  We report a temperature-dependent neutron diffraction (ND) study on
polycrystalline monoclinic BaIrO$_3$ which is famous for charge density wave
(CDW) and weak ferromagnetic phase transitions at T$_C$$\sim$180 K
simultaneously. A Rietveld analysis on the ND patterns reveals that even though
there is no symmetry breaking in crystal structure, a noticeable change in the
four kinds of IrO$_{6}$ octahedra is isolated as the temperature approaches to
T$_C$. Based on the structure analysis results, we calculated the $d$-orbital
energy level splittings by crystal electric field for each type of the IrO$_6$
octahedra. By taking into account the strong spin-orbit coupling in Ir 5$d$
orbitals and the lattice distortions obtained from the ND analysis, we propose
an electronic configuration model to understand the phase transition of the
system, where an effective $J_{\rm eff, 1/2}$ Mott insulating phase and a
charge gap phase induced by bonding states between the $J_{\rm eff,1/2}$ states
compete each other.
