ABSTRACT
In general, for a crystalline solid immersed in a heat-and pressure-bath, the location of the energy wells depends on the environmental temperature and pressure, regarded as control parameters. Bifurcation theory studies how the equilibria – here the critical points of the free energy density – change in number and stability character as the control parameters are varied continuously. An analysis in which both environmental temperature and pressure vary is given by Ericksen (1996a). For simplicity, here we assume pressure to be zero, temperature remaining the only control, and show how the energetics in chapter 6 can be used to describe a family of static bifurcations (phase transitions) in simple lattices, included in the larger class of martensitic phase transformations.
