In order to understand the close packing of the constituent particles in a crystal, it is assumed that these particles are hard spheres of identical size.

Close packing:- The packing of spheres in such away such that they occupy maximum available space and left minimum empty space it is called close packing.

  1. Close packing in one dimension:– In one dimension the spheres can be arranged in a row touching each other called packing in one dimension each sphere touch two of its neighbors so its coordination no. is 6
  2. Close – packing in two dimensions:- When the rows are stacked over each other a two dimensional close packed structure [called crystal plane] is formed. This stacking can be done in two ways.
    1. AAA type:-The sphere in second row may be placed in the way such that they are touching each sphere of first row and exactly above sphere of first row in this type coordination no. is 4
    2. ABA type:- The sphere in second row may be placed in depression of first row. This produces a different raw from 1st type in this coordination no. is 6.
  3. Close packing in three dimensions:- Three dimensional close packing from two dimensional (AAA) square close packed structure:-
    1. Starting from square close packed layer:- The second layer and all further layers are build up such that they are horizontally as well as vertically aligned on each other. Thus their lattice is of AAA type. It unit cell is primitive unit cell.
    2. Three dimensional close packing from two dimensional hexagonal close packed layer:-
      • Let in hexagonal close packing the sphere are marked as A and voids between spheres are marked as a, b alternatively.
      • When the second layer is placed in such a way that its spheres. Find place in a voids of first layer the b void left in occupied since in this arrangement no sphere can be placed in them.
      • Now come to have the two types of voids c and d.
    3. Tetrahedral void:- A simple triangular void like c in crystal is surrounded by four spheres and is called a tetrahedral void.
    4. Octahedral void:- Void like (d) is surrounded by six spheres and is called an octahedral void.

      The voids or holes in the crystals are also called interstices.Now when a third layer placed over second layer in such a way that sphere cover the tetrahedral (c) void a three dimensional close packing of ABAB patter or hexagonal close packing is obtained.

      Example:-Molybdenum, Magnesium have hcp [hexagonal close packing structure].

      When third layer is placed over the second layer in such a way that spheres covers the octahedral or (d) voids a three dimensional pattern of ABCABC or Cubic Close Packing (CCP) is formed. It is similar to FCC (Face Centred Packing).

      Iron, Nickel, Copper exists in CCP structures.

Coordination Number:-

The number of closest (or nearest) neighbors of any constituent particles in the crystal lattice is called the coordination number

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