Isochron Dating - Isochron Plots

Isochron Plots

To perform dating, a rock is crushed to a fine powder and minerals are separated by various physical and magnetic means. Each mineral has different ratios between parent and daughter concentrations. For each mineral, the ratios are related by the following equation:

(1)

where

is the initial concentration of the daughter isotope,

is the concentration of the non-radiogenic isotope of the daughter element (assumed constant),

is the initial concentration of the parent isotope, and

is the total amount of the parent isotope which has decayed by time .

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. To wit, and respectively correspond to the concentrations of parent, daughter and non-radiogenic isotopes found in the rock at the time of measurement.

The ratios (relative concentration of daughter and non-radiogenic isotopes) and (relative concentration of parent and non-radiogenic isotope) are measured by mass spectrometry and plotted against each other in a three-isotope plot known as an isochron plot. Ratios are used instead of absolute concentrations because mass spectrometers usually measure the former rather than the latter. (See particularly the section on isotope ratio mass spectrometry.)

If all data points lie on a straight line, this line is called an isochron. 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. The change in slope from initial conditions--assuming an initial isochron slope of zero (a horizontal isochron) at the point of intersection (intercept) of the isochron with the y-axis--to the current computed slope gives the age of the rock. The slope of the isochron, represents the ratio of daughter to parent as used in standard radiometric dating.

Whole rock isochron dating uses the same ideas but instead of different minerals obtained from one rock uses different types of rocks that are derived from a common reservoir; e.g. the same precursor melt. It is possible to date the differentiation of the precursor melt which then cooled and crystallized into the different types of rocks.

One of the best known isotopic systems for isochron dating is the rubidium-strontium system. Other systems that are used for isochron dating include samarium-neodymium, and uranium-lead. 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.