We investigate the high-pressure behaviour of beryllium, magnesium and calcium difluorides using ab initio random structure searching and density functional theory (DFT) calculations, over the pressure range 0-70 GPa. Beryllium fluoride exhibits extensive polymorphism at low pressures, and we find two new phases for this compound - the silica moganite and CaCl2 structures - which are stable over the wide pressure range 12-57 GPa. For magnesium fluoride, our searching results show that the orthorhombic `O-I TiO2 structure (Pbca, Z=8) is stable for this compound between 40 and 44 GPa. Our searches find no new phases at the static-lattice level for calcium difluoride between 0 and 70 GPa; however, a phase with P62m symmetry is close to stability over this pressure range, and our calculations predict that this phase is stabilised at high temperature. The P62m structure exhibits an unstable phonon mode at large volumes which may signal a transition to a superionic state at high temperatures. The Group-II difluorides are isoelectronic to a number of other AB2-type compounds such as SiO2 and TiO2, and we discuss our results in light of these similarities.
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