A simple method of determining the form of the phonon part of tensors describing quasicrystal properties.
It is shown that the restrictions on the form of property tensors of rank <5 that follow from the Neumann principle for the point groups describing quasicrystals can easily be deduced from the restrictions for the point groups describing ordinary crystals. For octagonal and dodecagonal point groups, this is true even for property tensors of rank<8 and <12, respectively. The results derived in a number of papers for various physical properties of quasicrystals with certain point-group symmetries are generalized to all quasicrystal point groups, and it is shown that the results become more lucid if the classification of quasicrystal point groups with a principal axis into pentagonal, decagonal, octagonal and dodecagonal ones is done appropriately. A comparison with other approaches shows that applying the Neumann principle for the point groups describing quasicrystals yields the form of the so-called phonon part of the tensor under consideration. Connections between the restrictions valid for property tensors of arbitrary rank are given for general Heesch-Shubnikov point groups in three dimensions.
Grimmer
Hans
H
Laboratory for Development and Methods, Condensed Matter Research with Neutrons and Muons, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland. hans.grimmer@psi.ch