Table of Contents
What is Bragg's Law?
Bragg's Law, formulated by William Lawrence Bragg and his father William Henry Bragg in 1913, describes the condition for constructive interference of X-rays scattered by crystal lattice planes. When X-rays strike a crystal, they are scattered by atoms in the lattice. At specific angles, the scattered waves from successive parallel planes reinforce each other, producing a strong diffracted beam.
This discovery earned the Braggs the Nobel Prize in Physics in 1915 and revolutionized our ability to determine the arrangement of atoms in crystalline materials. X-ray diffraction based on Bragg's Law has become the most powerful tool for determining crystal structures, enabling discoveries from DNA's double helix to protein structures used in drug design.
The Formula
Where n is the diffraction order (positive integer), λ is the X-ray wavelength, d is the spacing between crystal planes, and θ is the angle between the incident beam and the crystal planes (Bragg angle). Constructive interference occurs only when this condition is exactly satisfied.
Applications
| Technique | Application | Typical Source |
|---|---|---|
| Powder XRD | Phase identification, lattice parameters | Cu K-alpha (1.5406 A) |
| Single Crystal XRD | Full 3D structure determination | Mo K-alpha (0.7107 A) |
| Neutron Diffraction | Light element and magnetic structures | Reactor neutrons |
| Electron Diffraction | Thin film and surface analysis | Electron beam |
Frequently Asked Questions
Why are X-rays used for crystal diffraction?
X-ray wavelengths (0.1-10 Angstroms) are comparable to interatomic distances in crystals (1-5 Angstroms). For diffraction to occur, the wavelength must be on the same order as the spacing between scattering centers. Visible light (400-700 nm) is far too long to resolve atomic structure. Electrons and neutrons with appropriate energies also have de Broglie wavelengths suitable for crystal diffraction.
What is the significance of d-spacing?
The d-spacing is the perpendicular distance between adjacent parallel lattice planes. Each set of planes is identified by Miller indices (hkl). The d-spacing is characteristic of the crystal structure and relates to the unit cell dimensions. Measuring d-spacings from a diffraction pattern allows determination of the unit cell parameters and ultimately the crystal structure.
What determines the intensity of diffraction peaks?
While Bragg's Law determines the positions (angles) of diffraction peaks, the intensities depend on the structure factor, which accounts for the types and positions of atoms within the unit cell. Heavier atoms scatter more strongly. The Debye-Waller factor accounts for thermal vibrations that reduce peak intensities at higher angles. Peak intensities are crucial for solving crystal structures.