Sublattice polarization

The calculations physical properties of antiferroelectrics based on the Kittel model (i.e. with respect to antiparallel alignment of sublattices polarization vectors) can be done within the formalism of Chap. 1. The numerical calculations of phase diagrams of nanosized antiferroelectric systems of different shapes were carried out in Ref. [68] without consideration of either external or internal electric fields. Corresponding analytical calculations had been carried out in Ref. [69], However, the model used for calculations in [69] did not take into account both mechanical strains and surface piezoeffect generating built-in field. The consistent account for latter effects in Ref. [70] show that they are playing a decisive role in transformation of antiferroelectric phase into ferroelectric one in sufficiently thin Aims. With respect to the latter, the subsequent consideration will be done according to Ref. [70]. 

The spontaneous polarization in ferroelectrics and the sublattice polarizations in antiferroelectrics are analogous to their magnetic counterparts. As described above, however, these polarizations are a necessary... 

The neighboring chains of elementary units are exactly antiparallel in the antifer-roelectric phase. In three-dimensional case, it could be explained as two sublattices polarized in an antipaiallel direction. Resulting net polarization is therefore equal to zero. Typical polarization properties are given by the sublattice spontaneous polarizations rather than by the zero net polarization. If we denote Pa and Pb polarizations of sublattice a and b, it holds Pa = —Pb-... 

In an effort to understand the mechanisms involved in formation of complex orientational structures of adsorbed molecules and to describe orientational, vibrational, and electronic excitations in systems of this kind, a new approach to solid surface theory has been developed which treats the properties of two-dimensional dipole systems.61,109,121 In adsorbed layers, dipole forces are the main contributors to lateral interactions both of dynamic dipole moments of vibrational or electronic molecular excitations and of static dipole moments (for polar molecules). In the previous chapter, we demonstrated that all the information on lateral interactions within a system is carried by the Fourier components of the dipole-dipole interaction tensors. In this chapter, we consider basic spectral parameters for two-dimensional lattice systems in which the unit cells contain several inequivalent molecules. As seen from Sec. 2.1, such structures are intrinsic in many systems of adsorbed molecules. For the Fourier components in question, the lattice-sublattice relations will be derived which enable, in particular, various parameters of orientational structures on a complex lattice to be expressed in terms of known characteristics of its Bravais sublattices. In the framework of such a treatment, the ground state of the system concerned as well as the infrared-active spectral frequencies of valence dipole vibrations will be elucidated. 

For the polar vibrations of the two sublattices against each other, according to Huang the following equation of motion is valid... 

P is the macroscopic polarization. It consists of a lattice polarization b21 w originating from the electric dipole moment arising from the mutual displacement of the two sublattices, and of a second term b22 P originating from the pure electron polarization. According to definition, P and E are connected by... 

Ionic polarization is observed in ionic crystals and describes the displacement of the positive and negative sublattices under an applied electric field. 

When an electric field is applied to an ideal dielectric material there is no long-range transport of charge but only a limited rearrangement such that the dielectric acquires a dipole moment and is said to be polarized. Atomic polarization, which occurs in all materials, is a small displacement of the electrons in an atom relative to the nucleus in ionic materials there is, in addition, ionic polarization involving the relative displacement of cation and anion sublattices. Dipolar materials, such as water, can become polarized because the applied electric field orients the molecules. Finally, space charge polarization involves a limited transport of charge carriers until they are stopped... 

The concept of a zero-dimensional intrinsic point defect was first introduced in 1926 by the Russian physicist Jacov Il ich Frenkel (1894-1952), who postulated the existence of vacancies, or unoccupied lattice sites, in alkali-halide crystals (Frenkel, 1926). Vacancies are predominant in ionic solids when the anions and cations are similar in size, and in metals when there is very little room to accommodate interstitial atoms, as in closed packed stmctures. The interstitial is the second type of point defect. Interstitial sites are the small voids between lattice sites. These are more likely to be occupied by small atoms, or, if there is a pronounced polarization, to the lattice. In this way, there is little dismption to the stmcture. Another type of intrinsic point defect is the anti-site atom (an atom residing on the wrong sublattice). 

The presence of the polar mode oriented in the direction of maximum conductivity gives grounds to postulate the feasibility of the polaronic mechanism of motion of the protons in this crystal. As was shown in the previous subsection (see also Refs. 57,58, and 191) the proton can traverse a comparatively large distance between the nearest sites of the protonic sublattice (0.4 to 0.8 nm) with the participation of vibrational quanta, that is, phonons the virtual absorption of such a quantum can appreciably increase the resonance integral of overlapping of the wave functions of the proton on the nearest sites see expression (318). 

Fig. 8. Simple model of order-disorder or displacive ferroelectric phase transition. Left, ferroelectricity by relative displacement of the anion and cation sublattices (a) displacive model, where r — 0 in the HTP and the atoms are translated by r/0 in the LTP. The order parameter is r. (b) Order-disorder model in the high-temperature phase, the ions are symmetrically disordered with equal probabilities p+ — p — 1/2 over two positions r — +rQ. In the low-temperature phase, the occupancies of the sites become unequal with probabilities p p +. The order parameter is the difference Ap — p+—p. The spontaneous polarization Psocr and PsccAp for the displacive model and order-disorder model, respectively. Right, ferroelectricity by alignment of molecular dipoles (c) displacive model in the HTP, all the molecules are aligned with a = 0 in the LTP, the molecules are rotated around the center of inversion with angles +a/0, the order parameter is a. (d) Order-disorder model. The spontaneous polarization Ppx ct and PsccAp for the displacive model and order-disorder model, respectively.

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