Forces of Nature. Andrew Cohen

those doors would be opened by future generations. He asserts, correctly, that the structure of the snowflakes must be due at least in part to some underlying structure or shape, but given that atomic theory didn’t move into the realm of experimentally testable science until the early nineteenth century, and the structure of atoms themselves was a twentieth-century discovery, Kepler had no way of unlocking the doors. We now know that the building blocks of snowflakes are water molecules, and water molecules are capable of extremely complex behaviour when they get together. That may be a surprising statement if we think of water as the colourless, odourless liquid in a glass. Perhaps it shouldn’t be so surprising if we think of water molecules as the objects that come together spontaneously to produce the romantic flourishes of form and exquisite diversity of snowflakes.

      Single water molecules aren’t particularly complicated. They are molecules of hydrogen and oxygen, bonded together. Oxygen was first isolated in 1774 by Joseph Priestley, the son of a Yorkshire woollen cloth maker, and Henry Cavendish first identified hydrogen in 1766. The Nobel Prize in Physics in 1926 was awarded to Jean Baptiste Perrin for the confirmation of the physical reality of molecules, just about within living memory, which demonstrates how difficult it is to study the microscopic world and how quickly cutting-edge science can become common knowledge.

      A water molecule consists of two hydrogen atoms bonded to a single oxygen atom: H₂O (see illustration here). The water molecule isn’t linear – the hydrogen atoms are displaced at an angle of 104.5 degrees. The reason for this is the presence of two extra pairs of electrons that sit on the opposite side of the oxygen atom. To see why that is, let’s have a very brief tutorial on atomic physics and quantum mechanics.

      Atoms are made up of three constituents, as far as chemists are concerned (we’ll dig more deeply into this later on); they consist of a small, dense, atomic nucleus made up of protons and neutrons, with electrons orbiting a long way away. If the nucleus were the size of a tennis ball, the outer electron orbits would be several kilometres across. Hydrogen is the simplest element; its nucleus consists of a single proton. Next is helium, which contains two protons and two neutrons. Oxygen has eight protons and eight neutrons. The nucleus is surrounded by electrons, which are held in place by one of the four fundamental forces of Nature: electromagnetism. Electrons are negatively charged and protons are positively charged, and the negative electric charge of the electron is precisely equal in magnitude but opposite in sign to the positive electric charge of the proton. Nobody knows why these charges are precisely equal in magnitude; it’s one of the great mysteries of fundamental physics. The atoms of each chemical element are electrically neutral, which means that the number of protons in the nucleus is equal to the number of electrons that surround it. Hydrogen atoms have a single electron, therefore, whilst oxygen atoms have eight electrons.

      The structure of a water molecule, showing oxygen’s eight electrons, two of which are shared with the hydrogen atoms.

      The hexagonal crystalline structure of Ice 1_h. Water molecules are attached together by hydrogen bonds, with oxygen atoms from one water molecule lining up with hydrogen atoms from another.

      Now we need a little sprinkle of quantum theory. You can picture the electric charge of the atomic nucleus as creating a kind of box within which the electrons are trapped. Electrons, along with all of the fundamental building blocks of the Universe, obey the laws of quantum theory, which describe how they move. It turns out that the basic rules of quantum theory are counterintuitive and fly in the face of common sense. But that is okay because there is no reason at all to expect the laws that govern the Universe to be in accord with ‘common sense’. The most fundamental rule governing the behaviour of subatomic particles is that they don’t like to stand still. Unfettered, they are very likely to wander off, and the more we try to pin them down, the more they are inclined to wander. The presence of the nucleus tames the anarchic electrons somewhat, by confining them to the ‘nuclear box’.

      Another rule governing the behaviour of electrons is that they don’t much like each other’s company. This is known as the Pauli exclusion principle, also a consequence of the laws of quantum theory. Electrons will arrange themselves around the nucleus such that they stay away from each other, as best they can. There is a caveat, though, which is important for understanding the structure of atoms. Electrons of opposite spin are allowed to get close together (or ‘pair up’). Of course they cannot get too close because they have the same electric charge and ‘like-charges repel’. Spin is a property of subatomic particles that is easy to name but hard to picture. You could think of electrons as little spinning tops, if you like, but that’s a bad analogy on many levels, so you probably shouldn’t. Having said that, spin is a measure of how much an electron is spinning – it is just that the notion of a spinning point is not something we can easily imagine. For particles such as electrons, which are known as ‘spin ½’ particles or fermions, spin can have only two values; these are known as spin-up and spin-down. Spin is a direct, if rather subtle, consequence of the merger between Einstein’s Theory of Special Relativity and quantum theory, achieved by physicist Paul Dirac in his equation describing the electron in 1928. The details don’t matter here; what matters is that the negatively charged electrons get trapped by the positive electric charge of the protons in the atomic nucleus and that electrons tend to keep away from each other, although opposite-spin electrons can get closer together than same-spin electrons can. This is enough information for us to get a basic understanding of a water molecule. Oxygen has eight electrons. Two of the electrons sit close to the nucleus and do not play much of a role in binding the two hydrogen atoms to the oxygen. The remaining six are shared out as in the diagram here.³

       ANOTHER RULE GOVERNING THE BEHAVIOUR OF ELECTRONS IS THAT THEY DON’T MUCH LIKE EACH OTHER’S COMPANY. THIS IS KNOWN AS THE PAULI EXCLUSION PRINCIPLE.

      One of the basic concepts in chemistry, which again goes all the way back to the fundamental laws of quantum theory, is that electrons can be shared between atoms. This results in the formation of a chemical bond. Two hydrogen atoms will share their single electrons with an oxygen atom if they can, pairing up to fill the two remaining outer slots around the oxygen nucleus; the result is a water molecule, which is shown in the top illustration. The reason for the 104.5-degree ‘kink’ is the presence of the other two pairs of electrons in the outer level of the oxygen atom. They take up residence on the opposite side of the oxygen atom to the hydrogen atoms, giving the water molecule its distinctive shape, and its many unusual properties.

      The water molecule, like its constituent atoms, is electrically neutral, but the uneven distribution of electrons means that the hydrogen atom ‘legs’ have a very small net positive charge, whilst the oxygen end of things has a slight net negative charge. Water is known as a polar molecule for this reason – it has a negative end and a positive end. This opens up a world of complexity.

      An important consequence of water’s polarity is that water molecules like to stick together. The negatively charged oxygen ends of water molecules attract the positively charged hydrogen ends of other water molecules and they attach together through what is known as a hydrogen bond. This happens to an extent in liquid water, resulting in quite large and complex structures.

      The effects are even more dramatic when temperatures drop and water freezes to form ice. Water ice is very weird stuff. There are seventeen known forms of ice, the most common of which on Earth is called Ice 1_h (the structure of which is shown in the lower illustration). The regular crystalline structure leads to one of water’s most bizarre properties: ice floats. This is very unusual behaviour. Every other commonly occurring solid is denser in the solid phase than in the liquid phase, and therefore does not float