Prediction of an ultrahigh-pressure form of Al$_2$O$_3$*

We predict by first principles a pressure induced phase transition in alumina at $\sim$3.7 Mbar, relevant for interiors of the giant planets and terrestrial exoplanets, at room temperature from the CaIrO$_3$-type polymorph to another with the U$_2$S$_3$-type structure. This transformation should be important for the analysis of shock data in this pressure range, since alumina is used as window material. Our calculated compression curves agree with shock data excellently, indicating that the presence of two phase transitions (corundum--Rh$_2$O$_3$(II)-type and Rh$_2$O$_3$(II)-type--CaIrO$_3$-type) had gone unnoticed in shock data. Our prediction suggests that the multi-Mbar crystal chemistry of planet-forming minerals might be related to that of the rare-earth sulfides.