Surface Energies Arising in Microscopic Modeling of Martensitic Transformations in Shape-Memory Alloys

Abstract

In this study we construct and analyze a two-well Hamiltonian on a 2D atomic lattice.The two wells of the Hamiltonian are prescribed by two rank-one connected martensitic twins,respectively. By constraining the deformed con gurations to special 1D atomic chains withposition-dependent elongation vectors for the vertical direction, we show that the structure ofground states under appropriate boundary conditions is close to the macroscopically expectedtwinned con gurations with additional boundary layers localized near the twinning interfaces.In addition, we proceed to a continuum limit, show asymptotic piecewise rigidity of minimizingsequences and rigorously derive the corresponding limiting form of the surface energy.