Page 85 - Electrical Properties of Materials

General mechanical properties of bonds 67

from obvious. Unless you find these glimpses behind the scenes fascinating in
themselves you might come to the conclusion that the labour to be expended
is just too much. But try not to think in too narrow terms. Learning something
about the foundations may help you later when confronting wider problems.

5.2 General mechanical properties of bonds
Before classifying and discussing particular bond types, we can make a few
common-sense deductions about what sort of forces must be involved in a
bond. First, there must be an attractive force. An obvious candidate for this
role is the Coulomb attraction between unlike charges, which we have all met
–2
many times, giving a force proportional to r , where r is the separation.
We know that sodium easily mislays its outer-ring (often called valence)
+
electron, becoming Na , and that chlorine is an avid collector of a spare elec-
tron. So, just as we mentioned earlier with lithium and fluorine, the excess
electron of sodium will fill up the energy shell of chlorine, creating a posit-
ively charged sodium ion with a negatively charged chlorine ion. These two
ions will attract each other; that is obvious. What is less obvious, however, is
that NaCl crystallizes into a very definite structure with the Na and Cl ions
0.28 nm apart. What stops them getting closer? Surely the Coulomb forces are
great at 0.28 nm. Yes, they are great, but they are not the only forces acting.
When the ions are very close to each other and start becoming distorted, new
forces arise that tend to re-establish the original undistorted separate state of
the ions. These repulsive forces are of short range. They come into play only
when the interatomic distance becomes comparable with the atomic radius.
Thus, we have two opposing forces that balance each other at the equilibrium
separation, r 0 .
It is possible to put this argument into graphical and mathematical form. If
we plot the total energy of two atoms against their separation, the graph must
look something like Fig. 5.1. The ‘common-sense’ points about this diagram E(r)
are as follows:
1. The energy tends to zero at large distances—in other words, we define zero r 0
energy as the energy in the absence of interaction.
2. At large distances the energy is negative and increases with increasing dis- E c r
tance. This means that from infinity down to the point r 0 the atoms attract
each other. Fig. 5.1
3. At very small distances the energy is rising rapidly, that is, the atoms repel The essential general appearance of
each other up to the point r 0 . the energy versus separation curve if
4. The curve has a minimum value at r 0 corresponding to an equilibrium two atoms are to bond together. The
position. Here the attractive and repulsive forces just balance each other. equilibrium separation is r 0 and the
bond energy is E c .
In the above discussion we have regarded r as the distance between two
atoms, and r 0 as the equilibrium distance. The same argument applies, how-
ever, if we think of a solid that crystallizes in a cubic structure. We may then
interpret r as the interatomic distance in the solid.
Let us now see what happens when we compress the crystal, that is, when
we change the interatomic distance by brute force. According to our model,
illustrated in Fig. 5.1, the energy will increase, but when the external influence
is removed, the crystal will return to its equilibrium position. In some other