Discovery of time-reversal symmetry (TRS) breaking in Re-based noncentrosymmetric (NCS) α-Mn structure compounds has garnered much attention, due to the repeated occurrence of TRS breaking among all the members of Re6X (X = Ti.Hf,Zr). However the TRS breaking effects in Re6X, could also be a consequence of a subtle lattice distortion upon entering the superconducting state. Thus, leading to the possibility that these systems do not break TRS, but are conventional BCS isotropic gap superconductors, detailed study of the crystal structure near the phase transition (normal to superconducting) is highly desirable. In this proposal, we propose to use the high-resolution neutron diffraction technique to elucidate the fine details of a possible lattice distortion in Re3W, Re6Ti, pure Re element and Re0.82Nb0.18.