ABSTRACT
The properties of single crystals will generally depend on the direction in which the properties are measured. However, as a result of the crystal symmetry, there will be different directions in which the physical properties of the crystal are the same. Light passing through the crystal consists of transverse waves whose vibrations can be resolved into two perpendicular components, both orthogonal to the direction of motion of the wave. For the higher-rank tensors in particular, if all the components were to be independent when we applied the tensors to the properties of real crystals, then calculations would become alarmingly complex. It is necessary to relate the representation quadric and hence the second-rank symmetrical tensor to the situation in real crystals. In the application of tensors to monoclinic and triclinic crystals, coefficients other than the principal components are necessary in order to relate the tensors to the conventional crystallographic axes.
