Page 63 - Materials Science and Engineering An Introduction

2.6 Primary Interatomic Bonds • 35

Whereas, according to Equation 2.9,

A
E A = -
r
Now, taking the derivation of E A with respect to r yields the following expression for the
force of attraction F A :
A
da - b
dE A r -A A
F A = = = - a b = (2.12)
dr dr r 2 r 2
Now substitution into this equation the expression for A (Eq. 2.10) gives

1
F A = ( Z 1 e)( Z 2 e) (2.13)
4pP 0 r 2
Incorporation into this equation values for e and P 0 leads to

1 -19 -19
F A = -12 2 [ Z 1 (1.602 * 10 C)][ Z 2 (1.602 * 10 C)]
4p(8.85 * 10 F/m)(r )
-28 # 2
(2.31 * 10 N m )( Z 1 )( Z 2 )
= (2.14)
r 2
For this problem, r is taken as the interionic separation r 0 for KBr, which is equal to the

sum of the K and Br ionic radii inasmuch as the ions touch one another—that is,
r 0 = r K + r Br - (2.15)
+
= 0.138 nm + 0.196 nm
= 0.334 nm
= 0.334 * 10 m
-9
When we substitute this value for r into Equation 2.14, and taking ion 1 to be K and ion 2

as Br (i.e., Z 1 1 and Z 2 1), then the force of attraction is equal to

-28 # 2
(2.31 * 10 N m )( +1 )( -1 )
-9
F A = -9 2 = 2.07 * 10 N
(0.334 * 10 m)
(b) At the equilibrium separation distance the sum of attractive and repulsive forces is zero
according to Equation 2.4. This means that
-9
-9
F R = -F A = -(2.07 * 10 N) = -2.07 * 10 N

Covalent Bonding

covalent bonding A second bonding type, covalent bonding, is found in materials whose atoms have small
differences in electronegativity—that is, that lie near one another in the periodic table.
For these materials, stable electron configurations are assumed by the sharing of elec-
trons between adjacent atoms. Two covalently bonded atoms will each contribute at
least one electron to the bond, and the shared electrons may be considered to belong to
both atoms. Covalent bonding is schematically illustrated in Figure 2.12 for a molecule
of hydrogen (H 2 ). The hydrogen atom has a single 1s electron. Each of the atoms can
acquire a helium electron configuration (two 1s valence electrons) when they share
their single electron (right side of Figure 2.12). Furthermore, there is an overlapping of