LANDAU THEORY OF A CONSTRAINED FERROELASTIC IN 2 DIMENSIONS

The Landau expansion of the elastic energy in powers of the strains an d their derivatives is applied to the ferroelastic transformation of a grain constrained so that the displacement vanishes on the boundaries of the, grain; the model applies strictly only to the square-rectangu lar transformation, but some results may apply also to the tetragonal- orthorhombic transformation, The displacement and the strains are obta ined by numerical minimization of the elastic energy (with respect to the displacement) for a square column with edges parallel to the (100) and (010) planes of the tetragonal phase. The structure obtained is a sequence of twin boundaries [parallel to the (110) planes of the pare nt phase] with nonzero dilatational and sheer strains near the boundar ies. The mean-field transformation temperature T-c(L) is depressed fro m the bulk value due to the finite width L of the grain, behaving roug hly as T-c(L) = T-c(infinity) - const/L.