About Bragg Diffraction
When X-rays strike a crystal, they are scattered by electrons in the atoms. For most angles the scattered waves cancel by destructive interference. At special angles described by Bragg's law (nλ = 2d·sin θ), waves scattered from successive parallel planes are in phase and interfere constructively, producing diffraction peaks. William Lawrence Bragg derived this condition in 1913, and together with his father William Henry Bragg received the 1915 Nobel Prize in Physics.
Each set of crystal planes, identified by Miller indices (hkl), has a characteristic d-spacing. For a cubic lattice, d = a/√(h²+k²+l²), where a is the lattice parameter. The full set of diffraction peaks — their angles and intensities — constitutes a diffraction pattern that is unique to the crystal structure. Comparing a measured pattern to a database identifies unknown materials.
This simulation shows a 2D cross-section of a crystal lattice with an X-ray beam at the current 2θ angle, visualising the path-length geometry that underlies Bragg's condition. The diffraction pattern panel shows intensity vs. 2θ for all allowed reflections of the selected crystal structure. FCC and BCC lattices have selection rules that forbid certain peaks (systematic absences).
Frequently Asked Questions
What is Bragg's law?
Bragg's law states that constructive interference of X-rays reflected from parallel crystal planes occurs when nλ = 2d·sin(θ), where n is the diffraction order, λ is the X-ray wavelength, d is the spacing between crystal planes, and θ is the glancing angle. Derived by W.L. Bragg in 1913, it earned the 1915 Nobel Prize in Physics.
What are Miller indices?
Miller indices (hkl) specify the orientation of a crystal plane. For a cubic lattice, the d-spacing is d = a/√(h²+k²+l²), where a is the lattice parameter. The (100), (110), and (111) planes are the most commonly studied.
How does X-ray diffraction reveal crystal structure?
By measuring peak angles and applying Bragg's law, the d-spacings of all crystal planes are determined. The set of d-spacings and their intensities is unique to each crystal structure — a 'fingerprint'. Comparing the measured pattern to a database identifies the material.
What is the difference between powder and single-crystal diffraction?
Single-crystal diffraction uses one oriented crystal producing discrete spots (Laue pattern). Powder diffraction uses finely ground crystals in all orientations — the 3D pattern collapses to a 1D intensity vs. 2θ plot. Powder diffraction is simpler for phase identification; single-crystal gives full 3D structural information.
Why do different crystal structures give different diffraction patterns?
Different lattices have different sets of allowed d-spacings. FCC and BCC have systematic absences: FCC only shows peaks where h, k, l are all odd or all even; BCC only where h+k+l is even. These selection rules come from destructive interference due to extra atoms at face-centres or body-centres.
What is the structure factor in X-ray diffraction?
The structure factor F(hkl) = Σ fⱼ·exp[2πi(hxⱼ+kyⱼ+lzⱼ)] sums contributions from all atoms in the unit cell. |F|² gives the observed peak intensity. Systematic absences occur when F = 0 due to cancellation between atoms at different positions.
What wavelength of X-rays is used in crystallography?
X-ray wavelengths used in crystallography are typically 0.5–2.5 Å, comparable to atomic spacings. The most common laboratory source is copper Kα radiation at 1.54 Å. Synchrotron facilities can tune wavelengths precisely, enabling anomalous dispersion techniques for phase determination.
How was DNA's double helix discovered using X-ray diffraction?
Rosalind Franklin and Raymond Gosling produced X-ray diffraction patterns of DNA fibres in 1952. Photo 51 showed an X-shaped pattern characteristic of a helix. Watson and Crick used Franklin's measurements to build their correct double helix model in 1953, earning the 1962 Nobel Prize.
Can Bragg diffraction be observed with visible light?
Yes — opal gems show iridescent colours because regular arrays of silica spheres (250–350 nm spacing) diffract visible light. Holographic gratings, liquid crystal displays, and photonic crystal fibres all exploit this principle. Acoustic Bragg diffraction occurs in phononic crystals at ultrasonic frequencies.