Why broken crystals are stronger

Crystals may seem flawless, but deep inside they contain tiny structural imperfections that dramatically influence their strength and behavior. Researchers from The University of Osaka have used the sophisticated math of differential geometry to reveal how these defects—like dislocations and disclinations—interact in elegant, unified ways. Their findings could help scientists engineer tougher, smarter materials by intentionally leveraging these flaws rather than avoiding them.