Effects of symmetry on the structure amplitude

Considering the most general expression of the structure amplitude, Eq. 2.107, its value is defined by population and displacement parameters of all 

As a result of symmetry transformation (Eqs. 2.111 and 2.112), both the magnitude of the structure amplitude and its phase may change. Finite symmetry operations (t, tj and tj are all 0) usually affect the phase angle, while infinite operations, i.e. those which have a non-zero translational component, affect both the magnitude and the phase. 

We begin with considering the relationships between the structure amplitudes of two centrosymmetric reciprocal lattice points (hkl) and (hkl). 

Regardless of whether the crystal structure is centrosymmetric or not, in the absence of the anomalous scattering it directly follows from Eqs. 2.103, 2.104,2.105 and 2.113 that 

On the contrary, when the anomalous scattering is substantial, then considering Eq. 2.107 instead of Eq. 2.103, both the real and imaginary components of the structure amplitude are modified as follows 

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