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Diffraction Hoodie

SPOTS WHERE THE ROWS AGREE | Pixelated Physics

\[n\lambda = 2d\sin\theta\]
$54.99 USD
$54.99 USD
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Size guide S–5XL · inches

Shine waves at a crystal and they scatter from every atom. In almost every direction the scattered waves cancel. The far-field diffraction pattern of a hexagonal crystal: spots on the reciprocal lattice, first Brillouin zone outlined. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

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Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

X-rays reflecting from successive planes of atoms in a crystal add up only when the extra path between planes is a whole number of wavelengths. That Bragg condition lets you measure the spacing of atoms from the angles of bright spots.

Shine waves at a crystal and they scatter from every atom. In almost every direction the scattered waves cancel.

In a few directions they all add up, and those make bright spots. William Lawrence Bragg wrote the condition in 1913 as nλ = 2d sin θ. The modern form says the change in wavevector must equal a reciprocal lattice vector G.

The art is the exact intensity, the squared sum over every atom of a hexagonal crystal patch. The spots sit on the reciprocal lattice, which is hexagonal too. The faint ripples between them come from the patch having an edge.

The hexagon in the middle is the first Brillouin zone, the set of points closer to the origin than to any other spot.

Spots where the rows agree.

Equations

\[n\lambda = 2d\sin\theta\]
\[\mathbf{k} - \mathbf{k}_0 = \mathbf{G}\]
\[I(\mathbf{q}) \propto \Big|\sum_j e^{i\mathbf{q}\cdot\mathbf{r}_j}\Big|^2\]
SymbolMeaningUnit
\(n\) diffraction order \(\mathrm{1}\)
\(\lambda\) wavelength \(\mathrm{m}\)
\(d\) spacing between lattice planes \(\mathrm{m}\)
\(\theta\) angle between the beam and the planes \(\mathrm{rad}\)
\(\mathbf{k}_0, \mathbf{k}\) incoming and outgoing wavevectors \(\mathrm{m^{-1}}\)
\(\mathbf{G}\) reciprocal lattice vector \(\mathrm{m^{-1}}\)
\(\mathbf{q}\) scattering vector \(\mathrm{m^{-1}}\)
\(\mathbf{r}_j\) position of atom j \(\mathrm{m}\)

Sources

  1. Bragg & Bragg (1913) The Reflection of X-rays by Crystals, Proc. R. Soc. A 88, 428
  2. Friedrich, Knipping & Laue (1912) Interferenz-Erscheinungen bei Röntgenstrahlen, Sitzungsber. Bayer. Akad. Wiss., 303
  3. Ashcroft & Mermin, Solid State Physics (1976), Ch. 5–6
  4. Kittel, Introduction to Solid State Physics, Ch. 2

Source Bragg, W. H.; Bragg, W. L. (1913). The reflection of X-rays by crystals. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 88, 428–438.doi.org/10.1098/rspa.1913.0040

Field notes

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