Domains in Ferroic Crystals and Thin Films by Alexander Tagantsev, L. Eric Cross, Jan Fousek

By Alexander Tagantsev, L. Eric Cross, Jan Fousek

Domains in Ferroic Crystals and skinny Films provides experimental findings and theoretical knowing of ferroic (non-magnetic) domain names built in past times 60 years. It addresses the placement by means of taking a look in particular at bulk crystals and skinny motion pictures, with a specific specialise in recently-developed microelectronic purposes and strategies for remark of domain names with options similar to scanning strength microscopy, polarized gentle microscopy, scanning optical microscopy, electron microscopy, and floor adorning techniques.

Domains in Ferroic Crystals and skinny Films covers a wide region of fabric houses and results hooked up with static and dynamic houses of domain names, that are tremendous suitable to fabrics known as ferroics. In such a lot sturdy kingdom physics books, one huge staff of ferroics is quite often lined: these during which magnetic houses play a dominant position. a number of books are in particular dedicated to magnetic ferroics and canopy a large spectrum of magnetic area phenomena. by contrast, Domains in Ferroic Crystals and skinny motion pictures concentrates on domain-related phenomena in nonmagnetic ferroics. those fabrics are nonetheless inadequately represented in reliable nation physics, and this quantity fills that need.

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The experimental manifestation of the pyroelectric effect is a change dQ of bound charge density on the surface of a platelike sample cut obliquely to p when its temperature is changed by dT. Since dQ ¼ dDn ¼ "o dEn þ dPn , where dDn, dEn, and dPn are changes of components (normal to the plane of plate) of the electric displacement, electric field, and polarization, respectively, the condition E = 0 implies p = dQ/dT. The symmetry of a material puts serious restrictions on the existence and orientation of p.

We have in mind macroscopic properties which are described by the following material relations: "n ¼ snm sm þ din Ei þ an DT (2:1:12) Di ¼ dim sm þ "0 kij Ei þ pi DT   C DS ¼ am sm þ pj Ei þ DT: T (2:1:13) (2:1:14) Here the Einstein summation convention was applied with i and j changing from 1 to 3, n and m changing from 1 to 6. The system of 1–6 indexing for the elastic variables can be found in Nye’s book (Nye, 1992); for reference it is given in Appendix F. For the variables and material parameters in these expressions, the following notations have been accepted: "n — mechanical stress, Di — electric displacement, DS — change of the entropy density, sn — elastic strain, Ei — electric field, DT — temperature change, snm — elastic compliance taken at constant electric field and temperature, dim — piezoelectric moduli at constant temperature, an — coefficient of thermal dilatation, kij — relative dielectric permittivity at zero stress and constant temperature, pi — pyroelectric coefficients at constant stress, C — heat capacity at zero electric field and stress, "0 — permitivity of vacuum.

Some of their designations contain symbols P, ", d, or s. P means that this kind of transition is ferroelectric; ", d, and s denote ferroelastic, ferroelastoelectric, and ferrobielastic transitions, respectively. We may wish to assign a particular material a symbol which would show most of the information we have already discussed. This symbol contains the groups G and F. However, as we have seen above specifying these groups by their normal crystallographic notation may not be sufficient. Let us consider the phase transition from G ¼ " 42m to F = 2.

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