Crystal repulsion

Properties Colorless crystals repulsive astringent taste faint odor. D 1.59, mp 130-131C. Soluble in water, alcohol and acetone very slightly soluble in benzene. At temperatures shghtly higher than its melting point, it is converted partly to fumaric acid. Combustible. 

Crystal Repulsion according to the law BJrn Repulsion according to the law exp (-ar) Van der Waal s interaction Zero-point energy Difference between E calc, from equation 13.1 Band by Born and Mayer... 

Madeluag constant For an ionic crystal composed of cations and anions of respective change z + and z, the la ttice energy Vq may be derived as the balance between the coulombic attractive and repulsive forces. This approach yields the Born-Lande equation,... 

Gilman [124] and Westwood and Hitch [135] have applied the cleavage technique to a variety of crystals. The salts studied (with cleavage plane and best surface tension value in parentheses) were LiF (100, 340), MgO (100, 1200), CaFa (111, 450), BaFj (111, 280), CaCOa (001, 230), Si (111, 1240), Zn (0001, 105), Fe (3% Si) (100, about 1360), and NaCl (100, 110). Both authors note that their values are in much better agreement with a very simple estimate of surface energy by Bom and Stem in 1919, which used only Coulomb terms and a hard-sphere repulsion. In more recent work, however, Becher and Freiman [126] have reported distinctly higher values of y, the critical fracture energy. ... 

Many-body problems wnth RT potentials are notoriously difficult. It is well known that the Coulomb potential falls off so slowly with distance that mathematical difficulties can arise. The 4-k dependence of the integration volume element, combined with the RT dependence of the potential, produce ill-defined interaction integrals unless attractive and repulsive mteractions are properly combined. The classical or quantum treatment of ionic melts [17], many-body gravitational dynamics [18] and Madelung sums [19] for ionic crystals are all plagued by such difficulties. 

The fluoride ion is the least polarizable anion. It is small, having a diameter of 0.136 nm, 0.045 nm smaller than the chloride ion. The isoelectronic E and ions are the only anions of comparable size to many cations. These anions are about the same size as K" and Ba " and smaller than Rb" and Cs". The small size of E allows for high coordination numbers and leads to different crystal forms and solubiUties, and higher bond energies than are evidenced by the other haUdes. Bonds between fluorine and other elements are strong whereas the fluorine—fluorine bond is much weaker, 158.8 kj/mol (37.95 kcal/mol), than the chlorine—chlorine bond which is 242.58 kJ/mol (57.98 kcal/mol). This bond weakness relative to the second-row elements is also seen ia 0-0 and N—N single bonds and results from electronic repulsion. 

The reason for the formation of a lattice can be the isotropic repulsive force between the atoms in some simple models for the crystalhzation of metals, where the densely packed structure has the lowest free energy. Alternatively, directed bonds often arise in organic materials or semiconductors, allowing for more complicated lattice structures. Ultimately, quantum-mechanical effects are responsible for the arrangements of atoms in the regular arrays of a crystal. 

Data for some typical complexes are given in Table 26.5. The assignments are made, producing values of the inter-electronic repulsion parameter B as well as of the crystal-field splitting, 0Dq. 

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