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Close Packed Structures: Packing In One And Two Dimensions

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Close Packed Structures: Packing In One And Two Dimensions - Lesson Summary

A close packing is defined as a way of arranging equi-dimensional objects in space, such that the available space is filled very efficiently. Solids are three-dimensional objects, and we will develop their   structure in three steps.

Close packing in one dimension:
There is only one way of arranging the spheres in a one-dimensional close packed structure, that is, by arranging them in a row touching each other. In this arrangement, each sphere touches two neighbouring spheres. The number of nearest neighbours of a particle is defined as its co-ordination number. The coordination number of a particle or sphere in one-dimensional close packing is 2.
 

 
Close packing in two dimensions:
When a number of rows are stacked up, a two-dimensional crystal plane is generated. There are two ways of stacking the rows. One way is for the rows to lie one above the other, with one sphere exactly above another.
 
 
 
Here the spheres are aligned horizontally as well as vertically. Here each sphere is in contact with four other spheres – two on sides, one above and one below. Hence, the coordination number becomes four. If we join the centres of these four spheres, we will get a square. Therefore, this type of close packing is also referred to as square close packing.
 

 
The other way is for the spheres of the second row to be seated on the first row in a staggered manner, that is, in the depressions of the first layer.
 
The spheres of the third layer are placed in the depressions of the second layer, and so on. Evidently, the spheres in the third row are vertically aligned with the spheres in the first row. This pattern is followed throughout.
 

 
Here each sphere is in contact with six other spheres – two on either side, two in the layer below, and two more in the layer above. Hence, the coordination number of a sphere becomes six. If we join the centres of these six spheres, we get a hexagonal pattern. Therefore, this type of close packing is also referred to as hexagonal close packing.
 

 
Voids or interstitial sites
Some spaces are left vacant after the close packing of the spheres. These vacant spaces are called voids or interstitial sites. In the figure, the empty spaces are seen as curved triangular spaces. These spaces left between the spheres can be divided into two kinds - “b” and “c.”
 
  

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