The macroscopic response of a system is often expressible by linear or bilinear laws, of the form X = x.F or X=F.x.F’. The “forces” F and “responses” X may be scalars, polar or axial vectors, or tensors. Crystal symmetry then imposes severe restrictions on the form of x. Tables of basis functions for crystallographic point groups are provided in a form which directly dictates the form of % (and which requires no knowledge or application of group theory). Various special cases, such as that presented by a complex representation, are illustrated by concrete examples. If X and F are conjugate thermodynamic variables, the crystal symmetry is augmented by thermodynamic symmetry relations. If X and F are thermodynamically conjugate dynamical variables, crystal symmetry is augmented by Onsager reciprocity. These thermodynamic cases are most conveniently treated by applying symmetry considerations to the free energy or the dissipation function respectively, as is illustrated by specific applications. © 1968, American Association of Physics Teachers. All rights reserved.
