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There are three types of cubic unit cells: simple cubic (SC), body-centred cubic (BCC) and face-centred cubic(FCC). In the SC cell, the atoms are at the corners of a cube and adjacent atoms on an edge touch each other. If l is the edge length, then 2*r =l or r = l/2 , where r is the radius of the atom.
In the BCC lattice, atoms are at the corners and an extra atom is at the centre ( the point of intersection of the body diagonals).If l is the edge length, then a body diagonal is l√3, and the atom at the centre of the cube is at a distance of l√3/2 from the atoms at the corners.The nearest atoms touch each other, so 2*r =l√3/2. => r = l√3/4.
In FCC lattice there are atoms at the corners and at the face centres ( where face diagonals intersect). If l is the edge length then the nearest atoms (atom at a corner and at a face centre) are l√2/2 distance apart. The nearest atoms touch each other, so
2*r = l√2/2. => r = l√2/4
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