An Introduction to the Phenomenological Theory of by J. Grindlay

By J. Grindlay

''In this monograph the writer describes the root and derivation of the macroscopic or phenomenological thought 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 during the literature of this topic and this booklet provides them including their actual heritage in a single reference. The dialogue is specific to the idea required to explain the houses of homogeneous specimens topic to low frequency fields.'' acquired it?

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I) Suppose that 5 i i is the only non-vanishing component of Then a line element with components (dXx, dX^^, dXs) is, by definition. 26 T h e L i n e a r Elastic^Dielectric deformed to a line element with components [dXi{l +Sii), dX2, dXs], Thus the normal strain S n is the fractional elongation suffered by line elements parallel to the A'l-axis. (ii) Suppose that duijdX^ and duJdXi are the only non-vanishing components of duJdXj, Then a line element with components [dXi, dX2, dXs] is deformed to the line element [dXi-]-{duildX2)dX2, dX2-h (du2ldXi)dXu dXsl In particular the line elements [dXi, 0, 0] and [0, dX2, 0] are deformed to [dXu {du2ldXi)dXu 0] and [(Öwi/SZajäfJTa, dX2, 0] respectively.

12) is the unit vector parallel to the outward normal at a point on the surface Co. Because the fields E, D, ω and « ' are all small, these results are independent of the quantity We note that this linear theory also applies when the dielectric is in contact with the conductor. Z)^ = ω. Equations ( 2 . 5 . 8 ) to ( 2 . 5 . 1 2 ) are the field equations and boundary conditions characteristic of the standard linear theory of the elastic dielectric. T o complete the theory we require a set of equations o f state.

1 STRESS A N D B O D Y F O R C E S Consider the case of a finite body of volume V. We dhect our atten­ tion to an arbitrary volume ν of this body, bounded by an imaginary surface s. We shall suppose for the present that s does not include any part of the surface of F. We assume that the net force acting on the matter within ν can be represented by a body force of density and a surface traction field t. The fields / and t are defined by writing down expressions for (a) the net force F and net torque Γ acting on ν and (b) the work done 6W when υ is subjected to an infinitesimal displacement.

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An Introduction to the Phenomenological Theory of by J. Grindlay
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