Polarizability ionic

Jacucci G, McDonald IR, Singer K (1974) Introduction of the shell model of ionic polarizability into molecular dynamics calculations. Phys Lett A 50(2) 141—143... 

Figure 2.8 Shell model of ionic polarizability (a) unpolarized ion (no displacement of shell) (b) polarized (displaced shell) (c) interactions 1, core-core 2, shell-shell 3, core-shell.

The electron cloud of an ion subjected to an electric field undergoes deformations that may be translated into displacement of the baricenters of negative charges from the positions held in the absence of external perturbation, which are normally coincident with the centers of nuclear charges (positive). The noncoincidence of the two centers causes a dipole moment, determined by the product of the displaced charge (Z ) and the displacement d. The displacement is also proportional to the intensity of the electrical field (F). The proportionality factor (a) is known as ionic polarizability ... 

We have already introduced the concept of ionic polarizability (section 1.8) and discussed to some extent the nature of dispersive potential as a function of the individual ionic polarizability of interacting ions (section 1.11.3). We will now treat another type of polarization effect that is important in evaluation of defect energies (chapter 4). 

The terms in equation 1.166 represent total ionic polarizability, composed of electronic polarizability a plus an additional factor a , defined as a displacement term, due to the fact that the charges are not influenced by an oscillating electric field (as in the case of experimental optical measurements) but are in a static field (Lasaga, 1980) ... 

Lasaga A. C. and Cygan R. T. (1982). Electronic and ionic polarizabilities of silicate minerals. Amer. Mineral, 67 328-334. 

The rotational barrier increases with increasing ionic radius of the metal ion. We have noted above that rj is highly linear in the polarizability parameters a and Vm and are therefore unable to determine whether this dependence is due to ionic size or ionic polarizability. 

Combine your information to calculate the ionic polarizability, a . 

Plots of ionic polarizability against ionic volume are approximately linear with the slope oc/Vm increasing with cation charge. 

The magnitude of such electrostatic effects makes the question of ionic polarizability particularly important. Simulations have shown that while simulations employing nonpolarizable models adequately reproduce equilibrium properties in fused salts [86], ionic polarizability may have important... 

All polarizable models share the ability to polarize, by varying their charge distribution in response to their environment. In addition, shell models and EE models with charge-dependent radii have the ability to modify their polarizability—the magnitude of this polarization response—in response to their local environment. Consequently, it is reasonable to expect that shell models and mechanically coupled EE models may be slightly more transferable to different environments than more standard PPD and EE models. To date, it is not clear whether this expectation has been fully achieved. Although some shell-based models for both ionic and molecular compounds have been demonstrated to be transferable across several phases and wide ranges of phase points, " it is not clear that the transferability displayed by these models is better than that demonstrated in PPD- or EE-based models. And even with an environment-dependent polarizability, it has been demonstrated that the basic shell model cannot fully capture all of the variations in ionic polarizabilities in different crystal environments. ... 

Based on the position of an ion in the Hoftneister series, it is possible to foretell the relative effectiveness of anions or cations in an enormous number of systems. The rank of an ion was related to its kosmotropicity, surface tension increments, and salting in and salting out of salt solutions (see below) [25]. A quantitative physical chemistry description of this phenomenon is not far off. Molecular dynamics simulations that considered ionic polarizability were found to be valuable tools for elucidating salt effects [26,27]. 

Because charge defects will polarize other ions in the lattice, ionic polarizability must be incorporated into the potential model. The shell modeP provides a simple description of such effects and has proven to be effective in simulating the dielectric and lattice dynamical properties of ceramic oxides. It should be stressed, as argued previously, that employing such a potential model does not necessarily mean that the electron distribution corresponds to a fully ionic system, and that the general validity of the model is assessed primarily by its ability to reproduce observed crystal properties. In practice, it is found that potential models based on formal charges work well even for some scmi-covalent compounds such as silicates and zeolites. 

Finally, Shannon obtained 61 sets of ionic polarizabilities for 129 oxides and 25 fluorides using the Clausius-Mosotti equation and least square refinements, and suggested the periodic table of ionic polarizabilities. Therefore the dielectric constant of materials with compositional changes can be successfully predicted by Equation 22.17 and Equation 22.18. Erom another arrangement of Equation 22.16, the theoretical dielectric constant can be obtained from the total ionic polarizabilities in Equation 22.19. Erom Equation 22.17 through Equation 22.19, the theoretical values of dielectric constant and polarizabilities can be obtained as well as the measured values ... 

FIGURE 22.3 Dielectric constant deviation from theoretical ionic polarizability of (PbQ5CaQ5)(FeQ5TaQ j)03 specimen sintered at different temperatnres measured... 

Assuming the mixture of dielectrics and spherical pore with 3-0 connectivity, the dielectric constant (K) and loss quality (g) of (Pbo 5Cao.5)(Feo 5Tao.5)03 with different porosity were evaluated by the dielectric mixing rule. For the specimens with porosity, the ionic polarizabilities modified by Maxwell s Equation were closer to the theoretical values than those modified by Wiener s Equation. The predicted loss quality obtained from intrinsic ones and Maxwell s Equation agree with the observed ones. 

Therefore the dielectric constants and TCFs of PCCN and PCMT with compositional variation of the A-site cations are closely related to the bond valence of the A-site as well as ionic polarizability. With an increase in calcium content, the bond valence of the A-site decreases and A-site ions rattle easily, which results in an increase in the dielectric constant of specimens. Also, the TCP of PCCN and PCMT increases with an increase in the bond valence of the A-site. 

FIGURE 22.8 TCP and ionic polarizability deviation of CST specimens with octahedral bond valence. 

The interaction between a glass and light is related to the susceptibility of displacement of electrical charge, which in turn is related to the polarizability. Ionic polarizability increases with the size of ions involved however, structural considerations are also important. Refractive index (see Table 1), dielectric constant, polarizability, and molar volume are related in the molar refractivity, Rm. 

Our conclusion about existence of additional polarization of HB molecules follows from the relationship iiq > por for the fitted dipole moments pertinent, respectively, to VIB and LIB subensembles (see Tables V and VI). A similar conclusion is made in many works. Thus, the works Ruocco and Sette [36] and Sampoli et al. [37] refer to the electrostatic long-range interactions in Krasnoholovets [38] the spectrum of water around 200 cm-1 is ascribed to a strong ionic polarizability, since the pair potential of a water molecule is simulated in the form of an ionic crystal potential. We remind the reader that in our approach we postulate existence of oppositely charged molecules at both ends of the dimer shown in Fig. lb. 

We recall from Chapter 1 that for ionic materials, ionic polarizability can be taken into account using the shell model of Dick and Overhauser (1958), which treats each ion as a core and shell, coupled by a harmonic spring. The ion charge is divided between the core and shell such that the sum of their charges is the total ion charge. The free ion polarizability, a, is related to the shell charge, Y, and spring constant, k, by ... 

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