Thermodynamics of Ionic Crystal Formation

Formation of ionic compounds from the elements appears to be one of the simpler overall reactions, but can also be written as a series of steps adding up to the overall reaction. The Born-Haber cycle is the process of considering the series of component reactions that can be imagined as the individual steps in compound formation. For the example of lithium fluoride, the first five reactions added together result in the sixth overall reaction. 

Historically, such calculations were used to determine electron affinities when the enthalpies for all the other reactions could either be measured or calculated. Calculated lattice enthalpies were combined with experimental values for the other reactions and 

Such calculations were used historically to determine electron affinities after the enthalpies for the other reactions had been either measured or calculated. The improved experimental accuracy of modem electron affinity determinations permits these cycles to provide even more accurate lattice enthalpies. Despite the simplicity of this approach, it can be powerful in calculating thermodynamic properties for reactions that are difficult to measure directly. 

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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... 

Born-Haber s cycle — Hess s law establishes that the enthalpy of a reaction is the same independently whether the reaction proceeds in one or several steps. It is a consequence of the first law of thermodynamics, which states the conservation of energy. Born and -> Haber applied Hess s law to determine the - enthalpy of formation of an ionic solid. The formation of an ionic crystal from its elements according to Born-Haber s cycle can be represented by the following diagram. 

There are two major factors which have to be considered in the process of the electrolytic metal deposition (i) the thermodynamic and growth properties of the crystalline phase which can be treated as largely independent of the presence and character of the ambient phase and (ii) the properties of the ionic solution affecting primarily the structure of the interface boundary and the kinetics of the mass and charge transfer across it. In the first part of this chapter the problems connected with the formation and growth of the crystals of the metal deposit will be discussed more closely, while the problems arising from the ionic solution side will be treated as simply as possible (see also Vol. 1 of this series). 

In order to be able to calculate the concentrations of point defects at thermodynamic equilibrium, it is necessary to know the change in free energy of the crystal which accompanies the formation of point defects, since the equilibrium is determined by the minimization of the free energy when the pressure, the temperature, and the other independent thermodynamic variables are given. A theoretical calculation of the free energy of formation of defects is still one of the most difficult problems in solid state physics and chemistry. The methods of calculation for each group of materials - metals, covalent crystals, ionic crystals - are all very... 

If the range of homogeneity of the reaction product is sufficiently narrow, then the average diffusion coefficient as defined in eq. (8-9) can be calculated by means of defect thermodynamics, if it is assumed that the defects behave as the solute in ideally dilute solutions. In section 4.2 it was shown how the concentrations of the defect centers depend upon the component activities for a given type of disorder in binary ionic crystals. As an example, let us consider the formation of copper (I) oxide on copper sheet at 1000 °C in an oxidizing atmosphere whenis about 1 torr. The following defect equilibrium can be written ... 

Alternatively, Bratsch and Lagowski (1985a, b, 1986) proposed an ionic model to calculate the thermodynamics of hydration AGj, A/fJ and ASj using standard thermochemical cycles. This model is based on the knowledge of the values of quantities such as the enthalpy of formation of the monoatomic gas [A/f (M )], the ionization potential sum for the oxidation state under consideration and the crystal ionic radius of the metal ion. This approach, however, is difficult to apply for the actinides since the ionization potentials are, for the most part, unavailable. To overcome this problem, the authors back-calculated an internally consistent set of thermochemical ionization potentials from selected thermodynamic data (Bratsch and Lagowski 1986). The general set of equations developed are ... 

In 1973, Mikheev et al. reported that a stable, monovalent Md ion could be produced in ethanol solutions and that it co-crystallized with CsQ [45]. However, Samhoun and co-workers studied the overall reduction of Md to the amalgam using controlled potential electrolysis they concluded that Md could not be considered a cesium-like element and no evidence was obtained consistent with a monovalent state [46,47]. Hulet et al. have recently repeated some of the co-crystallization experiments of Mikheev and performed a series of new experiments in an attempt to prepare Md by reduction with Sm in ethanol solutions and also in fused KQ media [37]. In these experiments, the behavior of Md was compared to tracer amounts of 3-i-, 2-i-, and 1-i-ions and Md consistently followed the 2 -i- ions. They concluded that Md cannot be reduced to a monovalent state with Sm as daimed by Mikheev. However, on the basis of the results of thermodynamic studies of the co-crystallization process of mendelevium with chlorides of alkali metals, the Russian investigators maintain that Md can be reduced to the monovalent state in water-ethanol solutions and that the co-crystallization of Md with salts of divalent ions can be explained as being due to the formation of mixed crystals [102,103]. An ionic radius of 1.17 A was calculated for Md from the results of the co-crystallization studies [104]. 

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