Influence of point defects on the distribution of twin wall widths

A recent experimental measurement of the width of a twin wall suggests that the wall width can vary considerably as a function of position. This contradicts the previously held assumption that the wall width was a constant, taking the same value in adjacent walls and in different parts of the same wall. We explore the possibility that this variation in wall width is the result of the interaction of the order parameter with point defects. We do this in the context of a two-dimensional model on a square grid in which a continuous order parameter interacts with a lattice of Ising spins representing the presence or absence of point defects. We show that the key to reproducing the experimentally observed range of wall widths lies in two interactions. First, an interaction between the order parameter and the point defects causing the accumulation of point defects within the wall. Secondly, an interaction between point defects causing them to form clusters. When both these effects are included, simulations produce distributions of wall widths similar to those observed experimentally.