Twin wall of proper cubic-tetragonal ferroelastics

We derive solutions for the twin wall linking two tetragonal variants of proper cubic-tetragonal ferroelastics, including the dilatational and shear energies and strains. Our solutions satisfy the compatibility relations exactly and are obtained at all temperatures. They require four nonvanishing strains except at the Barsch-Krumhansl temperature ${T}_{\mathrm{BK}}$ (where only the two deviatoric strains are needed). Between the critical temperature and ${T}_{\mathrm{BK}},$ material in the wall region is dilated, while below ${T}_{\mathrm{BK}}$ it is compressed; we estimate a compression of $\ensuremath{\sim}1%$ for Fe-Pd alloys. In agreement with experiment and more general theory, the twin wall lies in a cubic 110-type plane. We obtain the wall energy numerically as a function of temperature and we derive a simple estimate which agrees well with these values.