Physical-property tensors and tensor pairs in crystals

Abstract

The form of physical-property tensors of rank 0, 1 and 2 invariant under the 32 crystallographic point groups and their subgroups are tabulated. This constitutes the basis for the tensorial classification of domain pairs in ferroic crystals which is given via a group theoretical classification of the corresponding physical-property tensor pairs. We tabulate this classification of tensor pairs for all physical-property tensors of rank 0, 1 and 2, and domain point-group symmetry.

Axial point groups: rank 1, 2, 3 and 4 property tensor tables

“…A considerable amount of literature exists on the derivation and tabulation of the form of physical property tensors invariant under non-magnetic crystallographic point groups (Jahn, 1949;Nye, 1957;Wooster, 1973;Kopský, 1979a;Sirotin & Shaskolskaya, 1982;Brandmü ller & Winter, 1985;Litvin & Litvin, 1990; and references contained in these sources) and under magnetic crystallographic point groups (Sirotin, 1962;Birss, 1964;Tenenbaum, 1966;Kopský, 1976Kopský, , 1979bLitvin & Litvin, 1991;Authier, 2003; and references contained in these sources). The symmetry of quasi-one-dimensional materials, such as polymers (Vainshtein, 1966) and nanotubes (Damnjanović & Milošević, 2010), is described by non-magnetic and magnetic line groups (Hermann, 1928;Alexander, 1929;Damnjanović & Vujičić, 1982).…”

Distinction of magnetic non-ferroelastic domains

“…This was extended to all non-magnetic non-ferroelastic domain pairs in Janovec et al (1993). Tabulations of the matrix form of physical property tensors (Litvin & Litvin, 1990, 1991 were used in listing the matrix forms of property tensors that distinguish non-ferroelastic magnetoelectric domain pairs (Litvin et al, 1994). From these latter tabulations, one can find not only which property tensors distinguish between the domains but also which components of the property tensors provide the distinction.…”