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).
Potassium–argon systematics
Potassium‐40 (40K) is a relatively rare radioactive isotope of potassium. Approximately 9.1% of40K atoms decay to the daughter isotope Argon‐40 (40Ar), almost entirely by electron capture that converts a proton into a neutron. This lowers the atomic number by one without changing the atomic mass number. Argon‐40 is produced only from the decay of potassium‐40, with a half‐life of 1.248 Ga. The other 88.9% of the radioactive40K atoms decay into the daughter isotope Calcium‐40 (40Ca) by β particle emission which converts a neutron into a proton. This increases the atomic number by one without changing the atomic mass number. Because calcium‐40 from other sources is abundant in variable amounts in most rocks its ratio with40K cannot be used to obtain rock ages.
Figure 3.15 Rubidium–strontium systematics, showing evolution in the composition of four representative minerals (1–4) from initial composition (blue line) to current composition (red line) as87Rb decays into87Sr over time. Whole rock compositions would lie somewhere between minerals 1 and 4 depending on the specifics of mineral composition and their proportions in the rock. Slope of red line yields provisional age of rock.
However, because argon‐40 is a Noble element it generally occurs as a gas and therefore rarely occurs in minerals at the time they form. Therefore, argon‐40 that exists in minerals is likely the product of the radioactive decay of the potassium‐40. Assuming that there is no loss of this argon‐40 from the mineral and no addition from other sources, the ratio of40K/40Ar in the mineral should increase over time and yield reliable ages for the minerals and/or rocks in which it occurs. This is especially true for volcanic rocks because, at high temperatures, argon is a gas that escapes easily from the lava into the atmosphere (where it is the third most abundant gas, after nitrogen and oxygen). On the other hand, when the lava crystallizes to form potassium‐bearing minerals, argon‐40 produced by the decay of potassium‐40 tends to be trapped in the crystal lattice because its radius is larger than the spacing between atoms. Ideally, this sets the stage for using40K/40Ar to date such rocks, but as we shall see, many challenges remain. This ratio is most useful for dating samples that formed more than 100 Ka in which enough time has elapsed for accurately measurable argon‐40 to accumulate, although some dates as young as 25 Ka have been reported.
Three isotopes of potassium exist and tend to occur in a known fixed ratio in mineral‐forming environments. The stable isotopes potassium‐39 and potassium‐41 constitute 93.25 815 and 6.73 025% of all potassium atoms. Radioactive potassium‐40 contributes only 0.0117% of all potassium atoms. The rarity of potassium‐40 means that its initial abundance in minerals or rocks must generally calculated from its known ratio to the other two isotopes that are much easier to measure accurately.
The abundance of argon‐40 in the sample is determined by mass spectrometry. The amount of potassium‐40 remaining in the sample is calculated by subtracting the amount of argon‐40 that has accumulated and the corresponding amount of calcium‐40 that would have formed in the double decay of potassium‐40. On the assumption that no argon‐40 existed in the sample at the time it was formed and that the mineral has behaved as a closed system with no gain or loss of argon‐40, the age of the sample can be calculated. Of course this assumption is not always valid. Two processes that produce excess argon‐40 and therefore anomalously old ages are (1) the incorporation of mantle xenoliths and xenocrysts that contain ungassed argon‐40 and (2) younger lavas that contain argon‐40 bearing gas‐bubble/vesicles. Processes that cause argon‐40 to leak from rocks and minerals, which produces anomalously young ages, include subsequent heating and alteration. For these reasons, care is taken to select samples that are unaltered and unfractured. This often requires extensive sample searching and preparation. Potassium feldspar (sanidine, orthoclase, and microcline) is the most commonly used mineral group, but biotite, muscovite, and illite clays can also be dated.
In recent decades, many techniques have been developed for the purpose of producing more accurate and refined age dates. Of these, the most significant has been the evolution of40Ar/39Ar dating methods which compare the ratios of these two argon isotopes from a small portion of a sample to avoid the inaccuracies inherent in inhomogeneous samples such as whole rocks, parts of which may not be representative. In this method, the sample and a standard of known age containing potassium‐40 are bombarded with neutrons in a nuclear reactor to produce argon‐39 which does not exist naturally. The amount of argon‐39 produced under a standard set of conditions is a proxy for the amount of potassium‐40 in the sample. From this information, the40K/40Ar ratio can be calculated and the age of the sample determined. On the whole,40Ar/39Ar dating methods appear to be more accurate than conventional40K/40Ar40 methods and can date samples as young as 25 Ka, but they do require access to a nuclear reactor.
There are many other isotope series utilized in determining rock ages, the history of magmatic source rocks, the conditions of sedimentation and/or the age of metamorphic events. Some of these are discussed in the chapters that follow in contexts where they are especially important.
CONTENT ASSESSMENT
1 What three conditions favor the complete substitution of different atoms/ions for one another in a particular coordination site as a mineral grows? What three conditions limit such substitutions? Why are some substitutions simple and other substitutions paired?
2 For an initial solid plagioclase of composition An60, use Figure 3.4 to:Describe the proportions of Na+ and Ca+2 in the large cation substitution site.Describe the proportions of Si+4 and Al+3 in the small cation substitution site.Write a formula for this plagioclase in the form (NaxCax) (SixAlx)AlSi2O8, similar to the formula for An35 shown in the figure.
3 In addition to the β‐quartz—cristobalite—liquid triple point show by the letter X in Figure 3.6, identify the two other triple points shown in the figure in terms of the three phases that exist in equilibrium and the unique temperature and pressure at which the three phases are equilibrium. Which of these sets of coexisting minerals might be expected to exist deep below the surface and which might be more likely to occur much nearer the surface? How might you recognize a rock that formed under triple point conditions?
