Structural origin of dipole x-ray resonant scattering in the low-temperature phase of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Nd</mml:mi></mml:mrow><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">MnO</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>

We have investigated the low-temperature phase of a ${\mathrm{Nd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_{3}$ single crystal by x-ray resonant scattering at the $\mathrm{Mn}$ $K$ edge of the $(3 0 0)$, $(0 3 0)$, and $(0 5∕2 0)$ reflections. Strong resonances were observed for the $\ensuremath{\sigma}--{\ensuremath{\sigma}}^{\ensuremath{'}}$ channel in the $(3 0 0)$ and $(0 3 0)$ reflections and for the $\ensuremath{\sigma}--{\ensuremath{\pi}}^{\ensuremath{'}}$ channel in the $(0 5∕2 0)$ reflection. These resonances show a $\ensuremath{\pi}$ periodicity on the azimuthal angle, having the intensity at the minimum position almost zero. The intensity dependence on the photon energy, azimuthal angle and polarization has been analyzed using a semi-empirical structural model. Contrary to previous claims of charge $({\mathrm{Mn}}^{3+}{\text{\ensuremath{-}}\mathrm{Mn}}^{4+})$ and orbital ordering in this compound, our results show that the dipole resonant superlattice reflections can be explained by the presence of two types of $\mathrm{Mn}$ sites with different local geometric structures. One of the $\mathrm{Mn}$ sites is surrounded by a tetragonal-distorted oxygen octahedron, whereas the other site has a nearly regular octahedral environment. This model also shows that no real space-charge ordering is needed to explain the experimental data. Intermediate-valence states according to a fractional charge segregation ${\mathrm{Mn}}^{+3.42}{\text{\ensuremath{-}}\mathrm{Mn}}^{+3.58}$ were deduced.