Zur rationellen Bestimmung der irreduziblen Bestandteile einer vorgegebenen Tensordarstellung in den 32 Kristallklassen

In terms of a group-theoretical notation of crystal symmetry a simple scheme is derived and discussed which allows to classify any given tensor with regard to irreducible representations of the crystallographic groups. To construct a complete decomposition-table for all 32 classes, a system of relating equations with universal constants has to be applied to a set of five numbers which sufficiently represent the specific properties (viz. order, intrinsic symmetry) of the tensor, and on which all results are dependent. Algebraic calculations with the representations are eliminated. The five characteristic values Nz, namely the number of independent components under the influence of a z-fold axis (z=1;2;3;4;6), can be calculated by means of elementary methods or special formulas given in the paper. Examples of third, fourth, sixth, & eighth order matter tensors illustrate the use of the scheme