Negative Thermal Expansion Behaviour in MZrF6 (M=Ca, Mg, Sr): Ab-initio Lattice Dynamical Studies

The thermal expansion behavior of metal fluorides can be tuned by choosing appropriate metal cation. We present ab-initio lattice dynamical studies on the metal fluorides (CaZrF6, MgZrF6 and SrZrF6) and identify the anharmonic phonon modes responsible for the negative thermal expansion in these materials. These phonons involve ZrF6 polyhedral rotational motion, which leads to large transverse amplitude of the vibrations of the fluorine atom in the Zr-F-Zr bond. The compounds with larger anisotropy in the thermal amplitude of the fluorine atoms show larger NTE behaviour. This has enabled to understand the large variation in thermal expansion behaviour of these compounds at high temperature. The calculations also predict decrease of the frequency of these anharmonic phonons with increasing temperature.