By Charles George Lamb
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Extra resources for Notes on Magnetism
Fig. 11 (a) Parent unit cell of an imaginary two-dimensional structure. A structural transition corresponding to either vertical or horizontal shifts of B atoms is considered. (b) Low-symmetry structure containing two orientational domain states in intimate contact. (c) Low-symmetry structure containing two translational domain states in intimate contact. Squares in (b) and (c) represent original unit cells. Dashes indicate orientations of shifts of the B atoms. In shaded squares the signs of these shifts are opposite to those in non-shaded squares As an illustration, Fig.
1 illustrates how matrices of natural spontaneous strain components are determined for the two just mentioned and two additional transitions. The symbols d"kl or "kl stand for symmetry-allowed changes of the unit cell, induced by a change of temperature in the phase of symmetry G or F. These matrices have the same structure as that of the thermal dilatation tensors. 1 Structural Phase Transitions and Domain States 23 However, compared to customary tables given in textbooks on crystal physics, for each subgroup F they are expressed in the reference frame of G.
The symmetry of a material puts serious restrictions on the existence and orientation of p. It can only have nonzero components in samples of materials represented by one of the point symmetry groups 1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm, or Curie groups 1 and 1m. These are referred to as polar groups. While point groups describe symmetries of crystalline media, the Curie groups 1 and 1m have been included since they play a role in nonuniform ferroelectric systems such as ceramics or polymers. If the group F is polar while G is not, we speak about a ferroelectric phase transition; F is then the symmetry of the ferroelectric phase.