Definition and expression of non-symmetric physical properties in space for uniaxial crystals

Abstract

The anisotropic physical property is the most noteworthy feature of crystals. In this paper, the subscript change method is used to analyze the sign changes of different tensors describing physical properties in uniaxial crystals. The distribution of some physical properties in special point groups exhibits non-symmetry in eight quadrants, which should attract the attention of crystal research. The difference between the crystallographic and physical coordinate systems and the lack of crystal symmetry operations are considered to be the origins of the non-symmetry. To avoid ambiguities and difficulties in characterizing and applying crystal physical properties, eight quadrants in space should be clarified. Hence, we proposed the use of piezoelectric properties to define the positive direction of the optical coordinate axis prior to the research and applications of optical properties.