Calculating Rb-Sr Isochrons
In this article we'll look at isochron dating. An isochron is a line on an isotope ratio diagram denoting rock samples. The slope of the line is related to the age of . Isochron dating is a common technique of radiometric dating and is applied to date certain . Isochron dating is useful in the determination of the age of igneous rocks, which have their initial origin in the cooling of liquid magma. It is also useful. Radioactive decay has become one of the most useful methods for determining the age of formation of rocks. However, in the very principal of radiometric dating .
The better the fit of the data to the line, the lower the uncertainty. For further information on fitting of lines to data also known as regression analysissee: Yorka short technical overview of a technique specially designed for assessing isochron fits. Note that the methods used by isotope geologists as described by York are much more complicated than those described by Gonick.
This will be discussed in more detail in the section on Gill's paper below. The "generic" method described by Gonick is easier to understand, but it does not handle such necessities as: Unfortunately, one must wade through some hefty math in order to understand the procedures used to fit isochron lines to data. General comments on "dating assumptions" All radiometric dating methods require, in order to produce accurate ages, certain initial conditions and lack of contamination over time.
The wonderful property of isochron methods is: This topic will be discussed in much more detail below. Where the simple methods will produce an incorrect age, isochron methods will generally indicate the unsuitability of the object for dating. Avoidance of generic dating's problems Now that the mechanics of plotting an isochron have been described, we will discuss the potential problems of the "simple" dating method with respect to isochron methods.
Initial daughter product The amount of initial D is not required or assumed to be zero. The greater the initial D-to-Di ratio, the further the initial horizontal line sits above the X-axis.
But the computed age is not affected. If one of the samples happened to contain no P it would plot where the isochron line intercepts the Y-axisthen its quantity of D wouldn't change over time -- because it would have no parent atoms to produce daughter atoms.
Whether there's a data point on the Y-axis or not, the Y-intercept of the line doesn't change as the slope of the isochron line does as shown in Figure 5. Therefore, the Y-intercept of the isochron line gives the initial global ratio of D to Di. For each sample, it would be possible to measure the amount of the Di, and using the ratio identified by the Y-intercept of the isochron plot calculate the amount of D that was present when the sample formed.
That quantity of D could be subtracted out of each sample, and it would then be possible to derive a simple age by the equation introduced in the first section of this document for each sample. Each such age would match the result given by the isochron. Contamination - parent isotope Gain or loss of P changes the X-values of the data points: Gain or loss of P. In order to make the figures easy to read and quick to drawthe examples in this paper include few data points.
While isochrons are performed with that few data points, the best ones include a larger quantity of data. If the isochron line has a distinctly non-zero slope, and a fairly large number of data points, the nearly inevitable result of contamination failure of the system to remain closed will be that the fit of the data to a line will be destroyed. For example, consider an event which removes P. The data points will tend to move varying distances, for the different minerals will have varying resistance to loss of P, as well as varying levels of Di: Loss of P in all samples The end result is that the data are nearly certain not to remain colinear: Loss of P destroys the fit to a line.
Even in our simple four-data-point example isochron, a change to two of the samples Migration of parent in two data points. Specific loss of P required to yield a different colinear plot. The two samples must each change by the indicated amount -- no more and no less -- if the data are to remain colinear. In the special case where the isochron line has a zero slope indicating zero agethen gain or loss of P may move the data points, but they will all still fall on the same horizontal line.
In other words, random gain or loss of P does not affect a zero-age isochron. This is an important point. If the Earth were as young as young-Earth creationists insist, then the "contamination" which they suggest to invalidate dating methods would have no noticeable effect on the results.
Moreover, the daughter atoms produced by decay in a mineral are isotopes of different elements and have different ionic charges and radii compared with their parents. The energy released during the decay may produce dislocations or even destroy the crystal lattice locally, thus making it all the more easy for the radiogenic daughters to escape. This will change the vertical position of the data points: Gain or loss of D. As with gain or loss of P, in the general case it is highly unlikely that the result will be an isochron with colinear data points: Exceptions for loss of daughter There are two exceptions, where it is possible for migration of D to result in an isochron with reasonably colinear data points: If the D is completely homogenized, then the isochron age is reset to zero.
When this happens, any later dating attempt will yield the age of that metamorphic event rather than the original time of crystallization: Complete homogenization of radiogenic daughter resets the isochron age to zero. If the D is partially homogenized in a reasonably regular manner, the isochron age can be partially reset and the samples will date to sometime in between the original time of crystallization and the time of metamorphism.
This is a very rare occurrence, but examples are known: 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 Canadian Shieldwhich have identical ages reflecting a common cooling history, have been identified.
Calculating Rb-Sr Isochrons
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 see also mass spectrometry. 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 vacuumwhere 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 1 cubic cm to 1 litre 0. 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 polytetrafluoroethylene metal-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 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. 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. Radiocarbon dates are obtained from such things as bones, teeth, charcoal, fossilized wood, and shells. Because of the short half-life of 14C, it is only used to date materials younger than about 70, years. Other Uses of Isotopes Radioactivity is an important heat source in the Earth.
Elements like K, U, Th, and Rb occur in quantities large enough to release a substantial amount of heat through radioactive decay. Thus radioactive isotopes have potential as fuel for such processes as mountain building, convection in the mantle to drive plate tectonics, and convection in the core to produce the Earth's magnetic Field.
Initial isotopic ratios are useful as geochemical tracers. Such tracers can be used to determine the origin of magmas and the chemical evolution of the Earth. Short-lived isotopes Isotopes made during nucleosynthesis that have nearly completely decayed away can give information on the time elapsed between nucleosynthesis and Earth Formation.
Ratios of stable, low mass isotopes, like those of O, S, C, and H can be used as tracers, as well as geothermometers, since fractionation of light isotopes can take place as a result of chemical process.
We can thus use these ratios of light isotopes to shed light on processes and temperatures of past events. Radioactivity is a source of energy and thus can be exploited for human use - good and bad. Examples of questions on this material that could be asked on an exam Which isotopic systems are most useful for radiometric dating and what are the limitations of each?
What is an isochron and what information can be obtained from an isochron? Why is zircon the preferred mineral for obtainting U - Pb dates?