Calculate Surface Density for SC, BCC & FCC Crystals

[sllow]

helppp

Homework Statement

Calculate the surface density of atoms on (111) and (110) planes for the following crystal structure.
a) simple cubic, b) body-centered cubic, c)face-centered cubic. Assume the lattice constant is x.

Homework Equations

well, from reading my lecture notes the general formula for surface density is (#atoms/cm2) . However, the notes doesn't seem to really help as the answer is really way off.

The Attempt at a Solution

Help please :(

 

[lippyka]

For a) Simple Cubic: The (111) plane has 1 atom per unit cell, and the (110) plane has 2 atoms per unit cell. So, the surface density of atoms on (111) and (110) planes can be calculated as follows: Surface density on (111) plane = (1 atom/unit cell) / (x cm/unit cell)^2 = 1/(x^2 cm^2)Surface density on (110) plane = (2 atoms/unit cell) / (x cm/unit cell)^2 = 2/(x^2 cm^2) For b) Body-Centered Cubic: The (111) plane has 2 atoms per unit cell, and the (110) plane has 4 atoms per unit cell. So, the surface density of atoms on (111) and (110) planes can be calculated as follows: Surface density on (111) plane = (2 atoms/unit cell) / (x cm/unit cell)^2 = 2/(x^2 cm^2)Surface density on (110) plane = (4 atoms/unit cell) / (x cm/unit cell)^2 = 4/(x^2 cm^2) For c) Face-Centered Cubic: The (111) plane has 4 atoms per unit cell, and the (110) plane has 8 atoms per unit cell. So, the surface density of atoms on (111) and (110) planes can be calculated as follows: Surface density on (111) plane = (4 atoms/unit cell) / (x cm/unit cell)^2 = 4/(x^2 cm^2)Surface density on (110) plane = (8 atoms/unit cell) / (x cm/unit cell)^2 = 8/(x^2 cm^2)