Madelung constant metals

The relationship between cubic close-packed (ccp) structures and ionic compounds of type B1 is obvious. Interstitial sites with respect to metal positions are at fractional coordinates of the type 00 and equivalent to the ionic sites in Bl. The Madelung constant of Al type metals with interstitially localized free electrons is therefore the same as that of rocksalt structures. It is noted that the interstitial sites define the same face-centred lattice as the metal ions. 

A serious limitation of (but not an objection to) the hydridic model is its inability to rationalize the nonstoichiometry of metallic hydrides. The difficulty arises in part because of the use of the Madelung constant (or an approximate equivalent) and a Born-Lande or exponential repulsion term. It is not yet clear how these may be calculated for a defect structure where ions are randomly missing from their sites. It is reasonable that mutual repulsion of outer electrons will be less in such a structure, but no quantitative interpretation has been made. 

From comparisons of the absorption and excitation spectra for the oxides, as shown in Table I (66) it appears that the energy decreases with an increase in the cation size from Mg to Ba in the alkaline earth metal cation series. This pattern has been satisfactorily explained by using the approach of Levine and Mark (84), whereby ions located on an ideal surface are considered to be equivalent to the bulk ions, except for their reduced Madelung constants. A more detailed analysis has been carried out by Garrone et al. (60, 79), who reinterpreted earlier reflectance spectra and suggested that there is evidence of three absorption bands corresponding to ions in live, four, and three coordination—aU three for MgO, CaO, and SrO. 

A few AB solids have body-centered cubic structures, with a CN of 8. An example is CsCl, which is calculated to be much more stable in the ionic model. Again ionic bonding seems to favor a high CN, since the Madelung constant increases, being 1.763 for bcc. This theory proves to be short-lived, however, when we consider bonding in the metals. By definition, the bonding here must be covalent, since identical atoms are bonded. 

The largest change is in the cohesive energy, which increases m all cases. For ionic solids, the increase is due to the larger Madelung constant. For metals, the increase is due to the better delocalization energy with a higher coordination number. For covalent solids, the increase occurs because all of the valence-shell... 

We can apply the Born-Haber cycle to a metal oxide having a structure type of known Madelung constant, and for which an electrostatic model is a reasonably valid approximation. Magnesium(II) oxide fits these criteria it has an NaCl structure type, /-Q has been accurately determined by X-ray diffraction methods, and compressibility data are available an electrostatic model gives At/(0K) = —3975kJmol . All other quantities in the appropriate Bom-Haber cycle are independently measurable and a value for E Aea (298 K) for reaction 6.21 can be evaluated. A series of similar values for E Aea- °(298 K) for reaction 6.21 can be obtained using different group 2 metal oxides. 

Table 5.2. Coordination numbers, C, Madelung constants, M, and calculated bond distance ratios, R R, for gaseous, monomeric alkali metal halides MX, gaseous square dimers M2X2, for cubic tetramers M4X4 and for MX crystals with rock-salt structures.

Carter (1972) established a tetragonal model of ordered cationic vacancies in the R3- cX4 compounds from considerations involving the stereohedral metal sites or Wigner-Seitz cells, and tested it by Madelung constant calculations. 

Contents Trifluoromethyl Aromatic Compounds (R. Filler) Aliphatic Fluoro-amino Acids (F. Loncrini and R. Filler) Fluoro-alcohols (S. K. De and S. R. Palit) Polyfluoroaromatic Derivatives of Metals and Metalloids (S. C. Cohen and A. G. Massey) The Chemistry of Organic Nitrogen Fluorides (J. P. Freeman) Fluorine Compounds of lenium and Tellurium (B. Cohen and R. D. Peacock) Madelung Constants as a New Guide in the Structural Chemistry of Solids (R. Hoppe). 

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