Complex Systems

The Free Energy Concept in Cellular Automaton Models of Solid-Solid Phase Transitions Download PDF

Daniel G. Maeder
Physics Section, University of Geneva,
CH-1211, Geneva 4, Switzerland


Landau theories can describe characteristic features of shape memory alloys associated with their thermoelastic martensitic phase transformation. Such theories, based on a continuously variable free energy function , explain global behaviour satisfactorily but neglect microscopic aspects of the lattice change where the order parameter can only switch between a few fixed values. In a corresponding {cellular} type theory, we replace the continuous by a discrete set of functions , each depending on continuous global variables such as temperature and stress . The processing algorithm minimizes for each cell the sum of and the interface energies with its neighbours. At a fixed -condition, this process is equivalent to a cellular automaton transition rule. The simple case of a 3-state, one-dimensional martensite model is discussed in detail; changes for two-dimensional extensions are outlined