  The alkali-trihalogeno-germanates AGeX$_3$ with A a large single positive ion
such as Rb, Cs, or organic radicals such as methyl ammonium (MA), and X a
halogen (I, Br, Cl, F) along with the corresponding stannates (ASnX$_3$) and
plumbates (APbX$_3$) exhibit a large variety of crystal structures, some of
which are of the perovskite type. These materials, better known as "halide
perovskites'' have recently gained worldwide attention as promising
photovoltaic and more broadly opto-electronic materials. But their stability
problems relative to the non-perovskite phases is a major issue. Here we show
that the phase relations in these materials can be understood in terms of the
relative orientation of the GeX$_3$ tetrahedral units, which is ferroelectric
in the perovskite phase but antiferroelectric in the competing phases. This
suggests that an applied electric field could be used to stabilize the desired
phases and trigger a phase transition between two phases of the material with
widely different optical and electronic properties.
