By J. Grindlay

''In this monograph the writer describes the root and derivation of the macroscopic or phenomenological concept of the elastic, dielectric and thermal homes of crystals as utilized within the box of ferroelectricity. many of the effects and ideas defined are scattered during the literature of this topic and this e-book 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.'' obtained it?

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**Extra info for An Introduction to the Phenomenological Theory of Ferroelectricity**

**Example text**

E. do not transform as tensor components under changes of coordinate axes, and (b) d o not provide a suitable measure of the local deformation when the deformation is finite as opposed to infinitesimal. This last remark applies also to the Sfj. Consider now the effect of the deformation on a mass element dm at X. Let dm occupy a volume dV at X and a volume dv at x, where dV = dXi dX2 dXs and dv = dxi dxz dxz. 6. t To prevent confusion we reserve italic letters for indices taking the values 1. 2 , 3, and Greek letters for indices taking the values 1, 2 , 3, 4, 5, 6.

In general both χ and ν are functions of t. We wish to calculate an expres sion for the time rate of change of H. e. dm = gdv = g^dv^. Clearly the solutions to the equa tions of motion for dm yield some relationship Xi = Xi(xJ, t^, t) {ij^ 1,2,3). ; hence Η II ¡h[xix^,t\t%t]g^dv^, 29 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 Since the limits of the integral are independent of t, dH dt The reverse transformation now yields dH dt hgdv, where h is the so-called material derivative.

E. t = t(x, n\ where η is the unit vector parallel to 30 The Linear Elastic Dielectric the outward normal to the surface of ν at JC. T O explore the restrictions on the physically permissible functions, ί,·, let us first of all consider the case where ν is a, small tetrahedron with three mutually perpendic ular faces, each of which is perpendicular to one of the coordinate axes. Let 0,· be the area of the face perpendicular to the Z/-axis (/ = 1 , 2 , 3 ) and a the area of the fourth face (Fig.