Geochronology A slight diversion into Isotope Geochemisty

1. Geochronology A slight diversion into Isotope Geochemisty

2. A Philosophical Question: How old is something? How long has it been in its current state? More precisely, the amount of time since a certain occurrence Rock – solidified from melt (igneous) indurated (sedimentary) last major thermal/pressure event (metamorphic) How can we tell how old something is if we didn’t observe it at the start? Need: Rate, and more precisely rate(t), and a boundary condition (a ground truth or a specification of something). The object has to change with time. e.g., how old is a proton? Specification of these conditions defines a “clock”. For the earth/rx, we call these geochronometers.

3. How we do this: • Relative (Geological) time scale: superposition, other simple physical rules. • Hutton – “no vestige of a beginning, no prospect of an end” • Geologists use uniformity – 100’s of millions of years based on sedimentary evidence. James Hutton and his unconformity

4. 2. Laws of physics: a. Cooling Earth from melt (Kelvin) < 100 Mya. More like 20-30 Mya b. Earth-Moon radius – Roche limit (G. Darwin and Kelvin). ~60 Mya (assumes Moon created from spinning Earth) c. Ocean salinity ~ 100 Mya (but oceans deposit seds as well). William Thomson, a.k.a. Lord Kelvin

5. About the same time that Kelvin made his announcement, Bequerel discovers radioactivity. Ernest Rutherford suggests its usefulness as a clock, and Boltwood gets ages of 450 my on rocks using U/Pb ratios. Geologists now say – whoa – too old! Henri Bequerel Ernest Rutherford

6. How Radioactive Age Dating Works The elements that make up matter are mostly stable, but a few (typically those with two many or too few neutrons in the nucleus – these are called isotopes), decay into other type of matter, releasing or absorbing energy and particles as they do so. This is called radioactive decay. For example, carbon has isotopes of weight 12, 13, and 14 times the mass of a proton, and we refer to them as carbon-12, carbon-13, or carbon-14 (abbreviated as 12C, 13C, 14C). It is only the 14C isotope that is radioactive. If there are a lot of atoms of the original element, called the parent or radioactive element, the atoms decay to another element, called the daughter or radiogenic element, at a predictable rate. The passage of time can be charted by the reduction in the number of parent atoms, and the increase in the number of daughter atoms.

7. Radioactive decay follows the simple rule that the rate at which the amount of parent material changes is proportional to the amount that is there. If N is the number of parent atoms, then or where l is a decay constant; the fraction of atoms that decay in a unit time. No is the original number of parent atoms (at t = 0). For convenience, we define the amount of time it takes for half of the available atoms to decay as a representative time called the "half-life".  This can be determined from

9. So what do you need to know? Well, if you can count all of the radioactive and radiogenic atoms in a rock, you could add them together to get No.  You know N, and if you also know the half-life (or, equivalently, the decay constant), the only thing left to determine is t.

10. What about a preexisting daughter product? Note we have assumed that there is no daughter product in the original formation of the rock (or mineral, if we are dating a certain mineral). In some cases this assumption is ok, for example because the radioactive and radiogenic atoms are different sizes and only one is likely to be the right size to fit in a given mineral.  Well, that may be true in some instances, but is not true in general.   What to do? In fact this is not so difficult.  All you do is subtract off the initial concentration and get an equation where the time dependence is linear.

11. Let D be the amount of daughter product at time t, and Do be the initial amount of daughter product that existed when the rock formed.  So, instead of presuming that N + D = No We write N + D - Do = No Substitution gives The final equation is a linear relation between N and D.  If we determine several values for N and D for different minerals in a rock (or from a pulverized powder of the rock) we can plot these and get a line, the slope of which can be used to determine t.  These lines are called isochrons.

12. The Radiometric Clocks There are now well over forty different radiometric dating techniques, each based on a different radioactive isotope. There is a large range in the half-lives of naturally occurring isotopes. Isotopes with long half-lives are useful for dating very old events. Isotopes with shorter half-lives cannot date very ancient events because all of the atoms of the parent isotope would have already decayed away, but are useful for dating correspondingly shorter intervals. The uncertainties on the half-lives determined are all better than about two percent. There is no evidence of any of the half-lives changing over time.

14. Examples of Dating Methods for Igneous Rocks For igneous rocks the event being dated is when the rock was formed from magma or lava. When the molten material cools and hardens, the atoms are no longer free to move about. Daughter atoms that result from radioactive decays occurring after the rock cools are frozen in the place where they were made within the rock.

15. Potassium-Argon (K-Ar) Method Potassium (K) is an abundant element in the Earth's crust. One isotope, 40K, is radioactive and decays to two different daughter products, 40Ca and 40Ar, by two different decay methods. This is not a problem because the production ratio of these two daughter products is precisely known, and is always constant: 11.2% becomes 40Ar and 88.8% becomes 40Ca. It is possible to date some rocks by the K-Ca method, but this is not often done because it is hard to determine how much calcium was initially present. Argon, on the other hand, is a gas. Whenever rock is melted to become magma or lava, the argon tends to escape. Once the molten material hardens, it begins to trap the new argon produced since the hardening took place. In this way the potassium-argon clock is reset when an igneous rock is formed.

16. In its simplest form, we measure the relative amounts of 40K and 40Ar to date the rock. The age is given by where t is the age and h is the half-life.

17. However, in reality there is often a small amount of argon remaining in a rock when it hardens. This is usually trapped in the form of very tiny air bubbles in the rock. One must have a way to determine how much air-Ar is in the rock. One approach is to recognize that argon has a couple of other isotopes, the most abundant of which is 36Ar. The ratio of 40Ar to 36Ar in air is known to be 295. Thus, if one measures 36Ar as well as 40Ar, one can calculate and subtract off the air-40Ar to get an accurate age.

18. Even so, Ar is sometimes contaminated with gas from deep underground rather than from the air. This gas can have a higher concentration of 40Ar escaping from the melting of older rocks. This is called parentless40Ar because its parent potassium is not in the rock being dated, and is also not from the air. In these cases, the date given by the normal potassium-argon method is too old. Because of all these difficulties, K-Ar is not used much except in special circumstances. Still, scientists in the mid-1960s came up with a way to use ratios of argon isotopes to produce very reliable ages. This is called the Ar-Ar method.

19. The Argon-Argon method This technique uses the ratio 40Ar/39Ar to estimate age. It has become quite popular in recent years because it appears to be quite robust and precise. 39Ar is unstable and does not exist in nature because its half life is only 269 years. Its daughter is 39K. 39K is stable, and because 39A has such a short half-life, for all intents all naturally occurring 39K can be considered non-radiogenic. But that means that if we make our own 39Ar then the amount will be stable over the duration of our experiments (usually several days).

20. The other crucial observation is that the ratio of many radioactive, but currently non-radiogenic, isotopes to a stable isotope of the same element is, at any point in time, everywhere the same on Earth. This is because of two reasons: • Most of these isotopes do not differentiate – meaning that there are no physical/chemical processes that preferentially concentrate any one type of isotope. Thus, their relative concentrations are everywhere the same in space (or at least on a planet like Earth). • 2. The rate of decay of a radioactive isotope is constant, and thus if no more of this isotope is made (i.e., it is non-radiogenic), then it is reducing at the same rate everywhere. • Thus, even though 40K is radioactive, neither it nor 39K is currently radiogenic, so the ratio 40K/39K is, at any particular time, the same everywhere (and hence in every rock).

21. Here’s how it works: First, create 39Ar by bombarding a sample with neutrons. In many rocks and minerals, 39K is very common, so you are pretty much guaranteed that 39Ar will be produced. We can write a conceptual equation for how much 39Ar we will produce: where f(e) is the neutron flux density at energy e s(e) is the capture cross section at energy e DT is the time interval of irradiation and the integral is over all possible energy levels.

22. We won’t actually need to know any of these terms, which is a good thing since they would be hard to measure, but we do need some way of expressing the fraction of 39K that turns into 39Ar. From the discussion of the K-Ar method, recall that 40K decays to 40Ar: where le is the decay constant for 40K to 40Ar (due to electron capture) and l is the total decay of 40K (remember it also decays to Ca). For our irradiated sample, we can divide the second equation by the first to get:

23. Let’s define J so that And then There are two unknowns in this equation: J and t. We can figure out what J is by simultaneously irradiating samples, called “flux monitors” of known age (tm) along with the sample we are trying to date. Note that all of the ratios in the above are the same for both the sample and the flux monitor, and hence J is the same for both.

24. Then and we recover the age of the sample from When we make our measurements we heat up the sample and monitor the release of Ar as a function of temperature. This provides a check to see if Ar has been released by past heating events. The idea is that at low temperatures the Ar at the edges of a mineral grain is released, but the core is intact. If the original Ar from the time the mineral cooled and became a closed system is retained, then the 40Ar/39Ar ratio will be independent of temperature or “plateau”.

26. Note that in this case no reliable age can be determined with the Ar-Ar technique.

27. Rubidium-Strontium (Rb-Sr) Rb-Sr provides a good example of how to handle pre-existing daughter products. In the Rb-Sr method, 87Rb decays with a half-life of 48.8 billion years to 87Sr. Strontium has several other isotopes that are stable. The ratio of 87Sr to one of the other stable isotopes, say 86Sr, increases over time as more 87Rb turns to 87Sr. But when the rock first cools, all parts of the rock have the same 87Sr/86Sr ratio because the isotopes were mixed in the magma. At the same time, some of the minerals in the rock have a higher initial Rb/Sr ratio than others. Rubidium has a larger atomic diameter than strontium, so rubidium does not fit into the crystal structure of some minerals as well as others.

28. At first, all the minerals will have a constant 87Sr/86Sr ratio but with varying 87Rb/86Sr. As the rock starts to age, rubidium gets converted to strontium. The amount of strontium added to each mineral is proportional to the amount of rubidium present. Thus, if we plot these ratios against each other for a selection of minerals in our sample, we will get a straight line, the slope of which can be used to deduce the age of the rock, and the intercept of which gives us the initial 87Sr/86Sr ratio.

30. The original amount of the daughter 87Sr can be determined from the present-day composition by extending the line through the data points back to 87Rb = 0. This works because if there were no 87Rb in the sample, the strontium composition would not change. The slope of the line is used to determine the age of the sample.

31. The Samarium-Neodymium, Lutetium-Hafnium, and Rhenium-Osmium Methods All of these methods work very similarly to the rubidium-strontium method. The samarium-neodymium method is the most-often used of these three. It uses the decay of samarium-147 to neodymium-143, which has a half-life of 105 billion years. The ratio of the daughter isotope, neodymium-143, to another neodymium isotope, neodymium-144, is plotted against the ratio of the parent, samarium-147, to neodymium-144. The samarium-neodymium method has been shown to be more resistant to being disturbed or reset by metamorphic heating events, so for some metamorphosed rocks the samarium-neodymium method is preferred.

32. The lutetium-hafnium method uses the 38 billion year half-life of lutetium-176 decaying to hafnium-176. This dating system is similar in many ways to samarium-neodymium, but since samarium-neodymium dating is somewhat easier, the lutetium-hafnium method is used less often. The rhenium-osmium method takes advantage of the very low osmium concentration in most rocks and minerals, so that a small amount of the parent rhenium-187 can produce a significant change in the osmium isotope ratio. The half-life for this radioactive decay is 42 billion years. The non-radiogenic stable isotopes, osmium-186 or -188, are used as the denominator in the ratios on the three-isotope plots. This method has been useful for dating iron meteorites, and is now enjoying greater use for dating Earth rocks due to development of easier rhenium and osmium isotope measurement techniques.

33. Uranium-Lead and related techniques (U-Pb) The uranium-lead method is the longest-used dating method. It was first used by Boltwood in 1907, about a century ago. The uranium-lead system is more complicated than other parent-daughter systems; it is actually several dating methods put together. Natural uranium consists primarily of two isotopes, 235U and 238U, and these isotopes decay with different half-lives to produce 207Pb and 206Pb, respectively. In addition, 208Pb is produced by thorium-232. Only one isotope of lead, 204Pb, is not radiogenic.

34. The U-Pb system has an interesting complication: none of the lead isotopes is produced directly from the uranium and thorium. Each decays through a series of relatively short-lived radioactive elements that each decay to a lighter element, finally ending up at lead. Since these half-lives are so short compared to 238U, 235U, and 232Th, they generally do not affect the overall dating scheme and we can use “effective” half lives to describe the decay. The result is that one can obtain three independent estimates of the age of a rock by measuring the lead isotopes and their parent isotopes.

35. The uranium-lead system in its simpler forms, using 238U, 235U, and 232Th, has proved to be less reliable than many of the other dating systems. This is because both U and Pb are less easily retained in many of the minerals in which they are found. Yet the fact that there are three dating systems all in one allows us to determine whether the system has been disturbed or not. One of the techniques used to do determine the time of a reset event is called the U-Pb Condordia technique.

36. Notes on U-Pb Concordia and Discordia We start with the U-Pb the decay relations: to produce the Concordia line: We plot vs or

37. Now, let’s suppose we start out with the some amount of Uranium (238Uo and 235Uo) and at time T1 there is a Pb loss event such that a given mineral Ma experiences partial lead loss a ( 0 < a < 1). We will assume that loss of lead isotopes is such that the proportion of 206Pb/207Pb is constant. On the Concordia plot, all possible points would lie on a straight line between the no-loss condition and the total loss condition. At time T1, we have

38. Ma has (a206PbT1,a 207PbT1,238UT1, and 235UT1). For Ma at a later time T2 Recall that

39. so Similarly So

40. This parametrically defines a straight line as a function of a. Note that if a = 1 which is just the formula for the Concordia. Thus we identify T2 as the age of the mineral, because that is what it would represent if no Pb were lost. If a = 0, then

41. Which again is the condordia, but now at a time T2-T1. This represents the time since the reset event, which is the date we expect to see because a = 0 means all lead was lost so we are starting again from scratch. (NOTE: This is the time SINCE the reset event, not the time OF the reset event). For 0 < a < 1, we have a parametrically defined straight line between the age of the rock (a = 1) and the time since the reset (a = 0).

42. Another way to see this as a straight line is to write the parametric equation as or where the slope m and intercept b are constants. We know from above that where m1 and m2 are constants, so that the slope of the above line is

43. The intercept will occur where or when which means at the intercept Hence the cord is given by:

44. Pb-Pb From the U-Pb the decay relations: We can look at the ratio of the above equations to the stable isotope of Lead (204Pb): If we then take the ratio of the above two equations, we get:

45. The ratio is a constant in nature (because of lack of fractionation of U) Thus the right side of the Pb-Pb equation is a constant for a given sample of age t: So, by plotting these isotopic ratios for different minerals in the rock, the age can be found from the slope (m) of the line (although you have to do this numerically as it involves ratios of exponentials).

46. The Oldest Rocks on Earth

47. The Age of the Earth When we began systematically dating meteorites we learned a very interesting thing: nearly all of the meteorites had practically identical ages, at 4.56 billion years. These meteorites are chips off the asteroids. When the asteroids were formed in space, they cooled relatively quickly (some of them may never have gotten very warm), so all of their rocks were formed within a few million years. The asteroids' rocks have not been remelted ever since, so the ages have generally not been disturbed. Meteorites that show evidence of being from the largest asteroids have slightly younger ages.

48. The moon is larger than the largest asteroid. Most of the rocks we have from the moon do not exceed 4.1 billion years. The samples thought to be the oldest are highly pulverized and difficult to date, though there are a few dates extending all the way to 4.4 to 4.5 billion years. We think that all the bodies in the solar system were created at about the same time. Evidence from the uranium, thorium, and lead isotopes links the Earth's age with that of the meteorites. This would make the Earth 4.5-4.6 billion years old.

49. Extinct Radionuclides: The Hourglasses That Ran Out If we find that a radioactive parent was once abundant but has since run out, we know that it too was set longer ago than the time interval it measures. In fact, most of them are no longer found naturally on Earth--they have run out. Their half-lives range down to times shorter than we can measure. Every single element has radioisotopes that no longer exist on Earth!