In terms of atoms, why are brittle materials stronger in compression than in tension?

Answer 1

Materials in the solid or liquid state have physical properties governed by several different kinds of bonds (not chemical bonds) among neighboring molecules. The nature of these bonds has the molecules nearly as close to their neighbors as they can possibly be. Forcing them closer causes the electrostatic repulsion between the nucleii increasing very rapidly. That's why most solids and liquids are incompressible.

For some materials, the bonding energy decreases gradually with distance. These materials can bend and stretch. For others, it decreases sharply. It takes a lot of energy to move them apart a little, but once the separate a little, the bond is broken. These are the brittle materials. The plastic materials can bend and stretch under pressure, but the brittle ones can't.

Answer 2

There are exceptions. Diamonds, for example, are both brittle and very strong. Many brittle materials, though, are made up of an aggregate of crystalline materials that individually are strong in both tension and compression, but are not bonded to each other very well (like concrete), or they tend to develop microscopic cracks (like glass). In either case, they can take great loads in compression, since this only pushes the crystals closer together and closes any cracks. Under tension, though, the crystals pull apart and cracks grow until the object breaks in half.

In terms of atoms, crystals, noncrystalline bonds, the definition of a glass, and why cracks tend to grow are all describable in terms of inter-atomic bond structure, which you may research on your own.