X-Ray Crystallography

X-ray crystallography is a powerful experimental technique used to determine the precise three-dimensional arrangement of atoms within a crystalline solid. The method relies on the principle of diffraction, where a beam of X-rays, with wavelengths comparable to interatomic distances, is directed at a crystal, causing the ordered lattice of atoms to act as a three-dimensional diffraction grating. By measuring the angles and intensities of the scattered X-ray beams, a unique diffraction pattern is produced, which can then be mathematically analyzed to reconstruct a map of the electron density within the crystal, thereby revealing the exact positions of individual atoms and the bonds connecting them. This structural information is fundamental to understanding the properties and functions of a vast range of materials, from simple salts to complex biological macromolecules like proteins and DNA.

1. Introduction to Crystallography and Crystals
   1. Core Concepts
      1. Definition of X-Ray Crystallography
      2. Historical Context and Key Discoveries
         1. Early Experiments with X-Rays
         2. Discovery of X-Ray Diffraction by Crystals
         3. Development of Crystallographic Methods
         4. Nobel Prizes and Landmark Achievements
      3. The Nature of Crystalline Solids
         1. Long-Range Order
         2. The Unit Cell
            1. Definition and Parameters
            2. Lattice Parameters
            3. Types of Unit Cells
         3. The Crystal Lattice
            1. Lattice Points
            2. Lattice Directions and Planes
            3. Crystal Faces and Habit
         4. Amorphous vs. Crystalline Solids
   2. Crystal Symmetry
      1. Symmetry Elements and Operations
         1. Rotation Axes
            1. 2-fold Axis
            2. 3-fold Axis
            3. 4-fold Axis
            4. 6-fold Axis
         2. Mirror Planes
         3. Inversion Centers
         4. Translation Symmetry
         5. Screw Axes
            1. Definition and Notation
            2. Examples in Crystal Structures
         6. Glide Planes
            1. Definition and Notation
            2. Examples in Crystal Structures
      2. Point Groups
         1. Definition and Classification
         2. Schoenflies Notation
         3. Hermann-Mauguin Notation
         4. Examples of Point Groups
      3. The Seven Crystal Systems
         1. Triclinic
         2. Monoclinic
         3. Orthorhombic
         4. Tetragonal
         5. Trigonal
         6. Hexagonal
         7. Cubic
      4. The Fourteen Bravais Lattices
         1. Primitive Lattices
         2. Body-Centered Lattices
         3. Face-Centered Lattices
         4. Base-Centered Lattices
         5. Lattice Types in Each Crystal System
      5. Space Groups
         1. Definition and Notation
         2. International Tables for Crystallography
         3. Symmetry Operations in Space Groups
         4. Numbering and Classification
         5. Examples of Common Space Groups