Self-polarization

In summary, density functional theory provides a natural framework to discuss solvent effects in the context of RF theory. A general expression giving the insertion energy of an atom or molecule into a polarizable medium was derived. This expression given in Eq (83), when treated within a first order perturbation theory approach (i.e. when the solute self-polarization... 

A complete treatment, including the solute self-polarization contribution, may be developped in the context of the KS theory. It was shown that within the LDA approximation, simple expressions for the effective KS potential may be obtained. 

T S)I. By making the identifications is self-polar), and applying the above... 

A tool to visualize the domains in thin films is the 3-D piezoresponse force microscope (pfm, see also Chapter 12). Figure 1.22 shows an epitaxial pzt thin films grown on a (001) single crystalline SrTiC>3 substrate coated with La0.5Sr0.5CoO3 oxide layer. A detailed analysis point out that a self-polarized polarization mechanism is observed because the out-of-plane polarization in c-domains are preferentially orientated towards the bottom electrode, i. e. a remanent polarization exists without applying an external field. The domain configuration is always of the head-to-tail type. 

However, no potential proposed up to the beginning of the 80 s, either ab initio or empirical and semiempirical, is entirely satisfactory. At the end of the 80 s new versions of two popular model were introduced, namely SPC/E and WK, that reparametrized SPC and TIP4P respectively, computing vaporization enthalpy in order to account for self-polarization energy (equation (40)). 

Enzymatic reactions will be considered in another chapter of this book. We shall only remark that continuum ASC models, and in particular the PCM, may be of some help in studying reactions involving large molecules. In the set of approximations we have considered no additional changes in the PCM formalism were introduced. In particular, the same definition of cavity in terms of interlocking spheres, its partition in tesserae resulting from the inscription of a pentakisdodecahedron in each sphere, and the self-polarization of apparent charges, have been used. 

Dielectrics can be self-polarizing this is the ferroelectric effect. These ceramics are used in capacitors because of their high dielectric constant. 

Here, s, Sgm, and s are the dielectric functions of the particles, the surrounding, and the effective medium, respectively, and gk (k = 1, 2, 3) is the geometric (shape) factor, which determines the self-polarizing effect of the ellipsoid and has a value between zero (needle) and unity (slab) so that gi -h g2 + gs = 1 ... 

The peculiarity of self-polarized films is an asymmetry of their hysteresis loop, so that the positive and negative coercive fields are not the same. This is illustrated in... 

Fig. 2.15, where the hysteresis loop of PZT (50/50) epitaxial film on (100)PT/MgO substrate with polarization along c-axes is presented. The loop has been measured by Souer-Tower method with 1 kHz a. c. electric field. The asymmetry of the loop in Fig. 2.15 shows that the polarization is stable in the direction towards the upper electrode. This direction occurs naturally without external field application. Previously, the self-polarization had been observed in the other pyroelectric lead containing thin films [39,40]. 

Kighelman, Z., Damianovich, D., Setter, N. Electromechanical properties and self-polarization in relaxor Pb(Mgi/3Nb2/3)03 thin films. J. Appl. Phys. 89(2), 1393-1401 (2001)... 

The typical shape of hysteresis loop P Eq) for the films with thickness smaller and larger than critical one is reported in Fig. 3.12a, b respectively. The characteristic feature of the loop is its shift to the larger fields with Pm/Ps increase. Such behavior corresponds to experimentally observed shift of hysteresis loop in self-polarized films [52] (see Fig. 3.13). The authors of Ref. [52] came to conclusion, that the shift of hysteresis loop shown in Fig. 3.13 is the manifestation of the film selfpolarization that arises without external field application. Self-polarization effect of ferroelectric films is very important for applications, for instance in the infrared devices, see e.g. Ref. [53]. 

---