By J. Grindlay

''In this monograph the writer describes the foundation and derivation of the macroscopic or phenomenological concept of the elastic, dielectric and thermal houses 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 offers them including their actual historical past in a single reference. The dialogue is specific to the idea required to explain the houses of homogeneous specimens topic to low frequency fields.'' obtained it?

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1), the electric field Ε can be written in the form Ε =E'-^S, where E' = - g r a d ¿ = - grad 1 4πεο dv' Γω(χ')α3' 4πει Φ where Ε' is the self-field of the dielectric and ¿ the applied field. We note that £ is the electric field of the charged conductor in the presence of the dielectric. The definitions given above are easily extended to the case of systems of several conductors and dielectrics. 3) curl £ = 0 at all points in space. 4) LC by means of the identity Φ PndS — Γ1 = ' —ái\Pdv r + Ρ · grad dv\ η is the unit vector parallel to the outward normal at the point x' on the surface of V.

36)]. Whereas if the dielectric is free of strain at that point, the relation is Z), = Σ ^'Ej- Clearly if the crystal is piezoelectric, j e[j ^ efj. We say that ε^(ε^) is the dielectric coefficient of the free (clamped) dielectric. e. "non-linear" terms) in the polynomial representation for the energy density. We shall refer to this theory as the quasi-linear theory. k μ|klmD|DJDkD|D„+i Σ Σ l,J,k,l,m Cfjk,mnO¡DjDkD,D,„D„. k μ^ΐη,ΟίθΗη,Ώ„ Σ ^UkiDjDkDi+ Σ k, ι ], k, I, m Σ ^k,n,nDjMD„D„. 45) The following symmetries under subscript interchanges are easily de duced from these equations: qij^ is invariant under the interchange /^ j ij^jt is invariant under the interchange i za: k :ÍÍ: ^fjki is invariant under the interchange i ^ j l^fjkim is invariant under the interchange i ^ j ^ k =^ I ^ m k I Cukintn is invariant under the interchange i^jziizk^l=^m:*^n Hence the arrays of coefficients q^j, n^jj,.

For some purposes it is convenient to replace the infinitesimal strain tensor S¡j by the closely related quantity ( a = 1, 2, 3, 4, 5, 6),í where 5Ί = 5 Ί ι , »S'2 = 522? = Ssz, Si = 2 5 2 3 » = 25*13, = 25*12. This is the Voigt notation for subscripts. We shall refer to the as infinitesimal strain components. 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.