Effects of atom position relaxations

We first showed the influence of vacancies or interstitial atoms on the diffracted and scattered signals by overlooking the effects of local cell deformations associated 

When the crystal cell contains vacancies or atoms in interstitial positions, the positions of the neighboring atoms of this localized defect are affected and these atoms are no longer exactly in their reference positiom This is called position relaxation. The farther away atoms are from the defect, the smaller the variations of their positions. Usually, only the first and second neighbors are assumed to be affected. 

In order to illustrate the influence of this effect on the diffracted intensity and on the diffuse scattering signal, we will consider the simple case where only the first two neighbors surrounding the interstitial atom are affected and we will assume that the atoms are moved by a distance of a/4. 

The diffracted intensity is then multiplied by the square of this expression, or  

The diffuse scattering distribution is expressed according to the equation  

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