Crystallite size effect on the monoclinic deformation of the bcc crystal structure of chromium

The modulated spin density wave magnetic orderings observed in chromium suggests that the crystal structure of chromium cannot be described by the cubic space group Im3m. Our experimental studies of polycrystalline and nanocrystalline chromium by synchrotron radiation (SR) and neutron powder diffraction show a hkl-dependent Bragg peak broadening which can be interpreted by the low-symmetry monoclinic space group P21∕n instead of the high symmetry cubic space group Im3m. The monoclinic angle is ??m = 90.05(1)◦ and 90.29(1)◦ for polycrystalline Cr and nanocrystalline Cr, respectively. The relative monoclinic distortion observed in chromium is 5 times larger than those reported for several oxides: BiFeO3, ??-Fe2O3, Cr2O3 and calcite. The symmetry of the magnetic transverse spin density wave (TSDW) and the longitudinal spin density wave (LSDW) observed in Cr are described by using the superspace groups P21∕n(0??0)00 and P2′ 1∕n′(0??0)00, respectively. These superspace groups describe both the magnetic modulations and the atomic position modulations reported in the literature. The monoclinic symmetry of chromium is a robust effect which is observed in the paramagnetic as well as in the TSDW and LSDW phases.