Close Packed Structure in Solid

Close Packed Structure

In solid, constituent particles are so closely packed that there is very low space between them.  

Let us consider the constituent particles as identical hard spheres and build a three dimension structure in three steps:

1)    Close packing in one dimension:

If we arrange spheres in a row touching each other, a one dimension structure is formed.

The number of nearest neighbours of a particle is called its coordination number. In one dimension structure a particle is in contact of two of its neighbours. Thus, its coordination number is 2.

2)    Close packing in two dimensions:

It can be generated by placing two rows of closed packed spheres together. It formed in two ways.

a)     When second row is placed just above the first row, a two dimension structure is formed.

If the centres of these 6 immediate neighbouring spheres are joined, a

square is formed hence this is called square close packing in two dimensions.

In this arrangement, each sphere is in contact with four of its neighbours. Thus, the two dimensional coordination number is 4.

If we called first row ‘A’ type, then second row will also called “A’ because second row is exactly same as the first row. So this type of arrangement is called ‘AAA’ type.

b)    When second row is placed above the first one in a staggered manner so that second row’s sphere fit in the depression of first one, a two dimension structure is formed.

              

In this arrangement, each sphere is in contact with six of its neighbours. Thus, the two dimensional coordination number is 6.

If the centres of these 6 immediate neighbouring spheres are joined, a

regular hexagon is formed hence this is called hexagonal packing in two dimensions.

If we called first row ‘A’ type, then second row will called “B’ because second row is different from the first row. Similarly if we place third row above the second one in staggered manner then its spheres are aligned with those of the first layer Hence this layer is also of ‘A’ type. The spheres of similarly placed fourth row will be aligned with those of the second row (‘B’ type). Hence this arrangement is of ‘ABAB’ type.

3)    Close packing in three dimensions:

They can be obtained by placing two dimensional layers one above the another. Let us find out.

a)     Three dimensional close packing from two dimensional square close packed structure:

It is formed when one row of square close packed is placed just above the other.

In this arrangement spheres of both layers are perfectly aligned horizontally as well as vertically.

If we called first row ‘A’ type, then second row will also called “A’ because second row is exactly same as the first row. So this type of arrangement is called ‘AAA’ type.

b)    Three dimensional close packing from two dimensional hexagonal close packed structure:

It is formed when one row of hexagon close packed is placed just above the other.

1)    Placing second layer over the first layer

If we take a two dimensional hexagonal close pack layer and place a similar layer above it such that the spheres of the second layer are placed in the depressions of the first layer, a three dimensional structure is formed.

           

             This type of arrangement is called “ABAB” type

When a sphere of second layer is place above the void of first layer (vice versa) a tetrahedral void “T” is formed. (Because if we joined centres of these four spheres, a tetrahedron is formed)

At other places, the triangular voids in the second layer are above the triangular voids in the first layer, and the triangular shapes of these do not overlap. One of them has the apex of the triangle pointing upwards and the other downwards. These voids are called octahedral void ‘O’. Such voids are surrounded by six spheres and are called octahedral voids.

If there are N number of close packed sphere, then

No. of octahedral void will be: N

No. of tetrahedral void will be: 2N

2)    Placing third layer over the second layer

When we place third layer over the second one, there are possibilities

A)   Covering tetrahedral void:

o   In this case, the spheres of third row are placed over the tetrahedral void of second layer.

o   In this manner, spheres of third layer come in straight line with spheres of first layer. Thus, this pattern is written as “ABAB” pattern.

o   This is called hexagonal close packed structure (hcp).

o   Example: Magnesium, zinc

o   The coordination number of this structure is 12. 

B)    Covering hexagonal void:

o   In this case, the spheres of third row are placed over the octaherdral void of second layer.

o   In this manner, third layer neither come in straight line with first layer nor with second layer. They form “C” type. But when fourth layeris placed, its spheres come in straight line with first layer. Thus, this pattern is written as “ABCABC……” pattern.

o   This structure is called cubic close packed (ccp) or face-centered cubic (fcc) structure.

o   Example: copper, silver etc.

o   The coordination number of this structure is 12.