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Question
Show that in a cubic close packed structure, eight tetrahedral voids are present per unit cell.
Solution
In ccp structure unit cell is divided into 8 small cubes. Each small cube has atoms at alternative corners [Figure]. In all, each small cube has 4 atoms. When joined to one another, they make a regular tetrahedron. Thus, there is one tetrahedral void in each small cube and 8 tetrahedral void in total. Each of the eight small cubes has one void in one unit cell of ccp structure. We know that ccp structure has four atoms per unit cell. Thus the number of tetrahedral voids is twice the number of atoms.
(a)
(b)
Again, the number of tetrahedral voids in ccp structure is equal to twice the total number of atoms.
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(i) A tetrahedral void is formed when a sphere of the second layer is present above triangular void in the first layer.
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