Page 61 - Materials Science and Engineering An Introduction

2.6 Primary Interatomic Bonds • 33

Coulombic bonding force

Na + Cl – Na + Cl – Na +

Cl – Na + Cl – Na + Cl –

Valence Electron
+ – + – +
Na Cl Na Cl Na

– + – + –
Cl Na Cl Na Cl
+ –
Na Atom CI Atom Na Ion CI Ion
(a) (b)
Figure 2.11 Schematic representations of (a) the formation of Na and Cl ions and (b) ionic bonding in sodium

chloride (NaCl).

Here P 0 is the permittivity of a vacuum (8.85 10 12 F/m), |Z 1 | and |Z 2 | are absolute values
of the valences for the two ion types, and e is the electronic charge (1.602 10 19 C). The
value of A in Equation 2.9 assumes the bond between ions 1 and 2 is totally ionic (see
Equation 2.16). Inasmuch as bonds in most of these materials are not 100% ionic, the
value of A is normally determined from experimental data rather than computed using
Equation 2.10.
An analogous equation for the repulsive energy is 5

Repulsive energy— B
interatomic E R = n (2.11)
separation r
relationship
In this expression, B and n are constants whose values depend on the particular ionic
system. The value of n is approximately 8.
Ionic bonding is termed nondirectional—that is, the magnitude of the bond is equal
in all directions around an ion. It follows that for ionic materials to be stable, all posi-
tive ions must have as nearest neighbors negatively charged ions in a three-dimensional
scheme, and vice versa. Some of the ion arrangements for these materials are discussed
Tutorial Video: in Chapter 12.
Bonding Bonding energies, which generally range between 600 and 1500 kJ/mol, are
What is Ionic Bonding?
6
relatively large, as reflected in high melting temperatures. Table 2.3 contains bonding
energies and melting temperatures for several ionic materials. Interatomic bonding is
typified by ceramic materials, which are characteristically hard and brittle and, further-
more, electrically and thermally insulative. As discussed in subsequent chapters, these
properties are a direct consequence of electron configurations and/or the nature of the
ionic bond.

5 In Equation 2.11, the value of the constant B is also fit using experimental data.
6 Sometimes bonding energies are expressed per atom or per ion. Under these circumstances, the electron volt (eV) is
a conveniently small unit of energy. It is, by definition, the energy imparted to an electron as it falls through an elec-
tric potential of one volt. The joule equivalent of the electron volt is as follows: 1.602 10 19 J 1 eV.