Born-von Karman boundary conditions

Born-von Karman boundary conditions are a mathematical way to model infinite crystal lattices by assuming that the ends of a finite chain of atoms wrap around and connect seamlessly. This means that an atom at one end is considered adjacent to the atom at the opposite end, creating a continuous, repeating pattern without edges. This approach simplifies calculations in solid-state physics, especially for studying vibrations and wave behavior in crystals, by effectively removing boundary effects and treating the material as an infinitely repeating structure.