Learn how fractional coordinates describe atom positions inside a unit cell — the foundation of crystallographic notation for engineers and researchers.
A clear guide to all 7 crystal systems — cubic, tetragonal, orthorhombic, hexagonal and more — with axis parameters and defining symmetry constraints.
Introduction to Bravais lattices and how they classify every possible periodic crystal structure. Visual, intuitive explanation for engineers and students.
Deep dive into all 14 Bravais lattice types. Covers cubic, tetragonal, and hexagonal families with diagrams and symmetry analysis.
Learn how to find Miller indices (hkl) step by step. Covers direction notation [uvw], families of planes {hkl}, bar notation, and d-spacing formula.
Understand close packing in crystals — HCP and CCP structures, coordination number, and packing efficiency. Clear derivations with visual explanations.
A complete guide to tetrahedral and octahedral voids in crystal structures — location, radius ratio, and significance in materials engineering.
Understand crystal density calculation and point defects — Schottky, Frenkel, and interstitial. Essential solid state physics for materials scientists.