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Figure 3.14 Uranium–lead concordia plot (blue) showing sample ages as a function²⁰⁶Pb/²³⁸U and²⁰⁷Pb/²³⁵U ratios and samples with lower²⁰⁶Pb/²³⁸U and²⁰⁷Pb/²³⁵U ratios (red), reset during a 2.5 Ga metamorphic event.

      Either decay series is capable of producing a sample age on its own. For example, a²⁰⁶Pb/²³⁸U ratio of 0.5 indicates an age of approximately 2.6 Ga (Figure 3.14), while a²⁰⁷Pb/²³⁵U ratio of 40 indicates an age of approximately 3.7 Ga. One advantage of these decay series is that the measurement of multiple, closely related isotopes permits ages to be checked against each other and provides robust sample ages when both methods yield a closely similar age. For example, if a sample possesses a²⁰⁶Pb/²³⁸U ratio of 0.7 and a²⁰⁷Pb/²³⁵U ratio of 32, a sample age near 3.5 Ga (Figure 3.14) is highly likely. When two age determinations are in agreement, their ages are said to be concordant. Another way to state this is that samples that plot on the concordia line when their²⁰⁶Pb/²³⁸U versus²⁰⁷Pb/²³⁵U ratios are plotted yield concordant ages. Such dating techniques are especially powerful in determining robust crystallization ages of igneous rocks that crystallized from magmas and lavas (Chapters 8 and 9).

A significant problem arises from the fact that subsequent events can alter the geochemistry of rocks, so that age determinations are no longer concordant. For example, when rocks undergo metamorphism, lead is commonly mobilized and lost from the minerals or rocks in question. This results in lower than expected amounts of daughter lead isotopes, lower Pb/U ratios and points that fall below the concordant age line on²⁰⁶Pb/²³⁸U versus²⁰⁷Pb/²³⁵U diagrams. When samples of similar real ages, affected differently during a single metamorphic event, are plotted on a concordia diagram, they fall along a straight line below the concordant age line. One interpretation of such data is that the right end of the dashed straight line intersects the concordant age line at the original age of the sample (4.0 Ga in Figure 3.14) and that the left end intersects the concordant age line at the time of metamorphism (2.5 Ga in Figure 3.14). Wherever possible, such interpretations should be tested against other data so that a robust conclusion can be drawn. One such independent radiometric decay series, with widespread application, is described in the section that follows.

       Rubidium–strontium systematics

      Several isotopes of the relatively rare element rubidium (Rb) exist; some 27% of these are radioactive⁸⁷Rb. Most Rb⁺¹ is concentrated in continental crust, especially in substitution for potassium ion (K⁺¹) in potassium‐bearing minerals such as potassium feldspar, muscovite, biotite, sodic plagioclase, and amphibole. Radioactive⁸⁷Rb is slowly (half‐life = 48.8 Ga) transformed by beta decay into strontium‐87 (⁸⁷Sr). Unfortunately, the much smaller strontium ion (Sr⁺²) does not easily substitute for potassium ion (K⁺¹) and therefore tends to migrate into minerals in the rock that contain calcium ion (Ca⁺²) for which strontium easily substitutes. This makes using⁸⁷Rb/⁸⁶Sr for age dating a much less accurate method than the U/Pb methods explained previously.

      One basic concept behind rubidium–strontium dating is that the original rock has some initial amount of⁸⁷Rb, some initial ratio of⁸⁷Sr/⁸⁶Sr and some initial ratio of⁸⁷Rb/⁸⁶Sr. These ratios evolve through time in a predictable manner. Over time, the amount of⁸⁷Rb decreases and the amount of⁸⁷Sr increases by radioactive decay so that the⁸⁷Sr/⁸⁶Sr

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