3  Fundamentals of Crystal Structure

NoteLearning Objectives

• Define a Bravais lattice, a basis, and a crystal structure in a mathematically precise real-space language.
• Distinguish primitive, conventional, and Wigner–Seitz cells and explain why they are not interchangeable.
• Recognize the seven crystal systems and the idea of the 14 Bravais-lattice types without yet developing full symmetry theory.
• Describe the real-space geometry of the common structure types SC, BCC, FCC, and HCP, as well as the simple binary prototypes CsCl, NaCl, fluorite, diamond, and zincblende.
• Explain why the basis matters physically, even when the underlying Bravais lattice is unchanged.
• Prepare for the next lecture by seeing how direct-lattice structure controls optical modes and later reciprocal-space selection rules.