Cubic Unit Cell

Cubic unit cell

There are three types of cubic unit cells which are (i) Simple cubic (ii) Body centered cubic (iii) Face centered cubic. These unit cells are formed by different number of atoms or ions, which are as follows:

(i)   Simple cubic unit cell: In this case one atom or ion lies at each corner of the cube. Since only 1/8 of each corner sphere lies within the unit cell hence simple cubic unit cell contains a total (1/8) 8 =1, atom or ion. The volume occupied by the particles in simple cubic unit cell is 52.4% and open space in this cell is 47.6%.

(ii)  Body centred cubic unit cell: In this case one atom or ion lies at each comer of the cube and one atom (or ion) lies at the centre of the cube (unshared atom or ion). Thus the contribution of the 8 corners is (1 / 8 ) X 8 = 1, while that of the body centred (unshared atom) is 1 in the unit cell. Hence total number of atoms per unit cell 1 + 1 = 2 atoms (or ions). The volume occupied by the particles in bcc is 68% and open space is 32%.

(iii)  Face centred cubic unit cell: In this case one atom or ion lies at each corner of the cube and one atom or ion lies at the centre of each face of the cube.

It may be noted that only 1/2 of each face sphere lies within the unit cell and there are six such faces. The total contribution of 8 comers is (1 / 8 ) x 8 =1 while that of 6-face-centred atoms is (1 / 2)×6 = 3 in the unit cell. Hence total number of atoms per unit cell is 1 + 3 = 4 atoms (or ions). The volume occupied by the particles in fcc is 74% and open space is 26%.

On the basis of above description the number of atoms (ions) per unit cell is summarized in the following table.

NUMBER OF ATOMS PER UNIT CELL IN CUBIC CLOSE PACKED STRUCTURE OF ATOMS

 Unit cell Number of atoms at Number of atoms per unit cell Volume occupied by particles (%) Corners Centers Faces Simple cube 1 0 0 1 52.4 Body centered (BCC) 1 1 0 2 68 Face centered (FCC) 1 0 3 4 74

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