THE SIXTH ELEMENT

© Lene Sælen

Diamond is the hardest material in nature and can only be cut by itself. This material, whose name is derived from the Greek word for ‘invincible’, is made solely of carbon. Graphite is also made of pure carbon, but is a distinctly softer material used for instance in pencils. Carbon is indeed a strange material, but it also happens to be the most important material in your life.

What’s so great about carbon?
Carbon is element number 6 in the periodic table, belongs to the non-metallic elements and has chemical symbol C. The most common isotopes of carbon is C-12, C-13 and C-14. Carbon has an atomic weight of 12.0107 atomic mass units and is solid at room temperature. Carbon has the highest melting point of all the elements, remaining solid at temperatures up to 4300°C. At this point carbon begins to sublimate, a process in which solid material transformes directly into wapour without going through a liquid phase.

Carbon as diamond is one of natures most desirable gemstones due to diamonds magnificent lustre, while artificial diamonds and diamond dust are used in drilling-, grinding- and cutting equipment due to their extreme hardness. In nuclear reactors carbon graphite is used as a neutron moderator, while steel is made by adding carbon to iron. Dust from diamonds conduct heat extremely well and is therefore used as coolants in computers, while the radioactive isotope C-14 is vital in the process of dating dead organic material.

But this does not make carbon any more special than your average element, of which there are 92 on earth. What separates carbon is its crucial partaking in the evolution of life as we know it. Carbon is found in 95% of all known chemical compounds on the planet and in every single lifeform. But why did carbon become the building block of life? It is not found in copious amounts on earth as one might think. In fact, carbon doesn’t even make it to the top seven list of the most abundant elements on earth.
In forming chemical bonds, carbon is superior to its fellow elements, as it easily bonds with other carbon atoms and non-metallic elements, especially nitrogen, phosphorus, oxygen, sulphur and hydrogen. Compared to carbon, the other more abundant elements on the list either form fewer or stronger bonds. In addition, some of them are trapped in minerals in the earth’s crust and are unavailable. Carbon based life therefore owes its success to the many bonds carbon makes, and the fact that the bonds are relatively weak. Because of this, carbon bonds are easily broken and reformed, creating an adaptable system.

Stardust
Where does carbon come from?
Some time ago, when the universe was mere three seconds old, only a hot soup of elementary particles existed. With temperatures reaching 7 billion°C, it would take the universe 300 000 years to cool enough for the simplest hydrogen- and helium atoms to form. Another 300 million years, and the force of gravity have amplified density fluctuations to a point where star formation could begin. Still we are 13.4 billion years from the present. Stars form from aggregates of matter compressed by gravity to such densities that atoms begin to fuse. Hydrogen, making up 90% of all the matter in the universe, come together in pairs and form helium by fusion – a process which releases huge amounts of energy. The energy is in the form of light, making the stars shine. The radiation pressure from the released light also prevents the stars from collapsing due to gravity. The period of time a star can exist in this harmonious state depends on its mass. Our own sun is fairly average in this respect, having a mass of about two-thousand-billion-billion-billion kilograms, the equivalent of 300 000 earth-sized planets. Every second our sun fuse 700 million tons of hydrogen into 695 tons of helium, while 5 tons are converted to highly energetic radiation. The sun has been doing this for 5 billion years, and will continue to do so for another 5 billion years before it becomes a red giant, devouring the earth in the process. It is during this violent phase that the sun produces heavier elements like carbon, nitrogen, oxygen, fluorine and sodium. Even heavier elements are produced in supermassive stars and gigantic star explosions knows as supernovas. The sun, briefly settling down as a planetary nebula, will eventually scatter its stardust throughout the universe, supplying planets like our own with maybe just the right amount of carbon to support the evolution of life. At least we can thank the stars for our carbon repository.

However, it all turns out to be crucially dependent on the finetuning of some of nature’s physical parameters.

The triple-alpha process and other difficulties
Firstly, star formation would not be possible at all if the gravitational constant – effectively the strength of gravity – was even slightly different. A bit lower, and gravity would be too weak to pull matter together forming stars; a bit higher, and every star would collapse much too soon. The process responsible for carbon production in stars is called the triple-alpha process. In this nuclear reaction three helium nuclei, sometimes called alpha-particles, fuse to become one carbon nucleus. The triple-alpha process happens in two stages, in which the first involves forming a beryllium-8 nucleus from two of the helium nuclei. A fusion between the third helium nucleus and the beryllium nucleus then results in carbon. The only problem is that the beryllium-8 nucleus is unstable and decays into two helium nuclei almost immediately. If you think one year is brief compared to the 13.7 billion years the universe has existed: beryllium-8 lives 10 times shorter compared to one second. In other words, it has a lifetime of 0.00000000000000026 seconds. In the core of a red giant this would meen that at any given time there is about one beryllium-8 nucleus per billion helium nuclei. To counteract this imbalance, the fusion between helium and beryllium should happen with a relatively high probability.

It doesn’t. In the 1950s, a British astronomer named Fred Hoyle calculated that the so far assumed process was far too slow to be responsible for the amounts of carbon found in nature. However, he came up with a clever explanation. Nature, it would seem, had another finely tuned lucky chance in store. Hoyle could make the process run fast enough if he assumed that there existed an excited state in carbon, which exactly matched the combined energies of the beryllium and helium nuclei. This, in the language of physics, is called a resonance. Mechanical systems exhibit resonances when an external periodical force has the same frequency as the natural frequency of the system. When on a swing, you change your center of weight in resonance with the system consisting of you and the swing. By doing so you gradually build up speed, and the swing goes higher and higher. Music instruments also utilize resonances. A guitar string mounted without a guitar case will barely be audible, but on a guitar it will emit a clear, strong note. It is the resonating chamber which amplifies the sound and creates a unique timbre. Similar resonances can occur in nuclear reactions, and it was just such a resonance Hoyle looked for to explain the observed amount of carbon in the universe. He discovered that in order for the world as we know it to exist, there had to be an excited state in carbon with the energy 7.65 mega electron volts. Mega electron volt is an energy unit often used when discussing nuclear reactions.

Let me explain the concept of an excited state a bit further. In the smallest of systems consisting of elementary particles, nature does not permit the particles to behave in any way they might wish. Not all energies are allowed, even those predicted from our ‘regular’ physics, which is Newtonian or Classical Mechanics. The system has been quantized, from which derives the name Quantum Mechanics, the theory to explain matter at very small scales. According to this theory, a system also has a smallest possible energy, which we call the ground state. Every other allowed energy corresponds to an excited state. Computing these states accurately is practically impossible even for the simplest systems. To accurately predict such a state, partly based on arguments that we wouldn’t exist otherwise, was quite an accomplishment. In fact, it was almost outrageous to make such claims concerning complex nuclear states, especially if you were not a nuclear physicist; Hoyle was an astronomer. But there was a nuclear physicist willing to listen to Hoyle. Willy Fowler was an experimental physicist at the California Institute of Technology. Together with his team he set up an experiment designed to discover the excited state predicted by Hoyle. After only ten days of testing Hoyle’s prediction was verified and scientific history was made.

Hoyle would later discover that several aspects of the triple-alpha process were dependent upon finely adjusted parameters. These parameters were not only critical to the carbon process, but also play a vital role in the creation of some 20 other elements essential to life. If the beryllium isotope formed from the two helium nuclei was stable, all the helium would instantly fuse to carbon once the first fusion step had started. This would free enormous amounts of energy, causing the star to explode and preventing any heavier elements from forming. But it does not end here. When carbon has formed from beryllium and helium, it will collide with new helium nuclei. Sometimes these collisions produce oxygen, another element vital to life. This reaction must proceed at a pace which does not cause an imbalance in the relative abundance of carbon and oxygen. Any resonant state in oxygen would disturb the delicate balance. As you might guess, no such state exists.

Fowler received the Nobel prize for his work on nuclear reaction in stars, and their significance to the formation of chemical elements in the universe. Like so many others, Hoyle was neglected, and he received no award for his groundbreaking ideas.

43 years after Hoyle and Fowler’s discoveries, in 2000, the physicists Oberhummer, Csoto and Schlattl investigated just how sensitive the triple-alpha process is to variation in the laws of physics. The force that binds nuclear particles together and governs the fusion process is called the strong nuclear force. It is one of four fundamental forces in nature. How much change would it take to critically alter the production of carbon, so essential to life? They found that a modest 0.4% change would render the development of carbon-based life impossible.
The production of carbon is just one of many prerequisites essential to life here on earth. All in all an uncanny amount of parameters seem to have tilted in our favor during the last 13.7 billion years, so that one day we would have the opportunity to wonder about all nature’s coincidences.

Lene Sælen
Department of Physics and Technology
University of Bergen