The Effect of Symmetry on Some Ferrotoroidial Properties of Quasicrystals

Abstract

In this work, the effect of symmetry on some ferrotoroidial properties of quasi-crystals with 5-fold, 8-fold, 10-fold and 12-fold symmetries using group theoretical methods are dealt with. The number of independent constants is calculated and tabulated which helps in describing the ferrotoroidial properties of the quasi-crystals. Like crystals, quasi-crystals are ordered structures in which continuous translational and rotational symmetries are broken.  In both cases, there remains a discrete set of transformations invariant.  The symmetries and group theory is of greatest importance to scientists who want to reveal the characteristic features of physical properties of quasi-crystals just from their symmetries but not from the details of atomic and inter-atomic interaction.  This chapter gives a brief account of group theoretical methods of studying the effect of symmetry of some ferrotoroidial properties of quasi-crystals with 5-fold, 8-fold, 10-fold and 12-fold symmetries and the number of independent constants required to describe the ferrotoroidial properties of quasi-crystals.