Phase transitions and equations of state of alkaline earth fluoridesCaF2,SrF2, andBaF2to Mbar pressures

Abstract

Phase transitions and equations of state of the alkaline earth fluorides ${\text{CaF}}_{2}$, ${\text{SrF}}_{2}$, and ${\text{BaF}}_{2}$ 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 $(Fm\overline{3}m)$ fluorite structure to the orthorhombic $(Pnam)$ cotunnite-type structure. This work has characterized an additional phase transition in ${\text{CaF}}_{2}$ and ${\text{SrF}}_{2}$: these materials were observed to transform to a hexagonal $(P{6}_{3}/mmc)$ ${\text{Ni}}_{2}\text{In}$-type structure between 63--79 GPa and 28--29 GPa, respectively, upon laser heating. For ${\text{SrF}}_{2}$, the ${\text{Ni}}_{2}\text{In}$-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 ${\text{CaF}}_{2}$ and ${\text{SrF}}_{2}$, the fluorite-cotunnite transition results in a volume decrease of $8--10\text{ }\mathrm{%}$, 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 ${\text{Ni}}_{2}\text{In}$-type phase is $\ensuremath{\sim}5\mathrm{%}$. The percentage increase in the bulk modulus $(\ensuremath{\Delta}K)$ across the transition is greater when the cation is smaller. While for ${\text{BaF}}_{2}$, $\ensuremath{\Delta}K$ is $10--30\text{ }\mathrm{%}$, $\ensuremath{\Delta}K$ values for ${\text{SrF}}_{2}$ and ${\text{CaF}}_{2}$ are $45--65\text{ }\mathrm{%}$ and $20--40\text{ }\mathrm{%}$. Although shock data for ${\text{CaF}}_{2}$ 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.