  The local structure of high pressure BaTiO$_3$ has been interrogated by
neutron total scattering methods, up to pressures of 4.18 GPa at ambient
temperature. Competitive refinements of cubic, tetragonal and rhombohedral
distortion modes against pair distribution functions indicate contrasting local
structure behaviour of temperature- and pressure-induced cubic BaTiO$_3$.
Suppression of the mode amplitude, isotropy of the order parameter direction
and loss of sensitivity to correlated Ti displacements at high pressure all
suggest a high-pressure local structure that is more consistent with the
harmonic approximation, rather than an order-disorder model which better
describes high-temperature cubic BaTiO$_3$ in the vicinity of the tetragonal
phase transition.
