as simple cubic structure as shown in fig. In simple cubic packing, each sphere is in contact with neighbouring spheres - Four in its own layer, one above and one below and hence the coordination number of the sphere in simple cubic arrangement is . Packing efficiency: There is some free space between the spheres of a single layer and the spheres of successive layers. The percentage of total volume occupied by these constituent spheres gives the packing efficiency of an arrangement.
Let us calculate the packing efficiency in simple cubic arrangement, Packing fraction (or) efficiency Total volume occup ied by spheres in a unit cell Volume of the unit cell × Let us consider a cube with an edge length ‘a’ as shown in fig. Volume of the cube with edge length a is = a a = a Let ‘r’ is the radius of the sphere. From the figure, a=2r ⇒ r (i) ABAB.. Type: In this type, the second row spheres are arranged in such a way that they fit in the depression of the first row as shown in the figure.
The second row is denoted as B type. The third row is arranged similar to the first row A, and the fourth one is arranged similar to second one. i.e., the pattern is repeated as ABAB….In this arrangement each sphere is in contact with of its neighbouring spheres. On comparing these two arrangements (AAAA...type and ABAB….type) we found that the closest arrangement is ABAB…type.
r r Simple Cubic (SC) XII U6 Solid State - XII U6 Solid State - - - - - ∴ Volume of the sphere with radius ‘r’ = π r = a = a = a π π π ... ( ) In a simple cubic arrangement, number of spheres belongs to a unit cell is equal to one ∴ Total volume occupied by the