4R 2 = 2( R + r) 2 2R 2 =( R + r) 2 R√2 = R + r R√2 – R = r r = R√2 – R Putting the value of √2, we derive r = R( 1.414-1) r = 0.414R
Placing third layer over the second layer: Covering Tetrahedral Voids
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Tetrahedral voids of the second layer can get covered by the spheres of the third layer.
Here the spheres of the third layer get exactly aligned with the spheres of the first layer.
Therefore it can be observed that the pattern of spheres is repeated in alternate layers.
This pattern is often written as ABAB....... pattern and the structure is called hexagonal close packed( hcp) structure found in many metals like magnesium and zinc.