Madelung constant The

Details of the calculation of Madelung constants for all of the common types of crystals are beyond the scope of this book. When the arrangement of ions differs from that present in NaCl, the number of ions surrounding the ion chosen as a starting point and the distances between them may be difficult to determine. They will most certainly be much more difficult to represent as a simple factor of the basic distance between a cation and an anion. Therefore, each arrangement of ions (crystal type) will have a different value for the Madelung constant. The values for several common types of crystals are shown in Table 7.3. 

The infinite series converges to A, the so-called Madelung constant. The interaction for an Avogadro number of formula units consisting of n ions (in this case n = 2) each, amounts to the Madelung energy ... 

The potential taking into account the Madelung constant the Madelimg constant is a representation of the distance of the ions from one another and thus depends on their geometric arrangement in a crystal structure or on a surface. 

Knowing that Cap2 crystallizes in the fluorite lattice, use the appropriate ionic radii from Table 5.2, the proper Madelung constant, the correct compressibility factor, and the Born—Lande equation to calculate the lattice enthalpy of CaF. ... 

The quantity -1.747 in Equation (20.5) is called the Madelung constant. The magnitude of the Madelung constant depends on the sy mmetry of the crystal lattice. 

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