Thursday, 28 January 2010

The Laue Equations

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:

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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