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The form of macroscopic physical property tensors of a crystalline structure can be determined from its magnetic or nonmagnetic point group symmetry. A ferroic crystal contains two or more equally stable domains of the same structure but of different spatial orientation. Macroscopic tensorial physical properties that are different in the domains provide a tensor distinction of the domains. The use of point group symmetries in this tensor distinction is reviewed in this chapter: 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 that 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 that focuses on the averaged point group symmetry and averaged physical properties of subsets of domains is also discussed.
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