Isochron dating

The Isochronenmethode is a method of radiometric dating of rocks frequently used. Advantage over the conventional radiometric dating is that no assumptions about the initial concentration of the decay product must be made in the rock, to date a rock safely. In addition, disturbances of the isotopic system used for dating can be discovered with the Isochronenmethode that would falsify a dating if they remained undetected. The Isochronenmethode is therefore a very powerful instrument of radiometric dating.

Usability

Isochronenmethode the isotope may be applied to such systems in which the element in which the parent nuclide decays, possesses at least one further non- radiogenic isotope stable isotope as a reference in addition to the daughter isotope. Example is the Rb -Sr system. In addition to 87Sr, which is the decay product of the radionuclide 87Rb, is found in nature nor the stable isotope 86Sr before, which is nichtradiogen, so do not even decay product of a radionuclide is present in the sample. Other examples are Sm- Nd and U- Pb.

End of the analysis

To date, the corresponding isotopic concentrations either in different minerals an individual rock sample ( Mineralisochrone, engl. " Mineral isochron " ) or in different rock types kogenetischen origin ( Gesamtgesteinsisochrone, engl. "Whole rock isochron " ), ie stemming from, for example, from a molten rock determined.

In a first Mineralisochrone different mineral fractions must be separated from the to predating rock. These mineral separation is done by various methods, such as density separation, magnetic separation, chemical separation, manually with tweezers and microscope etc. The aim is mineral fractions with the largest possible difference in the frequency ratio of parent isotope to gain reference isotope, which increases ultimately the accuracy of the dating.

The various fractions are then chemically dissolved and extracted the elements used for dating by chromatographic methods. The samples thus obtained are then, for example, with an atomic emission spectrometer, prepared for measuring the isotope ratio mass spectrometer, and the element with a frequency. The results obtained in the subsequent measurement are then plotted in a so-called Isochronenplot.

Isochronenplot

The Isochronenplot is a diagram in which the ratio of the daughter isotope to isotope reference () on the relationship of the parent isotope to the reference isotope () is applied. If the data in the Isochronenplot on a straight line, this is called Just when isochrone. The slope of the Isochronous is then a measure of the age of the sample. The intersection with the ordinate of the coordinate system represents the ratio of daughter -to reference isotope dated to the time.

It can be shown that for the slope m and the age t following relationship applies (see below):

It is worth noting that in this formula to determine the age and not only the slope of the initial ratio of daughter isotope enters to reference isotope. This initial ratio is obtained, although as a side result of Isochronenmethode, but do not need it to determine the age.

Immediately after the formation of a rock, the ratio of daughter isotope to isotope reference in all mineral fractions is the same, provided that a sufficient homogenization took place. The isochrone is thus beginning a horizontal line. Clearly, the relationship between age and slope of the isochron can be interpreted to mean that the greater the frequency of the parent isotope in each fraction is, the farther a mineral fraction is therefore right in Isochronenplot, the more decays into the daughter isotope will take place. A standing right in Isochronendiagramm fraction is therefore migrate faster upward and to the left at the same time, as a further left standing. Since this migration is proportional to the abscissa, the values ​​of all fractions always lie on a straight line, unless the isotopic system is not disturbed by environmental influences. The extrapolation of the isochrone to the intersection with the ordinate can be interpreted as an extrapolation to a hypothetical mineral fraction in which no parent isotope in any form, thus not take place decays and the initial ratio of daughter -to reference isotope therefore remains constant.

In principle, sufficient to determine the isochron slope and thus to determine the age of two points in Isochronendiagramm. In general, however, at least three or more fractions are separated, measured and registered in Isochronendiagramm. The reason for this is that there will always be a draw straight line through two points; can also be checked only after three or more points, whether it is actually a straight line is and the consistency is ensured. Is about a rock formation at the initial homogeneity, the ratio of daughter isotope does not ensure to reference isotope, or the isotope system after the formation of the rock has been disrupted, for example by diffusion, so the relevant soft fractions from the straight line. With only two measurement points, one would not realize this. But more measurement points were determined, and they are in Isochronenplot on a straight line, then it is known that this can be interpreted precisely as actual isochrone, excluding failure, as well as the initial homogeneity was ensured. The age determination is considered to be very reliable.

Sometimes a variation of Isochronenplot is used in the place of the parent isotope is a stable isotope of the same element is used in the diagram of isotopes. This is used especially in dating methods with " extinct " radionuclides.

Interpretation of dating

The resulting age of the Isochronenmethode dated, as with other radiometric dating methods also, the time of the " Financial Statements" of the isotope system used, ie the date on which the isotopes are fixed in the relevant minerals and rocks, and no longer be exchanged with the environment. Different isotope systems react very differently to environmental conditions, so that they complete under different conditions. Depending on the system used for isotopic dating, the " conclusion " therefore correspond to different physical events. If an isotope system used for dating closes for example at a higher temperature than another, so the former is a higher age for a crystallizing from a melt and extremely slow Cooling deliver rock than the latter. The age then specify the times at which the respective temperature was reached, which are used in such cases for the determination of cooling rates.

It is also noted that different events Gesamtgesteinsisochrone Mineralisochrone and date. While Mineralisochrone dated about crystallization of the individual stone, the Gesamtgesteinsisochrone dated splitting the source melt into various melts from which later crystallized to different types of rock. So it is not unusual if both datings provide different results.

Mathematical

After the decay law is valid for

The time-dependence

With = decay constant, and = frequency of the daughter isotope and parent isotope of the time, = Initial frequency of the daughter isotope. Both sides of the equation can be divided by the frequency of the reference isotope:

Thus, if the initial frequency of the daughter isotope is not known, one has a total of two unknown with the unknown age. The "conventional" radiometric age determination, in which only one value for and is determined only supplies a conditional equation, so there is no unique solution. When Isochronenemethode however, several fractions are measured, which results in a corresponding number of equations. When two fractions, and one has already two governing equations:

Because of the initial homogeneity, the following applies:

Thus the system of equations has a unique solution and can be deduced by subtracting the two equations, the following formula for the slope:

Transformation after the age results:

• Radiometric dating