Calculate planer density of 111 plane in FCC?

Answer 1

To calculate the planar density of the (111) plane in a face-centered cubic (FCC) structure, we first note that the (111) plane contains 3 atoms per unit cell. The area of the (111) plane in an FCC unit cell can be calculated as ( \frac{\sqrt{3}}{2} a^2 ), where ( a ) is the unit cell edge length. The planar density is then given by the formula:

[ \text{Planar Density} = \frac{\text{Number of atoms in the plane}}{\text{Area of the plane}} = \frac{3}{\frac{\sqrt{3}}{2} a^2} = \frac{6}{\sqrt{3} a^2} = \frac{2\sqrt{3}}{a^2} ]

Thus, the planar density of the (111) plane in FCC is ( \frac{2\sqrt{3}}{a^2} ).