  The greatest achievement of the “plumbologists” has been the calculation of the age of the earth, first proposed by Houtermans, a German physicist, and independently by Arthur Holmes, a British geologist, in 1946 and finally perfected by C. C. Patterson in 1953. It is actually a rather simple calculation, although the way to discovering it was far from easy. Before we look at it in detail, however, let’s consider some basic assumptions and explain what is meant by “the age of the earth”. From studying the mechanics of the solar system, scientists have become reasonably certain that the earth and the other planets and their satellites all were formed in a common process in a relatively short period of time, geologically speaking. Perhaps it took a dozen million Internal structure of the earth. The central core is probably an alloy of iron and nickel, surrounded by a mantle of less dense silicate material, with a thin crust of still lighter silicates. The time of this early and relatively rapid separation of uranium and lead on a worldwide scale is the event that plumbologists can determine, and the period since then is what they mean by “the age of the earth”. When Houtermans first wrote about it, he called it “the age of uranium”. How is this done? We have said that one of the isotopes of uranium, ²³5U, decays faster—about 6.3 times faster—than the other, ²³8U. They decay into two different isotopes of lead. Therefore, if we can determine the isotopic composition of average ordinary lead in the earth’s crust today, and if we can somehow obtain a sample of the kind of lead that is locked in the earth’s core, we can calculate Next, we must decide just what is average present-day lead? It isn’t enough to go to a lead mine and get a sample, because, unfortunately, leads from different mines have widely varied isotopic composition—that is, a different mixture of four natural isotopes, ²4Pb, ²6Pb, ²7Pb, and ²8Pb—as a result of their geologic histories. No, lead samples from a mine won’t do. However, geologists have been able to separate lead from recent marine sediments, obtained from the ocean bottom, far from land. These are of uniform composition, and are good samples of what the world’s rivers bring into the ocean. Other useful samples can be found in plateau basalts, which are enormous bodies of dark volcanic rock that make up the bedrock in many parts of the world. The lead from these basalts is isotopically very much like the lead in the oceans. Very well, but how about the lead from the core? Where can we hope to find a sample of it? It turns out to be easier than you might think. Astronomers believe it highly probable that most meteorites are fragments of a former planet that broke up for reasons that are not entirely clear. It is pretty definite, however, that this protoplanet (or these protoplanets, for there may have been more than one) had an iron core, and this core (or these cores) is the source of the iron meteorites sailing around in space. A large meteorite hit the earth not too long ago (geologically speaking) and caused the Meteor Crater near Canyon Diablo in Arizona. Examining ocean-bottom sediments obtained by lowering a tube-like instrument that brings up a long rod-shaped “core”, prior to nuclear age determination of the sample. Many fragments of the meteorite iron have been found around the crater, and it is reasonable to assume that this is the kind of iron we would expect to find in the core of the earth. Like the core iron, it is mixed with a little lead, which can be isolated and analyzed in a mass spectrometer for its isotopic composition. This lead is found to be much less contaminated with radiogenic lead, and hence is much more primitive than the oldest leads found on earth. Thus, meteorites presumably are as close as we can get to true primordial lead—the lead of the time when the earth (and the protoplanet) first formed. Once these measurements were available, it was easy to write the Houtermans equation for present-day and primordial leads in this way:
=137.7
The present ratio of ²³8U to ²³5U is 137.7.
Substituting the best experimental lead isotope ratios into the equation and solving for t, Patterson was able to calculate that the earth is 4550 million years (4.55 aeons) old. Subsequent calculations based on other procedures generally have confirmed that result. Analytical TechniquesEach method of nuclear age determination involves a different sequence of sample preparation. Wood, peat, charcoal, bones, or shells are cleaned for carbon-14 dating in order to remove every trace of possible contamination by modern carbon as well as extraneous old carbon. Rocks are crushed and ground, minerals are separated according to what is needed in any particular study, and the desired elements are extracted and separated by chemical procedures. Often there may be several different ways of doing the same thing; different laboratories use different procedures. In every case, however, long and complicated procedures must be followed before results are obtained from which an age can be calculated. There is no such thing as a black box into which you can throw a rock and read its age on a dial! Of all the elements that are part of the useful parent-daughter systems, only potassium is common enough to be analyzed by conventional chemical techniques. All the other elements, especially the radiogenic ones, are present in such small quantities that special processes had to be developed to measure them. The most valuable and generally used process is called Isotope DilutionThis is a process for analyzing an unknown material by incorporating uniformly into it a small amount of a radioactive test substance and determining how much the tracer radioactivity is altered by dilution in the original material. It works like this: Let’s say that we have an unknown number of atoms, x, of a given element. The normal isotopic composition of this element is accurately known, as it is for most elements, and the ratio of two of its isotopes can be expressed as A/B. We now add to x a known (but usually smaller) amount, c, of the same element. This quantity has a drastically different isotopic ratio, A'/B'. We mix x and c thoroughly together. The ratio A'/B' can have almost any value, but must be different from A/B and we must know exactly what it is. (There are many ways of determining this chemically, or we can use a sample isotope of known composition obtained from the U. S. Atomic Energy Commission’s Oak Ridge National Laboratory at Oak Ridge, Tennessee.) The substance added is known colloquially as the After the original material and the spike are thoroughly mixed we have: x(A/B) + c(A'/B') = (x + c) (AB) in which A/B will be the ratio of the two isotopes in the mixture. With this information in hand, we can perform any chemical purification or transfer process with the material (see photo on page 22), without having to worry about loss. (Even if 90% of the material should be lost in some operation, the isotopic composition would not be changed, and that is all we are interested in.) Now we can place the material containing the isotopic mixture in a A large (12-inch) mass spectrometer (at left) in use. Electronic equipment (right) charts results (see page 21). Essential parts of a mass spectrometer. Atoms to be analyzed are changed to ions in the source. Then the ions are accelerated by high voltage, deflected in a magnetic field according to their mass, and the intensity of the separated beams is measured in the collector. Mass SpectrometryThe mass spectrometer measures isotopic abundances using a magnetic field to sort electrically charged particles into groups according to their masses. It works this way: A small drop of material to be analyzed is placed on a metal filament and dried. The filament, in its holder, is placed inside the mass spectrometer, and heated electrically in a vacuum, like the filament in a light bulb. As the wire begins to glow, some of the sample begins to radiate, or “boil off”, losing an electron or two in the process. In other words, some of the atoms will be changed into positive An alternative method is to introduce the sample material into the vacuum chamber in the form of a gas (like argon, for example), and then bombard the gas with electrons Whichever way the ions were produced, they are next exposed to a strong electric field, accelerated, and electrostatically focused into a beam. These charged particles are directed into a magnetic field between the pole faces of an electromagnet. The magnet does the analyzing by the principle of magnetic deflection that was known to AndrÉ Ampere and Michael Faraday more than a century ago. Any moving electric charge has a magnetic field associated with it. This field interacts with the field of the analyzing magnet to impress a deflecting force on the charge. The force acts at right angles to the direction the charge travels and also at right angles to the direction of the impressed magnetic field. The pull of this force depends only on the electric charge and the speed of each particle: A light single-charged particle will be deflected more than a heavier particle with the same charge. In this way, the ions in the beam are sorted out into a number of separate beams, each made up of particles of the same charge/mass ratio. Each beam contains one isotope of the original material, because isotopes differ on the basis of their mass. By adjusting the current in the electromagnet we can direct these separate beams into a “collector” and electrically measure their intensity one by one. This gives the relative abundance of the separate isotopes in the sample. Minerals That Can Be DatedMeasuring age by one of the long-lived radioisotopes requires a closed system. Usually this is some kind of crystal formed in a period of time that is short, compared to the time that has elapsed since, and that has remained unchanged since it formed. Specifically, neither the parent isotopes can have been added nor the daughter isotopes removed by any process other than radioactive decay. The earth is a dynamic system, however. Things are always changing and moving—not very rapidly, perhaps, but fast enough, in geologic time, to raise mountains and shift oceans. Solutions are moving around, dissolving something here and depositing it again somewhere else. Temperatures are changing as one place is denuded by erosion and another area buried under layers of sediment. Under such conditions, few systems remain closed. It is perhaps surprising that we find any closed systems at all. Let us look at a few that are known to be reliable. (They are listed in Table I on page 4.) Potash FeldsparIn the early 1950s, when the potassium-argon (parent-daughter) method was being developed by scientists at the University of Chicago, it was thought that the potash-bearing variety of the mineral feldspar would be an ideal closed system, because it was usually optically clear and free of flaws. This widely shared, logical, and perfectly scientific deduction soon turned out to be quite wrong. The scientific workers discovered that when feldspar and mica from the same rock (and thus of the same age) were analyzed side by side, the mica always came out older! Investigation showed that feldspar “leaked” argon (lost some of its radiogenic argon) even at room temperature, but the mica retained all or nearly all of the argon that had been generated in it. MicaWith the development of the rubidium-strontium (parent-daughter) method by L. T. Aldrich and his co-workers at the Carnegie Institution of Washington, came the realization that mica was also very useful for this analysis, for it usually contains ample rubidium and not much original strontium that would mask the presence of the radiogenic strontium. As a result, mica, especially black mica (the mineral biotite), has enjoyed great popularity as a good and easy-to-find closed system. A scientist making adjustments on an “argon train”, a maze of glass tubing in which argon is released from minerals and purified for analysis. Everything has its limits, and mica is no exception: Even mica tends to leak argon at elevated, but still relatively low (geologically speaking), temperatures. These effects also depend on pressure and other factors, not all of which are well known; these elevated temperatures, pressures and other conditions of course act to some extent on all rocks buried in the earth’s crust. It is known that at only about 300°C at moderate pressures argon is leaked from mica faster than it is being generated in it by the decay of radioactive potassium. The temperature needed to cause the rapid loss of strontium from mica is not much higher. Mica, especially biotite, will recrystallize and lose all its radiogenic constituents (argon and strontium) at temperatures where many other minerals show little or no change. That means that we cannot always rely on mica to give the date of the original crystallization of a rock—the time when it cooled from a molten state. Instead, mica will tell us when the rock last cooled from, say, several hundred degrees centigrade, regardless of what may have happened to the rock before that. The mica may have been reheated as a result of being buried under a few miles of sediment, for example. The mica will show when the rock last cooled—in other words, when it came up again. Low-Strontium FeldsparIn spite of early disappointments with potash feldspar for argon dating, some of it is useful for rubidium-strontium procedures. It all depends on how much original strontium the potash feldspar contains. Most feldspars, unfortunately, contain far too much, but rapid screening by X-ray fluorescence or flame photometry methods can weed these out and identify specimens low enough in original strontium to be useful. Otherwise, feldspar is an excellent closed system for rubidium and strontium; it remains closed even at temperatures high enough to melt many other minerals. It is not affected at all by the same degree of heating that will drive argon out of biotite. The rubidium-strontium age of feldspar usually comes close to the time of original crystallization of the rock. Obviously, here is a geologically important tool. If we find feldspar and biotite in one rock, and if feldspar, tested by the rubidium-strontium method gives the same age as biotite tested by potassium-argon decay, then we can say with confidence that the rock has not been reheated since shortly after it crystallized. Conversely, if the biotite comes out much younger than the feldspar, we can be sure that something has happened to this rock long after it first crystallized. Such information is not only valuable to pure science—it can also be useful in locating areas favorable for ore prospecting and in other practical ways. ZirconAnother very interesting mineral is zircon (a silicate of zirconium), one of the accessory minerals found in small quantities in many crystalline rocks. Zircon usually occurs in very small grains and is heavy and hard, so that it can be separated from the other rock without much difficulty, even though it may take 100 pounds of rock to supply a gram of zircon. Zircon usually contains a fair amount of uranium and very little lead. It holds radiogenically produced lead well, even at relatively high temperatures. But that is not all. Even if some of the lead is lost, there is a mathematical way of correcting for it. This technique is called If we plot a graph of the radiogenic ²6Pb/²³8U ratio against the radiogenic ²7Pb/²³5U ratio for concordant (closed) systems of all ages, we obtain the curved line shown in the figure below. The curve is the locus of all concordant U-Pb ages and is called Concordia. Then if we test two or more particular zircons of the same age that have lost different amounts of lead, at about the same time, the plot of their ²6Pb/²³8U ratios against their ²7Pb/²³5U ratios will fall on a straight line that is a chord of the Concordia curve. The upper intersection of this chord with the curve then will mark the true age of the zircons. This is an elaborate technique utilizing difficult chemical procedures, but it has proved invaluable in solving some important geologic problems. The Concordia curve offers a useful way of analyzing results of age determinations on the mineral zircon. HornblendeThe mineral hornblende provides another useful system. Hornblende is a complex silicate of sodium, calcium, iron, magnesium, and aluminum, and usually contains a few tenths of 1% of potassium. It is unusual in that it tenaciously retains its radiogenic argon, even at relatively high temperatures. SanidineStill another good system is the rare feldspar, sanidine, which is excellent for both potassium-argon and rubidium-strontium age determination. Sanidine usually is found in volcanic ash falls and has been important in the establishment of the geologic time scale, as we shall see. Whole RocksFinally there is still another way of obtaining a closed system by using the whole rock, not just a crystal of a single mineral within it. A large body of granite or similar rock may contain a number of minerals, some or none of which may be closed systems. Yet as long as this body of rock remains impermeable to solutions (which in nature means mostly to water), no substance will be able to move very far in it because diffusion in solids is so slow. Consequently it will remain a closed system, as a whole, regardless of what happens to the individual mineral grains. If we take a piece from near the middle of this body of rock and if this piece is much larger than the largest constituent grain in it, then we have a fair sample of a closed system—the whole rock. The only difficulty arises from the fact that few rocks are sufficiently impermeable to solutions to retain argon, and many rocks contain so much common strontium that rubidium-strontium analysis |
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