the close-packed anion array
Pour a bag of oranges into a box and shake it gently. They settle into neat layers, each orange nestled into the dimples between three below it, filling space as tightly as round objects can. In most ceramics the big particles are the anions (usually oxygen, O2-, or a halide like Cl-), because a negative ion holds extra electrons and puffs up larger than the cation it pairs with. So a great many ceramic crystals are, at heart, a close-packed stack of anions with the small cations hidden in the gaps.
There are two ways to stack the layers so each is as tight as possible. If the third layer sits directly over the first (an ABAB rhythm) you get hexagonal close packing (HCP); if the third layer is offset into a new position (ABCABC) you get cubic close packing, which is the same as a face-centred-cubic (FCC) array. Both fill about 74 percent of space, leaving 26 percent as empty pockets called interstices. For every anion in the stack there is exactly one octahedral hole (surrounded by 6 anions) and two tetrahedral holes (surrounded by 4). So N anions create N octahedral and 2N tetrahedral sites waiting to be filled.
This one idea organises half of ceramic crystallography. Rock salt is FCC oxygen with every octahedral hole filled; corundum (Al2O3) is HCP oxygen with two-thirds of the octahedral holes filled; spinel is FCC oxygen with one-eighth of the tetrahedral and half the octahedral holes filled; zinc blende and wurtzite fill half the tetrahedral holes. Honest caveat: not every ceramic obeys this picture. Cesium chloride, fluorite, rutile and perovskite are not simple close-packed anion arrays, so treat close packing as a powerful organising theme, not an ironclad law.
Magnesium oxide, MgO, is nothing more than a face-centred-cubic stack of O2- ions with a tiny Mg2+ dropped into every octahedral gap. Knowing just that, you can predict its cubic shape, its 6-fold coordination, and even calculate its density.
Rock-salt MgO equals close-packed oxygen plus cations in the holes.
Close packing describes the anion sublattice, not the whole crystal. The cations that fill the holes push the anions slightly apart, so a real ceramic is rarely packed to the ideal 74 percent, and several important structures are not close-packed at all.