By J. Grindlay
''In this monograph the writer describes the foundation and derivation of the macroscopic or phenomenological conception of the elastic, dielectric and thermal homes of crystals as utilized within the box of ferroelectricity. lots of the effects and concepts defined are scattered in the course of the literature of this topic and this publication provides them including their actual heritage in a single reference. The dialogue is particular to the idea required to explain the homes of homogeneous specimens topic to low frequency fields.'' received it?
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Extra info for An Introduction to the Phenomenological Theory of Ferroelectricity
31) j β J β J l^d,ßTß+YerjEj. 1. The arrays of coefficients cf^, s^ß, jf^, efj, efj, ßjj are invariant under the interchange of indices a, β or /, y, whichever is appropriate. T o prove this we use the technique of Legendre transformations. F o r example, consider the quantity ρον^' = QoW—^^T^S^, F r o m eqns. +Y^EidDf. β ρο(Ον70ηί> = - . 5 . , and therefore (dSjdTß)n:=(dSß/dT^)0. 55 P h e n o m e n o l o g i c a l T h e o r y of F e r r o e l e c t r i c i t y TABLE 2 . 5 . 1 . Nomenclature, units and notation for the coefficients appearing in the linear representation of the elastic and dielectric equations of state.
L Diagram of the regions referred to in the text. Q and VQ are the regions occupied in the initial state by the conductor and dielectric respec tively (dashed lines). C, V and A are the regions occupied in some arbitrary state by the conductor, dielectric and free space respectively (full lines). in the initial state be denoted by Fo, Co and AQ respectively and the corresponding regions in any other state by F, C and A (Fig. 2 . 5 . 1 ) . In the linear theory we are concerned only with small deformations of the dielectric and conductor relative to their configurations in the initial state and hence F ~ Fo and C ~ Co.
Thus the matrices [c^ß] and [ßfj] are symmetric with at most twenty-one and six independent components respectively. has no analogous property and hence has at most eighteen independent components. This gives a total of forty-five independent coefficients appearing in the hnear equations of state. F o r a given crystal this number may be reduced by the demands of material symmetry.! Dielectrics for which there is at least one non-vanishing coefficient h¡^ are referred to as piezoelectric. That is to say, in piezoelectric materials there is linear coupling between the fields describing the mechanical behaviour and the fields describing the electrical behaviour.
An Introduction to the Phenomenological Theory of Ferroelectricity by J. Grindlay