Negative Thermal Expansion, Response to Pressure and Phase Transitions in CaTiF₆

Strong volume negative thermal expansion over a wide temperature range typically only occurs in ReO₃-type fluorides that retain an ideal cubic structure to very low temperatures, such as ScF₃, CaZrF₆, CaHfF₆, and CaNbF₆. CaTiF₆ was examined in an effort to expand this small family of materials. However, it undergoes a cubic ( Fm3̅ m) to rhombohedral ( R3̅) transition on cooling to ∼120 K, with a minimum volume coefficient of thermal expansion (CTE) close to -42 ppm K^-1 at 180 K and a CTE of about -32 ppm K^-1 at room temperature. On compression at ambient temperature, the material remains cubic to ∼0.25 GPa with K₀ = 29(1) GPa and K'₀ = -50(5). Cubic CaTiF₆ is elastically softer and shows more pronounced pressure induced softening, than both CaZrF₆ and CaNbF₆. In sharp contrast to both CaZrF₆ and CaNbF₆, CaTiF₆ undergoes a first-order pressure induced octahedral tilting transition to a rhombohedral phase ( R3̅) on compression above 0.25 GPa, which is closely related to that seen in ScF₃. Just above the transition pressure, this phase is elastically very soft with a bulk modulus of only ∼4 GPa as octahedral tilting associated with a reduction in the Ca-F-Ti angles provides a low energy pathway for volume reduction. This volume reduction mechanism leads to highly anisotropic elastic properties, with the rhombohedral phase displaying both a low bulk modulus and negative linear compressibility parallel to the crystallographic c-axis for pressures below ∼2.5 GPa. At ∼3 GPa, a further phase transition to a poorly ordered phase occurs.