Crystal structure and bonding are fundamental to understanding the physical properties of solid materials. A crystal is a solid material whose atoms, ions, or molecules are arranged in a highly ordered, repeating pattern extending in all three spatial dimensions. The smallest repeating unit of this structure is called the unit cell. The unit cell defines the crystal's lattice parameters, including the edge lengths a,b,ca, b, c and the angles between them α,β,γ\alpha, \beta, \gamma. The crystal lattice is generated by translating the unit cell along its edges, forming the complete crystalline structure.

Crystals are classified according to their symmetry into seven crystal systems: cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, and rhombohedral. Each system is characterized by specific symmetry elements such as mirror planes, rotation axes, and inversion centers. The Bravais lattices describe the 14 distinct lattice types that can fill three-dimensional space using translational symmetry. The atomic positions within a unit cell are described by fractional coordinates relative to the lattice vectors. In a face-centered cubic (FCC) lattice, atoms are located at the corners and the centers of the faces of the cube, while in a body-centered cubic (BCC) lattice, an additional atom is placed at the center of the cube.