For my April 2026 diary, go here.

Diary — May 2026

John Baez

May 14, 2026

I love quasicrystals — like crystals, but with patterns that never repeat, like Penrose tiles. But they've very rare in nature. They're created only by the most exotic and violent events: a high-speed collision of asteroids, lightning hitting a downed power cable in a sand dune — or an atomic bomb!

Amazingly, the first 3 kinds of naturally occurring quasicrystal were discovered in a single meteorite that landed in Khatyrka, in the far east of Russia. They've never been found anywhere else! And this meteorite is highly anomalous: it's the only meteorite known that contains metallic aluminum — and it seems to have been formed in a ultra-high-velocity collision between asteroids.

The only other quasicrystal I know that may be naturally created came from a bolt of lightning hitting a sand dune near a downed power cable in Nebraska. Then there was one found amid the fused desert sand and copper transmission cable left behind by the first atomic bomb test at Trinity, New Mexico. That's not quite 'naturally created'.

And that's all. As far as I can tell, all the rest have been made in labs!

Here are the 3 kinds of quasicrystal found in the Khatyrka meteorite, in order of their discovery:

The Nebraska quasicrystal shows how blurry the concept of 'natural' can be. It was found inside a 'fulgurite': a rock made when lightning hits sand. They found it in the Sand Hills near Hyannis, Nebraska, near a downed power line during a storm. It's unclear whether this fulgurite was created by a lightning strike or by the falling power line creating its own arc, so the 'natural vs manmade' status is genuinely ambiguous.

What's more important is it was a new kind of quasicrystal produced by a high-current, high-temperature, rapid-quench event on Earth's surface! It has a composition of roughly Mn72.3Si15.6Cr9.7Al1.8Ni0.6. Its atomic planes have 12-fold symmetry in a nonrepeating pattern, and these planes are stacked periodically along the perpendicular direction.

Here's a picture of this quasicrystal:

tunnelling electron microscope data obtained on a dodecagonal quasicrystal from a fulgurite. (A) The black circle in the acicular, quasicrystalline grain indicates the region where the electron diffraction pattern (Inset) has been collected. (B) A HAADF-TEM image of a portion of the quasicrystalline grain.  From here: www.pnas.org/doi/10.1073/pnas.2215484119

References

On icosahedrite, the first natural quasicrystal to be found in the meteorite from Khatyrka:

On decagonite, the second to be found:

On i-phase II, which is the provisional designation of the third quasicrystal found in that meteorite:

On the dodecagonal quasicrystal found in the dune in Nebraska:

On the quasicrystal found at the atomic bomb test site:

This has icosahedral symmetry, but it's quite different than the other quasicrystals I've mentioned, since it's mostly made of silicon! Its formula is Si61Cu30Ca2Fe2.

May 15, 2026

In 2025, researchers studied a quasicrystal forged in a hypervelocity asteroid collision 600 million years ago — and found that it contains 'phasons'!

It's not a perfect icosahedral quasicrystal: it's slightly distorted. 6 gentle 'phason waves' run through it, oriented along the 6 fivefold symmetry axes of an icosahedron. These waves were locked in when the alloy quickly cooled after impact, and they've been sitting there frozen in the structure ever since.

This quasicrystal is called 'icosahedrite'. The easiest way to describe it is the 'slice and project' method. You start with a lattice in 6 dimensions, choose a 3d slice, thicken that up a bit, take the lattice points that lie in the thickened slice, and project them down to 3d space. The atoms in the icosahedrite are exactly the projections of the 6d lattice points that happen to fall inside the thickened slice.

But now imagine wobbling the slice gently — not tilting it, but wiggling it sideways in the other three dimensions, the ones perpendicular to physical space. Some 6d lattice points slip out of the slice and others slip in. In physical space this looks like atoms suddenly hopping from one position to a nearby alternative one.

These atomic hops are called 'phason flips', and a wave of them is a 'phason'. Sound waves involve atoms swaying smoothly in place; phasons involve atoms jumping between alternative positions, and they exist only in quasicrystals.

These phasons are a fossil record of the collision that made the quasicrystal: the instant of cooling, preserved as a piece of warped 6-dimensional geometry, sitting inside a rock for 600 million years!

For my June 2026 diary, go here.


© 2026 John Baez
baez@math.removethis.ucr.andthis.edu

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