the lattice energy
The lattice energy is the glue budget of an ionic crystal: the energy released when a gas of separate positive and negative ions rushes together and snaps into an ordered solid, or, read the other way, the energy you would have to pour in to rip the crystal apart into free ions floating far away. A big lattice energy means the ions are bound tightly; that single number is behind a ceramic's high melting point, its stiffness, and its hardness.
Two levers dominate, both visible in the physics of Coulomb's law. First, the charges: energy scales with the product of the cation and anion charges, so going from singly charged NaCl (+1, -1) to doubly charged MgO (+2, -2) multiplies the ion-pair attraction roughly fourfold. Second, the spacing: energy scales inversely with the distance between ion centres, so smaller ions packed closer bind more strongly. This is why MgO, with double charges and a short Mg-O distance, has a lattice energy near 3800 kJ/mol against NaCl's near 790 kJ/mol, and why MgO melts at 2852 degrees C while table salt melts at 801.
You cannot just add up one ion pair: every ion feels attraction and repulsion from the whole infinite lattice. The Madelung constant sums that geometry, and the Born-Lande equation packages charges, spacing, the Madelung constant, and a short-range repulsion into a formula that predicts lattice energies to within a few percent for ionic solids. Lattice energy then feeds directly into the properties ceramists care about: strong, high-lattice-energy bonds resist thermal jostling (high melting point), resist stretching (high elastic modulus), and resist scratching (high hardness).
Compare by charge and size: LiF (small ions, +1/-1) has a lattice energy around 1030 kJ/mol, NaCl around 790, and MgO (doubled charges, small ions) around 3800, and their melting points climb in the same order, 845, 801, and 2852 degrees C.
Higher charges and shorter bonds mean a bigger lattice energy, and a higher melting point.
Lattice energy is a purely ionic quantity, computed as if bonds were 100 percent ionic. For covalent ceramics like SiC it is not the right bookkeeping: their cohesion comes from shared electrons, and you must reason with covalent bond energies instead.