GaAs/Fe$_{3}$Si core/shell nanowire structures were fabricated by molecular-beam epitaxy on oxidized Si(111) substrates and investigated by synchrotron x-ray diffraction. The surfaces of the Fe$_3$Si shells exhibit nanofacets. These facets consist of well pronounced Fe$_3$Si{111} planes. Density functional theory reveals that the Si-terminated Fe$_3$Si{111} surface has the lowest energy in agreement with the experimental findings. We can analyze the x-ray diffuse scattering and diffraction of the ensemble of nanowires avoiding the signal of the substrate and poly-crystalline films located between the wires. Fe$_3$Si nanofacets cause streaks in the x-ray reciprocal space map rotated by an azimuthal angle of 30{deg} compared with those of bare GaAs nanowires. In the corresponding TEM micrograph the facets are revealed only if the incident electron beam is oriented along [1$overline{1}$0] in accordance with the x-ray results. Additional maxima in the x-ray scans indicate the onset of chemical reactions between Fe$_{3}$Si shells and GaAs cores occurring at increased growth temperatures.
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