Crystals lattice energy

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. 

The Bom-Haber cycle follows the Law of Conservation of Energy, that is when a system goes through a series of changes and is returned to its initial state the sum of the energy changes is equal to zero. Thus the equation  

From this the crystal lattice energy, U, can be calculated from the following enthalpies  

The crystal lattice energy can be estimated from a simple electrostatic model When this model is applied to an ionic crystal only the electrostatic charges and the shortest anion-cation intemuclear distance need be considered. The summation of all the geometrical interactions between the ions is called the Madelung constant. From this model an equation for the crystal lattice energy is derived  

U = crystal lattice energy M = Madelung constant r = shortest intemuclear distance n = Bom exponent 

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The fluorite stmcture, which has a large crystal lattice energy, is adopted by Ce02 preferentially stahi1i2ing this oxide of the tetravalent cation rather than Ce202. Compounds of cerium(IV) other than the oxide, ceric fluoride [10060-10-3] CeF, and related materials, although less stable can be prepared. For example ceric sulfate [13590-82-4] Ce(S0 2> certain double salts are known. 

For crystalline compounds, they noted that an important factor to consider is the crystal lattice energy. From theoretical considerations and subsequent empirical studies, they discovered that melting point (mp) serves as an excellent proxy for this factor. While this is a significant advance in our understanding of water solubility, it falls short as a means to predict solubility from the chemical structure alone a compound must be made and a mp determined experimentally. 

Exothermic events, such as crystallization processes (or recrystallization processes) are characterized by their enthalpies of crystallization (AHc). This is depicted as the integrated area bounded by the interpolated baseline and the intersections with the curve. The onset is calculated as the intersection between the baseline and a tangent line drawn on the front slope of the curve. Endothermic events, such as the melting transition in Fig. 4.9, are characterized by their enthalpies of fusion (AHj), and are integrated in a similar manner as an exothermic event. The result is expressed as an enthalpy value (AH) with units of J/g and is the physical expression of the crystal lattice energy needed to break down the unit cell forming the crystal. 

Crystal lattice energy composition (including bile salts) ... 

Salt Measured M—X spacing in vapor", A d 7/subb kcal/mole Crystal lattice energy, UQ, kcal/mole (U-JH), kcal/mole Comp. M+—X-distance in vapor, A... 

Crystal defects and imperfections inLuence the crystal lattice energy. These defects, including dislocations, give rise to increased surface energy and may be a major factor in improving dissolution performance of poorly water-soluble, crystalline substances. 

A.P. Toropova et al., QSPR modeling mineral crystal lattice energy by optimal descriptors of the graph of atomic orbitals. Chem. Phys. Lett. 428, 183-186 (2006)... 

For more information see Crystallography Crystal Lattice Energy... 

Fig. 2-8. The relationship between standard molar Gibbs energies of solvation and solution and the crystal lattice energy of an ionophore A B AG =AG, -AG .

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