Droplet Free Energy Functional for the Morphology of Martensites

TL;DR

This paper introduces a free energy functional model incorporating strain and vacancy fields to predict and understand the characteristic morphologies of martensites, including twinned and single-interface structures, during phase transformations.

Contribution

It presents a novel coarse-grained free energy functional that accounts for vacancy effects, providing a framework to predict martensite morphologies during structural transitions.

Findings

Successfully modeled twinned martensites in 2D

Predicted morphology differences between hard and soft martensites

Demonstrated the role of vacancy fields in morphology formation

Abstract

Martensites are metastable phases, possessing a characteristic morphology, usually formed during a fast quench accross a structural transition. We attempt to understand these morphological features using a coarsegrained free energy functional ${\cal F}[\epsilon ; \Phi]$ which contains, in addition to the usual strain fields $\epsilon_{ij}$ (the `` order parameter'' for the transition), the ``vacancy'' field $\phi$ which arises due to the geometric mismatch at a parent-product interface. The relaxation of this mismatch is slow compared to typical front propagation times and hence $\phi$ is essentially frozen in the reference frame of the growing martensite front. Minimisation of ${\cal F}$ then automatically yeilds typical martensite morphologies. We demonstrate this in two dimensions for the square to rhombus transformation and obtain internally twinned martensites, which grow as thin strips, for ``hard'' martensites (e.g., Fe-based alloys) or with a `single-interface', for ``soft'' martensites (e.g., In-Tl alloys).