Ionic crystal systems

In periodic boimdary conditions, one possible way to avoid truncation of electrostatic interaction is to apply the so-called Particle Mesh Ewald (PME) method, which follows the Ewald summation method of calculating the electrostatic energy for a number of charges [27]. It was first devised by Ewald in 1921 to study the energetics of ionic crystals [28]. PME has been widely used for highly polar or charged systems. York and Darden applied the PME method already in 1994 to simulate a crystal of the bovine pancreatic trypsin inhibitor (BPTI) by molecular dynamics [29]. 

Fig. 17.1. (a) Dislocation motion is intrinsically easy in pure metals - though alloying to give solid solutions or precipitates con moke it more difficult. (b) Dislocation motion in covalent solids is intrinsically difficult because the interatomic bonds must be broken and reformed. ( ) Dislocation motion in ionic crystals is easy on some planes, but hard on others. The hard systems usually dominate. 

Electronegativity is a scale used to determine an atom s attraction for an electron in the bonding process. Differences in electronegativities are used to predict whether the bond is pure covalent, polar covalent, or ionic. Molecules in which the electronegativity difference is zero are considered to be pure covalent. Those molecules that exhibit an electronegativity difference of more than zero but less than 1.7 are classified as polar covalent. Ionic crystals exist in those systems that have an electronegativity difference of more than 1.7. 

Every ionic crystal can formally be regarded as a mutually interconnected composite of two distinct structures cationic sublattice and anionic sublattice, which may or may not have identical symmetry. Silver iodide exhibits two structures thermodynamically stable below 146°C sphalerite (below 137°C) and wurtzite (137-146°C), with a plane-centred I- sublattice. This changes into a body-centred one at 146°C, and it persists up to the melting point of Agl (555°C). On the other hand, the Ag+ sub-lattice is much less stable it collapses at the phase transition temperature (146°C) into a highly disordered, liquid-like system, in which the Ag+ ions are easily mobile over all the 42 theoretically available interstitial sites in the I-sub-lattice. This system shows an Ag+ conductivity of 1.31 S/cm at 146°C (the regular wurtzite modification of Agl has an ionic conductivity of about 10-3 S/cm at this temperature). 

Solid polymer and gel polymer electrolytes could be viewed as the special variation of the solution-type electrolyte. In the former, the solvents are polar macromolecules that dissolve salts, while, in the latter, only a small portion of high polymer is employed as the mechanical matrix, which is either soaked with or swollen by essentially the same liquid electrolytes. One exception exists molten salt (ionic liquid) electrolytes where no solvent is present and the dissociation of opposite ions is solely achieved by the thermal disintegration of the salt lattice (melting). Polymer electrolyte will be reviewed in section 8 ( Novel Electrolyte Systems ), although lithium ion technology based on gel polymer electrolytes has in fact entered the market and accounted for 4% of lithium ion cells manufactured in 2000. On the other hand, ionic liquid electrolytes will be omitted, due to both the limited literature concerning this topic and the fact that the application of ionic liquid electrolytes in lithium ion devices remains dubious. Since most of the ionic liquid systems are still in a supercooled state at ambient temperature, it is unlikely that the metastable liquid state could be maintained in an actual electrochemical device, wherein electrode materials would serve as effective nucleation sites for crystallization. 

The object of this paper is to discuss some of these problems. We start with the evidence for the new system of ionic radii. X-rays are diffracted by electrons in principle therefore X-ray diffraction should always locate the few outer electrons involved in bonding, but in fact this requires sophisticated treatment of meticulous measurements on crystals of high symmetry [6—9). But it has long been clear that some ionic crystals show round each ion an electron density which is approximately spherical but falls away to a very low background the following Table shows a typical example. 

Thirdly, there is the purely structural argument from Relative Size if ions of one type are much the largest, they will effectively fix the structure since the others can pack between them. This argument, which makes no assumption whatever about electron-clouds, is often referred only to lithium iodide, but much more evidence is available. Such questions of crystal-form and isomorphism are in fact the most important applications of ionic-radius systems in chemistry and mineralogy (cp. the classical work of V. M. Goldschmidt (2)). 

Systems of ionic radii have also been used to discuss the solvation-energies of ionic crystals. Fifty years ago Born 42) deduced for the free energy AG of transfer of an ion of valency Z from vacuum to a medium of dielectric constant C ... 

Up to this point we have discussed the formation of polarons in ionic crystals. Polarons of another type can also form in elements and other systems, such as the valence bands of alkali and silver halides, where the polarizability is not the relevant factor. In fact Holstein s (1959) original discussion of the small polaron was of this form. This kind of polaron is sometimes called a molecular polaron, and is illustrated in Fig, 2.3(a), and in Fig. 2.3(b) in the activated configuration of the atoms when the electron can move from one site to another. There is nothing analogous to the large polaron in this case in three-dimensional systems either a small polaron is formed or there is little effect on the effective mass from interaction with phonons. 

Ionic crystals can form solid solutions, too. KBr, in the presence of KG1, will form crystals, in which some of the Br ions are substituted by Cl ions. If KC1 is in excess, a KC1 crystal is formed with some of the chlorine ions replaced by bromine ions. Smaller ions, like F , or larger, like I"", do not replace Br ions in KBr in considerable quantities KF and KBr do not form solid solutions, unless at high temperature or between very narrow limits. In chloride bromide systems the composition of the solid solution may range from pure chloride to pure bromide. 

If all the packing atoms are no longer neutral (e.gn half are cations and half are anions), the closest packed structures are no longer the most stable, as can be seen from the similar two-dimensional case (see above). However, these structures may still be useful when considered as limiting cases for certain ionic crystals. Consider lithium iodide, in which the iodide anions are so much larger than the lithium cations that they may be assumed to touch or nearly touch. They can be considered to provide the framework for the crystal. The much smaller lithium ions can then fit irto the small interstices between the anions. If they expand the lattice slightly to remove the anion-anion contact, the anionic repulsion will be reduced and the crystal stabilized, but the simple model based on a closest packed system of anions may still be taken as the limiting case and a useful approximation. 

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. 

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