 First of all, diamond. In diamond, each carbon atom forms single bonds to four other carbon atoms, and the four bonds are arranged in a tetrahedral geometry. This is just like the methane molecule, except that in methane, the carbon bonded to four hydrogen atoms. Since hydrogen atoms can only form one bond, they represent a dead end. But when a carbon atom bonds to another carbon atom, that second one can bond to another three atoms, and they can each bond to another three and so on. As long as you have atoms, the molecule, or lattice, can keep on growing. So when many carbon atoms bond together in this formation, the result is a three-dimensional lattice held together by covalent bonds. We call this kind of covalent structure one that can be extended in all directions like a lattice, covalent network bonding. This is what makes diamonds so hard and so strong. A single diamond crystal is in effect a giant molecule, and in order to break it, you must break the covalent bonds between many carbon atoms. This is in contrast to, say, ice, which is made up of many separate water molecules. When you shatter an ice cube, you're merely separating the molecules from each other. You're not breaking the covalent bonds that hold the molecules together. Like most covalent compounds, diamond doesn't conduct electricity because the pairs, the electron pairs, are confined within the covalent bonds, and they can't move through the compound. Recall the difference with conductive metals, which have the delocalized valence electrons that can move through the lattice of positive metal ions, and thus conduct electricity. Graphite is another well-known allotrope of carbon, and it has a more complex structure. The bonding in graphite is a bit like the bonding in ethene. Each carbon atom bonds to three other carbon atoms using two single bonds and one double bond. The result of this is a continuous lattice of flat hexagons with alternating single and double bonds. Each lattice is a flat single sheet, only one carbon atom thick, and each layer is quite strong for its thickness because, like diamond, it's held together by covalent bonds. These 2D sheets of carbon can stack on top of one another to form the grey solid that we're familiar with, but neighbouring sheets are stuck together only by very weak attractions called van der Waals forces, and we're going to explore these more in semester two as well. There are no covalent bonds that tie the separate sheets together, only these weak attractions. So this means that the sheets can be separated from each other quite easily, and this is exactly what happens when you drag the tip of a pencil across some paper. Sheets of graphite are sheared off from the main lump and stick to the paper. In addition, there's something else about this bonding arrangement that gives graphite special properties. The pattern of single and double bonds in graphite is not fixed but can alternate, so that single becomes double and double becomes single. This means that the extra electrons that form these alternating single and double bonds are essentially able to move through the 2D lattice, and that means that graphite is conductive.