Intensity of the wave diffracted from a perfect crystal

7 Intensity of the wave diffracted from a perfect crystal 

We now consider the amplitude of the wave diffracted from a perfect crystal in directions that differ slightly from the exact Bragg angle. This 

Therefore, for one unit cell, the diffracted amplitude becomes 

Here r is the position of the nth atom in the unit cell with respect to some arbitrarily chosen origin. We now express r as the sum of two vectors 

Because g is a reciprocal lattice vector and tj is a lattice vector in real space, g r is an integer hence, Eq, (3.46) becomes 

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