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It is a measure of the cohesive forces that bind ionic solids. The size of the lattice energy is connected to many other physical properties including solubility, hardness, and volatility. Since it generally cannot be measured directly, the lattice energy is usually deduced from experimental data via the Born–Haber cycle. [1]
ε 0 = permittivity of free space 4 π ε 0 = 1.112 × 10 −10 C 2 /(J·m) r = distance separating the ion centers. For a simple lattice consisting ions with equal and opposite charge in a 1:1 ratio, interactions between one ion and all other lattice ions need to be summed to calculate E M, sometimes called the Madelung or lattice energy:
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The Born–Mayer equation is an equation that is used to calculate the lattice energy of a crystalline ionic compound.It is a refinement of the Born–Landé equation by using an improved repulsion term.
The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%. Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known.
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Born–Haber cycles are used primarily as a means of calculating lattice energy (or more precisely enthalpy [note 1]), which cannot otherwise be measured directly. The lattice enthalpy is the enthalpy change involved in the formation of an ionic compound from gaseous ions (an exothermic process ), or sometimes defined as the energy to break the ...
The energy of the electrons in the "empty lattice" is the same as the energy of free electrons. The model is useful because it clearly illustrates a number of the sometimes very complex features of energy dispersion relations in solids which are fundamental to all electronic band structures.