Part of JPC-09 — Solid State: Unit Cell, Packing & Defects

Crystal Systems and Unit Cells

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Crystalline solids have atoms/ions/molecules arranged in a regular, repeating 3D pattern. The smallest repeating unit is the unit cell. Seven crystal systems exist based on edge lengths and angles, but JEE focuses on the cubic system. Three cubic unit cells: Simple Cubic (SC) with Z=1 atom per cell 8cornersx18\frac{8 corners x 1}{8}, Body-Centred Cubic (BCC) with Z=2 (8 corners x 1/8 + 1 body centre), and Face-Centred Cubic (FCC) with Z=4 (8 corners x 1/8 + 6 faces x 1/2). Contribution rules: corner atom shared by 8 cells 18each\frac{1}{8 each}, face atom by 2 cells 12\frac{1}{2}, edge atom by 4 cells 14\frac{1}{4}, body centre atom unshared (1). Amorphous solids lack long-range order and behave as supercooled liquids (e.g., glass). They show isotropic properties and no sharp melting point. Crystalline solids are anisotropic with sharp melting points. Lattice = array of points, basis = atom(s) associated with each point. Crystal structure = lattice + basis. The 14 Bravais lattices represent all possible 3D lattice types. For JEE, memorise Z values, coordination numbers, and edge-radius relationships for SC, BCC, and FCC.

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