Dielectric constant crystals

The existence of an antiferroelectric state is possible. The antiferroelectric state occurs, for example, when neighboring lines of ions are displaced in opposite directions, resulting in no net spontaneous polarization below the Curie point, although the ordering may be accompanied by changes in the dielectric constant. Crystals... 

Fig. 3. Crystal structure and lattice distortion of the BaTiO unit ceU showiag the direction of spontaneous polarization, and resultant dielectric constant S vs temperature. The subscripts a and c relate to orientations parallel and perpendicular to the tetragonal axis, respectively. The Curie poiat, T, is also shown.

Most glass-ceramics have low dielectric constants, typically 6—7 at 1 MHz and 20°C. Glass-ceramics comprised primarily of network formers can have dielectric constants as low as 4, with even lower values (K < 3) possible in microporous glass-ceramics (13). On the other hand, very high dielectric constants (over 1000) can be obtained from relatively depolymerized glasses with crystals of high dielectric constant, such as lead or alkaline earth titanate (11,14). 

Perovskites have the chemical formula ABO, where A is an 8- to 12-coordinated cation such as an alkaU or alkaline earth, and B is a small, octahedraHy coordinated high valence metal such as Ti, Zr, Nb, or Ta. Glass-ceramics based on perovskite crystals ate characteri2ed by their unusual dielectric and electrooptic properties. Examples include highly crystalline niobate glass-ceramics which exhibit nonlinear optical properties (12), as well as titanate and niobate glass-ceramics with very high dielectric constants (11,14). 

Single-crystal sUicon has also been employed as substrate material, particularly in multichip module (MGM)-Si appUcations. As a substrate, sUicon offers good thermal conductivity and matches the GTE of the devices mounted on it it does, however, have a relatively high dielectric constant and is very britde. 

Fig. 4.3. Typical normalized piezoelectric current-versus-time responses are compared for x-cut quartz, z-cut lithium niobate, and y-cut lithium niobate. The y-cut response is distorted in time due to propagation of both longitudinal and shear components. In the other crystals, the increases of current in time can be described with finite strain, dielectric constant change, and electromechanical coupling as predicted by theory (after Davison and Graham [79D01]).

Numerous observations of the effect in ionic crystals were carried out by Mineev and Ivanov in the Soviet Union [76M01]. This is a class of crystals in which a number of materials factors can be confidently varied. By choice of crystallographic orientation, various slip directions can be invoked. By choice of various crystals other physical factors such as dielectric constant, ionic radius, and an electronic factor thought to be representative of dielec-... 

Fig. 5.20. The shock-induced polarization of a range of ionic crystals is shown at a compression of about 30%. This maximum value is well correlated with cation radius, dielectric constant, and a factor thought to represent dielectric strength. A mechanically induced point defect generation and migration model is preferred for the effect (after Davison and Graham [79D01]).

Figure 3.8 Anomalous temperature dependence of relative dielectric constant of ferroelectric crystals at the transition temperature (Curie point).

A ferroelectric crystal is one that has an electric dipole moment even in the absence of an external electric held. This arises because the centre of positive charge in the crystal does not coincide with the centre of negative charge. The phenomenon was discovered in 1920 by J. Valasek in Rochelle salt, which is the H-bonded hydrated d-tartrate NaKC4H406.4H 0. In such compounds the dielectric constant can rise to enormous values of lO or more due to presence of a stable permanent electric polarization. Before considering the effect further, it will be helpful to recall various dehnitions and SI units ... 

Similar observations hold for solubility. Predominandy ionic halides tend to dissolve in polar, coordinating solvents of high dielectric constant, the precise solubility being dictated by the balance between lattice energies and solvation energies of the ions, on the one hand, and on entropy changes involved in dissolution of the crystal lattice, solvation of the ions and modification of the solvent structure, on the other [AG(cryst->-saturated soln) = 0 = A/7 -TA5]. For a given cation (e.g. K, Ca +) solubility in water typically follows the sequence... 

Turning next to the unitary part of AS0, this is given in Table 36 under the heading — N(dL/dT). It was pointed out in Secs. 90 and 106 that, to obtain the unitary part of AS0 in aqueous solution, one must subtract 16.0 e.u. for a uni-univalent solute, and 24.0 e.u. for a uni-divalent solute. In methanol solution the corresponding quantities are 14.0 and 21.0 e.u. In Table 36 it will be seen that, except for the first two solutes KBr and KC1, the values are all negative, in both solvents. It will be recalled that for KBr and KC1 the B-coefficients in viscosity are negative, and we associate the positive values for the unitary part of the entropy, shown in Table 29, with the creation of disorder in the ionic co-spheres. In every solvent the dielectric constant decreases with rise of temperature and this leads us to expect that L will increase. For KBr and KC1 in methanol solution, we see from Table 36 that dL/dT has indeed a large positive value. On the other hand, when these crystals dissolve in water, these electrostatic considerations appear to be completely overbalanced by other factors. 

Let us now consider a pair of ions in aqueous solution from such a crystal. In the Debye-Hilckel theory it is assumed that in pure solvent, the mutual potential energy is — e2/ r, where e is the macroscopic dielectric constant of the solvent,2 until the ions come into contact with each... 

Strontium titanate, SrTi03, with a high dielectric constant (310 for single crystal) and high refractive index. 

Water is the most common solvent used to dissolve ionic compounds. Principally, the reasons for dissolution of ionic crystals in water are two. Not stated in any order of sequence of importance, the first one maybe mentioned as the weakening of the electrostatic forces of attraction in an ionic crystal known, and the effect may be alternatively be expressed as the consequence of the presence of highly polar water molecules. The high dielectric constant of water implies that the attractive forces between the cations and anions in an ionic salt come down by a factor of 80 when water happens to be the leaching medium. The second responsible factor is the tendency of the ionic crystals to hydrate. 

If a substance is to be dissolved, its ions or molecules must first move apart and then force their way between the solvent molecules which interact with the solute particles. If an ionic crystal is dissolved, electrostatic interaction forces must be overcome between the ions. The higher the dielectric constant of the solvent, the more effective this process is. The solvent-solute interaction is termed ion solvation (ion hydration in aqueous solutions). The importance of this phenomenon follows from comparison of the energy changes accompanying solvation of ions and uncharged molecules for monovalent ions, the enthalpy of hydration is about 400 kJ mol-1, and equals about 12 kJ mol-1 for simple non-polar species such as argon or methane. 

Dick BG, Overhauser AW (1958) Theory of the dielectric constants of alkali halide crystals. Phys Rev 112(1) 90-103... 

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