Modulated phases in multi-stage structural transformations

Abstract

For multistage displacive structural transitions we present a general framework that accounts for various intermediate modulated phases, elastic constant, phonon, and related thermodynamic anomalies. Based on the presence or absence of modulated phases we classify these transformations in four categories and apply this approach to four different representative materials Ni-Mn-Ga (or $\ensuremath{\alpha}\ensuremath{-}\mathrm{U}),$ NiTi(Fe), Ni-Al, and Cu-Zn-Al. We suggest that the anomalous increase in elastic constants and phonon frequency observed when approaching the martensitic transition from above is a signature of the commensurate modulated phase.