Solid state physics question

[tigger88]

Homework Statement

Given: Diamond structure with conventional lattice parameter a.
Show the Fourier component of the crystal potential at the reciprocal lattice point (4(pi)/a, 0, 0) is zero.

Homework Equations

(I don't know!)

The Attempt at a Solution

The Fourier component of potential = U_G1, U_-G1 (although I have no idea what G1 is... this was pulled from my notes)

G = (2hpi/a) where h is an integer
G = (2pi/a)(h, k, l) where h,k,l must either all be odd or all be even

This is as far as I got... any suggestions?
Thanks!

If it helps, I have been given the solution but I don't understand it, which is why I'm asking here. The solution mentions using the structure function (what is it?) and allowing Bragg reflection (but I don't know how to incorporate it).

 

[BigJDubs]

The solution is as follows: The structure function for a diamond lattice is given by f(G1) = 2δ(G1) - δ(G1-2pi/a) - δ(G1+2pi/a) Allowing for Bragg reflections, the Fourier component of the potential at (4(pi)/a, 0, 0) is U_G1 + U_-G1 = f(G1) = 0 Therefore, the Fourier component of the potential at (4(pi)/a, 0, 0) is zero.