Systematics of group-nonsubgroup transitions: Square to triangle transition

A variety of structural transitions in nature do not involve a group-subgroup relationship. A two-dimensional example is the transition between a square lattice and a triangular lattice, which is known to occur in vortex lattices, Wigner crystals, skyrmion lattices, colloids, diblock copolymers, etc. A three-dimensional analog is the shock-induced BCC to HCP transition in iron. We develop a systematic technique that incorporates site symmetry and yields displacive transition mechanisms and free energy forms for such structural changes. This procedure is demonstrated for the square to triangle transition.