More than two million years old is usually performed on the hot yes, but strongly rejects lead as u Mineral zircon. Question 14 3 feldspar quartz mica zircon 7 . Among the accessories,used for dating by the uranium-lead method,zircon has been theobject of many studies, the other minerals (sphene, allanite, monazite, Rb/Sr dating has been limited to biotite, with a few measurements performed on . instances, less than 2"„ quartz and feldspar impurity was present and analyzed . dating is most often performed on the mineral feldspar quartz mica zircon contact more whilst the file cum whites, is cum that plop cum the absolution least .
Uranium-lead radiometric dating is most often performed on the mineral
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. The mineral zircon datable by the uranium—lead method is one such mineral.
Successively higher blocking temperatures are recorded for another mica type known as muscovite and for amphibolebut the ages of both of these minerals can be completely reset at temperatures that have little or no effect on zircon. Vast areas within the Precambrian shield, which have identical ages reflecting a common cooling history, have been identified.
These are called geologic provinces. 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 inbut it was not until about 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. 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.
Lead 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.
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 dilutioninvisibly 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. 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. Certain minerals that are highly refractory both in nature and in the laboratory e.
In this case, the sample is confined in a solid Teflon trade name for a synthetic resin composed of polytetrafluoroethylenemetal-clad pressure vessel, introduced by the Canadian geochronologist Thomas E.
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, and nearly 1, This means that a single grain can now be analyzed with a lower contamination level or background correction than was possible before withsimilar 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.
The rate is related to the number of such atoms present through the half-life. 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, together with the stable nonradioactive isotopes carbon 12C and carbon 13Cas long as it is alive. 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 The introduction of an instrument called an accelerator mass spectrometer has brought about a major advance in radiocarbon dating.
Unlike the old detector e. This increase in instrument sensitivity has made it possible to reduce the sample size by as much as 10, times and at the same time improve the precision of ages measured.
For a detailed discussion of radiocarbon age determination, see below Carbon dating and other cosmogenic methods. 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 sincea 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 and zirconolite CaZrTi2O7 have been found to be widespread in the silica-poor mafic igneous rocks. In addition, perovskite CaTiO3a 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.
Age determinations also can now be made of low-uranium trace minerals such as rutile TiO2a 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 titanitemonaziteand even garnet in certain favourable cases.
Additional minerals have been tried with varying success. Double uranium-lead chronometers The reason why uranium—lead dating is superior to other methods is simple: In fact, U and Th both have isotopes of radium in their decay chains with half lives of a week or two, and 6.
Any process that is concentrating one isotope of radium will probably concentrate the others as well and invalidate these dating methods, too. Radium has a low melting point degrees K which may account for its concentration at the top of magma chambers. What radiometric dating needs to do to show its reliability is to demonstrate that no such fractionation could take place. Can this be done? With so many unknowns I don't think so. How Uranium and Thorium are preferentially incorporated in various minerals I now give evidences that uranium and thorium are incorporated into some minerals more than others.
This is not necessarily a problem for radiometric dating, because it can be taken into account. But as we saw above, processes that take place within magma chambers involving crystallization could result in a different concentration of uranium and thorium at the top of a magma chamber than at the bottom.
This can happen because different minerals incorporate different amounts of uranium and thorium, and these different minerals also have different melting points and different densities.
If minerals that crystallize at the top of a magma chamber and fall, tend to incorporate a lot of uranium, this will tend to deplete uranium at the top of the magma chamber, and make the magma there look older. Concerning the distribution of parent and daughter isotopes in various substances, there are appreciable differences. Faure shows that in granite U is 4. Some process is causing the differences in the ratios of these magmatic rocks.
Depending on their oxidation state, according to Faure, uranium minerals can be very soluble in water while thorium compounds are, generally, very insoluble. These elements also show preferences for the minerals in which they are incorporated, so that they will tend to be "dissolved" in certain mineral "solutions" preferentially to one another. More U is found in carbonate rocks, while Th has a very strong preference for granites in comparison.
I saw a reference that uranium reacts strongly, and is never found pure in nature. So the question is what the melting points of its oxides or salts would be, I suppose. I also saw a statement that uranium is abundant in the crust, but never found in high concentrations. To me this indicates a high melting point for its minerals, as those with a low melting point might be expected to concentrate in the magma remaining after others crystallized out.
Such a high melting point would imply fractionation in the magma. Thorium is close to uranium in the periodic table, so it may have similar properties, and similar remarks may apply to it. It turns out that uranium in magma is typically found in the form of uranium dioxide, with a melting point of degrees centrigrade. This high melting point suggests that uranium would crystallize and fall to the bottom of magma chambers. Geologists are aware of the problem of initial concentration of daughter elements, and attempt to take it into account.
U-Pb dating attempts to get around the lack of information about initial daughter concentrations by the choice of minerals that are dated. For example, zircons are thought to accept little lead but much uranium. Thus geologists assume that the lead in zircons resulted from radioactive decay. But I don't know how they can be sure how much lead zircons accept, and even they admit that zircons accept some lead. Lead could easily reside in impurities and imperfections in the crystal structure.
Also, John Woodmorappe's paper has some examples of anomalies involving zircons. It is known that the crystal structure of zircons does not accept much lead. However, it is unrealistic to expect a pure crystal to form in nature. Perfect crystals are very rare. In reality, I would expect that crystal growth would be blocked locally by various things, possibly particles in the way. Then the surrounding crystal surface would continue to grow and close up the gap, incorporating a tiny amount of magma.
I even read something about geologists trying to choose crystals without impurities by visual examination when doing radiometric dating. Thus we can assume that zircons would incorporate some lead in their impurities, potentially invalidating uranium-lead dates obtained from zircons.
Chemical fractionation, as we have seen, calls radiometric dates into question. But this cannot explain the distribution of lead isotopes. There are actually several isotopes of lead that are produced by different parent substances uraniumuraniumand thorium. One would not expect there to be much difference in the concentration of lead isotopes due to fractionation, since isotopes have properties that are very similar.
So one could argue that any variations in Pb ratios would have to result from radioactive decay. However, the composition of lead isotopes between magma chambers could still differ, and lead could be incorporated into lava as it traveled to the surface from surrounding materials. I also recall reading that geologists assume the initial Pb isotope ratios vary from place to place anyway.
Later we will see that mixing of two kinds of magma, with different proportions of lead isotopes, could also lead to differences in concentrations. Mechanism of uranium crystallization and falling through the magma We now consider in more detail the process of fractionation that can cause uranium to be depleted at the top of magma chambers.
Uranium and thorium have high melting points and as magma cools, these elements crystallize out of solution and fall to the magma chamber's depths and remelt. This process is known as fractional crystallization. What this does is deplete the upper parts of the chamber of uranium and thorium, leaving the radiogenic lead.
As this material leaves, that which is first out will be high in lead and low in parent isotopes. This will date oldest. Magma escaping later will date younger because it is enriched in U and Th. There will be a concordance or agreement in dates obtained by these seemingly very different dating methods. This mechanism was suggested by Jon Covey.
Tarbuck and Lutgens carefully explain the process of fractional crystallization in The Earth: An Introduction to Physical Geology.
They show clear drawings of crystallized minerals falling through the magma and explain that the crystallized minerals do indeed fall through the magma chamber.
Further, most minerals of uranium and thorium are denser than other minerals, especially when those minerals are in the liquid phase. Crystalline solids tend to be denser than liquids from which they came. But the degree to which they are incorporated in other minerals with high melting points might have a greater influence, since the concentrations of uranium and thorium are so low.
Now another issue is simply the atomic weight of uranium and thorium, which is high. Any compound containing them is also likely to be heavy and sink to the bottom relative to others, even in a liquid form.
If there is significant convection in the magma, this would be minimized, however. At any rate, there will be some effects of this nature that will produce some kinds of changes in concentration of uranium and thorium relative to lead from the top to the bottom of a magma chamber.
Some of the patterns that are produced may appear to give valid radiometric dates. The latter may be explained away due to various mechanisms.
Let us consider processes that could cause uranium and thorium to be incorporated into minerals with a high melting point. I read that zircons absorb uranium, but not much lead. Thus they are used for U-Pb dating. But many minerals take in a lot of uranium.
It is also known that uranium is highly reactive. To me this suggests that it is eager to give up its 2 outer electrons. This would tend to produce compounds with a high dipole moment, with a positive charge on uranium and a negative charge on the other elements. This would in turn tend to produce a high melting point, since the atoms would attract one another electrostatically.
I'm guessing a little bit here. There are a number of uranium compounds with different melting points, and in general it seems that the ones with the highest melting points are more stable. I would suppose that in magma, due to reactions, most of the uranium would end up in the most stable compounds with the highest melting points.
These would also tend to have high dipole moments. Now, this would also help the uranium to be incorporated into other minerals. The electric charge distribution would create an attraction between the uranium compound and a crystallizing mineral, enabling uranium to be incorporated. But this would be less so for lead, which reacts less strongly, and probably is not incorporated so easily into minerals. So in the minerals crystallizing at the top of the magma, uranium would be taken in more than lead.
These minerals would then fall to the bottom of the magma chamber and thus uranium at the top would be depleted. It doesn't matter if these minerals are relatively lighter than others. The point is that they are heavier than the magma. Two kinds of magma and implications for radiometric dating It turns out that magma has two sources, ocean plates and material from the continents crustal rock. This fact has profound implications for radiometric dating. Mantle material is very low in uranium and thorium, having only 0.
The source of magma for volcanic activity is subducted oceanic plates. Subduction means that these plates are pushed under the continents by motions of the earth's crust.
While oceanic plates are basaltic mafic originating from the mid-oceanic ridges due to partial melting of mantle rock, the material that is magma is a combination of oceanic plate material and continental sediments.
Subducted oceanic plates begin to melt when they reach depths of about kilometers See Tarbuck, The Earth, p. In other words, mantle is not the direct source of magma. Further, Faure explains that uraninite UO sub2 is a component of igneous rocks Faure, p.
Uraninite is also known as pitchblende. According to plate tectonic theory, continental crust overrides oceanic crust when these plates collide because the continental crust is less dense than the ocean floor. As the ocean floor sinks, it encounters increasing pressures and temperatures within the crust.
Ultimately, the pressures and temperatures are so high that the rocks in the subducted oceanic crust melt.
Uranium–lead dating - Wikipedia
Once the rocks melt, a plume of molten material begins to rise in the crust. As the plume rises it melts and incorporates other crustal rocks. This rising body of magma is an open system with respect to the surrounding crustal rocks. It is possible that these physical processes have an impact on the determined radiometric age of the rock as it cools and crystallizes.
Time is not a direct measurement. The actual data are the ratios of parent and daughter isotopes present in the sample. Time is one of the values that can be determined from the slope of the line representing the distribution of the isotopes. Isotope distributions are determined by the chemical and physical factors governing a given magma chamber. Uranium is believed to be able to incorporate itself as a trace material in many other minerals of low density, and so be relatively highly concentrated in the crust.
A lower mantle concentration of uranium is inferred because if the mantle contained the same uranium concentration as the crust, then the uranium's heat of radiactive decay would keep the crust molten.
Rhyolites in Yellowstone N. Most genetic models for uranium deposits in sandstones in the U. Most of the uranium deposits in Wyoming are formed from uraniferous groundwaters derived from Precambrian granitic terranes.
Uranium in the major uranium deposits in the San Juan basin of New Mexico is believed to have been derived from silicic volcanic ash from Jurassic island arcs at the edge of the continent. From the above sources, we see that another factor influencing radiometric dates is the proportion of the magma that comes from subducted oceanic plates and the proportion that comes from crustal rock. Initially, we would expect most of it to come from subducted oceanic plates, which are uranium and thorium poor and maybe lead rich.
Later, more of the crustal rock would be incorporated by melting into the magma, and thus the magma would be richer in uranium and thorium and poorer in lead.
So this factor would also make the age appear to become younger with time. There are two kinds of magma, and the crustal material which is enriched in uranium also tends to be lighter. For our topic on radiometric dating and fractional crystallization, there is nothing that would prevent uranium and thorium ores from crystallizing within the upper, lighter portion of the magma chamber and descending to the lower boundaries of the sialic portion.
The upper portion of the sialic magma would be cooler since its in contact with continental rock, and the high melting point of UO sub 2 uranium dioxide, the common form in granite: The same kind of fractional crystallization would be true of non-granitic melts.
I think we can build a strong case for fictitious ages in magmatic rocks as a result of fractional cystallization and geochemical processes. As we have seen, we cannot ignore geochemical effects while we consider geophysical effects. Sialic granitic and mafic basaltic magma are separated from each other, with uranium and thorium chemically predestined to reside mainly in sialic magma and less in mafic rock.
Here is yet another mechanism that can cause trouble for radiometric dating: As lava rises through the crust, it will heat up surrounding rock. Lead has a low melting point, so it will melt early and enter the magma. This will cause an apparent large age. Uranium has a much higher melting point. It will enter later, probably due to melting of materials in which it is embedded. This will tend to lower the ages. Mechanisms that can create isochrons giving meaningless ages: Geologists attempt to estimate the initial concentration of daughter product by a clever device called an isochron.
Let me make some general comments about isochrons. The idea of isochrons is that one has a parent element, P, a daughter element, D, and another isotope, N, of the daughter that is not generated by decay. One would assume that initially, the concentration of N and D in different locations are proportional, since their chemical properties are very similar.
Note that this assumption implies a thorough mixing and melting of the magma, which would also mix in the parent substances as well. Then we require some process to preferentially concentrate the parent substances in certain places. Radioactive decay would generate a concentration of D proportional to P. By taking enough measurements of the concentrations of P, D, and N, we can solve for c1 and c2, and from c1 we can determine the radiometric age of the sample.
Otherwise, the system is degenerate. Thus we need to have an uneven distribution of D relative to N at the start. If these ratios are observed to obey such a linear relationship in a series of rocks, then an age can be computed from them. The bigger c1 is, the older the rock is. That is, the more daughter product relative to parent product, the greater the age.
Thus we have the same general situation as with simiple parent-to-daughter computations, more daughter product implies an older age. This is a very clever idea. However, there are some problems with it. First, in order to have a meaningful isochron, it is necessary to have an unusual chain of events. Initially, one has to have a uniform ratio of lead isotopes in the magma.
Usually the concentration of uranium and thorium varies in different places in rock. This will, over the assumed millions of years, produce uneven concentrations of lead isotopes. To even this out, one has to have a thorough mixing of the magma. Even this is problematical, unless the magma is very hot, and no external material enters.
Now, after the magma is thoroughly mixed, the uranium and thorium will also be thoroughly mixed. What has to happen next to get an isochron is that the uranium or thorium has to concentrate relative to the lead isotopes, more in some places than others. So this implies some kind of chemical fractionation. Then the system has to remain closed for a long time.
This chemical fractionation will most likely arise by some minerals incorporating more or less uranium or thorium relative to lead. Anyway, to me it seems unlikely that this chain of events would occur. Another problem with isochrons is that they can occur by mixing and other processes that result in isochrons yielding meaningless ages. Sometimes, according to Faure, what seems to be an isochron is actually a mixing line, a leftover from differentiation in the magma.
Fractionation followed by mixing can create isochrons giving too old ages, without any fractionation of daughter isotopes taking place. To get an isochron with a false age, all you need is 1 too much daughter element, due to some kind of fractionation and 2 mixing of this with something else that fractionated differently. Since fractionation and mixing are so common, we should expect to find isochrons often.
How they correlate with the expected ages of their geologic period is an interesting question. There are at least some outstanding anomalies. Faure states that chemical fractionation produces "fictitious isochrons whose slopes have no time significance. As an example, he uses Pliocene to Recent lava flows and from lava flows in historical times to illustrate the problem.
He says, these flows should have slopes approaching zero less than 1 million yearsbut they instead appear to be much older million years. Steve Austin has found lava rocks on the Uinkeret Plateau at Grand Canyon with fictitious isochrons dating at 1.
Then a mixing of A and B will have the same fixed concentration of N everywhere, but the amount of D will be proportional to the amount of P.
This produces an isochron yielding the same age as sample A. This is a reasonable scenario, since N is a non-radiogenic isotope not produced by decay such as leadand it can be assumed to have similar concentrations in many magmas. Magma from the ocean floor has little U and little U and probably little lead byproducts lead and lead Magma from melted continental material probably has more of both U and U and lead and lead Thus we can get an isochron by mixing, that has the age of the younger-looking continental crust.
The age will not even depend on how much crust is incorporated, as long as it is non-zero. However, if the crust is enriched in lead or impoverished in uranium before the mixing, then the age of the isochron will be increased. If the reverse happens before mixing, the age of the isochron will be decreased.
Any process that enriches or impoverishes part of the magma in lead or uranium before such a mixing will have a similar effect. So all of the scenarios given before can also yield spurious isochrons.
I hope that this discussion will dispel the idea that there is something magical about isochrons that prevents spurious dates from being obtained by enrichment or depletion of parent or daughter elements as one would expect by common sense reasoning. So all the mechanisms mentioned earlier are capable of producing isochrons with ages that are too old, or that decrease rapidly with time.
The conclusion is the same, radiometric dating is in trouble. I now describe this mixing in more detail. Suppose P p is the concentration of parent at a point p in a rock. The point p specifies x,y, and z co-ordinates. Let D p be the concentration of daughter at the point p. Let N p be the concentration of some non-radiogenic not generated by radioactive decay isotope of D at point p. Suppose this rock is obtained by mixing of two other rocks, A and B.
Suppose that A has a for the sake of argument, uniform concentration of P1 of parent, D1 of daughter, and N1 of non-radiogenic isotope of the daughter. Thus P1, D1, and N1 are numbers between 0 and 1 whose sum adds to less than 1. Suppose B has concentrations P2, D2, and N2. Let r p be the fraction of A at any given point p in the mixture. So the usual methods for augmenting and depleting parent and daughter substances still work to influence the age of this isochron.
More daughter product means an older age, and less daughter product relative to parent means a younger age. In fact, more is true. Any isochron whatever with a positive age and a constant concentration of N can be constructed by such a mixing. It is only necessary to choose r p and P1, N1, and N2 so as to make P p and D p agree with the observed values, and there is enough freedom to do this. Anyway, to sum up, there are many processes that can produce a rock or magma A having a spurious parent-to-daughter ratio.
Then from mixing, one can produce an isochron having a spurious age. This shows that computed radiometric ages, even isochrons, do not have any necessary relation to true geologic ages. Mixing can produce isochrons giving false ages. But anyway, let's suppose we only consider isochrons for which mixing cannot be detected. How do their ages agree with the assumed ages of their geologic periods?
As far as I know, it's anyone's guess, but I'd appreciate more information on this. I believe that the same considerations apply to concordia and discordia, but am not as familiar with them. It's interesting that isochrons depend on chemical fractionation for their validity. They assume that initially the magma was well mixed to assure an even concentration of lead isotopes, but that uranium or thorium were unevenly distributed initially.
So this assumes at the start that chemical fractionation is operating. But these same chemical fractionation processes call radiometric dating into question. The relative concentrations of lead isotopes are measured in the vicinity of a rock. The amount of radiogenic lead is measured by seeing how the lead in the rock differs in isotope composition from the lead around the rock. This is actually a good argument. But, is this test always done?
How often is it done? And what does one mean by the vicinity of the rock? How big is a vicinity? One could say that some of the radiogenic lead has diffused into neighboring rocks, too. Some of the neighboring rocks may have uranium and thorium as well although this can be factored in in an isochron-type manner. Furthermore, I believe that mixing can also invalidate this test, since it is essentially an isochron.
Finally, if one only considers U-Pb and Th-Pb dates for which this test is done, and for which mixing cannot be detected. The above two-source mixing scenario is limited, because it can only produce isochrons having a fixed concentration of N p. To produce isochrons having a variable N pa mixing of three sources would suffice. This could produce an arbitrary isochron, so this mixing could not be detected.
Also, it seems unrealistic to say that a geologist would discard any isochron with a constant value of N pas it seems to be a very natural condition at least for whole rock isochronsand not necessarily to indicate mixing. I now show that the mixing of three sources can produce an isochron that could not be detected by the mixing test. First let me note that there is a lot more going on than just mixing. There can also be fractionation that might treat the parent and daughter products identically, and thus preserve the isochron, while changing the concentrations so as to cause the mixing test to fail.
It is not even necessary for the fractionation to treat parent and daughter equally, as long as it has the same preference for one over the other in all minerals examined; this will also preserve the isochron. Now, suppose we have an arbitrary isochron with concentrations of parent, daughter, and non-radiogenic isotope of the daughter as P pD pand N p at point p.
Suppose that the rock is then diluted with another source which does not contain any of D, P, or N. Then these concentrations would be reduced by a factor of say r' p at point p, and so the new concentrations would be P p r' pD p r' pand N p r' p at point p. Now, earlier I stated that an arbitrary isochron with a fixed concentration of N p could be obtained by mixing of two sources, both having a fixed concentration of N p.
With mixing from a third source as indicated above, we obtain an isochron with a variable concentration of N pand in fact an arbitrary isochron can be obtained in this manner. So we see that it is actually not much harder to get an isochron yielding a given age than it is to get a single rock yielding a given age.
This can happen by mixing scenarios as indicated above. Thus all of our scenarios for producing spurious parent-to-daughter ratios can be extended to yield spurious isochrons.
The condition that one of the sources have no P, D, or N is fairly natural, I think, because of the various fractionations that can produce very different kinds of magma, and because of crustal materials of various kinds melting and entering the magma. In fact, considering all of the processes going on in magma, it would seem that such mixing processes and pseudo-isochrons would be guaranteed to occur.
Even if one of the sources has only tiny amounts of P, D, and N, it would still produce a reasonably good isochron as indicated above, and this isochron could not be detected by the mixing test. I now give a more natural three-source mixing scenario that can produce an arbitrary isochron, which could not be detected by a mixing test. P2 and P3 are small, since some rocks will have little parent substance. Suppose also that N2 and N3 differ significantly. Such mixings can produce arbitrary isochrons, so these cannot be detected by any mixing test.
Also, if P1 is reduced by fractionation prior to mixing, this will make the age larger. If P1 is increased, it will make the age smaller. If P1 is not changed, the age will at least have geological significance. But it could be measuring the apparent age of the ocean floor or crustal material rather than the time of the lava flow.
I believe that the above shows the 3 source mixing to be natural and likely. We now show in more detail that we can get an arbitrary isochron by a mixing of three sources.
Thus such mixings cannot be detected by a mixing test. Assume D3, P3, and N3 in source 3, all zero. One can get this mixing to work with smaller concentrations, too. All the rest of the mixing comes from source 3. Thus we produce the desired isochron. So this is a valid mixing, and we are done.