Symmetry breaking in monoatomic 2-lattices

In this paper we describe all the possibilities for symmetry-breaking transformations in monoatomic 2-lattices (crystal structures with two identical points in their unit translational cell). This is done by establishing the symmetry hierarchies (partial ordering) for the arithmetic classes of symmetry groups of these crystals, shown in Fig. 1. We also study the ‘Ericksen–Pitteri neighbourhoods’ for monoatomic 2-lattices, thus making a local analysis of their configuration space. We give details about two physically relevant cases, analysing the neighbourhoods and the possible symmetry-breaking mechanisms for the hexagonal close-packed and the diamond structures (Figs. 2 and 3).