Disorder-Driven Pretransitional Tweed Microstructures in Martensitic Transformations.

Defying the traditionally accepted understanding of first-order transitions, solid-solid displacive transformations are often accompanied by pronounced pretransitional phenomena indicative of a mesoscopic lattice deformation that "anticipates" the upcoming phase transition. Among these precursive effects is the observation of the so-called "tweed" pattern arising in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. Within a Landau-Ginzburg framework, we develop a formalism which incorporates non-linearity and disorder. Analytically, we derive a formal, rigorous, mathematical mapping between this tweed system and an antiferromagnetic bipartite Sherrington -Kirkpatrick spin glass; a mapping which is exact in the limit of infinite elastic anisotropy. Even in real materials characterized by finite anisotropy, a glassy regime will still be present, as witnessed by hysteretic and frequency dependent experimental observations. We have employed numerical simulations to verify the predicted phase diagram and glassy behavior, and to produce diffraction patterns for comparison to experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.