Unconventional Thermal Expansion in quasi-one-dimensional monoclinic BaIrO$_3$

We have investigated the temperature dependence of the crystal structure of quasi-one-dimensional monoclinic BaIrO$_3$ using X-ray diffraction. Diffraction patterns were measured across a temperature range from 13 K to 300 K, with 5-degree steps, and Rietveld refinements were performed to extract the relevant lattice parameters. The resulting cell volumes exhibit a significant deviation from the Debye model predictions for lattice-specific heat within a reasonable range of the Debye temperature, Gr{\"u}neisen parameter, and bulk modulus. This suggests an invar-like, unconventional thermal expansion behavior. The deviation begins near the weak ferromagnetic transition temperature, indicating a strong correlation with changes in the electronic and magnetic structure of monoclinic BaIrO$_3$.