Why is the Fourier Component of the Crystal Potential Zero at (4(pi)/a, 0, 0)?

In summary, the problem is to show that at the reciprocal lattice point (4(pi)/a, 0, 0), the Fourier component of the crystal potential is zero. The solution involves using the structure function and allowing for Bragg reflections, which leads to the conclusion that the Fourier component at this point is indeed zero.
  • #1
tigger88
21
0

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).
 
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  • #2
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.
 

FAQ: Why is the Fourier Component of the Crystal Potential Zero at (4(pi)/a, 0, 0)?

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