lattice enthalpy
How much glue holds an ionic crystal together? Lattice enthalpy (often loosely called lattice energy) is the number that answers it. It is the energy involved when a mole of a solid ionic compound is built from, or pulled apart into, its separate gaseous ions. For NaCl it is the energy change for Na+(g) plus Cl-(g) coming together to form NaCl(s) — and it is huge, hundreds of kilojoules per mole, which is why ionic solids are hard, high-melting and tough.
Two sign conventions exist, so be careful. The lattice formation enthalpy is for gaseous ions coming together into the solid and is large and negative (energy released); the lattice dissociation enthalpy is for the solid breaking apart into gaseous ions and is the same magnitude but positive (energy required). Whichever convention, the magnitude depends on just two things, captured in the Coulomb law at the heart of the ionic model: the product of the ionic charges (doubling a charge roughly doubles the energy, so a 2+/2- pair binds far harder than 1+/1-) and the inverse of the distance between ion centres (smaller ions, closer together, bind harder). That is why MgO, with double charges and small ions, has a lattice enthalpy several times that of NaCl.
Lattice enthalpy is one of the most useful quantities in inorganic chemistry because it controls so much observable behaviour. It sets melting points and hardness; it governs thermal stability (carbonates of small cations decompose more easily because the small oxide left behind makes a much more stable lattice); and it competes with hydration energy to decide solubility (a salt dissolves when the energy released by hydrating its ions roughly matches the lattice enthalpy needed to break the crystal). It cannot be measured directly — no one can simply weigh gaseous ions assembling — so it is obtained from the Born-Haber cycle or calculated from the Born-Lande equation.
Group 2 carbonates decompose to the oxide on heating, and the small Mg2+ makes MgCO3 break down far below CaCO3. The reason is lattice enthalpy: the tiny oxide ion forms a much more stable lattice with small Mg2+ than the bigger carbonate ion can, so losing CO2 is favoured for the small cation.
Lattice enthalpy explains why small-cation carbonates (MgCO3) decompose at lower temperatures than large-cation ones.
Watch the sign convention: lattice formation enthalpy is negative, lattice dissociation enthalpy positive — they are equal in magnitude. Lattice enthalpy cannot be measured directly; it is inferred via a Born-Haber cycle or calculated.