Madelung constant defined

We have already defined the Madelung constant as the ratio of the energy released when a mole of crystal forms from the gaseous ions to that released when ion pairs form. In order to understand what this means, we will consider the following example. Suppose that a mole of Na+ and a mole of Cl... 

The geometry of the crystal introduces a factor multiplying the pairwise ionic interaction, which is the Madelung constant /t. It is a dimensionless constant, dependent on the geometry of the crystal under consideration. For an ionic binary crystal, consisting of N each positive and negative ions, fi is defined by... 

The results for the three models are summarized in Table 9.2, which lists the effective Madelung constant n (t, defined by eiectrosuiic = — peff/a the effective Born coefficient, defined by U = — NAncff/a(l — l/neff) and the lattice energy U. 

The electrostatic (Madelung) part of the lattice energy (MAPLE) has been employed to define Madelung potentials of ions in crystals (Hoppe, 1975). MAPLE of an ionic solid is regarded as a sum of contributions of cations and anions the Madelung constant. A, of a crystal would then be the sum of partial Madelung constants of cation and anion subarrays. Thus,... 

The Madelung constant is unique ftk ejj h crystal structure and is defined only for those whose interatomic vectors are fixed by symmetry. The Born exponent, n, can be cslimatcd Hfor alkali halides by the noblc-gas-likc electron configuration of the Vigny It can also be estimated from the compressibility of the crystal system. For NaCl, n equals 9.1. 

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. 

The Madelung constant a is defined as the ratio (a = EM/H) of the Madelung energy to the Coulomb attractive energy H between the nearest-neighbor anion and cation. Thus, for the monoatomic one-dimensional lattice of equidistant cations and anions of Eq. (8.10.3), a = 1.385294361. 

For further discussion of the problem of defining Madelung constants, see Quane. D. J. Chem. Educ. 1970. 47, 396. 

Factors Controlling the Formation and Structure of Phases The Madelung constant can be defined as... 

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