The Solid State

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Close Packing: In solids, the constituent particles are close-packed, leaving the minimum vacant space.

Close packing in one dimension: Only one way, arrange them in a row and touching each other.In this arrangement, each sphere is in contact with two of its neighbours. The number of nearest neighbours of a particle is called its coordination number.In one dimensional closed packed arrangement, the coordination number is 2.

Close packing in two dimensions: Two-dimensional close-packed structure can be generated by stacking (placing) the rows of close-packed spheres. This can be done in two different ways.

1. Square close packing: The coordination number is 4.
   
   
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3. Hexagonal close packing: The coordination number is 6. Hexagonal close packing structure is better than square close packing structure. In the hexagonal close packing 2-dimensional structure there are some voids which are triangular in shape.

Close packing in three dimensions: Three-dimensional close packing from a two-dimensional closed packed layer: - starting from the square close-packed layer the second layer and all further layers will be built up such that they are horizontally as well as vertically aligned with each other.

If the arrangement of spheres in the first layer is called ‘A’ type, all the layers have the same arrangement. Thus this lattice has AAA....type pattern. The lattice thus generated is the simple cubic lattice, and its unit cell is the primitive cubic unit cell.

Three-dimensional close packing from two-dimensional hexagonal close-packed layers: Three-dimensional close-packed structure can be generated by placing layers one over the other.

A stack of two layers of close-packed spheres and voids generated in them. T = Tetrahedral void; O = Octahedral void

When the third layer is placed over the second, there are two possibilities.
Covering Tetrahedral Voids: Tetrahedral voids of the second layer may be covered by the spheres of the third layer.The pattern of spheres is repeated in alternate layers.This pattern is often written as ABAB ....... pattern. This structure is called hexagonal close-packed hcp) structure	Covering Octahedral Voids: The third layer may be placed above the second layer in a manner such that its spheres cover the octahedral voids.This pattern of layers is often written as ABCABC ........... This structure is called cubic close packed (ccp) or face-centred cubic (fcc) structure.
This sort of arrangement of atoms is found in many metals like magnesium and zinc.	Metals such as copper and silver crystallise in this structure.