Periodic surfaces of simple and complex topology: Comparison of scattering patterns

We compute scattering patterns for six triply periodic minimal surfaces formed in oil/surfactant/water solutions: Three surfaces of a simple topology, Schwarz P $\left(Im3\mathrm{}¯m\right),$ Schwarz D–diamond $\left(Pn3\mathrm{}¯m\right),$ and Schoen G–gyroid $\left(Ia3\mathrm{}¯d\right),$ and three surfaces of a complex topology, SCN1 $\left(Im3\mathrm{}¯m\right),$ CD $\left(Pn3\mathrm{}¯m\right),$ and GX6 $\left(Ia3\mathrm{}¯d\right).\mathrm{}$ We show that in the case of the complex structures, scattering intensity is shifted towards the higher $\mathrm{hkl}$ peaks. This might cause their misidentification and wrong estimates about the cell size of the structure.