Structure Factor Explained: Scattered Rays, Zero Values & Wave Vector

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The structure factor in solid state physics quantifies the amplitude of scattered rays from a crystal lattice, indicating how waves interact with the atomic arrangement. A zero structure factor at specific points means that scattered waves interfere destructively, resulting in no intensity in those directions. To determine allowable scattering directions given an incident wave vector, one should indeed utilize the structure factor. Understanding these concepts is crucial for analyzing diffraction patterns in crystallography. This foundational knowledge aids in interpreting how atomic structures influence wave scattering behavior.
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The structure factor in solid state physics (https://en.wikipedia.org/wiki/Structure_factor) apparently gives information on the scattered ray from a lattice.

How exactly does it do that?

Does a structure factor of zero at certain points imply that rays cannot be scattered in those directions?

If I know the incident wave vector, how do I determine the allowable scattering directions? (Should this be done with the structure factor?)I'm just confused about some general concepts, so a qualitative discussion would be nice. Thanks
 
The structure factor determines the amplitude of a Bragg diffracted ray, i.e. coherent and elastic scattering off the atoms of the crystal.
A zero structure factor implies that the waves scattered by the different atoms interfere destructively such that this amplitude becomes zero, hence no intensity.
 

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