Surface Energy and Microstructure

Bulk energy considerations can predict the gross features of microstructures observed in martensitic phase transitions, but not finer details such as the length scale on which twinning occurs. These are determined by surface energy. A standard approach is to minimize the sum of bulk and surface energy within the class of “twinned” configurations. This leads to the conclusion that the twin width w and the twin length L should satisfy w ∼L∼. While that seems to be the rule, a different structure is sometimes observed, for example in In-Tl and Cu-Al-Ni. It involves successive coarsening of the twins away from an austenite/twinned-martensite interface.We re-examine the minimization of bulk plus surface energy. Our analysis differs from prior ones in that it permits configurations which are not essentially “onedimensional” to compete in the minimization. We find that the global minimum of energy can be either “one-dimensional” or “branched,” depending on the relative values of the elastic moduli and surface energy density.