isochrons

An isochron is a diagnostic plot used in radiometric geochronology. It is a straight line on a graph that connects multiple rock or mineral samples derived from a common geological event and that share a uniform initial isotopic composition. The typical isochron plots the ratio of a radiogenic daughter isotope to a stable non-radiogenic isotope against the ratio of the parent isotope to that same non-radiogenic isotope, for several samples from the same rock body or related rocks. If the system has remained closed since formation and the samples started with the same initial non-radiogenic ratio, the data form a straight line.

The slope of the isochron is related to time through the radiometric decay equation, while the intercept gives the initial ratio of the daughter to the non-radiogenic isotope. Specifically, the age t is given by t = (1/λ) ln(slope + 1), where λ is the decay constant of the parent isotope. The intercept reflects the initial isotopic composition, thus enabling the method to avoid assumptions about initial daughter concentrations.

Isochrons are widely used in geochronology. Common systems include rubidium–strontium (Rb–Sr), samarium–neodymium (Sm–Nd), and uranium–lead (U–Pb) dating. They are particularly useful for checking the consistency of ages across samples and for identifying mixtures, inheritance, or disturbance that cause data to deviate from a single straight line.

Limitations include the need for multiple suitable samples that share a common history, potential perturbations from open-system behavior, and analytical uncertainties. A well-defined isochron supports robust age estimates and initial isotopic compositions.