Non-weak phase transformations

  • Sergio Conti
  • Giovanni Zanzotto
G3 10 (Lecture hall)


Non-weak solid-to-solid phase transitions are characterized by the absence of a finite supergroup of all the symmetry groups of the phases involved, as for example in the face-centered-cubic to body-centered-cubic of iron. Non-weak transformations necessarily involve large lattice distortions, and their properties are markedly different from those of the "weak" transitions, typical of shape-memory compounds.
We show that all transitions where the parent and product phases are in a group-subgroup relation can be accomplished as weak transformations, and study a general framework for the analysis of non-weak transformations. We present a nonlinear elastic model for a square-to-hexagonal transition in planar simple lattices, which gives a two-dimensional example of non-weak phase changes. Our constitutive framework and the ensuing analysis illustrate some general propertis of non-weak transformations, showing their link to the development of dislocations and plasticity phenomena in crystalline lattices.

Stefan Müller

Max Planck Institute for Mathematics in the Sciences