Bragg's Law Calculator | SolidState3D

Understanding Bragg's Law

Bragg's Law is a fundamental principle in solid-state physics and crystallography that explains the relationship between an X-ray light's wavelength and its diffraction pattern from a crystal surface.

The Equation

The condition for constructive interference of scattered waves is given by Bragg's Law:

$n\lambda = 2d \sin(\theta)$

Where:

$n$ is the order of reflection (an integer: 1, 2, 3...)
$\lambda$ is the wavelength of the incident wave (e.g., X-rays, electrons, neutrons)
$d$ is the interplanar spacing (the distance between parallel planes of atoms in the crystal lattice)
$\theta$ is the scattering angle (the angle between the incident ray and the scattering planes)

Application in X-Ray Diffraction (XRD)

In an X-Ray Diffraction experiment, a crystal sample is bombarded with X-rays of a known wavelength (often Cu Kα with $\lambda \approx 1.54 \mathring{A}$ ). By measuring the angles ( $\theta$ ) at which the X-rays are strongly diffracted (constructive interference), researchers can calculate the interplanar spacing ( $d$ ) of the crystal planes.

Because different crystal structures have unique sets of interplanar spacings, XRD serves as a highly effective "fingerprinting" technique to identify unknown crystalline materials.