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
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angle to the lattice planes
- Scattering angle 2θ
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- Path difference 2d sin θ
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- n integer diffraction order · λ radiation wavelength · d spacing between parallel lattice planes · θ angle between the incident beam and those planes
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.
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