In chemistry, the lattice energy is the energy change (released) upon formation of one mole of a crystalline compound from its infinitely separated constituents, which are assumed to initially be in the gaseous state at 0 K. It is a measure of the cohesive forces that bind crystalline 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.
Lattice energy and lattice enthalpy
The concept of lattice energy was originally applied to the formation of compounds with structures like rocksalt (NaCl) and sphalerite (ZnS) where the ions occupy high-symmetry crystal lattice sites. In the case of NaCl, lattice energy is the energy change of the reaction:
Na + ( g ) + Cl − ( g ) ⟶ NaCl ( s ) {\displaystyle {\ce {Na^+ (g) + Cl^- (g) -> NaCl (s)}}}
which amounts to −786 kJ/mol. Some chemistry textbooks as well as the widely used CRC Handbook of Chemistry and Physics define lattice energy with the opposite sign, i.e. as the energy required to convert the crystal into infinitely separated gaseous ions in vacuum, an endothermic process. Following this convention, the lattice energy of NaCl would be +786 kJ/mol. Both sign conventions are widely used. The relationship between the lattice energy Δ U l {\displaystyle \Delta U_{l}} and the lattice enthalpy Δ H l {\displaystyle \Delta H_{l}} at pressure P {\displaystyle P} is given by the following equation:
Δ U l = Δ H l − P Δ V m {\displaystyle \Delta U_{l}=\Delta H_{l}-P\Delta V_{m}} , where Δ U l {\displaystyle \Delta U_{l}} is the lattice energy (i.e., the molar internal energy change), Δ H l {\displaystyle \Delta H_{l}} is the lattice enthalpy, and Δ V m {\displaystyle \Delta V_{m}} the change of molar volume due to the formation of the lattice. Since the molar volume of the solid is much smaller than that of the gases, Δ V m < 0 {\displaystyle \Delta V_{m}<0} . The formation of a crystal lattice from ions in vacuum must lower the internal energy due to the net attractive forces involved, and so Δ U l < 0 {\displaystyle \Delta U_{l}<0} . The − P Δ V m {\displaystyle -P\Delta V_{m}} term is positive but is relatively small at low pressures, and so the value of the lattice enthalpy is also negative (and exothermic). Both, lattice energy and lattice enthalpy are identical at 0 K and the difference may be disregarded in practice at normal temperatures.
Theoretical treatments
Lattice energy of ionic compounds The lattice energy of an ionic compound depends strongly upon the charges of the ions that comprise the solid, which must attract or repel one another via Coulomb's law. More subtly, the relative and absolute sizes of the ions influence Δ H l {\displaystyle \Delta H_{l}} . London dispersion forces also exist between ions and contribute to the lattice energy via polarization effects. For ionic compounds made up of molecular cations and/or anions, there may also be ion-dipole and dipole-dipole interactions if either molecule has a molecular dipole moment. The theoretical treatments described below are focused on compounds made of atomic cations and anions, and neglect contributions to the internal energy of the lattice from thermalized lattice vibrations.
Born–Landé equation
In 1918 Max Born and Alfred Landé proposed that the lattice energy could be derived from the electric potential of the ionic lattice and a repulsive potential energy term. This equation estimates the lattice energy based on electrostatic interactions and a repulsive term characterized by a power-law dependence (using a Born exponent, n {\displaystyle n} ). It was published building on earlier work by Born on ionic lattices.
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