Lattice energy


The lattice energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound. It is a measure of the cohesive forces that bind ions. Lattice energy is relevant to many practical properties including solubility, hardness, and volatility. The lattice energy is usually deduced from the Born–Haber cycle.
CompoundExperimental Lattice EnergyStructure typeComment
LiF−1030 kJ/molNaCldifference vs. sodium chloride due to greater charge/radius for both cation and anion
NaCl−786 kJ/molNaClreference compound for NaCl lattice
NaBr−747 kJ/molNaClweaker lattice vs. NaCl
NaI−704 kJ/molNaClweaker lattice vs. NaBr, soluble in acetone
CsCl−657 kJ/molCsClreference compound for CsCl lattice
CsBr−632 kJ/molCsCltrend vs CsCl like NaCl vs. NaBr
CsI−600 kJ/molCsCltrend vs CsCl like NaCl vs. NaI
MgO−3795 kJ/molNaClM2+O2- materials have high lattice energies vs. M+O−. MgO is insoluble in all solvents
CaO−3414 kJ/molNaClM2+O2- materials have high lattice energies vs. M+O−. CaO is insoluble in all solvents
SrO−3217 kJ/molNaClM2+O2- materials have high lattice energies vs. M+O−. SrO is insoluble in all solvents
MgF2−2922 kJ/molrutilecontrast with Mg2+O2-
TiO2−12150 kJ/molrutileTiO2 and some other M4+2 compounds are refractory materials

Lattice energy and lattice enthalpy

The formation of a crystal lattice is exothermic, i.e., the value of ΔHlattice is negative because it corresponds to the coalescing of infinitely separated gaseous ions in vacuum to form the ionic lattice.
The concept of lattice energy was originally developed for rocksalt-structured and sphalerite-structured compounds like NaCl and ZnS, where the ions occupy high-symmetry crystal lattice sites. In the case of NaCl, lattice energy is the energy released by the reaction
which would amount to -786 kJ/mol.
The relationship between the molar lattice energy and the molar lattice enthalpy is given by the following equation:
where is the molar lattice energy, the molar lattice enthalpy and the change of the volume per mole. Therefore, the lattice enthalpy further takes into account that work has to be performed against an outer pressure.
Some textbooks and the commonly 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. The lattice energy for ionic crystals such as sodium chloride, metals such as iron, or covalently linked materials such as diamond is considerably greater in magnitude than for solids such as sugar or iodine, whose neutral molecules interact only by weaker dipole-dipole or van der Waals forces.

Theoretical treatments

The lattice energy of an ionic compound depends upon charges of the ions that comprise the solid. More subtly, the relative and absolute sizes of the ions influence ΔHlattice.

Born–Landé equation

In 1918 Born and Landé proposed that the lattice energy could be derived from the electric potential of the ionic lattice and a repulsive potential energy term.
where
The Born–Landé equation shows that the lattice energy of a compound depends on a number of factors
Barium oxide, for instance, which has the NaCl structure and therefore the same Madelung constant, has a bond radius of 275 picometers and a lattice energy of -3054 kJ/mol, while sodium chloride has a bond radius of 283 picometers and a lattice energy of -786 kJ/mol.

Kapustinskii equation

The Kapustinskii equation can be used as a simpler way of deriving lattice energies where high precision is not required.

Effect of polarisation

For ionic compounds with ions occupying lattice sites with crystallographic point groups C1, C1h, Cn or Cnv the concept of the lattice energy and the Born–Haber cycle has to be extended. In these cases the polarization energy Epol associated with ions on polar lattice sites has to be included in the Born–Haber cycle and the solid formation reaction has to start from the already polarized species. As an example, one may consider the case of iron-pyrite FeS2, where sulfur ions occupy lattice site of point symmetry group C3. The lattice energy defining reaction then reads
where pol S− stands for the polarized, gaseous sulfur ion. It has been shown that the neglection of the effect led to 15% difference between theoretical and experimental thermodynamic cycle energy of FeS2 that reduced to only 2%, when the sulfur polarization effects were included.