Bonding Between Atoms

Chapter 4
Bonding between atoms

Introduction
In order to understand the origin of material properties like Young’s moduZus, we need
to focus on materials at the atomic level. Two things are especially important in
influencing the modulus:
(1) The forces which hold atoms together (the interatomic bonds) which act like little
springs, linking one atom to the next in the solid state (Fig. 4.1).

Fig. 4.1. The spring-like bond between two atoms.

and

(2) The ways in which atoms pack together (the atom packing), since this determines
how many little springs there are per unit area, and the angle at which they are
pulled (Fig. 4.2).
In this chapter we shall look at the forces which bind atoms together - the springs. In
the next we shall examine the arrangements in whichthey can be packed.

Fig. 4.2. Atom packing and bond-angle.

Bonding between atoms

37

The various ways in which atoms can be bound together involve

(I) Primary bonds - ionic, covalent or metallic bonds, which are all relatively strong
(they generally melt between 1000 and 4000K, and
(2) Secondary bonds - Van der Waals and hydrogen bonds, which are both relatively
weak (they meltbetween 100 and 500K).
We should remember, however, when drawing up a list of distinct bond types like this
that many atoms are really bound together by bonds which are a hybrid, so to speak,
of the simpler types (mixed bonds).

Primary bonds
Ceramics and metals are entirely held together by primary bonds - the ionic and
covalent bond in ceramics, and the metallic and covalent bond in metals.These strong,
stiff bonds give high moduli.
The ionic bond is the most obvious sort of electrostaticattraction between positive and
negative charges. It is typified by cohesion in sodium chloride. Other alkali halides
(such as lithium fluoride), oxides (magnesia, alumina) and components of cement
(hydrated carbonates and oxides) are wholly or partly held together by ionic bonds.
Let us startwith the sodium atom. It has a nucleus of 1 protons, each with a + charge
1
(and 12 neutrons with no charge at all) surrounded by 11 electrons each carrying a charge (Fig. 4.3).
The electrons are attracted to the nucleus by electrostatic forces and therefore have
negative energies. But the energies of the electrons are not all the same. Those furthest
from the nucleus naturally have thehighest (least negative) energy. The electron that
we can most easily remove from the sodium atom is therefore the outermost one: we

Sodium atom

Fig. 4.3. The formation of a n ionic bond
sodium chloride.

Chlorine atom

- in t his case between a sodium atom a nd a chlorine atom, making

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Engineering Materials 1

can remove it by expending 5.14eV* of work. This electron can be mostprofitably
transferred to a vacant position on a distant chlorine atom, giving us back 4.02eV of
energy. Thus, we can make isolated Na' and C1- by doing 5.14 eV - 4.02 eV = 1.12eV of
work, Ui.
So far, we have had to do work to create the ions which will make the ionic bond: it
does not seem to be a very good start. However, the + and - charges attract each other
and if we now bring themtogether, the force of attraction does work. This force is
simply that between two opposite point charges:

where q is the charge on each ion, eo is the permittivity of vacuum, and r is the
separation of the ions. The work done as the ions are brought to a separation r (from
infinity) is:
U=

1" F dr

= q2/4mOr.

(4.2)

Figure 4.4 shows how the energy of the pair of ions falls as rdecreases, until, at r =
1nm for a typical ionic bond, we have paid off the 1.12eV of work borrowed to form
Na' and Cl- in the first place. For r < 1nm (1nm = 10-9m),it is all gain, and the ionic
bond now becomes more and more stable.
Why does r not decrease indefinitely, releasing more and more energy, and ending
in the fusion of the two ions? Well, when the ions get close enough together, the...