The reason why ionic compounds are brittle is because the ions in the compound are already held rigidly in place in a lattice due to the strong electrostatic forces of attraction in between the cations and the anions as well as the repulsion in the ions with like charges . However, if a large enough force is applied along a certain plane, this causes the ions to shift along that layer, displacing that layer with respect to the next, and there will hence be a repulsion between like charges within the ionic compound. This repulsion will shatter the crystal lattice of the ionic compound.
