Science calculator

Bragg's law.

Relate diffraction order, wavelength, crystal-plane spacing and Bragg angle. Enter three values and leave one blank.

Bragg angle θSolved
angle to the lattice planes
Scattering angle 2θ
Path difference 2d sin θ
nλ=2dsin(θ)

Assumptions

  • Elastic, monochromatic scattering from a regular family of parallel crystal planes.
  • θ is measured between the incident beam and the lattice planes, not between the beam and their normal.
  • A physical reflection uses a positive integer order n and requires nλ ≤ 2d.
  • The common diffractometer reading is the angle between incident and diffracted beams, 2θ; instrument broadening and structure-factor intensity are not modelled.

How it works

Waves scattered from neighbouring crystal planes travel different distances. Their path difference is 2d sin θ.

A diffraction maximum occurs when that path difference is a whole number of wavelengths. This selects particular angles for each plane spacing and wavelength.

Leave one field blank to rearrange Bragg's law. A solved non-integer order indicates that the entered geometry is not a diffraction maximum.