Packing of Constituent Particles in Crystals

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

Assumption

It is assumed that the atoms are hard spheres of identical size. Packing is done in such a way that they occupy maximum available space. This type of packing is called close packing.

The packing of the spheres of equal size latices place as follows:

1.

fig 2.5 - Close packing of spheres in one dimension

Spheres are placed in a row forming the crystal edge.

fig 2.6

fig 2.7

2. Rows can be combined in two ways to form crystal planes

a) Square close packing - Particles when placed in the adjacent rows show a horizontal as well as vertical alignment and form squares.

b) Hexagonal close packing - Packing in every next row are placed in the depression between the particles of the first row. Hexagonal close packing with triangular voids is more efficient.

3. Three-dimensional packing

Hexagonal close packing is the most efficient two dimensional close packing.

Let us now consider a three dimensional packing keeping a hexagonal close packed pattern for layers.

Two types of arrangements are possible.

a) Hexagonal close packing - AB AB type of arrangement.

b) Cubic close packing - ABC-ABC type of arrangement.

Solid circles represent layer A

Dotted circles represent layer B

fig 2.8

Hexagonal Close Packing

In two-dimensional packing, hexagonal close packing is more efficient. In three dimensions the second layer spheres are placed in the A voids and B voids are unoccupied.

In the second layer there are C and D voids.

The third layer is placed such that it covers the C voids. The third layer spheres are directly over the first layer leading to AB AB type of arrangement or hexagonal close packing.

Cubic Close Packing

When the third layer spheres are placed on the D voids a layer different from layers A and B is produced leading to ABC ABC ....... type of arrangement or cubic close packing (CCP) similar to face centered cubic. It is similar to face centered cubic packing.

Examples of HCP - Mg, Zn, Cd

Examples of CCP - Na, K, Fe, Cr;

In both the above patterns of arrangements the maximum occupied shape is 76% of the available volume.

In both HCP and CCP the coordination number is 12 because a sphere is in contact with 6 spheres in its own layer. It touches three spheres in the layer above and three in the layer below.

fig 2.9 - Co-ordination number in hcp and ccp

fig 2.10 - (i) Hexagonal close packing

fig 2.10 - (ii) Cubic close packing