(1) A two dimensional crystal has the structure shown below. Atom A are at the
corners of a square cell. The length of each side of the square cell is a. Atom B is
in the center of the square cell. An x-ray with a wavelength $\lambda$ is incident on the
crystal with an angle of $\theta$.
(a) How many fold symmetry does the solid have ? (2%)
(b) If atom A and atom B are the same, what is the area of the 1st BZ in k-space ?
(3%)
(c) If atom A and atom B are the same, what are the possible values of $\lambda$ to have
constructive interference? Express your result in terms of a. (2%)
(d) If atom A and atom B are different, what are the possible values of $\lambda$ to have
constructive interference? Express your result in terms of a. (3%)
(e) If A=B and $\theta=\pi/4$, the incident x-ray is found to be diffracted backward, as
shown below, what is the possible value of $\lambda$? (please use Laue equation in
your derivation) (10%)
(f) If A$\neq$B and $\theta=\pi/4$, what is the result in (e). (5%)
