10.4 Covalent Materials

In covalent materials, the atoms are held together by covalent chemical bonds. Such bonds are strong. Note that the classification is somewhat vague; many crystals, like quartz (silicon dioxide), have partly ionic, partly covalent binding. Another ambiguity occurs for graphite, the stable form of carbon under normal condition. Graphite consists of layers of carbon atoms arranged in a hexagonal pattern. There are four covalent bonds binding each carbon to three neighboring atoms in the layer: three sp$\POW9,{2}$ hybrid bonds in the plane and a fourth $\pi$-​bond normal it. The $\pi$-​electrons are delocalized and will conduct electricity. (When rolled into carbon nanotubes, this becomes a bit more complicated.) As far as the binding of the solid is concerned, however, the point is that different layers of graphite are only held together with weak Van der Waals forces, rather than covalent bonds. This makes graphite one of the softest solids known.

Under pressure, carbon atoms can form diamond rather than graphite, and diamond is one of the hardest substances known. The diamond structure is a very clean example of purely covalent bonding, and this section will have a look at its nature. Other group IV elements in the periodic table, in particular silicon, germanium, and grey tin also have the diamond structure. All these, of course, are very important for engineering applications.

One question that suggests itself in view of the earlier discussion of metals is why these materials are not metals. Consider carbon for example. Compared to beryllium, it has four rather than two electrons in the second, L, shell. But the merged 2s and 2p bands can hold eight electrons, so that cannot be the explanation. In fact, tin comes in two forms under normal conditions: covalent grey tin is stable below 13 $\POW9,{\circ}$C; while above that temperature, metallic white tin is the stable form. It is often difficult to guess whether a particular element will form a metallic or covalent substance near the middle of the periodic table.

Figure 10.14: Schematic of crossing bands.
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Figure 10.14 gives a schematic of the energy band structure for a diamond-type crystal when the spacing between the atoms is artificially changed. When the atoms are far apart, i.e. $d$ is large, the difference from beryllium is only that carbon has two electrons in 2p states versus beryllium none. But when the carbon atoms start coming closer, they have a group meeting and hit upon the bright idea to reduce their energy even more by converting their one 2s and three 2p spatial states into four hybrid sp$\POW9,{3}$ states. This allows them to share pairs of electrons symmetrically in as much as four strong covalent bonds. And it does indeed work very well for lowering the energy of these states, filled to the gills with electrons. But it does not work well at all for the “anti-bonding” states that share the electrons antisymmetrically, (as discussed for the hydrogen molecule in chapter 5.2.4), and who do not have a single electron to support their case at the meeting. So a new energy gap now opens up.

At the actual atom spacing of diamond, this band gap has become as big as 5.5 eV, making it an electric insulator (unlike graphite, which is a semi-metal). For silicon however, the gap is a much smaller 1.1 eV, similar to the one for germanium of 0.7 eV; grey tin is considerably smaller still; recent authoritative sources list it as zero. These smaller band gaps allow noticeable numbers of electrons to get into the empty conduction band by thermal excitation, so these materials are semiconductors at room temperature.

Figure 10.15: Ball and stick schematic of the diamond crystal.
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The crystal structure of these materials is rather interesting. It must allow each atom core to connect to 4 others to form the hybrid covalent bonds. That requires the rather spacious structure sketched in figure 10.15. For simplicity and clarity, the four hybrid bonds that attach each atom core to its four neighbors are shown as blue or dark grey sticks rather than as a distribution of grey tones.

Like for lithium, you can think of the spheres as representing the inner electrons. The grey gas represents the outer electrons, four per atom.

To understand the figure beyond that, first note that it turns out to be impossible to create the diamond crystal structure from a basis of a single atom. It is simply not possible to distribute clones of a single carbon atom around using a single set of three primitive vectors, and produce all the atoms in the diamond crystal. A basis of a pair of atoms is needed. The choice of which pair is quite arbitrary, but in figure 10.15 the clones of the chosen pair are linked by blue lines. Notice how the entire crystal is build up from such clones. (Physically, the choice of basis is artificial, and the blue sticks indicate hybrid bonds just like the grey ones.) One possible choice for a set of three primitive translation vectors is shown in the figure. The more usual choice is to take the one in the front plane to the atom located at 45 degrees instead.

Now notice that the lower members of these pairs are located at the corners and face centers of the cubic volume elements indicated by the fat red lines. Yes, diamond is another example of a face-centered cubic lattice. What is different from the NaCl case is the basis; two carbon atoms at some weird angle, instead of a natrium and a chlorine ion sensibly next to each other. Actually, if you look a bit closer, you will notice that in terms of the half-size cubes indicated by thin red frames, the structure is not that illogical. It is again that of a three-di­men­sion­al chess board, where the centers of the black cubes contain the upper carbon of a basis clone, while the centers of the white cubes are empty. But of course, you would not want to tell people that. They might think you spend your time playing games, and terminate your support.

If you look at the massively cross-linked diamond structure, it may not come as that much of a surprise that diamond is the hardest substance to occur naturally. Under normal conditions, diamond will supposedly degenerate extremely slowly into graphite, but without doubt, diamonds are forever.