Anomalous X-ray scattering

Wavelength-dependent complex atomic scattering, written $f=f_0+f^{\prime }+i{f}^{\prime \prime }$. Its imaginary component can break equality of Friedel-pair intensities.

For positional structure factors $A,B$, a real scattering factor $a$, and a complex factor $b+i{b}^{\prime \prime }$, the amplitudes are $F_{+}=aA+(b+i{b}^{\prime \prime })B$ and $F_{-}=a{A}^{\ast }+(b+i{b}^{\prime \prime })B^{\ast }$. Expanding their squared moduli gives the displayed difference. Resonance and lack of inversion allow a difference but do not force one: proportional positional sums with a real proportionality factor give zero.

A phase-determination method combining intensities measured at wavelengths with different anomalous-scattering contributions. Both dispersive and Friedel-pair differences provide constraints.