X-ray diffraction and theoretical studies of the high-pressure structures and phase transitions in magnesium fluoride

Abstract

Magnesium fluoride is an archetypal simple ionic solid and as such has been subject to numerous theoretical studies with particular emphasis on the rutile to fluorite phase transition. In the present study by angle-dispersive, x-ray powder diffraction and density-functional plane-wave methods, it is shown that the high-pressure behavior of ${\mathrm{MgF}}_{2}$ is much more complex. A second-order transition from the tetragonal rutile-type to an orthorhombic ${\mathrm{CaCl}}_{2}$-type phase is observed at 9.1 GPa, prior to the transformation at close to 14 GPa to the cubic phase, which is found to have a modified fluorite structure of the ${\mathrm{PdF}}_{2}$ type. The structures of these three phases were refined by the Rietveld method, and the pressure dependence of the structural parameters is in good agreement with theory. A denser, cotunnite $(\ensuremath{\alpha}\ensuremath{-}{\mathrm{PbCl}}_{2})$- type phase is observed at pressures above 35 GPa. Upon decompression, retransformation to the ${\mathrm{PdF}}_{2}$-type phase is observed and a mixture of the rutile- and $\ensuremath{\alpha}\ensuremath{-}{\mathrm{PbO}}_{2}$-type forms is recovered at ambient pressure. The results of density-functional calculations yield the following sequence of stable phases: ${\mathrm{rutil}\stackrel{\ensuremath{\rightarrow}}{e}\mathrm{\ensuremath{\alpha}}\ensuremath{-}\mathrm{P}\mathrm{b}\mathrm{O}}_{2}{\ensuremath{\rightarrow}\mathrm{PdF}}_{2}{\ensuremath{\rightarrow}\mathrm{\ensuremath{\alpha}}\ensuremath{-}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_{2}$ and indicate that fluorite-type structure always has a higher energy than the ${\mathrm{PdF}}_{2}$-type structure and is never stable for ${\mathrm{MgF}}_{2}.$