Time evolution of twin domains in cordierite: a computer simulation study

The time and temperature evolution of twinning in cordierite is simulated using three computer models. The orientation of walls between twin domains in natural cordierite follows mainly the ferroelastic pattern which minimises the strain energy of the walls between twin-related domains. Such ferroelastic twinning is simulated in an elastic three-states Potts model in which each structural six-membered ring is represented by a three state pseudo-spin. The resulting twin pattern in a sample with 3169 structural rings shows sector trilling and fine scale ferroelastic wall patterns which coarsen with increasing annealing time. The poorly defined wall directions observed in cordierite were found to be related to twin walls which do not minimise the strain energy. Instead, these walls are located along the corners of pseudo-hexagonal rings and appear as the consequence of local rather than global interatomic interactions. Simulations using two-dimensional (38028 atoms) and three-dimensional (408 228 atoms) structural models show a predominance of these topological walls over the strain walls at early stages in the ordering process. The domain structure in the simulation is patchy rather than corresponding to repeated stripe structures found in other ferroelastic and co-elastic materials. In all models, a strong tendency for sector trilling is observed. In kinetic tweed patterns a novel 60 degrees tweed is found at atomic length scales while the usual strain-mediated 90 degrees tweed appears at mesoscopic length scales. An unusual surface tension effect in domain formation and 'writhing', fluid-like motion was found in the three-dimensional structural model. This motion, along with the existence of non strain-mediated walls may contribute to cordierite's poorly defined domain wall directions at the early stages of domain coarsening.