Material Symmetry and Crystals

Abstract

When a crystal undergoes a change of symmetry during a phase transition, it suffers a change in the point group that characterizes the crystal structure. This kind of phase transition also is associated with the existence of variant forms whose particular arrangements are closely related to the symmetry change itself [1, 21]. Thus, the standard practice of considering a fixed point group as the material symmetry group clearly is inadequate to describe such phenomena. This observation was given an interesting perspective ten years ago by Ericksen [2] when he suggested that a more local theory of material symmetry was needed. Others [19, 20], already had begun to question the classical development of constitutive theory concerning material symmetry on the grounds that the symmetry was not allowed to change with either the temperature or the deformation gradient. The ideas of Ericksen in [2], and later in [17, 18], have motivated some additional development of the local theory for crystals by Pitteri [3] and others, wherein point groups serve as local material symmetry groups that are embedded in a basic global invariance group; the latter group identifies the crystal lattice structure. We, also, shall pursue this direction here.