Incommensurate modulated structure of BaMnF4 with monoclinic symmetry at 100 and 210 K

The incommensurate modulated structure of BaMnF 4 has been refined at 210 K and at 100 K using symmetry properties of the four-dimensional superspace groups. Two main assumptions have been made: orthorhombic P2,nb" symmetry (U l qq) and monoclinic symmetry (U A2'~h 1 11/" The symmetry of the X-ray diffraction pattern is better described with the monoclinic hypothesis assuming a twinning of the crystal. Refinement results have confirmed this analysis [Rv=4.51% for 4321 reflections at 100 K (monoclinic), R v = 5.61% for 3844 reflections at 210 K (monoclinic), Rv= 8.1% for 2217 reflections at 210 K (orthorhombic)]. The modulation is coherent with a rigid-body rotation of the MnF 6 octahedra and a related rectilinear motion of the Ba ion. A comparison of the shape and amplitude of the modulation waves at both temperatures is discussed.