Bragg's Law Calculator

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Determine the interplanar spacing of crystals based on X-ray diffraction patterns.

Diffraction Parameters

Diffraction Order (n)

X-ray Wavelength (λ)

Incident Angle (θ)

Calculation Results

Enter the diffraction parameters to calculate the crystal lattice spacing

About this calculator

Overview

Bragg's Law is the fundamental principle of X-ray crystallography, describing how X-rays are diffracted by the regular arrangement of atoms in crystalline solids. When X-rays strike crystal lattice planes at specific angles, they undergo constructive interference, producing diffraction patterns that reveal the crystal's atomic structure. This law revolutionized our understanding of matter at the atomic level and earned the Braggs father-son team the Nobel Prize in Physics.

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Pro Tips

The Bragg angle (θ) is measured between the incident X-ray beam and the crystal plane, not between the beam and the crystal surface.
Diffraction order (n) is typically 1 for fundamental reflections, but higher orders (n=2, 3) can occur at the same angle for different wavelengths.
Common X-ray wavelengths: Cu Kα = 0.154 nm, Mo Kα = 0.071 nm, Co Kα = 0.179 nm - choose based on your sample and desired resolution.
For powder diffraction, the angle in Bragg's equation is actually 2θ (the scattering angle), so the equation becomes nλ = 2d sin(θ) where θ is half the measured angle.
Crystal quality affects diffraction - perfectly ordered crystals produce sharp, intense reflections, while disordered materials give broad, weak patterns.
Temperature can affect lattice spacing through thermal expansion, so samples are often cooled to reduce atomic vibrations and improve diffraction quality.
The maximum resolution achievable depends on the wavelength and maximum scattering angle - shorter wavelengths allow study of finer details.

Fun Facts

"William Lawrence Bragg was just 25 years old when he and his father William Henry Bragg won the Nobel Prize in Physics in 1915 for their work on X-ray crystallography - making him the youngest Nobel laureate ever."
"The Bragg equation (nλ = 2d sinθ) was derived by Lawrence Bragg while still an undergraduate student at Cambridge University in 1912."
"X-ray crystallography revealed that table salt (NaCl) consists of alternating sodium and chloride ions in a cubic lattice, not molecules as previously believed."
"The technique was crucial in determining the double-helix structure of DNA by Watson and Crick, who used data from Rosalind Franklin's X-ray diffraction patterns."
"Bragg's Law explains why crystals can act like three-dimensional diffraction gratings, scattering X-rays in predictable patterns based on their atomic spacing."
"Modern protein crystallography uses synchrotron X-ray sources that are billions of times brighter than the X-ray tubes used by the Braggs, enabling the study of increasingly complex molecules."
"The law applies not just to X-rays but to any wave phenomenon interacting with periodic structures, including neutron diffraction and electron microscopy."

Formula: nλ = 2d sinθ