Lines That Tell Time
When a rock crystallizes, its constituent minerals incorporate different amounts of rubidium and strontium depending on their crystal chemistry. Biotite is Rb-rich, plagioclase is Rb-poor, but all minerals start with the same ⁸⁷Sr/⁸⁶Sr ratio — the ratio of the parent magma. Over time, ⁸⁷Rb decays to ⁸⁷Sr, and Rb-rich minerals accumulate more radiogenic strontium. Plotting the present-day ratios of all minerals yields a line — the isochron — whose slope encodes the age.
Slope Equals Age
The isochron equation ⁸⁷Sr/⁸⁶Sr = (⁸⁷Sr/⁸⁶Sr)₀ + ⁸⁷Rb/⁸⁶Sr × (e^(λt) − 1) is a straight line with slope m = e^(λt) − 1. Measuring the slope and inverting gives t = (1/λ) × ln(m + 1). The beauty of this method is that the initial ratio drops out — it is simply the y-intercept. No assumption about initial conditions is needed, only that all samples were co-genetic.
What Can Go Wrong
If the rock was reheated (metamorphosed), some minerals may partially or fully re-equilibrate their Sr isotopes, rotating the isochron toward a younger slope. This produces scatter (high MSWD) or a mixed age. Careful petrography and comparison of mineral vs. whole-rock isochrons can detect and sometimes correct for such disturbance. Undisturbed systems yield isochrons with MSWD near 1.
Beyond Rb-Sr
The isochron approach applies to any parent-daughter system: Sm-Nd isochrons are particularly resistant to metamorphic resetting, Lu-Hf provides complementary age and source information, and Re-Os dates sulfide minerals and organic-rich sediments. Each system has unique strengths, and modern geochronology typically combines multiple isochron systems to tell the complete thermal history of a rock.