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DIFFRACT

hold an unknown crystal · turn it under the X-ray sun · name it from the diffraction

the specimen☼ X-ray beam → into screen

Drag to turn the crystal in the fixed beam. The beam travels into the screen; the detector behind it catches the reflected spots (right). Coloured stubs are the crystal axes a b c.

Laue diffraction pattern

Each spot is a family of lattice planes reflecting the one wavelength (from the white beam) that satisfies Bragg's law. Rotate until the pattern snaps into n-fold symmetry — that names the system.

name that crystal

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Rotate the specimen, read its symmetry, then pick the crystal system.

symmetry along the beam

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Align a rotation axis with the beam (into the screen) to lock the pattern's symmetry.

X-ray source & detector

How this works — Bragg, Laue, and reading symmetry

This is the transmission Laue method, the oldest trick in X-ray crystallography (von Laue, 1912). A single crystal sits still in a white (polychromatic) X-ray beam — the “X-ray sun.” Every family of parallel lattice planes selects, from the whole spectrum, the one wavelength that satisfies Bragg's law and mirrors the beam into a sharp spot on the detector.

Bragg's law

A family of planes with spacing d reflects constructively when

nλ = 2 d sinθ

In Laue diffraction θ and d are fixed by the crystal's orientation, so each plane family simply picks its own λ out of the white beam. That's why a still crystal lights up dozens of spots at once.

The reflection, in vectors

Write the incident beam as the unit vector s₀ and a set of planes by its reciprocal-lattice vector G = h·a* + k·b* + l·c* (its length is |G| = 1/d). The elastic Laue condition k − k₀ = G works out to a pure mirror reflection of the beam across the planes:

s = s₀ − 2 (s₀ · Ĝ) Ĝ,    λ = −2 (s₀ · G) / |G|²

The spot only appears if that required λ falls inside the beam's band [λmin, λmax]. Lowering λmin (harder X-rays) admits more, higher-order planes — so the pattern fills in. This page computes exactly that, live, for the rotating reciprocal lattice.

Why the pattern names the crystal

A Laue pattern carries the point symmetry of the crystal as seen down the beam. Turn a cubic crystal so a cube axis ⟨100⟩ points into the screen and the spots lock into 4-fold symmetry; a body diagonal ⟨111⟩ gives 3-fold; a face diagonal ⟨110⟩ gives 2-fold. Each system has a signature highest axis:

cubic → 4,3,2  hexagonal → 6  trigonal → 3  tetragonal → 4  orthorhombic → 2,2,2  monoclinic → one 2  triclinic → none

So the game is real crystallography in miniature: rotate to find the highest-order rotation axis, count its spokes, and that narrows the seven systems. The spacing of the spots scales with 1/a, so a small unit cell throws a wide pattern — a second clue once you've got the symmetry.

Honest caveats

Spot positions here are exact reflection geometry. Spot brightness uses a simplified Kramers white-beam spectrum and a crude form-factor falloff, plus lattice-centering extinctions (P / I / F / C / R and the diamond rule) — enough to make face-centred and primitive cells look different, but not a full structure-factor calculation. Laue resolves the Laue class, not the exact compound; the specimen name in the reveal is the mineral the lattice was taken from.