  We report the results of both angle-dispersive x-ray diffraction and x-ray
absorption near-edge structure studies in BaWO4 and PbWO4 at pressures of up to
56 GPa and 24 GPa, respectively. BaWO4 is found to undergo a pressure-driven
phase transition at 7.1 GPa from the tetragonal scheelite structure (which is
stable under normal conditions) to the monoclinic fergusonite structure whereas
the same transition takes place in PbWO4 at 9 GPa. We observe a second
transition to another monoclinic structure which we identify as that of the
isostructural phases BaWO4-II and PbWO4-III (space group P21/n). We have also
performed ab initio total energy calculations which support the stability of
this structure at high pressures in both compounds. The theoretical
calculations further find that upon increase of pressure the scheelite phases
become locally unstable and transform displacively into the fergusonite
structure. The fergusonite structure is however metastable and can only occur
if the transition to the P21/n phases were kinetically inhibited. Our
experiments in BaWO4 indicate that it becomes amorphous beyond 47 GPa.
