Bragg's Law
Definition
nλ = 2d sin(θ). A monochromatic X-ray beam diffracted off the parallel lattice planes of a crystal produces constructive interference only at angles where the path-length difference is an integer number of wavelengths. The single equation behind every powder XRD pattern in a crystallography lab.
- Equation
- nλ = 2d sin(θ), where n is an integer
- Core principle
- Constructive interference of X-rays scattered from crystal planes
- Primary forensic application
- X-ray diffraction (XRD) for material identification
Common questions
What does Bragg's Law tell us?+
Bragg's Law (nλ = 2d sin θ) describes when X-rays bouncing off crystal planes will amplify each other instead of canceling out. This constructive interference happens only at specific angles that depend on the wavelength and the spacing between atomic layers. It's the principle that makes X-ray crystallography work.
Why is Bragg's Law important in forensic analysis?+
Forensic scientists use X-ray diffraction (XRD) to identify unknown minerals, drugs, and crystalline materials in evidence. Bragg's Law is the foundation of every diffraction pattern. By measuring which angles produce peaks, labs can determine what materials are present and confirm their identity.
What are the variables in Bragg's Law?+
In the equation nλ = 2d sin θ: λ is the X-ray wavelength (fixed by the instrument), d is the spacing between crystal planes (unique to each material), θ is the angle at which diffraction occurs, and n is a whole number (1, 2, 3...) representing the order of interference. Each material produces peaks at predictable angles.
Related terms
- D-Spacing
- The perpendicular distance between adjacent parallel planes of atoms in a crystal lattice, measured in angstroms or nanometres. Each set of planes...
- Anode Target
- The metal block (commonly Cu, Mo or Rh) that electrons strike inside an X-ray tube to produce the X-ray beam. Choice of...
- Basal Reflection
- The diffraction peak arising from the repeat distance along the stacking direction of clay layer silicates (the c-axis or 001 reflection). Its...
- Characteristic X-Ray
- An X-ray photon emitted when an outer-shell electron drops into an inner-shell vacancy created by ionisation. Energy is set by the difference...
- Characteristic X-Rays
- Sharp emission lines produced when an inner-shell vacancy in an atom is filled by an outer electron. Their energies are element-specific (Moseley's...
- Continuous (Bremsstrahlung) Radiation
- Smooth background X-ray spectrum produced when high-energy electrons decelerate in the anode. Element-independent. The 'hump' under the characteristic lines.
- EDXRF
- Energy-dispersive X-ray fluorescence. A solid-state detector resolves the entire emission spectrum at once by photon energy. Cheap, portable, faster.
- EDXRF vs WDXRF
- Energy-dispersive XRF reads all photon energies in parallel with a Si(Li) or silicon-drift detector; fast, cheap, lower resolution. Wavelength-dispersive XRF uses a...
- GSR Pb-Sb-Ba Signature
- The classical elemental signature of inorganic gunshot residue: lead from the bullet core, antimony from the priming compound, barium from the priming...
- ICDD PDF-4
- The Powder Diffraction File maintained by the International Centre for Diffraction Data. A reference database of more than 400,000 crystalline phases that...
- K-Alpha Line
- The characteristic X-ray emitted when an electron drops from the L-shell to fill a K-shell vacancy. Brightest line for most elements; the...
- Mixed-Layer Clay
- A clay mineral in which two different layer types (for example smectite and illite layers) are interstratified in a regular or random...
Explained in these topics
- X-Ray Spectroscopy: XRF, XRD and X-Ray Absorptionnλ = 2d sin(θ). A monochromatic X-ray beam diffracted off the parallel lattice planes of a crystal produces constructive interference only at angles where the...
- X-ray Techniques in Forensic Analysis: XRD, XRF and X-ray Imagingnλ = 2d sin θ. The condition under which X-rays scattered from successive crystal planes interfere constructively. Foundation of XRD.
- X-ray Diffraction and Clay MineralogyThe relationship n*lambda = 2d*sin(theta), where lambda is the X-ray wavelength, d is the interplanar spacing, and theta is the diffraction angle. It defines t...