Different crystals have different symmetries and these can be read off from the structure factor. For example, a perfect single crystal with the symmetry called body-centred cubic (bcc) shows, when viewed from one angle, a structure factor with a set of sharp points including six arranged at the corner of a hexagon.
The calculator to the left is solar powered, via the little solar panel at the top right. Small cheap solar panels like those in calculators are made from amorphous silicon, because its a lot cheaper than its more efficient but pricey, cousin crystalline silicon. In crystalline silicon the silicon atoms are arranged in a regular crystal lattice — as it happens the arrangement is similar to that of water molecules in ice.
We take crystals for granted, maybe because they are so common. The Earth’s crust is crystalline, as are our cutlery, and even our bones and teeth are partly crystalline. But crystals are remarkable things. Although most crystalline materials are made of many tiny crystals mushed together (our bones are like this), sometimes huge single crystals can grow. There are crystals in the Naica mine in the Chihuahua state* of Mexico that are over 10 cubic metres in volume. This corresponds to maybe 1030 atoms. And in a single crystal, all atoms are on the same crystal lattice, all 1030 of them here. So the relative positions of pairs of atoms in one corner of the crystal are the same as in the opposite corner over 10 metres or more than 10 billion layers of atoms away. That’s a lot of layers, and presumably they grew one at a time. These big crystals may have started growing before the first civilisations arose in what is now Egypt and Iraq, thousands of years ago. The growth of large perfect crystals can be a slow business.
One of the things I work on is the nucleation of crystals. Nucleation is how crystals start to form, and so control over nucleation basically means being able to start a crystal growing where we want and when we want. We scientists have tried really quite hard to do this, for decades, and to be honest we are still pretty rubbish at it. We still can’t predict what we need to do to make a crystal on command. Sometimes nothing happens when we want a crystal to nucleate, other times when we want one crystal to form, instead we get dozens. It is a bit of a tale of woe.
Water is everywhere – we have been inundated with the stuff over the last few months. But maybe we should not take it for granted. In Britain water is everywhere but in the universe as whole liquids of any sort are extremely rare. And even on Earth, water is pretty much the only liquid around.