Alladi Ramakrishnan Hall

Domain-wall evolution in structural phase transitions: Anisotropic interactions, entropy barriers and final geometric strain-patterns

Subodh R Shenoy

TCIS, TIFR Hyderabad

Structural phase transitions such as in martensites, are spontaneous changes of the crystal-lattice unit cell on cooling, to lattices of lower symmetry. The relative changes in the unit-cell axes define a strain tensor, with some subset defined as the order parameter(s) or OP, that enter the non-harmonic Landau free energy. A minimization of the remaining (non-order-parameter) harmonic strains, subject to a ‘lattice-integrity’ or Compatibility constraint, generates a power-law, anisotropic interaction between the OPs, that orients the elastic domain-walls between competing crystal variants.

We evaluate strain magnitudes at degenerate minima of the symmetry-allowed Landau free energy, thus inducing discretized-strains that are clock-like spins, pointing to competing crystal variants, in OP space. The full free energies then generate families of generalized clock model hamiltonians, with power-law anisotropic interactions.

We show that the experimentally observed, domain-wall final patterns in different materials, can be understood in terms of a local mean-field treatment of the relevant clock-like hamiltonian.

We show that a puzzling delayed-conversion to martensite on quenching to above transition,
can be understood by entropy barriers, or rare domain-wall pathways to conversion; with a natural appearance of protein folding concepts like golf holes and funnels,
in configuration space.