Crystals, electric field ionic

Crystal field theory A theory of bonding in transition metal complexes in which ligands and metal ions are treated as point charges a purely ionic model. Ligand point charges represent the crystal (electric) field perturbing the metal s d orbitals that contain nonbonding electrons. 

The crystal electric field (CEF). The ionic states are split by the interaction (S states excepted) with the CEF. We will name the corresponding energy Hcf-... 

Plastics can be used to make erasable printing media by a number of different techniques. Photo changing dyes could be incorporated into the structure of the plastics. The printer could change the dye to the colored form to read, and the material can be bleached with another unit that would reverse the photo coloring process. An ionic type plastic can be incorporated into the plastics and used to color the printed area by the use of an indicator type reaction with an organic acid or base. Another method would be to use a thermal printer in conjunction with liquid crystal type materials that would alter the state of the liquid crystals in the printed areas. Applying heat and electrical fields to the printed sheet would erase the printing. 

The ionic conductivities of most solid crystalline salts and oxides are extremely low (an exception are the solid electrolytes, which are discussed in Section 8.4). The ions are rigidly held in the crystal lattices of these compounds and cannot move under the effect of applied electric fields. When melting, the ionic crystals break down, forming free ions the conductivities rise drastically and discontinuously, in some cases up to values of over 100 S/m (i.e., values higher than those of the most highly conducting electrolyte solutions). 

As mentioned earlier in this chapter dislocations in ionic crystal may carry a net electric charge. Therefore, their motion may be influenced by applied electric fields, and may generate observable fields external to a specimen during plastic flow. These effects have been studied by Li (2000) and others. 

When applied to the motion of ions in a crystal, the term drift applies to motion of ions under the influence of an electric field. Although movement of electrons in conduction bands determines conductivity in metals, in ionic compounds it is the motion of ions that determines the electrical condu-ctivity. There are no free or mobile electrons in ionic crystals. The mobility of an ion, ji, is defined as the velocity of the ion in an electric field of unit strength. Intuitively, it seems that the mobility of the ion in a crystal should be related to the diffusion coefficient. This is, in fact, the case, and the relationship is... 

The Na+ and Cl- ions can be considered as negatively and positively charged spheres that attract each other. Since positive (+) and negative (-) charges form an electric field in all directions, the electrostatic force of attraction (ionic bond) is not just in one direction. In the NaCl crystal, each Na+ ion is surrounded by six Cl- ions and each Cl- ion is surrounded by six Na+ ions (Figure 2). Because of this, the structure of NaCl is not a molecule but it is in the form of an ionic crystal in which many ions are found together. 

In a crystal, the electronic and ionic conductivities are generally tensor quantities relating the current density Iq to the applied electric field E in accordance with Ohm s law. The scalar expression for the mobile-ion current density in the different principal crystallographic directions has the form... 

One of the most important aspects of point defects is that they make it possible for atoms or ions to move through the structure. If a crystal structure were perfect, it would be difficult to envisage how the movement of atoms, either diffusion through the lattice or ionic conductivity (ion transport under the influence of an external electric field) could take place. Setting up equations to describe either diffusion or conductivity in solids is a very similar process, and so we have chosen to concentrate here on conductivity, because many of the examples later in the chapter are of solid electrolytes. 

Ionic radii in the figure are measured by X-ray diffraction of ions in crystals. Hydrated radii are estimated from diffusion coefficients of ions in solution and from the mobilities of aqueous ions in an electric field.3-4 Smaller, more highly charged ions bind more water molecules and behave as larger species in solution. The activity of aqueous ions, which we study in this chapter, is related to the size of the hydrated species. 

In 1937, dost presented in his book on diffusion and chemical reactions in solids [W. lost (1937)] the first overview and quantitative discussion of solid state reaction kinetics based on the Frenkel-Wagner-Sehottky point defect thermodynamics and linear transport theory. Although metallic systems were included in the discussion, the main body of this monograph was concerned with ionic crystals. There was good reason for this preferential elaboration on kinetic concepts with ionic crystals. Firstly, one can exert, forces on the structure elements of ionic crystals by the application of an electrical field. Secondly, a current of 1 mA over a duration of 1 s (= 1 mC, easy to measure, at that time) corresponds to only 1(K8 moles of transported matter in the form of ions. Seen in retrospect, it is amazing how fast the understanding of diffusion and of chemical reactions in the solid state took place after the fundamental and appropriate concepts were established at about 1930, especially in metallurgy, ceramics, and related areas. 

In chemically homogeneous ionic crystals, may be the only driving force. In inhomogeneous systems, the electrochemical potential gradient Vrij = Vnt+ZjF-Vtp acts upon the mobile charged species i. The additivity of Vp, and stems from the very small electric charge number needed to establish the internal electric field, which is on the order of 1 [V/cm]. These charges are too small to interfere with the concentrations that determine the chemical potentials p,. 

There is still another type of internal solid state reaction which we will discuss and it is electrochemical in nature. It occurs when an electrical current flows through a mixed conductor in which the point defect disorder changes in such a way that the transference of electronic charge carriers predominates in one part of the crystal, while the transference of ionic charge carriers predominates in another part of it. Obviously, in the transition zone (junction) a (electrochemical) solid state reaction must occur. It leads to an internal decomposition of the matrix crystal if the driving force (electric field) is sufficiently high. The immobile ionic component is internally precipitated, whereas the mobile ionic component is carried away in the form of electrically charged point defects from the internal reaction zone to one of the electrodes. 

A gradient of electrical potential constitutes the classic (external) force field for ionic solids. Let us study the effect of this electric field on the interface morphology and stability. The thermodynamic driving force in ionic crystals is Vi/,(= +... 

The driving forces necessary to induce macroscopic fluxes were introduced in Chapter 3 and their connection to microscopic random walks and activated processes was discussed in Chapter 7. However, for diffusion to occur, it is necessary that kinetic mechanisms be available to permit atomic transitions between adjacent locations. These mechanisms are material-dependent. In this chapter, diffusion mechanisms in metallic and ionic crystals are addressed. In crystals that are free of line and planar defects, diffusion mechanisms often involve a point defect, which may be charged in the case of ionic crystals and will interact with electric fields. Additional diffusion mechanisms that occur in crystals with dislocations, free surfaces, and grain boundaries are treated in Chapter 9. 

FERROELECTRIC EFFECT. The phenomenon whereby certain crystals may exhibit a spontaneous dipole moment twhich is called ferroelectric by analogy with ferromagnetic—exhibiting a permanent magnetic moment). The effect in the most typical case, barium manate. seems to he due to a polarization catastrophe, in which the local electric fields due lo the polarizuiion itself increase faster than die elastic restoring forces on the ions in Ihe crystal, thereby leading to an asymmetrical shift in ionic positions, and hence lo a permanent dipole moment. Ferroelectric crystals... 

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