Thermodynamics, of ionic crystal

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. 

The basis of defect thermodynamics is the concept of regular and irregular SE s and the constraints which crystallography and electroneutrality (in the case of ionic crystals) impose on the derivation of the thermodynamic functions. Thermodynamic potential functions are of particular interest, since one derives the driving forces for the chemical processes in the solid state from them. 

After 14 years on the faculty of Imperial College, Jacobs moved from London, England, to London, Ontario, where his research program focused on the optical and electrical properties of ionic crystals, as well as on the experimental and theoretical determination of thermodynamic and kinetic properties of crystal defects.213 Over the years his research interests have expanded to include several aspects of computer simulations of condensed matter.214 He has developed algorithms215 for molecular dynamics studies of non-ionic and ionic systems, and he has carried out simulations on systems as diverse as metals, solid ionic conductors, and ceramics. The simulation of the effects of radiation damage is a special interest. His recent interests include the study of perfect and imperfect crystals by means of quantum chemical methods. The corrosion of metals is being studied by both quantum chemical and molecular dynamics techniques. 

Yet more important was the publication by Schottky and Wagner (1930) of their classical paper on the statistical thermodynamics of real crystals (41). This clarified the role of intrinsic lattice disorder as the equilibrium state of the stoichiometric crystal above 0° K. and led logically to the deduction that equilibrium between the crystal of an ordered mixed phase—i.e., a binary compound of ionic, covalent, or metallic type—and its components was statistical, not unique and determinate as is that of a molecular compound. As the consequence of a statistical thermodynamic theorem this proposition should be generally valid. The stoichiometrically ideal crystal has no special status, but the extent to which different substances may display a detectable variability of composition must depend on the energetics of each case—in particular, on the energetics of lattice disorder and of valence change. This point is taken up below, for it is fundamental to the problems that have to be considered. 

In the discussions of the kinetic theory of gases and of intermolecular forces, we obtained expressions for properties of matter in bulk in terms of the properties of the individual molecules. In this chapter we will describe the cohesive energy of ionic crystals in terms of the interactions of the ions in the crystals, and some of the properties of metals and covalent crystals in terms of the quantum mechanical picture obtained from the Schrodinger equation. In Chapter 29 we will describe the method for calculating the thermodynamic properties of bulk systems from a knowledge of structure. 

Chebotin s scientific interests were characterized by a variety of topics and covered nearly all aspects of solid electrolytes electrochemistry. He made a significant contribution to the theory of electron conductivity of ionic crystals in equilibrium with a gas phase and solved a number of important problems related to the statistical-thermodynamic description of defect formation in solid electrolytes and mixed ionic-electronic conductors. Vital results were obtained in the theory of ion transport in solid electrolytes (chemical diffusion and interdiffusion, correlation effects, thermo-EMF of ionic crystals, and others). Chebotin paid great attention to the solution of actual electrochemical problem—first of all to the theory of the double layer and issues related to the nature of the polarization at the interface of the solid electrol34e and gas electrode. 

Energy Changes in the Formation of Ionic Crystals— Lattice energies of ionic crystals can be related to certain atomic and thermodynamic properties by means of the Born-Fajans-Haber cycle (Fig. 12-51). 

Stem layer adsorption was involved in the discussion of the effect of ions on f potentials (Section V-6), electrocapillary behavior (Section V-7), and electrode potentials (Section V-8) and enters into the effect of electrolytes on charged monolayers (Section XV-6). More speciflcally, this type of behavior occurs in the adsorption of electrolytes by ionic crystals. A large amount of wotk of this type has been done, partly because of the importance of such effects on the purity of precipitates of analytical interest and partly because of the role of such adsorption in coagulation and other colloid chemical processes. Early studies include those by Weiser [157], by Paneth, Hahn, and Fajans [158], and by Kolthoff and co-workers [159], A recent calorimetric study of proton adsorption by Lyklema and co-workers [160] supports a new thermodynamic analysis of double-layer formation. A recent example of this is found in a study... 

Crystal structure, crystal defects and chemical reactions. Most chemical reactions of interest to materials scientists involve at least one reactant in the solid state examples inelude surfaee oxidation, internal oxidation, the photographie process, electrochemieal reaetions in the solid state. All of these are critieally dependent on crystal defects, point defects in particular, and the thermodynamics of these point defeets, especially in ionic compounds, are far more complex than they are in single-component metals. I have spaee only for a superficial overview. 

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). 

After discussing the thermodynamic properties of the boundary, let us concentrate on the change in thermodynamic potentials across the boundary. For this, we formulate the Gibbs energy for the bulk phase a of an ionic crystal as the sum... 

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/,(= +... 

An important property of an ionic crystal is the energy required to break the crystal apart into individual ions, this is the crystal lattice energy. It can be measured by a thermodynamic cycle, called the Born-Haber cycle. 

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