Assume a row of scatterers separated by constant repeat, a. Radiation of wavelength l is incident on this row at an angle ao. Examine the the scatter from this row at an angle an.
The path difference of rays scattering at points A and D is just AB-CD. If the incoming rays are in phase, the path difference must be some integral multiple of the wavelength for constructive interference to occur. This leads to the first Laue equation:
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This result is valid for any scattered ray that makes an angle an with the unit cell axis. Thus the Laue condition is consistent with a cone of scattered rays centered about the a axis. This equation can be restated in vector terms. The repeat distance a, becomes a unit cell vector a. Call a unit vector parallel to the incoming rays, S0, and one parallel to the scattered rays, S. There are then some simple vector dot products:
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