I am trying to understand diffraction a little better and eventually Kikuchi lines. I am confused about something -- namely the difference between the Ewald sphere and the so-called sphere of reflection -- and the role of Brillouin zone boundaries.
In order to satisfy constructive interference conditions due to (elastic) diffraction we must conserve energy -- so the incident beam and diffracted beam must have the same amplitude: $|k_i| = |k_f|$.
We also know that if the path difference between a $k_i$ and $k_f$ is equal to a reciprocal lattice vector G we get constructive interference.
If we combine these conditions we get: $2 k_i \cdot G= G^2$ which describes Brillouin zone boundaries -- since in essence we are bisecting $G$. Does this mean that every Ewald Sphere is centred at a Broullin Zone Boundary?
My final goal is to understand the difference between the Ewald Sphere and the Sphere of Reflection which explains kikuchi lines.