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Origin of Laue equations?

The Bragg condition (by Bragg in 1913) can be derived by the Laue equations that is making use of the Miller indices and all the latice/crystal stuff (so basically it's bringing Bragg's law to more ...
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Laue diffraction/equations: Path difference, why a minus sign and not a plus?

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 ...