The path length of wave 2 is larger by AB + BC = 2d sin Q, Constructive interference will occur only if the path length difference is a multiple of the wavelength (l), this leads to Bragg's Law

nl = 2d sin Q

For practical purposes we shall only consider the situation where n=1, furthermore, we can calculate the value of d from the formulas given for d-spacings of a cubic system:

1/d² = (0² + 0² + 1²)/(3²) = 1/9d = 3 Å

Returning to Bragg's law and assuming we are using Cu Ka1 radiation (l = 1.5406 Å)

Q = sin^-1[1.54056/(2x3)]=14.87 degrees

Therefore, in a powder pattern we expect to see the (001) reflection at 29.74 degrees two-theta.
 

It is important to remember that although Bragg's law gives the right answer it is not a very accurate description of the physics involved. That is the electrons on the atoms actually act as point scatterers.
 

 

Consider diffraction from the (001) plane of a body centered cubic lattice (a = 3 A)
 

 

Path Length (wave 2) ® larger than 1 by 2d sin Q
Path Length (wave 3) ® larger than 1 by 2(d/2) sin Q
Thus leading to destructive interference.
This results in a systematic absence of the (001) reflection.

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