Isochron dating
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.
[1][2][3] All forms of isochron dating assume that the source of the rock or rocks contained unknown amounts of both radiogenic and non-radiogenic isotopes of the daughter element, along with some amount of the parent nuclide.
Thus, at the moment of crystallization, the ratio of the concentration of the radiogenic isotope of the daughter element to that of the non-radiogenic isotope is some value independent of the concentration of the parent.
Thus, the ratio of the radiogenic to non-radiogenic isotopes of the daughter element will become larger with time, while the ratio of parent to daughter will become smaller.
For rocks that start out with a small concentration of the parent, the radiogenic/non-radiogenic ratio of the daughter element will not change as quickly as it will with rocks that start out with a large concentration of the parent.
An isochron diagram will only give a valid age if all samples are cogenetic, which means they have the same initial isotopic composition (that is, the rocks are from the same unit, the minerals are from the same rock, etc.
), all samples have the same initial isotopic composition (at t0), and the system has remained closed.
(See the section on isotope ratio mass spectrometry.)
As such, isochrons are typically defined by the following equation, which normalizes the concentration of parent and radiogenic daughter isotopes to the concentration of a non-radiogenic isotope of the daughter element that is assumed to be constant:
To perform dating, a rock is crushed to a fine powder, and minerals are separated by various physical and magnetic means.
The proof of (1) amounts to simple algebraic manipulation.
It is useful in this form because it exhibits the relationship between quantities that actually exist at present.
respectively correspond to the concentrations of parent, daughter and non-radiogenic isotopes found in the rock at the time of measurement.
(relative concentration of present daughter and non-radiogenic isotopes) and
The better the fit of the data points to a line, the more reliable the resulting age estimate.
Since the ratio of the daughter and non-radiogenic isotopes is proportional to the ratio of the parent and non-radiogenic isotopes, the slope of the isochron gets steeper with time.
, represents the ratio of daughter to parent as used in standard radiometric dating and can be derived to calculate the age of the sample at time t. The y-intercept of the isochron line yields the initial radiogenic daughter ratio,
It is possible to date the differentiation of the precursor melt which then cooled and crystallized into the different types of rocks.
Some isotopic systems based on short-living extinct radionuclides such as 53Mn, 26Al, 129I, 60Fe and others are used for isochron dating of events in the early history of the Solar System.
However, methods using extinct radionuclides give only relative ages and have to be calibrated with radiometric dating techniques based on long-living radionuclides like Pb-Pb dating to give absolute ages.
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 can be used to determine the age of grains in sedimentary rocks and understand their origin by a method known as a provenance study.
