Calculate and compare the planar densities of the 100 and 11

Calculate and compare the planar densities of the (100) and (110) planes for a BCC crystal.

Solution

planar density of (100) iron

sol :

at T < 912⁰C iron has the BCC structure

radius of iron R - 0.1241 nm

planar density   = (atoms / 2D repeat unit ) / (area / 2D repeat unit)

                       =1 / a²       

                       =1/(43 R / 3)²

                     =12.1 atoms / nm²

                    = 1.21*10¹⁹ atoms / nm²

planar density of (110) iron

PD 110(BCC)=(3 / (8R²2))

                     =0.27 / R²

                      =17.53 atoms / nm²

                  =1.753*10¹⁹ atoms / nm²

comparision

planar densities of the (100) ---> = 1.21*10¹⁹ atoms / nm²

planar densities of the (110) ---> =1.753*10¹⁹ atoms / nm²