SpgFoldINSD:A Folding algorithm of Neutron Inelastic Scattering Data to the Primitive Brillouin Zone

Measured Inelastic Neutron Scattering Data (INSD) is obtained in energy-momentum space by neutron spectroscopy methods. With recent advances in time-of-flight chopper spectrometers (i.e. ARCS, CNCS, HYSPEC), the entire 4-dimensional (Q_x,Q_y,Q_z,E) space can be efficiently collected. With that said, the spatial dimensions of the detectors limit the span of the crystal’s reciprocal space {H_hkl} covered. Depending on the crystallographic space group of the measured crystal, the tiling of INSD in reciprocal space must display a corresponding set of symmetry relations. In this thesis, we detail the construction of a post-processing algorithm that overlaps the dataset of a given crystal sample to its Primitive Brillouin Zone (PBZ). Furthermore, to ensure crystal symmetry is preserved, an average of the overlapped dataset over the crystal’s symmetry equivalent q_l points inside the PBZ is then obtained by applying the rotational symmetry operations to the folded dataset. The method we apply is consistent with band-unfolding methods for supercell calculations where the primitive cell’s translational symmetry is preserved (Ikeda & Popescu & Allen). We fold INSD of Germanium and Niobium, both crystals whose supercells preserve the translational symmetry of the primitive lattice, and present the improvement of the statistical quality of the data through the evolution of the folding.