Radiocarbon (C14) Dating
|Of course you know how radiocarbon or C14 dating works on principle. I did credit you with a halfway decent education, remember? So in what follows I only want to refresh your memory.|
|The first thing to remember is that
plants turn the carbon dioxide or CO2 contained in the air into
solid organic stuff like barley (for making beer), leaves (for shading beer
gardens), grass, cauliflower. Or worse, leeks, celery, Brussels sprouts and all
kinds of salad. Then your wife (or kids if they study medicine like mine) force
you to eat that.
Fortunately animals like chicken, cows and pigs also eat the plant stuff, turning it into something useful like steaks or ham which some of us also eat.
|Whatever the food chain looks like
in detail, one fact applies to everything that was once alive. As soon as
something organic like you dies in some (hopefully far away) time in the
future, or the tree you felled with your car, or the grass that withered in the
sun, there is now some dead body around that contains a lot of carbon that came
exclusively from the carbon dioxide in the air via the food chain.
Now something special happens. The carbon in the dead organic matter slowly changes over the years. And with carbon I mean the individual carbon atoms, no matter in what kind of molecules they find themselves as time goes by. When you're dead you rot and turn to compost but this involves only chemical reactions that change the molecules but not the atoms. The basic insight is that all the oxygen, hydrogen, phosphorous, nitrogen and so on atoms do not change at all - except for the carbon atoms.
We need to answer two basic questions now:
|1. How can an atom
change itself? There are two basic ways:
|You might wonder about the electrons surrounding any atom - what's their role in this? None. They just rearrange to whatever is needed. The energy involved for this is minuscule compared to what's going on in the nucleus and thus can be neglected.|
|2. How can some carbon atom be different from any other carbon atom?
|The last thing to remember now is that some isotopes are stable forever, some decay radioactively. As it turns out, the carbon isotopes 12C and 13C are stable. 14C, however, decays with a halftime of 5 730 ± 40 years. In other words, if you start with 1 000 14C atoms, you will only have 500 left after 5 730 years. 250 after 2 ×5 730 years = 11 460 years, and so on.|
|How It Works|
|All elements where made some time ago
(like 10 billion years or so), either in the big bang or inside a sun. The
ratio of the isotopes of a given element was fixed right then, and all the
radioactive ones have long since disappeared (with a few exceptions that are of
no interest here). The ratio of 12C to 13C thus is fixed
at 99 : 1, and this ratio is immutable.
There is no 14C left over from the times when all the carbon atoms were made.
|However, the atmosphere of our
planet consists of 78.08% nitrogen molecules (N2), 20.95% oxygen
molecules (O2), 0.93% argon (Ar), 0.038% carbon dioxide molecules
(CO2) plus traces of other stuff of no importance here. What is of
importance here is that all these molecules and atoms in the upper strata of
the atmosphere get hit by highly energetic particles of the cosmic radiation
that bombard the earth relentlessly all the time. The atmospheric layers up
there stops most of this radiation. That is generally a good thing for normal
people because we would not be here or last very long if we would be hit by
It is also a good thing for archeologists because some of that radiation hits nitrogen atoms and turns them into the 14C isotope. The precise reaction is
|In words: A nitrogen atom with (per
definition) 7 protons and 7 neutrons (adding up to 14N) gets hit be
a neutron (n) that was supplied by cosmic radiation, and turns into the
unstable 15N isotope that decays immediately into 14C by
emitting a proton (p).
In yet other words: In the upper atmosphere 14C is generated at a constant rate. It trickles down, forms carbon dioxide, and gets incorporated into plants and finally into everything alive. It decays inside you but as long as we live, we replenish it and essentially keep up a constant level of 14C in our organic bodies. As soon as we die, no more 14C is added to the remains and whatever was there now decreases in concentration by a factor of two every 5 730 years.
|Radiocarbon dating now is easy. Measure the relative concentration of the14C isotope in living (or freshly dead) organic material, and you have the starting point. It is about 1 part per trillion, i.e. you have about 600 billion radioactive carbon atoms in one mol of carbon. A mol is a defined amount of stuff.|
|If the organic matter you unearthed
somewhere (typically coal from some old fire, bones or wood remains; all
containing carbon) happens to be 5 730 years old, you would find only half of
that concentration or only 300 billion radioactive carbon atoms in one mol of
With a little simple math, the "Before Present" or BP age tBP of a sample comes out to
|N is the measured 14C concentration; N / N0 thus the relative concentration of how much 14C is left. This follows straight from our old beer math.|
|Is that cool or what? So of course you know everything about the hero of science who came up with that monumental recipe for dating old organic things: Willard Frank Libby and his team at the University of Chicago first came up with the method in 1946; Libby got the Nobel price in 1960.|
|The basics are clear now. It only
remains to look at the small print coming with the general recipe for
14C dating. We need to answer two big questions:
|How It Is Done|
|How is it done? Well - the stuff is radioactive after all! So get a Geiger counter or whatever else registers radioactive decay, hold it over your sample, and measure how many "clicks" you get per time unit (= N). Repeat with a sample of modern carbon that contains exactly as much carbon as the sample you want to date to give you the N0. Use the equation form above and you are done.|
|OK - that's how Libby did it, and
there are problems, of course. From tiny samples you don't get that much
signal, so your N value has an error of roughly
N0 value has an error - and how do you determine the
exact weight you need (or just the exact carbon weight of your sample)? Than
your halftime value may be a bit off. In fact, Libby used a value of
5568±30 years that was later corrected to 5730±40 years.
Maybe your sample as contaminated with a bit of "fresh" carbon? The tree those Greek guys used to barbecue their rabbit was a 500 year old oak that was felled by a flash of lightning - your are 500 years off the proper date of the fire! An so on.
The most tricky source of error, however, is that the 14C/12C ratio for "fresh" carbon is not really constant as was assumed as a matter of course. This may have several reasons:
|Since we have some more methods to date things, and since more and more details become clear, we now have a calibration curve:|
|As the examples show, a radiocarbon age of 20 000 (10 000) years translates into 23 900 (11 400) BP years or 21 900 (9 400) BC. So be careful about the BP and the BC! With this curve we get rid of the fluctuating 14C/12C ratio problem, at least to some extent. We are also rather certain that the halftime is now as correct as it can be. The only problem that remains is to measure the amount of 14C still there. That gets more difficult for old thing because most of it has already decayed and thus disappeared, and for very small specimen that do not contain much to start with. The decay rates then are so low that they do not register anymore in your Geiger counter or more sophisticated equipment.|
|That's when "accelerator mass spectrometry" (AMS) kicks in. This is rather tricky (and very expensive) but allows a far better analysis of the 14C/12C ratio for far smaller samples than the direct method.|
|How does it work? You atomize your
specimen, ionize the carbon (and whatever else will get ionized), accelerate
those ions by high voltage, run them through a thin film to strip off electrons
in order to destroy all charged molecules (like 13C1H)
that might be in there and would be confused with 14C, accelerate
the pure ions now once more with a really high voltage (several million Volts),
and separate different atoms and their various isotopes by magnetic fields into
individual ions beams. Measure how much 14C and 12C flies
along and you have the ratio.
Here is an impression of what is involved (from the Leibniz Laboratory for Radiometric Dating and Stable Isotope Research of my University (Christian-Albrechts-University of Kiel, Germany).
|Doesn't look cheap, isn't cheap, and is not all that easy to operate. You need to know exactly what your are doing, in particular with respect to specimen preparation. The data you get are only as good as your specimen. Breath at it once in the wrong way, and its contaminated with fresh carbon, yielding faulty results.|
|Not sparing time and money, how good can it be? Well, after about ten half-lives, approximately 60,000 years, not much 14C is left (1/ 210) » 1/1 000). That gives sort of the lower limit for a 1 mg sample. Very young stuff is problematic too, but why should you want to date that?|
|Pure iron, copper, gold and so on, not containing any carbon, cannot be dated this way at all, of course. But what about steel? It contains carbon and that we can dated. Yes - but where did that carbon come from? If it came exclusively from the charcoal used in the smelting process, you get the age of the tree the charcoal was made from, and that should be close enough. However, if some of the carbon came from the limestone or calcium carbonate (CaCO3) that was added for some reason, or if you used coal (from trees that died many million years ago) your results are useless.|
General Remarks to Literature and Sources
Diffusion in Iron
10.2 Making Iron 10.2.1 Early Iron
Phosphorous Steel; 9.4.1 General Remarks
11.1.4 Swords of Major Near East Powers in the 1st Millennium BC
Early Copper Sites
Large Pictures 1
11.4.2 Blades of Viking Era Swords
Large Pictures chapter 11.4
10.3 Iron and Steel in Early Europe; 10.3.1 Technology Transfer and Trading
11.1.3 The The Luristan Iron Sword
Old Copper Complex of the Western Great Lake
Rosh Horesha, Shanidar Cave
More Luristan Swords
© H. Föll (Iron, Steel and Swords script)