The clocks in the rocks

kw: book reviews, nonfiction, geology, geological history, radioactive dating

In the early 19^th century, once William Smith had discovered the correlation of strata by index fossil assemblages, and published Strata Identified by Organized Fossils, you could use illustrations such as these to identify the key fossils for rocks of a certain formation. "Formation", to a geologist, refers to a sequence of rock strata with a certain range of ages. In 1820 those ages were not known, but their relative order was known. Cambrian rocks were the oldest layers with fossils, Permian was in the middle, and the Tertiary and Quaternary formations were the youngest. Debates over just how old these were went on for generations, until the discovery of radioactivity. This image is from a lovely site that reproduces William Smith's book for us: William Smith on the Web.

By 1950 it was possible to measure the amount of trace elements in certain rocks to determine their ages. Some radioactive isotopes, primarily C¹⁴, have half-lives of a few thousand years, making them ideal for dating (determining the age) artifacts younger than forty or fifty thousand years. Others have much longer half-lives: U²³⁵, for example, has a half-life of 710 million years, making it one of several very long-lived isotopes that are ideal for measuring the ages of rocks as old as the formation of the Earth 4,540 million years ago.

The main Uranium isotope, U²³⁸, decays through a dozen steps to produce an isotope of Lead, Pb²⁰⁶, with a half-life of 4,470 million years. When only this was known, the first age date on a Uranium-bearing mineral was done by extracting the lead and weighing it. In the two or three generation since that was first done, our techniques have improved somewhat...

This image, scanned from a recent (2003) article, shows a magnified Zircon crystal and associated facts discovered from it. The crystal was mounted in plastic, sectioned and polished, then attacked with an ion microprobe that made the eight pits that are numbered in the illustration. The pits are small, just twenty microns in diameter, and perhaps equally deep, but Zircons typically contain as much as a percent of Uranium, or sometimes a few percent. That means, among the Zirconium and Oxygen vaporized to make each pit, there were a few billion atoms each of Uranium and Lead, and millions of atoms of the rarer isotopes.

Modern instruments count each atom of an isotope of interest. Poisson statistics indicate that the uncertainty in a counted measurement is roughly the square root of the number counted. If you count a million atoms of Pb²⁰⁷, the uncertainty (formally, the standard deviation) is about a thousand counts, or 0.1%. In pits this size you can zap several times each, getting several counts for each isotope, and get a very precise result. All that from a crystal nearly too small to see! No more dissolving a big lump of Uraninite to extract a few grams of lead!! The curved line on the chart is a Concordia Curve, and deviations from it indicate either contamination or reheating of a sample. One typically measures a number of samples because trends of the measurements can often help discern both the age of reheating and the age of original formation, and distinguish reheating from contamination.

The development of these and other methods of dating using radioactive isotopes is outlines beautifully by Doug MacDougall in Nature's Clocks: How Scientists Measure the Age of Almost Everything. Dr. MacDougall, a retired professor of Geology, takes a strictly geological and radiological approach, so this book actually doesn't cover all the kinds of "natural clocks" that exist (such as mitochondrial DNA mutation rates or circadian rhythms). The radioactive elements decay with mathematical precision; other processes are more variable.

Come to think of it, although C¹⁴ decays with a half-life of 5,730 years, it is not produced at a very steady rate. Let us first suppose that C¹⁴ were produced at exactly the same rate always. Then it would be incorporated into all plants in exactly the same proportion to C¹², and spread throughout the herbivorous and carnivorous animals in short order, so that every creature when it died would contain exactly the same proportion. All one need do then is measure how much of it is left to calculate the time since the creature died. There is the tiny complication that some of the Carbon in your bones and teeth has been there for decades, but compared to the 5,730-year half life, it is insignificant.

As author MacDougall explains so well, however, C¹⁴ is produced at a slightly variable rate. It forms when cosmic rays hit Nitrogen atoms in the upper atmosphere. The rate that cosmic rays reach Earth varies with several things: variations in Earth's magnetic field, the 11-year solar-magnetic cycle, and longer cycles that probably have cosmic origins. So calibration is needed.

This image shows a small part of a calibration curve known as Intcal98. It is used thus: The remnant C¹⁴, say in a piece of old bone or charcoal, is measured and used to calculate a "C¹⁴ age". Such ages are always referenced to 1950 as the zero age, meaning you subtract out any years from 1950 to the current year. Then, roughly speaking, you draw a line across from that age on the Y axis to the calibration data shown, and read off the age range from the X axis. So from this graph, a C¹⁴ age of 11,000 years turns into a Calendar age of about 12,850 years. In actual practice, the 11,000-year age would have some uncertainty, and this would be combined with the calibration data using an operation called convolution.

What is that telling us? When the C¹⁴ age is smaller than Calendar age, it means that more C¹⁴ was found than the true age would indicate, because there was more C¹⁴ being produced some 13,000 years ago. The symbols on the graph show the calibration data, mostly from tree rings, which have ages that are known exactly. At the lower left you can see part of the Intcal98 consensus curve without its "data cloak".

This image is a small portion of a more recent revision called Intcal04. See this PDF for the whole thing. The different data sets used for calibration are distinguished, and they are explained at the PDF's web site.

For both of these calibration curves, the wiggly nature of the data mean that some eras can be dated more accurately than others. On this curve, you can see that if you were to measure a C¹⁴ date of 6,250 years, the Calendar age would be quite uncertain, ranging from 7,000 to 7,150 years before 1950 (or 5050BC to 5200BC). On the other hand, a C¹⁴ age near 6,500 years would be much more accurately converted to a date near 5450BC (7,400 years BP).

And let us not forget the people (a tendency of mine). The very human stories, the triumphs and troubles of the players who worked all this out over the past hundred years make for enjoyable reading. The earliest measurements of radioactive isotopes and their decay products required nearly superhuman laboratory skills and skull-cracking effort. With today's knowledge, building an instrument to measure Uranium and Lead isotopes is tedious and rather costly, but not particularly difficult. What is difficult is gathering "clean" specimens and maintaining their cleanliness. The processing isn't hard, otherwise. But what big shoulders we are standing on!