# Laue Diffractograms in Crystallography

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In the Laue backscattering method, a polychromatic x-ray beam impinges on a single crystal through a small hole in a disc-like detector or photographic film. For specific wavelengths within the spectrum of the beam (fulfilling the Bragg condition), the lattice planes of the crystal behave like mirrors and reflect beams with corresponding wavelengths back onto the detector. From the resulting diffractogram ("Laue" pattern), the orientation of the crystal can be determined. This Demonstration assumes an FCC (face-centered cubic) crystal and generates diffractograms that include all reflections from lattice plane types {111}, {200}, {220}, {422}, {311}, {442}, {331}, {420}, {620}. These reflections are significant in Laue diffractograms from simple FCC metals, e.g. Al, Cu, Ag, Au. Observe that the reflections representing "zones" (planes with a common direction) line up along hyperbolas. In this Demonstration, you can rotate the crystal in order to observe the effect of lattice orientation on the pattern. In spite of the distortion introduced by the backscatter setting, high-symmetry zone-axis reflections (e.g. 111) locally reveal the symmetry of the corresponding crystal axis.

Contributed by: Frank Ernst (March 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: Laue diffraction pattern for the primary x-ray beam impinging on the FCC crystal in a <001> direction, that is, parallel to an edge of the cubic unit cell of the crystal structure. The diffraction pattern reflects the four-fold symmetry of the crystal structure with respect to these directions.

Snapshot 2: Simulated pattern for a crystal orientation where the primary x-ray beam impinges parallel to a <111> direction, that is, parallel to a space diagonal of the FCC unit cell. Corresponding to the 3-fold symmetry of cubic crystals about such directions, this pattern exhibits 3-fold symmetry.

Snapshot 3: Laue pattern for the primary beam parallel to a <110> direction of the FCC unit cell, exhibiting 2-fold symmetry.

See also "Laue Method" on Wikipedia.

## Permanent Citation

"Laue Diffractograms in Crystallography"

http://demonstrations.wolfram.com/LaueDiffractogramsInCrystallography/

Wolfram Demonstrations Project

Published: March 24 2014