  The deceptively simple inorganic salt ammonium sulfate undergoes a
ferroelectric phase transition associated with a very large entropy change and
both electrocaloric and barocaloric functionality. While the structural origins
of the electrical polarisation are now well established, those of the entropy
change have been controversial for over fifty years. This question is resolved
here using a combination of DFT phonon calculations with inelastic neutron
scattering under variable temperature and pressure, supported by complementary
total and quasielastic neutron scattering experiments. A simple model of the
entropy in which each molecular ion is disordered across the mirror plane in
the high symmetry phase, although widely used in the literature, proves to be
untenable. Instead, the entropy arises from low-frequency librations of
ammonium ions in this phase, with harmonic terms that are very small or even
negative. These results suggest that, in the search for molecular materials
with functionality derived from large entropy changes, vibrational entropy
arising from broad energy minima is likely to be just as important as
configurational entropy arising from crystallographic disorder.
