  Changes in stoichiometric NiTi allotropes induced by hydrostatic pressure
have been studied employing density functional theory. By modelling the
pressure-induced transitions in a way that imitates quasi-static pressure
changes, we show that the experimentally observed B19' phase is (in its bulk
form) unstable with respect to another monoclinic phase, B19". The lower
symmetry of the B19" phase leads to unique atomic trajectories of Ti and Ni
atoms (that do not share a single crystallographic plane) during the
pressure-induced phase transition. This uniqueness of atomic trajectories is
considered a necessary condition for the shape memory ability. The forward and
reverse pressure-induced transition B19'{$\leftrightarrow$}B19" exhibits a
hysteresis that is shown to originate from hitherto unexpected complexity of
the Born-Oppenheimer energy surface.
