  Diffusionless phase transitions are at the core of the multifunctionality of
(magnetic) shape memory alloys, ferroelectrics and multiferroics. Giant strain
effects under external fields are obtained in low symmetric modulated
martensitic phases. We outline the origin of modulated phases, their connection
with tetragonal martensite and consequences for their functional properties by
analysing the martensitic microstructure of epitaxial Ni-Mn-Ga films from the
atomic to macroscale. Geometrical constraints at an austenite-martensite phase
boundary act down to the atomic scale. Hence a martensitic microstructure of
nanotwinned tetragonal martensite can form. Coarsening of twin variants can
reduce twin boundary energy, a process we could follow from the atomic to the
millimetre scale. Coarsening is a fractal process, proceeding in discrete steps
by doubling twin periodicity. The collective defect energy results in a
substantial hysteresis, which allows retaining modulated martensite as a
metastable phase at room temperature. In this metastable state elastic energy
is released by the formation of a 'twins within twins' microstructure which can
be observed from the nanometre to millimetre scale. This hierarchical twinning
results in mesoscopic twin boundaries which are diffuse, in contrast to the
common atomically sharp twin boundaries of tetragonal martensite. We suggest
that observed extraordinarily high mobility of such mesoscopic twin boundaries
originates from their diffuse nature which renders pinning by atomistic point
defects ineffective.
