Ionic Solids and Lattice Energetics
Ionic solids are held together by the electrostatic attraction of oppositely charged ions, and their lattice energy—quantified by electrostatic models and thermodynamic cycles—governs their stability and properties.
Definition
Lattice energetics is the quantitative treatment of the energy of ionic solids—the energy required to separate the crystal into gaseous ions—using electrostatic models and thermodynamic cycles to relate structure to stability.
Scope
This topic covers the ionic model and its energetics: the electrostatic Madelung summation, the Born–Landé and Born–Mayer expressions that add short-range repulsion, the experimental determination of lattice energy through the Born–Haber cycle, and the use of lattice energies to rationalize melting points, solubilities, and the stability of unusual oxidation states. It treats energetics specifically, leaving the geometric description of structures to the close-packing topic.
Core questions
- What is lattice energy and how is it defined?
- How does the Born–Landé equation combine attraction and repulsion?
- How does a Born–Haber cycle determine lattice energy experimentally?
- How do lattice energies explain solubility and oxidation-state stability?
Key concepts
- Ionic model
- Madelung constant
- Born–Landé and Born–Mayer equations
- Born–Haber cycle
- Lattice enthalpy
- Charge and size effects
Key theories
- Madelung electrostatics and the Born–Landé equation
- Summing the Coulomb interactions over an infinite ionic lattice gives the Madelung energy, and adding a Born repulsion term yields the Born–Landé equation, which predicts lattice energies in good agreement with experiment.
- Born–Haber cycle
- A Hess's-law thermodynamic cycle relating atomization, ionization, electron-gain, and formation enthalpies allows lattice energy to be determined from measurable quantities, testing the ionic model.
- Lattice energy and chemical trends
- Lattice energy rises with ionic charge and falls with ionic size, explaining trends in melting point, hardness, and solubility and the thermodynamic stabilization of high- or low-charge species in the solid state.
Clinical relevance
Lattice energetics explains why some salts are soluble and others insoluble, guides the formulation of materials and pharmaceuticals, and underpins the thermodynamic stability of pigments, ceramics, and battery electrode materials.
History
The electrostatic theory of ionic crystals was developed in the 1910s by Madelung, Born, and Landé, who computed lattice energies from crystal geometry. Haber's thermodynamic cycle, refined with Born, gave an experimental route to the same quantity, establishing lattice energy as a cornerstone of inorganic solid-state thermodynamics.
Key figures
- Max Born
- Alfred Landé
- Fritz Haber
- Erwin Madelung
Related topics
Seminal works
- born1918
- west2014
- weller2018
Frequently asked questions
- Why do salts of small, highly charged ions have such high melting points?
- Lattice energy increases with the product of the ionic charges and decreases with the distance between ions, so small, highly charged ions produce especially strong electrostatic binding, which must be overcome to melt the solid, giving high melting points.
- What does a Born–Haber cycle let you calculate?
- By applying Hess's law to a closed loop of enthalpy steps connecting the elements, their gaseous ions, and the solid compound, the cycle lets you solve for the lattice energy, which cannot be measured directly, from quantities that can.