Part 4: Crystallography
Crystallography is the science of determining the arrangement of atoms in solids. Understanding crystal structure is essential for predicting material properties such as mechanical strength, electronic behavior, and optical characteristics. X-ray diffraction provides the experimental tool to probe atomic arrangements at the angstrom scale.
What You Will Learn
- βThe 7 crystal systems and 14 Bravais lattices
- βMiller indices for planes and directions
- βPacking fractions for common crystal structures
- βBragg's law and X-ray diffraction techniques
- βStructure factors and systematic absences
- βPowder diffraction and space group determination
Key Equations
Bragg's law
$$n\lambda = 2d\sin\theta$$
Interplanar spacing (cubic)
$$d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$$
Structure factor
$$F_{hkl} = \sum_j f_j\,e^{2\pi i(hx_j + ky_j + lz_j)}$$
Moseley's law
$$\sqrt{\nu} = a(Z - b)$$
Topics
4.1 Crystal Structure & Symmetry
Bravais lattices, unit cells, Miller indices, packing fractions, and common crystal structures (NaCl, CsCl, diamond, zinc blende, wurtzite).
4.2 X-ray Diffraction
X-ray generation, Bragg's law, structure factors, systematic absences, powder diffraction, and space group determination.