Two dimensional close packed structures can be generated by stacking (placing) the rows of one dimensional close packed spheres. This can be done in two different ways.
i. Square close packing (AAAA type arrangement):
a. The second row may be placed in contact with the first one such that the spheres of the second row are exactly above those of the first row.
b. Thus, all the spheres of different rows are aligned horizontally as well as vertically.
c. If the first row is called as ‘A’ type row, the second row being exactly the same as the first one, is also of ‘A’ type.
d. The planar two dimensional arrangement is called AAAA type of arrangement.
e. In this arrangement, each sphere is in contact with four of its neighbours. Thus, the coordination number of the sphere is four.
f. If the centre of these 4 immediate neighbouring spheres are joined, a square is formed. Hence, this packing is called square close packing in two dimensions and it occupies 52.4 % of available space.
ii. Hexagonal close packing (ABAB type arrangement):
a. The second row may be placed above the first one in staggered manner such that its spheres fit in the depressions of the first row.
b. If the arrangement of spheres in the first row is called ‘A’ type, the one in the second row is different and may be called ‘B’ type.
c. When the third row is placed adjacent to the second in staggered manner, 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).
d. Hence, this arrangement is of ABAB type.
e. Each sphere is in contact with six of its neighbours and therefore the coordination number of the sphere is six.
f. The centres of these six spheres are at the corners of a regular hexagon. Hence, this packing is called hexagonal close packing in two dimensions and it occupies 60.4 % of available space. Hence, packing is more efficient than that in square close packing in two dimensions.
