10 September 2007

I have never quite understood radiocarbon (C₁₄) dating. The thing that I had a problem with was: How do you use the measurement of how much C₁₄ is left now to determine the age of an object when you were not around to know how much C₁₄ was in the object when it died. In my readings I have found two descriptions of the process that have helped me.

The first description I will quote comes from Chapter XI, Megaliths Come of Age, in Peter Lancaster Brown’s book Megaliths, Myths and Men (©1976). [This book was written by a Brit and the quoted passage may have contained some British spellings that my spell checker has converted to American English spellings but otherwise it is unchanged.]

Radiocarbon was discovered in the 1930s. This material has an atomic weight of 14 instead of the normal 12 of carbon, and for this reason it is referred to as carbon-14 (C-14). The first to find radiocarbon in nature was W. F. Libby, the American nuclear chemist. Libby knew that cosmic rays, which bombard the upper atmosphere, produce large numbers of neutrons. He reasoned that when these collide with nitrogen atoms in the atmosphere, some of them were transmuted into radiocarbon. Nitrogen is changed to carbon by replacing one of the positively charged protons in the nucleus of the nitrogen-14 atom with an uncharged neutron of almost the same mass. It was Libby’s belief that radiocarbon combined with oxygen to form carbon dioxide which is diffused throughout the atmosphere. Plants absorb carbon dioxide by the process of photosynthesis. Plants in turn are consumed by animals and humans, and as a result radiocarbon is acquired in all their tissues.

But what happens to radiocarbon when a living organism dies? It is obvious that death would stop further intake of radiocarbon. Libby found that what remained in the tissues after death slowly leaked away. The carbon-14 atom in fact is unstable and throws out its negatively charged electrons and becomes stable nitrogen. It was this characteristic which he realized could be put to good use.

Libby’s value for the breakdown indicated a ‘half-life’ of 5,568 years. In this period half the radiocarbon in any given sample disappears. Half of what is left then disintegrates in the next 5,568 years, now leaving only one-quarter of the original; this disintegration then continues until all the radiocarbon is gone (in c. 70,000 years or more). Thus Libby realized that by determining the amount of radioactivity left at any point, and by measuring that amount against a calibrated scale based on the radioactivity of modern carbon, it is possible to gauge the age of the host substance. It was in thes way that radiocarbon dating (C-14 dating) was born.

Any organic material is suitable for radiocarbon dating, such as wood, flesh, bone, antler, peat, excreta, grain, even beeswax. Each substance can be made to reveal its age. To check out the theory, Libby experimented with objects of known chronological age, but some early results were disappointing; eventually, however, as laboratory techniques improved, it was believed Libby’s method could provide radiocarbon dates accurate to within a few per cent of the true value. One test was to attempt to date precisely when Hammurabi, the Babylonian king, lived; this is also a subject closely related to the controversial Venus tablets of Ammizaguga (see below). Libby’s results in the 1950s finally gave a figure of c. -1750 for Hammurabi – plus or minus a century. Libby also attempted to provide conclusive evidence for an exact correlation of the Western calendar to the Maya calendar which is still subject to controversy. His result (+415 ±110 years) indicated that the Spinden correlation of +418 seemed to be a better fit than the Goodman-Thompson correlation of +741 (see below).

In general usage Libby’s radiocarbon dating method was subject to practical contamination problems that gave anomalous results. Again, however, as laboratory techniques slowly improved, it was accepted that the method was accurate enough. Libby assumed that carbon-14 had been in the atmosphere in similar amounts at different periods, or in other words, a more or less steady flux of cosmic rays produced a constant proportion of carbon-14 relative to other isotopes of carbon. But this assumption proved to be an oversimplification. Cosmic radiation intensities likely varied in the past; for example, outbursts from the Sun and distant astronomical bodies such as novae, supernovae, pulsars, quasars and enigmatic X-ray bodies may have significant effects on the intensity of cosmic radiation. It has also been shown that lightning bolts can enhance the level of carbon-14 in wood. Dates via radiocarbon methods gave chronological fixes for Egyptian material which were later than historical calendar dates – that was both a puzzle and a nuisance. However, dates for European Megalithic societies seemed just right if equated with the assumed dated derived from prehistoric studies. For example, a date of about -2400 seemed right for Iberia, and likewise dates of -1620 and -1720 for the main structure at Stonehenge. Carbon-14 dating also appeared valid to establish relative chronology. Nevertheless, it soon began to look suspect for exact chronological datings. The solution to the difficulty was resolved by falling back on tree-ring dating. This proved to be the salvation for the radiocarbon method. Particularly in the role played by the bristlecone pine (Pinus aristata) found in the White Mountains in California, the oldest living example of which is 4,600 years old. Earlier in the twentieth century, A. E. Douglas, an American astronomer, pioneered a method of tree-ring dating. Douglas noted that trees of certain species showed marked variations in ring width, reflecting wet and dry years. This he found especially true of the Rocky Mountain Douglas fir and some of the pines. By coring trees with a simple instrument, growth rings can be checked against those in neighboring trees. It is possible to trace missing rings, extra rings and other growth irregularities and so date the rings exactly. By this method it was possible to dat the time the prehistoric Indians built their pueblos.

The method was later applied to bristlecone pines; several of these are some thousands of years old. Long time spans can be cross-calibrated using many tree samples of old living trees and dead wood which overlap in age with samples from young trees. This is possible because of the recurring characteristic recognition rings brought about by various weather conditions. Trees in the same area are affected in much the same way, therefore all carry the same signature. In such a way the bristlecone pine has produced a chronology going back 8,200 years. The bristlecone rings provide samples of wood that can be dated by counting tree rings and by measuring their carbon-14 content, and the two results then compared.

These comparisons yielded results which were so surprising that the whole method was immediately called into question. If one accepted the C-14 correction indicated by the tree rings, the whole structure of prehistoric archaeology was upset.

The check was made: an independent tree-ring calendar was constructed using different wood samples. But the results were the same; the two calendars agreed exactly. These results also confirmed that contrary to widely held belief, each tree ring does not correspond to one year. It confirmed, too, that large radiocarbon discrepancies observed between dendrochronological and radiocarbon ages could not be explained by major systematic errors in tree-ring dating.

For archeology – for astro-archeology – the consequences were far-reaching. Radiocarbon dates before -1000 are too young. All corrections necessary are believed to be applicable uniformly on a world-wide basis. Nevertheless, there remain some minor anomalies to explain away, and it is not certain (c. 1975) that the calibration curve has yet reached its final, definitive shape. The Libby half-life of 5,568 years is thought to be in error. The magnitude of error is still not absolutely clear, but it appears that the Libby value is probably too small. Until everyone has agreed about the value of this all-important half-life, radio carbon dates are still expressed in terms of the standard Libby figure. In the literature carbon datings have a special nomenclature such as bp (before present—reckoned as epoch 1950) and bc/ad (all lower case for carbon dated); these are cited as against BP and BC/AD notations for calendar years. With carbon-date citations the laboratory which published the radiocarbon data is also quoted wherever possible.

This second quote obviously came from my readings on Moon cratering but the file on my PDA doesn’t contain a citation and may no be the complete file I keyed it (I have found that either the PDA or Outlook will truncate long memo files without telling you it is doing it).

Most of the ages of Moon rocks have been deduced through the analysis of radioactive elements with long half-lives, such as rubidium 87, which decays into strontium 87 with a half life of 49 billion years. This means that a rock will loose half of its original composition of rubidium 87 in that time. Of course, Moon rocks are not anywhere near that old. If a Moon rock had, say, 95 percent of its original component of rubidium 87 then its age would work out to be 3.6 billion years, typical of a mare basalt.

You might have noticed a flaw in this dating scheme. How can you tell what the “original” amount of rubidium 87 in the rock is? You can’t go back in a time machine and measure the amount of rubidium when the rock first crystallized from the magma ocean.

The actual technique that isotope chemists use is a bit more complicated and clever. It starts by taking several different mineral samples from the same rock. (This is not hard, because all rocks, when looked at under a microscope, are a mixed-up jumble of different minerals.) All the samples presumably are the same age, but they have different initial rubidium concentrations, because rubidium has a different affinity for different minerals. Over the eons, the crystals that had a lot of rubidium to start with will accumulate a larger fraction of strontium 87 than the ones that started with a small amount of rubidium. When the concentrations of rubidium and strontium 87 in the different samples are plotted on a graph, they form a straight line called an “isochron” (meaning “equal age”). The older the sample, the steeper the line is, and vice versa. So the chemist can use the slope of the isochron to determine the age of the rock – in other words, the amount of time since it last melted Melting resets the slope of the isochron to zero because it lets the excess strontium escape the mineral crystals and be replaced by rubidium again.

As a rule of thumb a radioactive dating system is reliable for only about five half-lives of the “parent” element, because after that time not enough of the parent will remain to be measured accurately. That is why geologists use elements with very long half-lives, such as rubidium 87, to figure out the age of a rock. The most famous radioactive tating technique, carbon 14 dating, is virtually useless for geologists. Because carbon 14 has a half-life of 5,730 years, it cannot be used reliably to date objects more than 28,000 years old. That is fine for dating human artifacts, which are almost always younger than this, but not for dating rocks.

In spite of the five-half-life rule of thumb, the most exciting recent developments in lunar chronology do involve elements with shorter half-lives, such as hafnium 182, which decays to tungsten182 with a half-life of 9 million years. Hafnium 182 is an “extinct radionuclide,” an isotope that no longer exists naturally because it decays so rapidly. But it does have a fingerprint. Any time an isotope chemist finds an atom of tungsten 182, he knows that it came from a hafnium 182 atom, because the normal flavors of tungsten have atomic weights of 183, 184 and 186.

Now hafnium is a rock-loving element, while tungsten is metal loving. [Thus the decay of hafnium 182 can be used to tell when a planet’s core formed. To see why, consider two possibilities.

1. The core formed early, when the hafnium 182 was still “alive.” In this case, rocks in the mantle would become enriched with hafnium 182, because hafnium is rock-loving; they would be depleted in tungsten 183, 184 and 185. As the hafnium decays, it would be replaced by tungsten 182. But this tungsten would stay in the mantle, because the iron it likes to alloy with has already filled the planet’s core. As a result, the planet’s mantle would have a disproportionately high amount of tungsten 182 compared to the ordinary isotopes.
2. The core formed late, more than 45 million years (or five half-lives of hafnium 182) after Time Zero. In this case, all the hafnium 182 would be converted to tungsten 182 before the core formed. This tungsten would escape into the core along with the ordinary isotopes, because chemically they are no different from one another. (The missing neutrons in tungsten 182 make it lighter but do not affect its iron-loving properties.) Thus only a small amount of tungsten would remain in the mantle and there would be no excess of tungsten 182.

To state things succinctly, radioactive dating techniques that use long-lived elements, such as strontium, measure the time between a rock’s crystallization and the present. Dating techniques that use short-lived elements, such as hafnium, measure the time between the rock’s crystallization and the beginning of the solar system.