Phasons in Quasicrystals

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 made of ‘icosahedrite’. The easiest way to describe this 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 wiggling the slice gently—letting it ripple 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 these hops is a ‘phason’. Sound waves involve atoms swaying smoothly in place; phasons involve atoms jumping between alternative positions, and they’re special to quasicrystals.

These phasons give 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!

References

For more about quasicrystals in this particular meteorite, which is called the Khatyrka meteorite, read my post:

• Naturally occurring quasicrystals.

This paper reported the discovery of icosahedrite in the Khatyrka meteorite:

• L. Bindi, J. M. Eiler, Y. Guan, L. S. Hollister, G. MacPherson, P. J. Steinhardt and N. Yao, Evidence for the extraterrestrial origin of a natural quasicrystal, Proceedings of the National Academy of Sciences 31 (2012), 1396-401.

This is the paper that first reported phasons in this sample of icosahedrite:

• Hiroyuki Takakuru, Asuka Ishikawa, Tsutomu Ishimasa, Luca Bindi and Paul J. Steinhardt, High-resolution synchrotron X-ray study of natural icosahedrite, IUCrJ 12 (2025), 435–443.

Quasicrystal phasons had already been understood long before:

• Dov Levin, T. C. Lubensky, Stellan Ostlund, Sriram Ramaswamy, Paul J. Steinhardt and John Toner, Elasticity and dislocations in pentagonal and icosahedral quasicrystals, Physical Review Letters 54 (1985), 1520–1523.

• T. C. Lubensky, Sriram Ramaswamy and John Toner, Hydrodynamics of icosahedral quasicrystals, Physical Review Letters 32 (1985), 7444–7452.

These paper use some nice math. The lattice I mentioned above is the D₆ lattice in 6 dimensions: a ‘checkboard’ lattice consisting of all points with integer coordinates that sum to an even integer. To understand phasons in icosahedral quasicrystals we need the representation theory of the rotational symmetry group of the icosahedron, which is the alternating group A₅. This group has an obvious 3-dimensional representation, called 3, where group elements just rotate an icosahedron and drag 3d Euclidean space along with that. But it also has another 3-dimensional representation, the Galois conjugate 3′, where we replace by in every formula describing the representation 3.

Beautifully, the 6d space containing the D₆ lattice transforms as the representation 3 ⊕ 3′. Using this we can classify all the possible formulas, allowed by symmetry, for how an icosahedral quasicrystal can oscillate. It turns out that we get phonons (sound waves) and phasons, and their motions are described by various constants: two that describe the behavior of phonons, two for phasons, and one for phonon-phason interactions.

I feel like saying more, but this is not the right place!