Analysis of Microstructures in Cu-14.0%Al-3.9%Ni by Energy Minimization

Abstract
During the past few years, a new theory of martensite has been developed in which microstructure is predicted by energy minimization ([1, 2]). The theory is based on a crystallographic model, and the continuum theory is obtained from this model by using the Cauchy-Born rule to relate atomic to macroscopic deformation. The theory treats the geometry of deformation exactly, regardless of the size of the transformation strain. The authors believe that this theory could be widely used by experts on martensite to analyze and predict microstructures. To illustrate one way the theory can be used, the authors take several of the commonly observed microstructures in CuAlNi and show how each of them can be obtained directly by energy minimization of a given energy function. In particular, we consider the austenite-martensite interface (the theory subsumes the crystallographic theory of martensite), the divided wedge, laminates of compound twins, layers within layers of Type II twins, and simple and complex twin crossings. In each of these cases the theory gives precise information on deformed geometry, orientation of interfaces, and volume fractions.