Martensitic transformations are diffusionless, solid-to-solid phase transitions, and have been observed in metals, alloys, ceramics and proteins1,2. They are characterized by a rapid change of crystal structure, accompanied by the development of a rich microstructure. Martensitic transformations can be irreversible, as seen in steels upon quenching1, or they can be reversible, such as those observed in shape-memory alloys3,4. In the latter case, the microstructures formed on cooling are easily manipulated by loads and disappear upon reheating. Here, using mathematical theory and numerical simulation, we explain these sharp differences in behaviour on the basis of the change in crystal symmetry during the transition. We find that a necessary condition for reversibility is that the symmetry groups of the parent and product phases be included in a common finite symmetry group. In these cases, the energy barrier to lattice-invariant shear is generically higher than that pertaining to the phase change and, consequently, transformations of this type can occur with virtually no plasticity. Irreversibility is inevitable in all other martensitic transformations, where the energy barrier to plastic deformation (via lattice-invariant shears, as in twinning or slip) is no higher than the barrier to the phase change itself. Various experimental observations confirm the importance of the symmetry of the stable states in determining the macroscopic reversibility of martensitic transformations.
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This work was largely carried out when J.Z. held a position at the California Institute of Technology. The work of S.C. and J.Z. was partially supported by the Deutsche Forschungsgemeinschaft. G.Z. acknowledges the partial support of the Italian MIUR (CoFin Modelli Matematici per i Materiali). S.C. and G.Z. acknowledge the partial support of the IV Framework Programme of the EU. K.B. and J.Z. acknowledge the partial financial support of the US Air Force Office of Scientific Research and the US Office of Naval Research. All authors contributed equally to this work.
The authors declare that they have no competing financial interests.
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