Question

Compute the Structure Factor for the (200) plane in a zincblende structure of A and B atoms. The lattice constant is 3 angstroms.

Answer 1

The structure factor reflects the interference between atoms in the unit cell. All of the information regarding where the atoms are located in the unit cell that is contained in structure factor. The structure factor is given by following summation over all atoms in the unit cell.

F_(h,k,l) = _{$\sum_{j=1}^{atoms}$} f( _$\hat{j}$ ) exp [2 $\pi$ . $\hat{i}$ (h x_{( $\hat{j}$ )} + k y_{( $\hat{j}$ )} + l z_{( $\hat{j}$ )}]

For Face centered unit cell, we have

Four atoms of the same kind located at (0 0 0), (1/2 1/2 0), (1/2 0 1/2) and (0 1/2 1/2).

F = f exp [2 $\pi$ i(0) + 2 $\pi$ i(h/2 + k/2) + 2 $\pi$ i(h/2 + l/2) + 2 $\pi$ i(k/2 + l/2)]

If h, k & l are unmixed, then the sum (h + k), (h + l) and (k + l) are even integers.

Each term in the above equation which has the value 1.

F = 4f   (Unmixed indices)

If h, k & l are mixed, then the sum of three exponentials is -1.

F = 0   (mixed indices)

Thus, reflections may occur for such planes as (111), (200) and (220) but not for the planes (100), (210), (112) etc. Structure factor is independent of the shape and size of the unit cell.