The Laue diffraction (that reduces to the Bragg refraction in the end) has for the path difference of the incoming and outgoing beam
$$\Delta s = \vec R \cdot ( \vec k_0/k_0 - \vec k^\prime/k^\prime )$$
with $\vec R$ being the translation vector of the lattice and the two $\vec k$ being the incoming and outgoing wave vector.
My question now: Why is there a minus and not a plus between the wave vectors? In the Bragg way of describing such diffraction you add the two paths contributing (incoming + outgoing) to get $\Delta s = d\sin \Theta + d\sin\Theta=2d\sin\Theta$ (with scattering angle $\Theta$ and lattice distance $d$), but on the Laue way you take the difference between the scalar products. For pictures see Wikipedia, for example.
