Crystal symmetry and physical properties: application of group theory

The paper gives a brief account of group-theoretical methods of studying the effect of symmetry on all possible physical properties (known and already measured or not known) which depend on crystal symmetry; based on the fact that all such properties represent the relation between two quantities each of which may be a scalar, a vector, or a tensor. Tables are given showing the character of the transformation matrices for each possible combination of the above quantities, the number of independent constants needed to describe the corresponding phenomenon in each of the 32 classes, and actual examples (where known) of physical properties corresponding to the different possible combinations. The 32 crystal classes are reduced to 11 in all cases where centro-symmetrical properties are dealt with. When comparison is made with results of other methods of considering the same problems, discrepancies are found in the case of the photo-elastic coefficients and the third-order elastic coefficients. All the properties considered above are such as will remain invariant under a transformation of axes according to any symmetry operation. There are other properties, such as enantiomorphism and optical activity, which change sign for an operation of rotation reflexion. The numbers of independent constants in each of the 32 classes are deduced for these properties also.