Page 89 - Electrical Properties of Materials

Bond types 71

The properties of the covalent bond, also called the valence or homopolar
bond on occasions, is the most important single topic in chemistry, yet its
mechanism was completely inexplicable before the rise of quantum mechanics.
The exact mathematical description is immensely difficult, even for people
with degrees, so in an undergraduate course we must be modest. The most
we can hope for is to get a good physical picture of the bond mechanism,
and perhaps an inkling of how a theoretical physicist would start solving the
problem.
The simplest example of the covalent bond is the hydrogen molecule, where
two protons are kept together by two electrons. The bond comes about because
both electrons orbit around both atoms. Another way of describing the bond is
to appeal to the atoms’ desire to have filled shells. A hydrogen atom needs two
electrons (of opposite spin) to fill the 1s shell, and lacking any better source of
electrons, it will consider snatching that extra electron from a fellow hydrogen
atom. Naturally the other hydrogen atom will resist, and at the end they come to
a compromise and share both their electrons. It is as if two men, each anxious
to secure two wives for himself, were to agree to share wives. ∗ ∗ The analogy also works, as a femin-
Another example is chlorine, which has five 3p electrons and is eagerly ist friend has pointed out, if two women,
each anxious to secure two husbands for
awaiting one more electron to fill the shell. The problem is again solved by
herself, were to agree to share husbands.
sharing an electron pair with another chlorine atom. Thus, each chlorine atom
for some time has the illusion that it has managed to fill its outer shell.
Good examples of covalent bonds in solids are carbon, silicon, and ger-
manium. Their electron configurations may be obtained from Table 4.1. They
are as follows:

2
2
C: 1s ,2s ,2p 2
2
2
2
6
Si: 1s ,2s ,2p ,3s ,3p 2
2
6
2
2
2
2
10
6
Ge: 1s ,2s ,2p ,3s ,3p ,3d ,4s ,4p .
It can be easily seen that the common feature is two s and two p electrons
in the outer ring. The s shells (2s, 3s, 4s, respectively) are filled; so one may
expect all three substances to be divalent, since they have two extra electrons
in the p shells. Alas, all of them are tetravalent. The reason is that because
of interaction (which occurs when several atoms are brought close together),
the spherical symmetry of the outer s electrons is broken up, and they are per-
suaded to join the p electrons in forming the bonds. Hence, for the purpose
of bonding, the atoms of carbon, silicon, and germanium may be visualized
with four dangling electrons at the outside. When the atoms are brought close
to each other, these electrons establish the bonds by pairing up. The four elec-
trons are arranged symmetrically in space, and the bonds must therefore be
tetrahedral, as shown in Fig. 5.3.
In covalent bonds all the available electrons pair up and orbit around a pair
of atoms; none of them can wander away to conduct electricity. This is why car-
†
bon in the form of diamond is an insulator. The covalent bonds are weaker in † Incidentally, carbon can have another
silicon and germanium, and some of the electrons might be ‘shaken off’ by the type of bond as well. In its graphite form,
thermal vibrations of the crystal. This makes them able to conduct electricity consisting of layers on top of each other,
it is a fairly good conductor.
to a certain extent. They are not conductors; we call them semiconductors.