Madelung energy
/ MAH-deh-loong EN-er-jee /
Imagine standing in the middle of a vast checkerboard where the red squares pull you in and the black squares push you away, and you must add up every single tug and shove from the entire board to know which way you are pulled overall. An ion in a salt crystal faces exactly this task, and the Madelung energy is the grand total: the combined electric energy of one ion feeling all the other ions in the crystal at once.
Each ion is attracted to its nearest neighbors of opposite charge but repelled by the next ones of the same charge, then attracted again farther out, in an endless alternating pattern. Adding up all these contributions across the whole lattice gives a single net number that, surprisingly, comes out attractive — the pulls win over the pushes. The exact result depends only on the geometry of the crystal, captured in a fixed number called the Madelung constant, which differs for each crystal shape.
The Madelung energy matters because it is the dominant ingredient in the binding of ionic crystals; it is the main reason salt holds together so firmly. A common misconception is that an ion is bound mainly by its closest neighbor — in fact the long reach of electric forces means distant ions contribute meaningfully too, and only by summing the entire infinite array do you get the true energy. That subtle infinite sum is exactly what the Madelung constant tames into one tidy figure.
In table salt, a sodium ion is hugged by six chlorine ions just next door (a strong attraction), surrounded by twelve sodium ions a little farther out (a repulsion), then eight more chlorines beyond, and so on. Summing this never-ending alternating series gives the Madelung constant of about 1.748 for the salt structure — the single number that captures the whole electric tally.
Summing salt's alternating shells of ions yields a Madelung constant near 1.748.
Madelung energy counts only the electrostatic pulls and pushes between point-like ions. The full lattice energy also subtracts a smaller repulsion that appears because ions cannot overlap, so the Madelung energy is a leading piece, not the entire story.