Point group symmetries

The form of macroscopic physical property tensors of a crystalline structure can be determined from its magnetic or non-magnetic point group symmetry. In a ferroic crystal containing two or more equally stable domains of the same structure but of different spatial orientation, macroscopic tensorial physical properties that are different in domains, provide a tensor distinction of the domains. The use of point group symmetries in this tensor distinction is reviewed in this paper: Point group symmetry based classifications of domains have been defined to determine if specific macroscopic tensorial physical properties can provide a tensor distinction of all or some domains which arise in a phase transition. For pairs of domains, the tensor distinction is determined from a point group symmetry relationship, called a twin law. Recent work on domain average engineering in ferroics which focuses on the averaged point group symmetry and averaged physical properties of subsets of domains is also discussed.