Hierarchical microstructure in structural phase transitions

We consider a model in the context of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential in local deviatoric (rectangular) strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation-induced strain gradient terms. The last term favors branching of domain walls which enables communication between macroscopic and microscopic regions essential for shape memory. Below the transition temperature (T₀) we obtain the conditions under which branching of twins is energetically favorable. Above T₀ a hierarchy of branched domain walls also stabilizes tweed formation (criss-cross patterns of twins). External stress or pressure modulates (“patterns”) the spacing of domain walls. Results based on 2D time-dependent Ginzburg-Landau simulations are shown for twins, tweed and hierarchy formation.