Computer Simulation of a “Tweed- Transformation” in an Idealized Elastic Crystal

Abstract

A tweed-like transformation in a simple two-dimensional solid is simulated by distributing coherent rectangular particles over a square lattice and permitting them to undergo a step-wise reconfiguration so as to decrease the elastic energy. The equations determining the elastic energy of an arbitrary distribution of coherent tetragonal precipitates in a cubic crystal are developed under the assumptions that the precipitates are coherent, that the elastic constants are uniform, and that linear elastic relations apply; these include the example of rectangular precipitates in a square lattice as a special case. The model system is shown to relax into a tweed-like configuration in which like-variant particles align along (11) lines. The relaxed configuration yields simulated diffraction patterns and bright-field electron images which strongly resemble those obtained experimentally from the “tweed” transformation in Cu-Be.