On the Co-Existence and Stability of Trijunctions and Quadrijunctions in a Simple Model
John W. Cahn, E S. Vanleck
Junctions of four domain walls (quadrijunctions) are shown to be stable in Ising-type ordering models with weak first and strong second neighbor interactions that give rise to certain ordered structures with four or more domains, such as the striped rectangular phase on ordering of two-dimensional square lattice and the B32 (NaTl) structure on ordering of BCC. Wen first neighbor interactions in the model are set to zero, quadrijunctions are stable with respect to dissociation into two trijunctions for all orientations and all temperatures below the critical ordering temperature. When the magnitude of first neighbor interactions in the model is increased, the stable range of orientation for quadrijunctions diminishes, and quadrijunctions coexist with trijunctions in a microstructure. When the magnitude of the first neighbor interaction reaches the limit of the existence of the ordered phases, the range of orientation for which the quadrijunction is stable vanishes. Results of confirming computer simulations are presented.