Problem 1ΒΆ
Consider a 2D triangle lattice with basis vectors \(\mathbf{a}_1 = (a, 0)\) and \(\mathbf{a}_2 = (1/2, \sqrt{3}/2)a\).
Calculate the reciprocal lattice vectors for this lattice. Plot the lattice in real space and reciprocal space.
Consider a photon incident on the lattice with wavevector \(\mathbf{k}_{in} = [0, 4\pi/\sqrt{3}a]\). Find the possible outgoing wavevectors for elastic scattering of the photon from this lattice and plot them on the reciprocal lattice.