what is the difference between 3 dimensional close packing and 2 dimensional close packing?

Asked by Jogy Jacob | 29th Mar, 2013, 10:03: AM

Expert Answer:

When the rows are combined touching each other, the crystal plane is obtained. The rows can be combined in two different ways

(i)   The particles when placed in the adjacent rows, show a horizontal as well as vertical alignment and form squares. This type of packing is called square close packing   

(ii)   The particles in every next row are placed in the depressions between the particles of the first row. The particles in the third row will be vertically aligned with those in the first row. This type of packing gives a hexagonal pattern and is called hexagonal close packing

 


In two dimensional packing, a more efficient packing is given by hexagonal close packing. In order to develop three dimensional close packing let us retain the hexagonal close packing in the first layer. If the spheres in the second layer are just placed over the spheres in the first layer so that the spheres in the two layers are vertically aligned, its voids will come above the voids in the first layer. This is an inefficient way of filling the space.

 

When the second layer is placed in such a way that its spheres find place in the ‘b’ voids of the first layer, the ‘c’ voids will be left unoccupied. Since under this arrangement no sphere can be placed in them, (c voids), i.e. only half the triangular voids in the first layer are occupied by spheres in the second layer (i.e. either b or c)

 

Answered by  | 31st Mar, 2013, 06:17: AM

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