Question

Surface energy is the sum of the energies of all surfaces and the preferred shape of a crystal that is bounded by free surfaces is the one that minimizes its total interfacial energy.

a) In simple metal solids, the preferred shape is nearly spherical. Please explain why.

b) Ionic solids tend to have polygonal shapes with large, flat facets parallel to the low-energy planes. Please explain why.

c) Use the NaCl ionic structure to explain what you described in (b).

Answer 1

Wulff construction:

This is a method to determine the equilibrium shape of a crystal. The shape of an equilibrium crystal is obtained by minimizing the total surface energy associated with the crystal.

If surface of the crystal is made up of facets, consider an n^th face having interfacial tension and area A_n. Then the energy is given by:

To minimise the energy we need to minimise interfacial tension or surface area according to the above equation.

a) When crystal is a simple metal, which have isotropic . So to minimise energy they need to minimise surface area. The optimum shape for minimizing the surface energy is sphere. This is why the preferred shape of simple metal solid is spherical.

b) To minimize the interfacial energy (thereby decreasing the surface energy), ionic solids tend to have polygonal shapes with large, falt facets parallel to the low energy plane. These have anisotropic .

c) The natural macroscopic shape is compound solids are polygonal (crystalline) due to their anisotropic . According to Wulff construction for crystalline solids depends on the orientation of (hkl) of the surafce. Then is a function of orientation of surface, n.

The shape of NaCl is cubic. This is because of the low energy of (100) surface in NaCl structure.