Phase transitions and equations of state of alkaline earth fluorides CaF_2, SrF_2, and BaF_2 to Mbar pressures

摘要

Phase transitions and equations of state of the alkaline earth fluorides CaF_2, SrF_2, and BaF_2 were examined by static compression to pressures as high as 146 GPa. Angle-dispersive x-ray diffraction experiments were performed on polycrystalline samples in the laser-heated diamond-anvil cell. We confirmed that at pressures less than 10 GPa all three materials undergo a phase transition from the cubic (Fm3m) fluorite structure to the orthorhombic (Pnam) cotunnite-type structure. This work has characterized an additional phase transition in CaF_2 and SrF_2: these materials were observed to transform to a hexagonal (P6_3/mmc) Ni_2In-type structure between 63-79 GPa and 28-29 GPa, respectively, upon laser heating. For SrF_2, the Ni_2In-type phase was confirmed by Rietveld refinement. Volumes were determined as a function of pressure for all high-pressure phases and fit to the third-order Birch-Murnaghan equation of state. For CaF_2 and SrF_2, the fluorite-cotunnite transition results in a volume decrease of 8-10 %, while the bulk modulus of the cotunnite-type phase is the same or less than that of the fluorite phase within uncertainty. For all three fluorides, the volume reduction associated with the further transition to the Ni_2In-type phase is ～5%. The percentage increase in the bulk modulus (△K) across the transition is greater when the cation is smaller. While for BaF_2, △K is 10-30 %, △K values for SrF_2 and CaF_2 are 45-65 % and 20-40 %. Although shock data for CaF_2 have been interpreted to show a transition to a highly incompressible phase above 100 GPa, this is not consistent with our static equation of state data.