Isochron
A straight-line plot of isotope ratios measured in several cogenetic samples, whose slope gives an age and whose intercept gives the initial isotopic composition.
An isochron (equal-time line) solves a basic problem in radiometric dating: a rock usually contains some daughter isotope from the start. For a system such as rubidium-87 decaying to strontium-87, each mineral or whole-rock sample is plotted with its parent-to-reference ratio (⁸⁷Rb/⁸⁶Sr) on the x-axis and its daughter-to-reference ratio (⁸⁷Sr/⁸⁶Sr) on the y-axis, where ⁸⁶Sr is a stable, non-radiogenic isotope. If the samples formed together with the same initial ratio and have remained closed systems, they fall on a straight line. The slope equals e^(λt) − 1, giving the age t from the decay constant λ, while the y-intercept gives the initial ratio.
The method builds in a test of validity. Scatter about the line, quantified by the mean square weighted deviation (MSWD), suggests disturbance, such as later heating, shock or weathering. Internal isochrons use minerals separated from one meteorite; whole-rock isochrons use several related meteorites. The same approach works for samarium–neodymium, lutetium–hafnium and, in a modified form, for extinct isotopes such as aluminium-26.
Eucrites illustrate it well: mineral isochrons from Juvinas and others give crystallisation ages close to 4.56 billion years. Recognise an isochron by its ratio-versus-ratio axes and fitted line.
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Level: Expert Advanced