal rocks. The radiogenic daughter, 87Sr, is produced in this decay process and was produced in rounds of stellar nucleosynthesis predating the formation of the Solar System.

Different minerals in a given geologic setting can acquire distinctly different ratios of radiogenic strontium-87 to naturally occurring strontium-86 (87Sr/86Sr) through time; and their age can be calculated by measuring the 87Sr/86Sr in a mass spectrometer, knowing the amount of 87Sr present when the rock or mineral formed, and calculating the amount of 87Rb from a measurement of the Rb present and knowledge of the 85Rb/87Rb weight ratio.

If these minerals crystallized from the same silicic melt, each mineral had the same initial 87Sr/86Sr as the parent melt. However, because Rb substitutes for K in minerals and these minerals have different K/Ca ratios, the minerals will have had different Rb/Sr ratios.

During fractional crystallization, Sr tends to become concentrated in plagioclase, leaving Rb in the liquid phase. Hence, the Rb/Sr ratio in residual magma may increase over time, resulting in rocks with increasing Rb/Sr ratios with increasing differentiation. Highest ratios (10 or higher) occur in pegmatites.

Typically, Rb/Sr increases in the order plagioclase, hornblende, K-feldspar, biotite, muscovite. Therefore, given sufficient time for significant production (ingrowth) of radiogenic 87Sr, measured 87Sr/86Sr values will be different in the minerals, increasing in the same order.

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Radiometric dating

From Wikipedia, the free encyclopedia

Radiometric dating, radioactive dating or radioisotope dating is a technique which is used to date materials such as rocks or carbon, in which trace radioactive impurities were selectively incorporated when they were formed. The method compares the abundance of a naturally occurring radioactive isotope within the material to the abundance of its decay products, which form at a known constant rate of decay.[1] The use of radiometric dating was first published in 1907 by Bertram Boltwood[2] and is now the principal source of information about the absolute age of rocks and other geological features, including the age of fossilized life forms or the age of the Earth itself, and can also be used to date a wide range of natural and man-made materials.

Together with stratigraphic principles, radiometric dating methods are used in geochronology to establish the geologic time scale.[3] Among the best-known techniques are radiocarbon dating, potassium–argon dating and uranium–lead dating. By allowing the establishment of geological timescales, it provides a significant source of information about the ages of fossils and the deduced rates of evolutionary change. Radiometric dating is also used to date archaeological materials, including ancient artifacts.

Different methods of radiometric dating vary in the timescale over which they are accurate and the materials to which they can be applied.
Contents

1 Fundamentals
1.1 Radioactive decay
1.2 Decay constant determination
1.3 Accuracy of radiometric dating
1.4 Closure temperature
1.5 The age equation
2 Modern dating methods
2.1 Uranium–lead dating method
2.2 Samarium–neodymium dating method
2.3 Potassium–argon dating method
2.4 Rubidium–strontium dating method
2.5 Uranium–thorium dating method
2.6 Radiocarbon dating method
2.7 Fission track dating method
2.8 Chlorine-36 dating method
2.9 Luminescence dating methods
2.10 Other methods
3 Dating with decay products of short-lived extinct radionuclides
3.1 The 129I – 129Xe chronometer
3.2 The 26Al – 26Mg chronometer
4 See also
5 References
6 Further reading

Fundamentals
Radioactive decay
Example of a radioactive decay chain from lead-212 (212Pb) to lead-208 (208Pb) . Each parent nuclide spontaneously decays into a daughter nuclide (the decay product) via an α decay or a β− decay. The final decay product, lead-208 (208Pb), is stable and can no longer undergo spontaneous radioactive decay.

All ordinary matter is made up of combinations of chemical elements, each with its own atomic number, indicating the number of protons in the atomic nucleus. Additionally, elements may exist in different isotopes, with each isotope of an element differing in the number of neutrons in the nucleus. A particular isotope of a particular element is called a nuclide. Some nuclides are inherently unstable. That is, at some point in time, an atom of such a nuclide will undergo radioactive decay and spontaneously transform into a different nuclide. This transformation may be accomplished in a number of different ways, including alpha decay (emission of alpha particles) and beta decay (electron emission, positron emission, or electron capture). Another possibility is spontaneous fission into two or more nuclides.

While the moment in time at which a particular nucleus decays is unpredictable, a collection of atoms of a radioactive nuclide decays exponentially at a rate described by a parameter known as the half-life, usually given in units of years when discussing dating techniques. After one half-life has elapsed, one half of the atoms of the nuclide in question will have decayed into a "daughter" nuclide or decay product. In many cases, the daughter nuclide itself is radioactive, resulting in a decay chain, eventually ending with the formation of a stable (nonradioactive) daughter nuclide; each step in such a chain is characterized by a distinct half-life. In these cases, usually the half-life of interest in radiometric dating is the longest one in the chain, which is the rate-limiting factor in the ultimate transformation of the radioactive nuclide into its stable daughter. Isotopic systems that have been exploited for radiometric dating have half-lives ranging from only about 10 years (e.g., tritium) to over 100 billion years (e.g., samarium-147).[4]

For most radioactive nuclides, the half-life depends solely on nuclear properties and is essentially constant.[5] This is known because decay constants measured by different techniques give consistent values within analytical errors and the ages of the same materials are consistent from one method to another. It is not affected by external factors such as temperature, pressure, chemical environment, or presence of a magnetic or electric field.[6][7][8] The only exceptions are nuclides that decay by the process of electron capture, such as beryllium-7, strontium-85, and zirconium-89, whose decay rate may be affected by local electron density. For all other nuclides, the proportion of the original nuclide to its decay products changes in a predictable way as the original nuclide decays over time.

This predictability allows the relative abundances of related nuclides to be used as a clock to measure the time from the incorporation of the original nuclides into a material to the present. Nature has conveniently provided us with radioactive nuclides that have half-lives which range from considerably longer than the age of the universe, to less than a zeptosecond. This allows one to measure a very wide range of ages. Isotopes with very long half-lives are called "stable isotopes," and isotopes with very short half-lives are known as "extinct isotopes."
Decay constant determination
See also: Radioactive decay law

The radioactive decay constant, the probability that an atom will decay per year, is the solid foundation of the common measurement of radioactivity. The accuracy and precision of the determination of an age (and a nuclide's half-life) depends on the accuracy and precision of the decay constant measurement.[9] The in-growth method is one way of measuring the decay constant of a system, which involves accumulating daughter nuclides. Unfortunately for nuclides with high decay constants (which are useful for dating very old samples), long periods of time (decades) are required to accumulate enough decay products in a single sample to accurately measure them. A faster method involves using particle counters to determine alpha, beta or gamma activity, and then dividing that by the number of radioactive nuclides. However, it is challenging and expensive to accurately determine the number of radioactive nuclides. Alternatively, decay constants can be determined by comparing isotope data for rocks of known age. This method requires at least one of the isotope systems to be very precisely calibrated, such as the Pb-Pb system.
Accuracy of radiometric dating
Thermal ionization mass spectrometer used in radiometric dating.

The basic equation of radiometric dating requires that neither the parent nuclide nor the daughter product can enter or leave the material after its formation. The possible confounding effects of contamination of parent and daughter isotopes have to be considered, as do the effects of any loss or gain of such isotopes since the sample was created. It is therefore essential to have as much information as possible about the material being dated and to check for possible signs of alteration.[10] Precision is enhanced if measurements are taken on multiple samples from different locations of the rock body. Alternatively, if several different minerals can be dated from the same sample and are assumed to be formed by the same event and were in equilibrium with the reservoir when they formed, they should form an isochron. This can reduce the problem of contamination. In uranium–lead dating, the concordia diagram is used which also decreases the problem of nuclide loss. Finally, correlation between different isotopic dating methods may be required to confirm the age of a sample. For example, the age of the Amitsoq gneisses from western Greenland was determined to be 3.60 ± 0.05 Ga (billion years ago) using uranium–lead dating and 3.56 ± 0.10 Ga (billion years ago) using lead–lead dating, results that are consistent with each other.[11]: 142–143 

Accurate radiometric dating generally requires that the parent has a long enough half-life that it will be present in significant amounts at the time of measurement (except as described below under "Dating with short-lived extinct radionuclides"), the half-life of the parent is accurately known, and enough of the daughter product is produced to be accurately measured and distinguished from the initial amount of the daughter present in the material. The procedures used to isolate and analyze the parent and daughter nuclides must be precise and accurate. This normally involves isotope-ratio mass spectrometry.[12]

The precision of a dating method depends in part on the half-life of the radioactive isotope involved. For instance, carbon-14 has a half-life of 5,730 years. After an organism has been dead for 60,000 years, so little carbon-14 is left that accurate dating cannot be established. On the other hand, the concentration of carbon-14 falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades.[13]
Closure temperature
Main article: Closure temperature

The closure temperature or blocking temperature represents the temperature below which the mineral is a closed system for the studied isotopes. If a material that selectively rejects the daughter nuclide is heated above this temperature, any daughter nuclides that have been accumulated over time will be lost through diffusion, resetting the isotopic "clock" to zero. As the mineral cools, the crystal structure begins to form and diffusion of isotopes is less easy. At a certain temperature, the crystal structure has formed sufficiently to prevent diffusion of isotopes. Thus an igneous or metamorphic rock or melt, which is slowly cooling, does not begin to exhibit measurable radioactive decay until it cools below the closure temperature. The age that can be calculated by radiometric dating is thus the time at which the rock or mineral cooled to closure temperature.[14][15] This temperature varies for every mineral and isotopic system, so a system can be closed for one mineral but open for another. Dating of different minerals and/or isotope systems (with differing closure temperatures) within the same rock can therefore enable the tracking of the thermal history of the rock in question with time, and thus the history of metamorphic events may become known in detail. These temperatures are experimentally determined in the lab by artificially resetting sample minerals using a high-temperature furnace. This field is known as thermochronology or thermochronometry.
The age equation
Lu-Hf isochrons plotted of meteorite samples. The age is calculated from the slope of the isochron (line) and the original composition from the intercept of the isochron with the y-axis.

The mathematical expression that relates radioactive decay to geologic time is[14][16]
D* = D0 + N(t) (eλt − 1)

where

t is age of the sample,
D* is number of atoms of the radiogenic daughter isotope in the sample,
D0 is number of atoms of the daughter isotope in the original or initial composition,
N(t) is number of atoms of the parent isotope in the sample at time t (the present), given by N(t) = N0e−λt, and
λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the parent isotope[17] times the natural logarithm of 2.

The equation is most conveniently expressed in terms of the measured quantity N(t) rather than the constant initial value No.

To calculate the age, it is assumed that the system is closed (neither parent nor daughter isotopes have been lost from system), D0 must be either negligible or can be accurately estimated, λ is known to a high precision, and one has accurate and precise measurements of D* and N(t).

The above equation makes use of information on the composition of parent and daughter isotopes at the time the material being tested cooled below its closure temperature. This is well-established for most isotopic systems.[15][18] However, construction of an isochron does not require information on the original compositions, using merely the present ratios of the parent and daughter isotopes to a standard isotope. An isochron plot is used to solve the age equation graphically and calculate the age of the sample and the original composition.
Modern dating methods

Radiometric dating has been carried out since 1905 when it was invented by Ernest Rutherford as a method by which one might determine the age of the Earth. In the century since then the techniques have been greatly improved and expanded.[17] Dating can now be performed on samples as small as a nanogram using a mass spectrometer. The mass spectrometer was invented in the 1940s and began to be used in radiometric dating in the 1950s. It operates by generating a beam of ionized atoms from the sample under test. The ions then travel through a magnetic field, which diverts them into different sampling sensors, known as "Faraday cups", depending on their mass and level of ionization. On impact in the cups, the ions set up a very weak current that can be measured to determine the rate of impacts and the relative concentrations of different atoms in the beams.
Uranium–lead dating method
Main article: Uranium–lead dating
A concordia diagram as used in uranium–lead dating, with data from the Pfunze Belt, Zimbabwe.[19] All the samples show loss of lead isotopes, but the intercept of the errorchron (straight line through the sample points) and the concordia (curve) shows the correct age of the rock.[15]

Uranium–lead radiometric dating involves using uranium-235 or uranium-238 to date a substance's absolute age. This scheme has been refined to the point that the error margin in dates of rocks can be as low as less than two million years in two-and-a-half billion years.[20][21] An error margin of 2–5% has been achieved on younger Mesozoic rocks.[22]

Uranium–lead dating is often performed on the mineral zircon (ZrSiO4), though it can be used on other materials, such as baddeleyite and monazite (see: monazite geochronology).[23] Zircon and baddeleyite incorporate uranium atoms into their crystalline structure as substitutes for zirconium, but strongly reject lead. Zircon has a very high closure temperature, is resistant to mechanical weathering and is very chemically inert. Zircon also forms multiple crystal layers during metamorphic events, which each may record an isotopic age of the event. In situ micro-beam analysis can be achieved via laser ICP-MS or SIMS techniques.[24]

One of its great advantages is that any sample provides two clocks, one based on uranium-235's decay to lead-207 with a half-life of about 700 million years, and one based on uranium-238's decay to lead-206 with a half-life of about 4.5 billion years, providing a built-in crosscheck that allows accurate determination of the age of the sample even if some of the lead has been lost. This can be seen in the concordia diagram, where the samples plot along an errorchron (straight line) which intersects the concordia curve at the age of the sample.
Samarium–neodymium dating method
Main article: Samarium–neodymium dating

This involves the alpha decay of 147Sm to 143Nd with a half-life of 1.06 x 1011 years. Accuracy levels of within twenty million years in ages of two-and-a-half billion years are achievable.[25]
Potassium–argon dating method
Main article: Potassium–argon dating

This involves electron capture or positron decay of potassium-40 to argon-40. Potassium-40 has a half-life of 1.3 billion years, so this method is applicable to the oldest rocks. Radioactive potassium-40 is common in micas, feldspars, and hornblendes, though the closure temperature is fairly low in these materials, about 350 °C (mica) to 500 °C (hornblende).
Rubidium–strontium dating method
Main article: Rubidium–strontium dating

This is based on the beta decay of rubidium-87 to strontium-87, with a half-life of 50 billion years. This scheme is used to date old igneous and metamorphic rocks, and has also been used to date lunar samples. Closure temperatures are so high that they are not a concern. Rubidium-strontium dating is not as precise as the uranium-lead method, with errors of 30 to 50 million years for a 3-billion-year-old sample. Application of in situ analysis (Laser-Ablation ICP-MS) within single mineral grains in faults have shown that the Rb-Sr method can be used to decipher episodes of fault movement.[26]
Uranium–thorium dating method
Main article: Uranium–thorium dating

A relatively short-range dating technique is based on the decay of uranium-234 into thorium-230, a substance with a half-life of about 80,000 years. It is accompanied by a sister process, in which uranium-235 decays into protactinium-231, which has a half-life of 32,760 years.

While uranium is water-soluble, thorium and protactinium are not, and so they are selectively precipitated into ocean-floor sediments, from which their ratios are measured. The scheme has a range of several hundred thousand years. A related method is ionium–thorium dating, which measures the ratio of ionium (thorium-230) to thorium-232 in ocean sediment.
Radiocarbon dating method
Main article: Radiocarbon dating
Ale's Stones at Kåseberga, around ten kilometres south east of Ystad, Sweden were dated at 56 CE using the carbon-14 method on organic material found at the site.[27]

Radiocarbon dating is also simply called carbon-14 dating. Carbon-14 is a radioactive isotope of carbon, with a half-life of 5,730 years[28][29] (which is very short compared with the above isotopes), and decays into nitrogen.[30] In other radiometric dating methods, the heavy parent isotopes were produced by nucleosynthesis in supernovas, meaning that any parent isotope with a short half-life should be extinct by now. Carbon-14, though, is continuously created through collisions of neutrons generated by cosmic rays with nitrogen in the upper atmosphere and thus remains at a near-constant level on Earth. The carbon-14 ends up as a trace component in atmospheric carbon dioxide (CO2).

A carbon-based life form acquires carbon during its lifetime. Plants acquire it through photosynthesis, and animals acquire it from consumption of plants and other animals. When an organism dies, it ceases to take in new carbon-14, and the existing isotope decays with a characteristic half-life (5730 years). The proportion of carbon-14 left when the remains of the organism are examined provides an indication of the time elapsed since its death. This makes carbon-14 an ideal dating method to date the age of bones or the remains of an organism. The carbon-14 dating limit lies around 58,000 to 62,000 years.[31]

The rate of creation of carbon-14 appears to be roughly constant, as cross-checks of carbon-14 dating with other dating methods show it gives consistent results. However, local eruptions of volcanoes or other events that give off large amounts of carbon dioxide can reduce local concentrations of carbon-14 and give inaccurate dates. The releases of carbon dioxide into the biosphere as a consequence of industrialization have also depressed the proportion of carbon-14 by a few percent; conversely, the amount of carbon-14 was increased by above-ground nuclear bomb tests that were conducted into the early 1960s. Also, an increase in the solar wind or the Earth's magnetic field above the current value would depress the amount of carbon-14 created in the atmosphere.
Fission track dating method
Main article: fission track dating
Apatite crystals are widely used in fission track dating.

This involves inspection of a polished slice of a material to determine the density of "track" markings left in it by the spontaneous fission of uranium-238 impurities. The uranium content of the sample has to be known, but that can be determined by placing a plastic film over the polished slice of the material, and bombarding it with slow neutrons. This causes induced fission of 235U, as opposed to the spontaneous fission of 238U. The fission tracks produced by this process are recorded in the plastic film. The uranium content of the material can then be calculated from the number of tracks and the neutron flux.

This scheme has application over a wide range of geologic dates. For dates up to a few million years micas, tektites (glass fragments from volcanic eruptions), and meteorites are best used. Older materials can be dated using zircon, apatite, titanite, epidote and garnet which have a variable amount of uranium content.[32] Because the fission tracks are healed by temperatures over about 200 °C the technique has limitations as well as benefits. The technique has potential applications for detailing the thermal history of a deposit.
Chlorine-36 dating method

Large amounts of otherwise rare 36Cl (half-life ~300ky) were produced by irradiation of seawater during atmospheric detonations of nuclear weapons between 1952 and 1958. The residence time of 36Cl in the atmosphere is about 1 week. Thus, as an event marker of 1950s water in soil and ground water, 36Cl is also useful for dating waters less than 50 years before the present. 36Cl has seen use in other areas of the geological sciences, including dating ice and sediments.
Luminescence dating methods
Main article: Luminescence dating

Luminescence dating methods are not radiometric dating methods in that they do not rely on abundances of isotopes to calculate age. Instead, they are a consequence of background radiation on certain minerals. Over time, ionizing radiation is absorbed by mineral grains in sediments and archaeological materials such as quartz and potassium feldspar. The radiation causes charge to remain within the grains in structurally unstable "electron traps". Exposure to sunlight or heat releases these charges, effectively "bleaching" the sample and resetting the clock to zero. The trapped charge accumulates over time at a rate determined by the amount of background radiation at the location where the sample was buried. Stimulating these mineral grains using either light (optically stimulated luminescence or infrared stimulated luminescence dating) or heat (thermoluminescence dating) causes a luminescence signal to be emitted as the stored unstable electron energy is released, the intensity of which varies depending on the amount of radiation absorbed during burial and specific properties of the mineral.

These methods can be used to date the age of a sediment layer, as layers deposited on top would prevent the grains from being "bleached" and reset by sunlight. Pottery shards can be dated to the last time they experienced significant heat, generally when they were fired in a kiln.
Other methods

Other methods include:

Argon–argon (Ar–Ar)
Iodine–xenon (I–Xe)
Lanthanum–barium (La–Ba)
Lead–lead (Pb–Pb)
Lutetium–hafnium (Lu–Hf)
Hafnium–tungsten dating (Hf-W)
Potassium–calcium (K–Ca)
Rhenium–osmium (Re–Os)
Uranium–uranium (U–U)
Krypton–krypton (Kr–Kr)
Beryllium (10Be–9Be)[33]

Dating with decay products of short-lived extinct radionuclides

Absolute radiometric dating requires a measurable fraction of parent nucleus to remain in the sample rock. For rocks dating back to the beginning of the solar system, this requires extremely long-lived parent isotopes, making measurement of such rocks' exact ages imprecise. To be able to distinguish the relative ages of rocks from such old material, and to get a better time resolution than that available from long-lived isotopes, short-lived isotopes that are no longer present in the rock can be used.[34]

At the beginning of the solar system, there were several relatively short-lived radionuclides like 26Al, 60Fe, 53Mn, and 129I present within the solar nebula. These radionuclides—possibly produced by the explosion of a supernova—are extinct today, but their decay products can be detected in very old material, such as that which constitutes meteorites. By measuring the decay products of extinct radionuclides with a mass spectrometer and using isochronplots, it is possible to determine relative ages of different events in the early history of the solar system. Dating methods based on extinct radionuclides can also be calibrated with the U-Pb method to give absolute ages. Thus both the approximate age and a high time resolution can be obtained. Generally a shorter half-life leads to a higher time resolution at the expense of timescale.
The 129I – 129Xe chronometer
See also: Iodine-129 § Meteorite age dating

129
I
beta-decays to 129
Xe
with a half-life of 16 million years. The iodine-xenon chronometer[35] is an isochron technique. Samples are exposed to neutrons in a nuclear reactor. This converts the only stable isotope of iodine (127
I
) into 128
Xe
via neutron capture followed by beta decay (of 128
I
). After irradiation, samples are heated in a series of steps and the xenon isotopic signature of the gas evolved in each step is analysed. When a consistent 129
Xe
/128
Xe
ratio is observed across several consecutive temperature steps, it can be interpreted as corresponding to a time at which the sample stopped losing xenon.

Samples of a meteorite called Shallowater are usually included in the irradiation to monitor the conversion efficiency from 127
I
to 128
Xe
. The difference between the measured 129
Xe
/128
Xe
ratios of the sample and Shallowater then corresponds to the different ratios of 129
I
/127
I
when they each stopped losing xenon. This in turn corresponds to a difference in age of closure in the early solar system.
The 26Al – 26Mg chronometer

Another example of short-lived extinct radionuclide dating is the 26
Al
– 26
Mg
chronometer, which can be used to estimate the relative ages of chondrules. 26
Al
decays to 26
Mg
with a half-life of 720 000 years. The dating is simply a question of finding the deviation from the natural abundance of 26
Mg
(the product of 26
Al
decay) in comparison with the ratio of the stable isotopes 27
Al
/24
Mg
.

The excess of 26
Mg
(often designated 26
Mg
*) is found by comparing the 26
Mg
/27
Mg
ratio to that of other Solar System materials.[36]

The 26
Al
– 26
Mg
chronometer gives an estimate of the time period for formation of primitive meteorites of only a few million years (1.4 million years for Chondrule formation).[37]