The analysis of the cubic system

         (1) The number of atoms in per unit cell

         Total number of atoms enclosed in the unit cell for the simple cubic called as unit cell content.

         The simplest relation which can be determine for it is, 

         Here n_c = Number of the atoms at corners of the cube=8

         n_f = Number of the atoms at six the faces of the cube = 6

         n_i = Number of the atoms inside the cube = 1

         (2) Co-ordination number (C.N.) : The co-ordinate number is defined as the number of the nearest neighbours or touching particles with other particle present in the crystal is known as its co-ordination number. It depends upon the structure of the crystal.

         For simple cubic system Cubic number = 6.

         For body centred cubic system Cubic number = 8

         For face centred cubic system Cubic number = 12.

      (3) Density of the unit cell     : It can be defined as the ratio of mass per unit cell to the total volume of the unit cell.

         Where Z = Number of particles per unit cell

         M = Atomic mass or molecular mass

         N_o = Avogadro number (6.023 * 10²³ mol^-1) 

         a = Edge length of the unit cell= a pm = a * 10^-10 cm

         a³ =  volume of the unit cell

i.e. 

         The density of substance is same as the density of the unit cell.

         (4) Packing fraction (P.F.): It can be defined as ratio of the volume of the unit cell that is occupied by spheres of the unit cell to the total volume of the unit cell.   

         Let radius of the atom in the packing = r

         Edge length of the cube = a

         Volume of the cube V = a³

         Volume of the atom  (spherical)  =  

         Packing density 

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