Primary and secondary bonds in solids

Atoms bond to lower their energy. Bonds are primary (strong, 100-1000 kJ/mol) or secondary (weak, below about 40 kJ/mol).

Primary bonds

• Ionic bond: a metal atom transfers electrons to a non-metal atom, and the resulting opposite ions are held together by electrostatic attraction (NaCl, MgO). The bond is non-directional; ionic solids are hard, brittle, high melting and insulating in the solid state.
• Covalent bond: atoms share electrons in a fixed direction (diamond, Si, SiC). Very hard, high melting, poor ductility.
• Metallic bond: valence electrons form a free "electron cloud" shared by positive ion cores (Cu, Fe). Gives ductility, good electrical and thermal conductivity, and lustre.

Secondary bonds

• Van der Waals forces between temporary or permanent dipoles, and hydrogen bonds (H bonded to O, N, F). They are responsible for the bonding between polymer chains and in ice, and they explain the low melting point of polymers.

Force and energy curves

When two atoms are far apart they attract each other; when they come very close their electron clouds overlap and they repel. The net force is $F_N = F_A + F_R$. The attractive force dominates at large distance and the repulsive force at small distance. At the equilibrium spacing $r_0$ the net force is zero and the potential energy is minimum.

Force against interatomic distance:

 Force F
  ^
  | attraction (+)      _.-----.__
  |                  .-'          `--..___
  0 ----------------+------------------------> r
  |                /| r0  (net force F = 0)
  |               /
  |              /   net force F_N
  | repulsion (-)|
  |              |

Potential energy against interatomic distance:

 Energy E
  ^
  |  repulsion |
  |            \
  |             \
  0 -------------\---------------------------> r
  |               \            ___.....-----
  |                \       _.-'
  |                 `-.__.'   net energy E_N
  |                    |
  |      -Eb (minimum) r0

$$E_N = -\frac{A}{r^m} + \frac{B}{r^n} \quad (n > m), \qquad \frac{dE_N}{dr} = 0 \ \ (\text{net force zero})\ \text{at}\ r = r_0$$

Bond (binding) energy $E_b$ is the energy needed to separate two atoms from the equilibrium spacing $r_0$ to infinity, i.e., the depth of the energy well. Materials with deep, narrow wells have a high melting point, high modulus and low thermal expansion.