Ionic bonds Madelung constants

When we have an ordered assembly of atoms called a lattice, there is more than one bond per atom, and we must take into account interactions with adjacent atoms that result in an increased interionic spacing compared to an isolated atom. We do this with the Madelmg constant, ckm. This parameter depends on the structure of the ionic crystal, the charge on the ions, and the relative size of the ions. The Madelung constant fits directly into the energy expression (Eq. 1.25) ... 

This energy is termed the Madelung energy since it represent a (attice energy" internal to the molecule with a Madelu ng constant, course, ecjual to I.OO. It is a maximum in a purely ionic bond (5 -> Z ) and decreases to whatever extent the charges on X and Y decrease. 

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. 

In the general case of a Debye solid the temperature dependence of G is determined via the parameter 0d (see Chapter 3). Hence, the free enthalpy of a perfect sohd is determined for all temperatures by the parameters effective pair bonding energy, co-ordination number and Debye-temperature. While (e) is a meaningful parameter in the case of co radent crystals (for elemental crystals x-x> cf. Section 2.2.4), in the case of ionic crystals charge numbers, lattice constant and Madelung number are the appropriate parameters. Hence... 

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