Читать книгу Earth Materials - John O'Brien - Страница 81

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 ratio increases. At the same time, the⁸⁷Rb/⁸⁶Sr ratio decreases by an amount proportional to sample age. A second basic concept is that the initial amount of⁸⁷Rb varies from mineral to mineral, being highest in potassium‐rich minerals. As a result, the rate at which the⁸⁷Sr/⁸⁶Sr ratio increases depends on the individual mineral. For example, in a potassium‐rich (rubidium‐rich) mineral, the⁸⁷Sr/⁸⁶Sr ratio will increase rapidly, whereas for a potassium‐poor mineral it will increase slowly. For a mineral with no⁸⁷Rb substituting for K, the⁸⁷Sr/⁸⁶Sr ratio will not change; it will remain the initial⁸⁷Sr/⁸⁶Sr ratio. The⁸⁷Rb/⁸⁶Sr ratio of the whole rock however decreases at a constant rate that depends on the decay constant.

In a typical analysis, the amounts of⁸⁷Rb,⁸⁷Sr, and⁸⁶Sr in the whole rock and in individual minerals are determined by mass spectrometry, and the⁸⁷Rb/⁸⁶Sr and⁸⁷Sr/⁸⁶Sr ratios are calculated for each. These are plotted on an⁸⁷Sr/⁸⁶Sr versus⁸⁷Rb/⁸⁶Sr diagram (Figure 3.15). At the time of formation, assuming no fractionation of strontium isotopes, the⁸⁷Sr/⁸⁶Sr in each mineral and in the whole rock was a constant initial value, while the⁸⁷Rb/⁸⁶Sr values varied from relatively high for rubidium‐rich minerals such as biotite and potassium feldspar to zero for minerals with no rubidium. These initial⁸⁷Sr/⁸⁶Sr and⁸⁷Rb/⁸⁶Sr values are shown by the horizontal line in Figure 3.15. As the rock ages,⁸⁷Rb progressively decays to⁸⁷Sr, which causes the⁸⁷Sr/⁸⁶Sr ratio to increase at rates proportional to the initial amount of⁸⁷Rb, while the⁸⁷Rb/⁸⁶Sr ratio decreases at a constant rate. Over time, the⁸⁷Sr/⁸⁶Sr ratios and⁸⁷Rb/⁸⁶Sr ratios for each mineral and the whole rock evolve along paths shown by the arrowed lines in Figure 3.15. If each mineral acts as a closed system, points representing the current⁸⁷Sr/⁸⁶Sr versus⁸⁷Rb/⁸⁶Sr ratios will fall on a straight line whose slope increases through time (Figure 3.15). The slope of the best‐fit line, called an isochron (line of constant age), yields the age of the sample. The y‐intercept of any isochron yields the initial⁸⁷Sr/⁸⁶Sr ratio, which is unchanging for a theoretical sample that contains no⁸⁷Rb. The initial⁸⁷ Sr/⁸⁶ Sr is especially important in identifying the source regions from which magmas are derived in the formation of igneous rocks (Chapter 8).