The calculation that led to Eq. 2 can be extended to more realistic threedimensional
arrays of ions with different charges. The result has the same form but
with different values of A and 0z1z2 0 (that is, the absolute value of z1z2, its value without
the negative sign) in place of z2. The factor A is a numerical coefficient called the
Madelung constant; its value depends on how the ions are arranged about one another
(TABLE 3.2). In all cases, the energy lowering that occurs when an ionic solid forms is
greatest for small, highly charged ions. For example, there is a strong interaction
between the Mg2 and the O2 ions in magnesium oxide, MgO, because the ions have
high charges and small radii. This strong interaction is one reason why magnesium
oxide survives at such high temperatures that it can be used for furnace linings. It is an
example of a “refractory” material, a substance that can withstand high temperatures.