  For multi-stage, 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, NiTi(Fe),Ni-Al, Cu-Zn-Al and alpha-U. We suggest that the anomalous
increase in elastic constant(s) and phonon frequency observed when approaching
the martensitic transition from above is a signature of the conmensurate
modulated phase.
