Negative thermal expansion behavior in M Zr F6 (M =Ca ,Mg,Sr) : Ab initio lattice dynamical studies

The thermal expansion behavior of metal fluorides can be tuned by choosing an appropriate metal cation. We present ab initio lattice dynamical studies on the metal fluorides (CaZr F₆,MgZr F₆ , and SrZr F₆ ) and identify the anharmonic phonon modes responsible for the negative thermal expansion (NTE) in these materials. These phonon modes involve Zr F₆ polyhedral rotational motion, which leads to large transverse amplitude of the vibrations of the fluorine atom in the Zr-F-M bond in these compounds. The compounds with larger anisotropy in the thermal amplitude of the fluorine atom show larger NTE behavior. This has enabled us to understand the substantial variation in thermal expansion behavior of these compounds at high temperature. We have also calculated the potential energy profile of selected phonon modes, which enables us to derive the cubic and quartic anharmonic coefficients.