THEORY AND COMPUTER-SIMULATION OF TWEED TEXTURE

An analytical theory of the ordering interaction J(R(ij)) in structura l phase transitions mediated by elastic relaxation in the material is outlined. The ordering process in cell i sets up a local stress field due to the sizes, shapes or displacements of atoms or atomic groups, w hich is propagated elastically to a distant cell j. The atomistic theo ry for ferro- and antiferro-elastic transitions takes into account two types of singularity, one due to elastic anisotropy and the other to the Zener interaction J(Z) of infinite range in ferroelastic transitio ns. The form of J(k) in Fourier space is highly anisotropic with a few ''soft'' directions coinciding with the orientation of twin boundarie s. The asymptoptic J(R) at large R is shown to be very anisotropic as well and decays as R(-3) in ferroelastic and R(-5) in antiferroelastic systems. Computer simulations for a three-dimensional model of about 29,000 particles show a strong tendency to form tweed texture, as obse rved experimentally. Well above the structural phase transition temper ature, the strain fluctuations show well-developed embryos of the twee d texture. On quenching to below the transition temperature, a pronoun ced micro-twinning appears which follows almost exactly the shape of t he embryos and then develops towards a stripe texture. After a certain time needle-shaped domains are formed and a peculiar step-wise proces s of generating new stripes is observed.