Theories of Ferroelectrics

The second-order ferroelectric transitions can be modeled using the Curie-Weiss theory of ferromagnetism. It is assumed that there is a local field that is proportional to the polarization or E-Loc = E + yP/so, where y is the constant of proportionality. For T Tq, Equation 23.28 gives P = Np Eux /kT and the susceptibility is given by 

Polarization versus temperature predicted using the Curie-Weiss model for spontaneous polarization. 

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Il is interesting to discuss, next, the available e data for the various compositions in the light of the classical theory of ferroelectricity. According to this theory [100] for T > Tc the temperature dependence of e can be written as... 

Our brief review of Bersuker s academic life won t be complete, without mention to his excellent reviews and books on the Jahn-Teller effect and vibronic interactions in molecules and solids, on vibronic theory of ferroelectricity, on electron properties of coordination compounds, and on the electron-conformational approach to the problem of identification of biologically active units in a large set of molecules. However, the most important creation of Isaac Bersuker is his school, the world-known group of scholars that hold his system of views and follow his high... 

Determination of the critical temperature after equation (1), T0 = En/Syl, is considered in the cooperative JT and PJT effects [2,3,8,9]. In particular, the origin of structural ferroelectric phase transitions as due to the PJT effect (the vibronic theory of ferroelectricity) was suggested first in the sixties [10] (see also Ref. [9]). JT structural phase transitions are reviewed in Ref. [8]. 

These important, but not completely understood, problems are considered here by using the novel, quantum chemical, approach to the microscopical theory of ferroelectrics and related materials [1], The isomorphous H-bonded crystals M3(H/D)(A04)2 (M = K, Rb A = S, Se) are taken as examples. There are two reasons of such choice. This family is investigated actively at present. Moreover, it is a suitable subject of theoretical examination because of simple chemical constitution of the TKHS-like compounds (zero-dimensional H-bond network). 

V. G. Vaks, Introduction to Microscopical Theory of Ferroelectrics, Nauka, Moscow, 1973, in Russian. 

Cochran W (1960) Crystal stability and the theory of ferroelectricity. Adv Phys 9 387... 

The well-known Landau-Ginsburg-Cochran-Anderson theory is a phenomenological approach. Of the first-principle theories, just one, the vibronic theory of ferroelectricity (e.g., see [1,51]), is consistently based upon electronic structure and chemical nature of the respective compounds. 

In the OOA, as it was discussed above, ligands are omitted. The vibrational motion of low-symmetry distortions is averaged out. Electron wave functions do not follow nuclear displacements. Therefore, in the OOA, the abovementioned crystal-lattice mechanism of spontaneous polarization is lost. The only possibility left in the OOA is polarization of electron wave functions. Without lattice distortion involved, this pure electron-shell mechanism was discussed in literature long ago, back about 45 years. Lacking supporting evidence from experimental data and electron-structure evaluation, it was rejected. On the contrary, the vibronic theory of ferroelectricity cumulated overwhelming experimental evidence. (For an updated review, see Sect. 8.3 in Bersuker s book [1].)... 

Cohen RE (2000) Theory of ferroelectrics A vision for the next decade and beyond. J Phys Chem Sol 61 139-146... 

In the present review article 1985 s results obtained in applications of the concept of vibronic interactions to the investigation of electric properties of molecules (dipole and multipole moments and polarizabilities) are presented. Molecular aspects of these topics are almost untouched in the publications listed in the preceding paragraph. The idea of dipole instability was used first as a basis of the so-called vibronic theory of ferroelectricity (Bersuker, 1966 Bersuker and Vekhter, 1978). Meanwhile, the manifestation of the electronic or vibronic degeneracy in the electric responses of molecules, being no less essential than other vibronic effects, has some special features. 

L.M. Lopatina, J.V. Selinger, Theory of ferroelectric nanoparticles in nematic liquid crystals. Phys. Rev. Lett. 102, 197802 (2009)... 

Indenbom, V.L. Phase transitions without atoms number change in elementary cell of crystals. Crystallography 5(1), 115-125 (1960) On thermodynamic theory of ferroelectricity, Izvestiya AN SSSR, ser. Phys. 24(10), 1180-1183 (1960) (in Russian)... 

Bratkovsky, A.M., Levanuk, A.P. Continuous theory of ferroelectric states in ultrathin films with real electrodes. J. Comput. Theor. Nanosci. 6(3), 465 89 (2009)... 

Li, J. and Bhattacharya, K. 2002. A mesoscopic electromechanical theory of ferroelectric films and ceramics. Fundamental Physics of Ferroelectrics, R.E. Cohen, ed. AIP. 

The fundamental problem of the theory of ferroelectricity is the origin of stmc-tural phase transition, when the spontaneous polarization appears or disappears. At first, we will describe such phase transition from the thermodynamic point of view. Phenomenological ferroelectricity theory is based on the works of Landau and Lifshitz (1974) and Devonshire (1949,1951). Starting point of the theory is the elastic Gibbs potential G, where we would select polarization P (except of electric displacement D) as an independent variable. Therefore the Gibbs potential is... 

Busch G (1938) Neue seignette-elektrika. Helv Phys Acta 11 269-298 Busch G, Scherrer P (1935) Eine neue seignette-elektrische Substanz. Naturwiss 23 737 Cochran W (1959) Crystal stability and the theory of ferroelectricity. Phys Rev Lett 3 412-414 Cochran W (1960) Crystal stability and the theory of ferroelectricity. Adv Phys 9 387 23 Cochran W (1961) Crystal stability and the theory of ferroelectricity part II. Piezoelectric crystals. Adv Phys 10 401 20... 

R. Zbatig and P.LThylor. Theory of ferroelectric-paraelectricttansitians in VFi/F E random oopolymera, J. AppL Pkys 73 1395 (1993)... 

H. Zewdic and F. Brouers. Theory of ferroelectric polymer-ceramic oompoaiies, / AppL Pkys. 68 713 (1990). 

Yacoby, Y. and Girshberg, Y., Theory of ferroelectric phase transitions in pure and mixed perovskites. Mat. Res. Soc. Symp. Proc., Vol. 718, Materials Research Society, Warrendale, Pennsylvania, 2002. 

Lin Y, Boker A, Sill K, Xiang H, Abetz C, Li X, Wang J, Emrick T, Balazs AC, Russell TP (2005) Self-directed self-assembly of nanoparticle/copolymer mixtures. Nature 434(1 ) 55-59 Lopatina LM, Selinger JM (2011) Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals. Phys. Rev E 84 041703/1-041703/7 Lorenz A, Zimmermann N, Kumar S, Evans DR, Cook G, Martinez ME, Kitzerow H-S (2013) X-ray scattering of nematic liquid crystal nanodispersion with negative dielectric anisotropy. Appl Opt 52(22) E1-E5... 

The statistical theory of ferroelectricity (see Volume 2, Chapter 3) relates 7 to the mass m of ions and the bonding between ions. The temperature 7 is proportional to m and inversely proportional to a force constant. Heavier ions lead to increased 7 and strong bonds to lowered 7. This is an important result because it allows for an understanding of the effect of changes in composition on ferroelectric properties. Lowering of 7 raises the dielectric constant at room temperature. For a fuller discussion of these points the reader is referred to Volume 2, Chapter 3. 

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