Single Phase and Isochron Dating

If a material contains only the radioactive parent at the time of its formation, then the age of the material (or system ) can be determined by measuring the parent/ daughter ratio, provided that the system remained closed since its formation. If both parent and daughter are present in the system at the time of its formation, we must know the initial amount of daughter present. The derivation of the pertinent equations can be found in several textbooks on geochronology [1-3], with the essential one for geochronological purposes being 

As it is easier to determine precisely the ratio of two isotopes relative to each other than the absolute concentration of an individual isotope, both sides of the equation above are generally divided by a stable isotope of the element to which the daughter belongs. In the case of the radioactive decay of Rb to Sr, for instance, everything is normalized to Sr, so the equation becomes 

The subscript t refers to the time at which we perform the measurement, to distinguish it from time zero, at which the system became closed. 

The minimum and maximum ages of materials that can be dated depend on the decay constant/half-life of the parent isotope (Table 9.1) and the relative enrichment of parent over daughter isotope, apart from the precision of the isotope ratio measurements. The materials most suitable for dating purposes are those that only incorporate the parent isotope at the time of formation, as a single sample (mineral) suffices to obtain an age, whereas at least two, but preferably three or more, samples are necessary to obtain an age by the isochron method. 

The slope of the line connecting the open boxes depends on the time elapsed since the six minerals last equilibrated with each other or, in other words, since closure of the Rb-Sr system for these minerals. In this example, 40 million years (Ma) elapsed since closure. 

---