Potassium–argon dating , abbreviated K–Ar dating , is a radiometric dating method used in geochronology and archaeology . It is based on measurement of the product of the radioactive decay of an isotope of potassium (K) into argon (Ar). Potassium is a common element found in many materials, such as feldspars , micas , clay minerals , tephra , and evaporites . In these materials, the decay product Ar is able to escape the liquid (molten) rock but starts to accumulate when the rock solidifies ( recrystallizes ). The amount of argon sublimation that occurs is a function of the purity of the sample, the composition of the mother material, and a number of other factors. These factors introduce error limits on the upper and lower bounds of dating, so that the final determination of age is reliant on the environmental factors during formation, melting, and exposure to decreased pressure or open air. Time since recrystallization is calculated by measuring the ratio of the amount of Ar accumulated to the amount of K remaining. The long half-life of K allows the method to be used to calculate the absolute age of samples older than a few thousand years.
49-568: 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. The geomagnetic polarity time scale was calibrated largely using K–Ar dating. Potassium naturally occurs in 3 isotopes: K (93.2581%), K (0.0117%), K (6.7302%). K and K are stable. The K isotope
98-449: A crystal lattice. When K decays to Ar ; the atom typically remains trapped within the lattice because it is larger than the spaces between the other atoms in a mineral crystal. But it can escape into the surrounding region when the right conditions are met, such as changes in pressure or temperature. Ar atoms can diffuse through and escape from molten magma because most crystals have melted and
147-539: A finite value to zero when the temperature is increased above the Curie temperature. That heating destroys magnetism was already described in De Magnete (1600): Iron filings, after being heated for a long time, are attracted by a loadstone, yet not so strongly or from so great a distance as when not heated. A loadstone loses some of its virtue by too great a heat; for its humour is set free, whence its peculiar nature
196-456: A history of volcanic activity such as Hadar, Ethiopia . The K–Ar method continues to have utility in dating clay mineral diagenesis . In 2017, the successful dating of illite formed by weathering was reported. This finding indirectly led to the dating of the strandflat of Western Norway from where the illite was sampled. Clay minerals are less than 2 μm thick and cannot easily be irradiated for Ar–Ar analysis because Ar recoils from
245-422: A magnetic field is absent the material has a spontaneous magnetism which is the result of ordered magnetic moments; that is, for ferrimagnetism one ion's magnetic moments are aligned facing in one direction with certain magnitude and the other ion's magnetic moments are aligned facing in the opposite direction with a different magnitude. As the magnetic moments are of different magnitudes in opposite directions there
294-479: A material's intrinsic magnetic moments change direction. Permanent magnetism is caused by the alignment of magnetic moments, and induced magnetism is created when disordered magnetic moments are forced to align in an applied magnetic field. For example, the ordered magnetic moments ( ferromagnetic , Figure 1) change and become disordered ( paramagnetic , Figure 2) at the Curie temperature. Higher temperatures make magnets weaker, as spontaneous magnetism only occurs below
343-452: A net magnetism of zero at all temperatures below the Néel temperature. Antiferromagnetic materials are weakly magnetic in the absence or presence of an applied magnetic field. Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions preventing thermal disorder from overcoming the weak interactions of magnetic moments. When disorder occurs it is at
392-576: A rock retains all of its Ar after cooling past the closing temperature and that this was properly sampled during analysis. This technique allows the errors involved in K-Ar dating to be checked. Argon–argon dating has the advantage of not requiring determinations of potassium. Modern methods of analysis allow individual regions of crystals to be investigated. This method is important as it allows crystals forming and cooling during different events to be identified. One problem with argon-argon dating has been
441-466: A sample of known age for a standard. Because this (primary) standard ultimately cannot be determined by Ar/ Ar, it must be first determined by another dating method. The method most commonly used to date the primary standard is the conventional K/Ar technique . An alternative method of calibrating the used standard is astronomical tuning (also known as orbital tuning ), which arrives at a slightly different age. The primary use for Ar/ Ar geochronology
490-476: A spontaneous magnetism; the material is ferrimagnetic. Above the Curie temperature the material is paramagnetic as the atoms lose their ordered magnetic moments as the material undergoes a phase transition. Materials are only antiferromagnetic below their corresponding Néel temperature or magnetic ordering temperature , T N . This is similar to the Curie temperature as above the Néel Temperature
539-415: Is also measured to assess how much of the total argon is atmospheric in origin. According to McDougall & Harrison (1999 , p. 11) the following assumptions must be true for computed dates to be accepted as representing the true age of the rock: Both flame photometry and mass spectrometry are destructive tests, so particular care is needed to ensure that the aliquots used are truly representative of
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#1732772028801588-410: Is analogous to Curie temperature. Ferromagnetic, paramagnetic, ferrimagnetic, and antiferromagnetic structures are made up of intrinsic magnetic moments. If all the electrons within the structure are paired, these moments cancel out due to their opposite spins and angular momenta. Thus, even with an applied magnetic field, these materials have different properties and no Curie temperature. A material
637-401: Is dating metamorphic and igneous minerals. Ar/ Ar is unlikely to provide the age of intrusions of granite as the age typically reflects the time when a mineral cooled through its closure temperature . However, in a metamorphic rock that has not exceeded its closure temperature the age likely dates the crystallization of the mineral. Dating of movement on fault systems is also possible with
686-723: Is defined as C = μ 0 μ B 2 3 k B N A g 2 J ( J + 1 ) {\displaystyle C={\frac {\mu _{0}\mu _{\mathrm {B} }^{2}}{3k_{\mathrm {B} }}}N_{\text{A}}g^{2}J(J+1)} The Curie–Weiss law is then derived from Curie's law to be: χ = C T − T C {\displaystyle \chi ={\frac {C}{T-T_{\mathrm {C} }}}} where: T C = C λ μ 0 {\displaystyle T_{\mathrm {C} }={\frac {C\lambda }{\mu _{0}}}} λ
735-646: Is generally crushed and single crystals of a mineral or fragments of rock are hand-selected for analysis. These are then irradiated to produce Ar from K via the (n-p) reaction K(n,p) Ar. The sample is then degassed in a high-vacuum mass spectrometer via a laser or resistance furnace. Heating causes the crystal structure of the mineral (or minerals) to degrade, and, as the sample melts, trapped gases are released. The gas may include atmospheric gases, such as carbon dioxide, water, nitrogen, and radiogenic gases like argon and helium, generated from regular radioactive decay over geologic time. The abundance of Ar* increases with
784-418: Is marred. (Book 2, Chapter 23). At the atomic level, there are two contributors to the magnetic moment , the electron magnetic moment and the nuclear magnetic moment . Of these two terms, the electron magnetic moment dominates, and the nuclear magnetic moment is insignificant. At higher temperatures, electrons have higher thermal energy. This has a randomizing effect on aligned magnetic domains, leading to
833-404: Is named after Pierre Curie , who showed that magnetism is lost at a critical temperature. The force of magnetism is determined by the magnetic moment , a dipole moment within an atom that originates from the angular momentum and spin of electrons. Materials have different structures of intrinsic magnetic moments that depend on temperature; the Curie temperature is the critical point at which
882-406: Is paramagnetic only above its Curie temperature. Paramagnetic materials are non-magnetic when a magnetic field is absent and magnetic when a magnetic field is applied. When a magnetic field is absent, the material has disordered magnetic moments; that is, the magnetic moments are asymmetrical and not aligned. When a magnetic field is present, the magnetic moments are temporarily realigned parallel to
931-486: Is radioactive; it decays with a half-life of 1.248 × 10 years to Ca and Ar . Conversion to stable Ca occurs via electron emission ( beta decay ) in 89.3% of decay events. Conversion to stable Ar occurs via electron capture in the remaining 10.7% of decay events. Argon, being a noble gas , is a minor component of most rock samples of geochronological interest: It does not bind with other atoms in
980-419: Is still a spontaneous magnetism and a magnetic field is present. Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions. The orientations of moments however are anti-parallel which results in a net momentum by subtracting their momentum from one another. Below the Curie temperature the atoms of each ion are aligned anti-parallel with different momentums causing
1029-582: Is sufficient to overcome the ordered alignments. As the temperature approaches 0 K, the entropy decreases to zero, that is, the disorder decreases and the material becomes ordered. This occurs without the presence of an applied magnetic field and obeys the third law of thermodynamics . Argon%E2%80%93argon dating Argon–argon (or Ar/ Ar ) dating is a radiometric dating method invented to supersede potassium–argon (K/Ar) dating in accuracy. The older method required splitting samples into two for separate potassium and argon measurements, while
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#17327720288011078-515: Is the Ar*/ Ar ratio. The J factor relates to the fluence of the neutron bombardment during the irradiation process; a denser flow of neutron particles will convert more atoms of K to Ar than a less dense one. The Ar/ Ar method only measures relative dates. In order for an age to be calculated by the Ar/ Ar technique, the J parameter must be determined by irradiating the unknown sample along with
1127-782: Is the Weiss molecular field constant. For full derivation see Curie–Weiss law . As the Curie–Weiss law is an approximation, a more accurate model is needed when the temperature, T , approaches the material's Curie temperature, T C . Magnetic susceptibility occurs above the Curie temperature. An accurate model of critical behaviour for magnetic susceptibility with critical exponent γ : χ ∼ 1 ( T − T C ) γ {\displaystyle \chi \sim {\frac {1}{(T-T_{\mathrm {C} })^{\gamma }}}} The critical exponent differs between materials and for
1176-460: Is used to compute the amount of time that has passed since a rock sample has solidified. Despite Ca being the favored daughter nuclide, it is rarely useful in dating because calcium is so common in the crust, with Ca being the most abundant isotope. Thus, the amount of calcium originally present is not known and can vary enough to confound measurements of the small increases produced by radioactive decay. The ratio of
1225-395: Is volatilized in vacuum. The potassium is quantified by flame photometry or atomic absorption spectroscopy . The amount of K is rarely measured directly. Rather, the more common K is measured and that quantity is then multiplied by the accepted ratio of K / K (i.e., 0.0117%/93.2581%, see above). The amount of Ar
1274-429: The Ar/ Ar method. Different minerals have different closure temperatures; biotite is ~300°C, muscovite is about 400°C and hornblende has a closure temperature of ~550°C. Thus, a granite containing all three minerals will record three different "ages" of emplacement as it cools down through these closure temperatures. Thus, although a crystallization age is not recorded, the information is still useful in constructing
1323-552: The K/ Ar* ratio, and thus to calculate the age of the unknown sample. Ar* refers to the radiogenic Ar, i.e. the Ar produced from radioactive decay of K. Ar* does not include atmospheric argon adsorbed to the surface or inherited through diffusion and its calculated value is derived from measuring the Ar (which is assumed to be of atmospheric origin) and assuming that Ar is found in a constant ratio to Ar in atmospheric gases. The sample
1372-515: The magnetic susceptibility , χ , in the immediate vicinity of the Curie point because of correlations in the fluctuations of neighboring magnetic moments. Neither Curie's law nor the Curie–Weiss law holds for T < T C . Curie's law for a paramagnetic material: χ = M H = M μ 0 B = C T {\displaystyle \chi ={\frac {M}{H}}={\frac {M\mu _{0}}{B}}={\frac {C}{T}}} The Curie constant C
1421-443: The mean-field model is taken as γ = 1. As temperature is inversely proportional to magnetic susceptibility, when T approaches T C the denominator tends to zero and the magnetic susceptibility approaches infinity allowing magnetism to occur. This is a spontaneous magnetism which is a property of ferromagnetic and ferrimagnetic materials. Magnetism depends on temperature and spontaneous magnetism occurs below
1470-486: The Curie temperature, the atoms are aligned and parallel, causing spontaneous magnetism; the material is ferromagnetic. Above the Curie temperature the material is paramagnetic, as the atoms lose their ordered magnetic moments when the material undergoes a phase transition. Materials are only ferrimagnetic below their corresponding Curie temperature. Ferrimagnetic materials are magnetic in the absence of an applied magnetic field and are made up of two different ions . When
1519-566: The Curie temperature, the atoms are excited, and the spin orientations become randomized but can be realigned by an applied field, i.e., the material becomes paramagnetic. Below the Curie temperature, the intrinsic structure has undergone a phase transition , the atoms are ordered, and the material is ferromagnetic. The paramagnetic materials' induced magnetic fields are very weak compared with ferromagnetic materials' magnetic fields. Materials are only ferromagnetic below their corresponding Curie temperatures. Ferromagnetic materials are magnetic in
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1568-479: The Curie temperature. Magnetic susceptibility above the Curie temperature can be calculated from the Curie–Weiss law , which is derived from Curie's law . In analogy to ferromagnetic and paramagnetic materials, the Curie temperature can also be used to describe the phase transition between ferroelectricity and paraelectricity . In this context, the order parameter is the electric polarization that goes from
1617-490: The Curie temperature. An accurate model of critical behaviour for spontaneous magnetism with critical exponent β : M ∼ ( T C − T ) β {\displaystyle M\sim (T_{\mathrm {C} }-T)^{\beta }} The critical exponent differs between materials and for the mean-field model as taken as β = 1 / 2 where T ≪ T C . The spontaneous magnetism approaches zero as
1666-413: The Néel temperature. Listed below are the Néel temperatures of several materials: The Curie–Weiss law is an adapted version of Curie's law . The Curie–Weiss law is a simple model derived from a mean-field approximation, this means it works well for the materials temperature, T , much greater than their corresponding Curie temperature, T C , i.e. T ≫ T C ; it however fails to describe
1715-413: The absence of an applied magnetic field. When a magnetic field is absent the material has spontaneous magnetization which is a result of the ordered magnetic moments; that is, for ferromagnetism, the atoms are symmetrical and aligned in the same direction creating a permanent magnetic field. The magnetic interactions are held together by exchange interactions ; otherwise thermal disorder would overcome
1764-463: The age of the sample, though the rate of increase decays exponentially with the half-life of K, which is 1.248 billion years. The age of a sample is given by the age equation: where λ is the radioactive decay constant of K (approximately 5.5 x 10 year , corresponding to a half-life of approximately 1.25 billion years), J is the J-factor (parameter associated with the irradiation process), and R
1813-480: The amount of Ar to that of K is directly related to the time elapsed since the rock was cool enough to trap the Ar by the equation: where: The scale factor 0.109 corrects for the unmeasured fraction of K which decayed into Ca ; the sum of the measured K and the scaled amount of Ar gives the amount of K which
1862-473: The applied field; the magnetic moments are symmetrical and aligned. The magnetic moments being aligned in the same direction are what causes an induced magnetic field. For paramagnetism, this response to an applied magnetic field is positive and is known as magnetic susceptibility . The magnetic susceptibility only applies above the Curie temperature for disordered states. Sources of paramagnetism (materials which have Curie temperatures) include: Above
1911-433: The atoms are no longer trapped. Entrained argon – diffused argon that fails to escape from the magma – may again become trapped in crystals when magma cools to become solid rock again. After the recrystallization of magma, more K will decay and Ar will again accumulate, along with the entrained argon atoms, trapped in the mineral crystals. Measurement of the quantity of Ar atoms
1960-686: The crystal lattice. In 2013, the K–Ar method was used by the Mars Curiosity rover to date a rock on the Martian surface, the first time a rock has been dated from its mineral ingredients while situated on another planet. Curie point In physics and materials science , the Curie temperature ( T C ), or Curie point , is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism . The Curie temperature
2009-458: The disruption of order, and the phenomena of the Curie point. Ferromagnetic , paramagnetic , ferrimagnetic , and antiferromagnetic materials have different intrinsic magnetic moment structures. At a material's specific Curie temperature ( T C ), these properties change. The transition from antiferromagnetic to paramagnetic (or vice versa) occurs at the Néel temperature ( T N ), which
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2058-470: The material undergoes a phase transition and becomes paramagnetic. That is, the thermal energy becomes large enough to destroy the microscopic magnetic ordering within the material. It is named after Louis Néel (1904–2000), who received the 1970 Nobel Prize in Physics for his work in the area. The material has equal magnetic moments aligned in opposite directions resulting in a zero magnetic moment and
2107-401: The newer method requires only one rock fragment or mineral grain and uses a single measurement of argon isotopes . Ar/ Ar dating relies on neutron irradiation from a nuclear reactor to convert a stable form of potassium ( K) into the radioactive Ar. As long as a standard of known age is co-irradiated with unknown samples, it is possible to use a single measurement of argon isotopes to calculate
2156-428: The sample. Ar–Ar dating is a similar technique that compares isotopic ratios from the same portion of the sample to avoid this problem. Due to the long half-life of K , the technique is most applicable for dating minerals and rocks more than 100,000 years old. For shorter timescales, it is unlikely that enough Ar will have had time to accumulate to be accurately measurable. K–Ar dating
2205-519: The temperature increases towards the materials Curie temperature. The spontaneous magnetism, occurring in ferromagnetic, ferrimagnetic, and antiferromagnetic materials, approaches zero as the temperature increases towards the material's Curie temperature. Spontaneous magnetism is at its maximum as the temperature approaches 0 K . That is, the magnetic moments are completely aligned and at their strongest magnitude of magnetism due to lack of thermal disturbance. In paramagnetic materials thermal energy
2254-428: The thermal history of the rock. Dating minerals may provide age information on a rock, but assumptions must be made. Minerals usually only record the last time they cooled down below the closure temperature, and this may not represent all of the events which the rock has undergone, and may not match the age of intrusion. Thus, discretion and interpretation of age dating is essential. Ar/ Ar geochronology assumes that
2303-452: The weak interactions of magnetic moments. The exchange interaction has a zero probability of parallel electrons occupying the same point in time, implying a preferred parallel alignment in the material. The Boltzmann factor contributes heavily as it prefers interacting particles to be aligned in the same direction. This causes ferromagnets to have strong magnetic fields and high Curie temperatures of around 1,000 K (730 °C). Below
2352-418: Was instrumental in the development of the geomagnetic polarity time scale . Although it finds the most utility in geological applications, it plays an important role in archaeology . One archeological application has been in bracketing the age of archeological deposits at Olduvai Gorge by dating lava flows above and below the deposits. It has also been indispensable in other early east African sites with
2401-411: Was present at the beginning of the elapsed time period. In practice, each of these values may be expressed as a proportion of the total potassium present, as only relative, not absolute, quantities are required. To obtain the content ratio of isotopes Ar to K in a rock or mineral, the amount of Ar is measured by mass spectrometry of the gases released when a rock sample
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