Download PDF by J. Grindlay: An Introduction to the Phenomenological Theory of

By J. Grindlay

ISBN-10: 0080063624

ISBN-13: 9780080063621

''In this monograph the writer describes the root and derivation of the macroscopic or phenomenological thought 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 e-book provides them including their actual historical past in a single reference. The dialogue is specific to the speculation required to explain the homes of homogeneous specimens topic to low frequency fields.'' acquired it?

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Additional resources for An Introduction to the Phenomenological Theory of Ferroelectricity

Example text

In this case the electric field is given by the expression Et = ¿ i - ^ ' - ( / = 1,2,3). 5 T h e L i n e a r E l a s t i c Dielectric^ 2 . 5 . 1 ASSUMPTIONS The standard theory of the linear time-dependent behaviour of a homogeneous dielectric is based on four main assumptions which we list below. These assumptions, together with the conservation laws for linear momentum, angular momentum and energy, yield the field equations, boundary conditions and equations of state characteristic of this theory.

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. Extending the notation introduced in § 2 .

The displace­ ment vector is defined w = JC—Λ;' the components of u in F a r e denoted by Ufi clearly, u^ = Xi—X^ {i = 1, 2, 3); du¡/dXj are the displacement gradients. F r o m the definition of i/,, dujdxj = dxJdXj—dy, where is the Kronecker delta (ó^y = 1, / = y; d^j = 0, i 9^ J), The deformation is infinitesimal or vanishingly small if | duJdXj\ « : 1 (/, j = I, 2, 3). Consider the line element dX at X. In a general deformation dX is translated, rotated and altered in length to become a line element dx at x.

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An Introduction to the Phenomenological Theory of Ferroelectricity by J. Grindlay


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