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Geometry

  Geometry of Diffraction: Braggs Law 2     3 of 18
 

Many layers of atomsRays on many rows atoms image

Consider many layers of regularly spaced atoms, such as we might encounter in a crystalline material. We already know that a diffracted beam from a single layer of atoms has qOUT = qIN. We need to know what spacing of the layers of atoms will give rise to scattered waves being in phase, when interacting with many layers of atoms.

• Consider two waves C and D, scattered from particles in adjacent planes separated by a distance d. They are only in phase if the extra path length of wave D over C (= x + y) equals a whole number of wavelengths.  

• The equation for this path difference gives the Bragg law:

x + y = 2dsinq = nl

• This condition which gives rise to diffracted beams depends on the wavelength, l; the spacing of the planes of atoms, d; and the angle of incidence of the beam, q. This condition is known as Bragg's law:

nl = 2dsinq

• For a particular pair of d and l values there may be several values of q at which diffraction occurs.

 

 
 

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