Polarizability of the lattice

Piezoelectric coefficients are also temperature dependent quantities. This is true for both the intrinsic and the extrinsic contributions. Typically, the piezoelectric response of a ferroelectric material increases as the transition temperature is approached from below (See Figure 2.3) [3], Where appropriate thermodynamic data are available, the increase in intrinsic dijk coefficients can be calculated on the basis of phenomenology, and reflects the higher polarizability of the lattice near the transition temperature. The extrinsic contributions are also temperature dependent because domain wall motion is a thermally activated process. Thus, extrinsic contributions are lost as the temperature approaches OK [4], As a note, while the temperature dependence of the intrinsic piezoelectric response can be calculated on the basis of phenomenology, there is currently no complete model describing the temperature dependence of the extrinsic contribution to the piezoelectric coefficients. 

Instead of modifying the density of states, local disorder might also lead to a poorer screening of the core hole as a result of reduced polarizability of the lattice. This might also account for the larger BEvb(CL) values of films deposited at room temperature in pure Ar. 

Energy of ionization. a = Polarizability of the lattice units, ro = Distance of the lattice units. 

In eq. 2 E51 is added to realize the quasi static contribution of permittivity due to polarizability of the lattice plus electronic part. Additional dipole contribution with relaxations between frequencies as realized here and the far infrared could contribute. A separation of the frequency independent and frequency dependent contributions could be obtained using first derivatives of eq. 1 and 2, namely... 

The solubilities of the ionic halides are determined by a variety of factors, especially the lattice enthalpy and enthalpy of hydration. There is a delicate balance between the two factors, with the lattice enthalpy usually being the determining one. Lattice enthalpies decrease from chloride to iodide, so water molecules can more readily separate the ions in the latter. Less ionic halides, such as the silver halides, generally have a much lower solubility, and the trend in solubility is the reverse of the more ionic halides. For the less ionic halides, the covalent character of the bond allows the ion pairs to persist in water. The ions are not easily hydrated, making them less soluble. The polarizability of the halide ions and the covalency of their bonding increases down the group. 

The alkali halides cire noted for their propensity to form color-centers. It has been found that the peak of the band changes as the size of the cation in the alkali halides increases. There appears to be an inverse relation between the size of the cation (actually, the polarizability of the cation) and the peak energy of the absorption band. These are the two types of electronic defects that are found in ciystcds, namely positive "holes" and negative "electrons", and their presence in the structure is related to the fact that the lattice tends to become charge-compensated, depending upon the type of defect present. 

From the fit one obtains values of and a. Note how the electronic polarizability of the adsorbed molecules gives the absorptance a nonlinear coverage dependence. However, there exist several systems that do not follow Eqs. (2) and (3). This can be caused either by a coverage dependent change in the electronic structure, that is an additional chemical shift, or because the system exhibits clustering or the molecules occupy more the one adsorption site, since the theory assumes a random filling of the adsorbate lattice. 

Abstract This chapter describes the experimentai compiement of theoretical models of the microscopic mechanism of ferroelectric transitions. We use the hydrogen-bonded compounds as examples, and attempt to show that the new experimental data obtained via recently developed high resolution nuclear magnetic resonance techniques for solids clearly support the hypothesis that the transition mechanism must involve lattice polarizability (i.e. a displacive component), in addition to the order/disorder behaviour of the lattices. 

The effects of pressure on the properties of perovskite fes and rls are manifestations of the influence of pressure on the soft fe mode frequency of the host lattice [14,24], This frequency is determined by a delicate balance between short-range and long-range forces, and these forces exhibit markedly different dependences on interatomic separation, or pressure. Specifically, pressure increases the soft-mode frequency at constant temperature, which reduces the polarizability of the host lattice, thereby reducing Ac. The result is a shift of the transition temperature, Tc (or Tm), to lower temperatures and a suppression of the e (T) response in the high temperature paraelectric phase [14,24],... 

Bersohn 76) has calculated the crystal field created by the molecular dipoles in the lattice of CH3C1. The static dipole moment of the molecules induces through the polarizability of the molecules an additional dipole moment which increases the dipole moment of the free molecule by a factor of about 1.05. This in turn means that the C—Cl bond has increased in ionic character under the influence of the intermolecular electric fields and therefore (see Eq. (II.9 the quadrupole coupling constant will be lower relative to the gaseous state. Besides the dipole moment induced in the direction of the static dipole, a perpendicular partial moment should be induced, too. Therefore the axial symmetry of the C—Cl bond will be disturbed and the asymmetry parameter 77 may become unequal zero. A small asymmetry parameter 17 = 0.028 has been observed for the nuclear quadrupole interaction in solid CH3I. Bersohn also calculated from the known crystal structure of 1,3,5-trichlorobenzene the induced... 

As a result of the small polarizability of the complex ions formed by fluorine and oxygen this contribution to the lattice energy is small for the complex compound. 

Summarizing, we may say that in ionic lattices the ratio is closely related to the crystal structure. The fundamental data are therefore the number, the diameter, and the polarizability of the individual constituents. Our point of view differs from that of Fajans and Joos, Grimm, Goldschmidt, c., who are concerned with the electronic polarization (P ), whereas this paper is intended to throw some light on the motion of the elementary constituents in the lattice (P ). 

In the crystal lattice of diamond, each atom of carbon is surrounded tetrahedrally by four other atoms to which the central atom is bound by four (7 bonds. Each crystal is thus a large single molecule in which every atom is joined to four others by homopolar bonds. The bond between the carbon atoms is almost identical in properties with that of the single C—G bond in hydrocarbons, thus the interatomic distance in diamond is i 54 A and the value of the dielectric constant, 5 3, leads to a value for the polarizability of the bond of i cc, which is only slightly less than the value for the G—G bond in hydrocarbons. 

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