The Free Energy Concept in Cellular Automaton Models of Solid-Solid Phase Transitions
Daniel G. Maeder
Physics Section, University of Geneva,
CH-1211, Geneva 4, Switzerland
Abstract
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
