Nanocrystals in the size range 12–21 nm of a model binary ionic material in the wurtzite (B4) structure were constructed with morphologies which minimize the surface energy. These were then embedded in a pressurization medium, consisting of a binary Lennard-Jones-type fluid and progressively pressurized in “constant pressure” molecular dynamics simulation runs. Phase transitions to the rocksalt (B1) phase were confirmed by examining calculated powder diffraction patterns, which show the same changes in features as seen for experimental systems. By directly observing the atomic trajectories throughout the duration of the transition the local mechanism has been identified. The transition proceeds via a trigonal bipyramidal intermediate, denoted as the h-MgO structure. It is initiated by a single nucleation event at a [11-20]B4 surface with subsequent growth of the B1 region throughout the remainder of the nanocrystal. The consequences of this mechanism for the particle shape of the product phase are detailed and contrasted with those previously found for initially zincblende (B3) structured nanoparticles, using the same interaction potential. The observed transition pressures are elevated relative to the thermodynamically predicted pressure for the bulk, but there is no observable system size effect on the transition pressure across the size range of nanocrystals investigated.