Posted on 28 June 2022 by Andrei Mihai

Adversity, Quasicrystals and a Nobel ─ the Forbidden Fivefold Symmetry that Was

Dan Shechtman during his lecture at the 69th Lindau Nobel Laureate Meeting

The quasicrystal debate: how Nobel Laureate Dan Shechtman fought to prove the existence of the “forbidden symmetry”.

In what would eventually become a seminal paper in 1984, chemist Dan Shechtman presented a striking structure: a new class of ordered solids that were ordered and not periodic. The paper challenged the “traditional” definition of what a crystal is and the structures quickly became known as “quasicrystals” – it also made Shechtman a bit of a celebrity in the world of chemistry, but not only for good reasons.

The paper drew the ire of another leading chemist: two-time Nobel Laureate Linus Pauling, who not only disagreed with Shechtman’s findings but made him the target of ridicule. It was a hostility unusual for the world of science, with two leading researchers having not different, but opposite opinions.

Perhaps this is why Shechtman’s own journey to the Nobel Prize is all the more remarkable: not only did he produce outstanding contributions in the field of chemistry, but he did so while overcoming strong adversity coming from many corners of science.

Crystals and Quasicrystals

Crystals are a weird thing. They’re solid materials with a microscopic structure that is ordered and periodic. Essentially, crystals have a structural lattice that extends in all directions. In an ideal crystal, every atom has exactly the same repeating pattern.

Atomic image of a micron-sized grain of the natural Al71Ni24Fe5 quasicrystal
Atomic image of a micron-sized grain of the natural Al71Ni24Fe5 quasicrystal (shown in the inset) from a Khatyrka meteorite fragment. The corresponding diffraction patterns reveal a ten-fold symmetry. Photo/Credits: Wiki Commons / Paul Steinhardt et al.

Since ancient times, humans have been fascinated by crystals, and it’s not hard to understand why, especially as this lattice sometimes translates to remarkable macroscopic structures. Take, for instance, the surreal-looking but perfectly natural pyrite crystals. They look like perfect cubes with straight edges and faces, sometimes intertwining with each other and other minerals.

How could nature, which is so often messy and irregular, produce something like this?

The key is the crystal lattice, the pattern in which atoms (or molecules or other constituents) are distributed microscopically. Pyrite is a mineral that crystallises in the “cubic crystal system,” one of the seven types of crystal lattice systems. All crystals fall into one of seven lattice systems. Quartz, for instance, is famously in the hexagonal crystal system.

Pyrite cubic crystals on marlstone.
Pyrite cubic crystals on marlstone. Photo/Credits: Wiki Commons / Carles Millan.

These crystal lattices can be described in different ways, but one way of looking at them is through something called rotational symmetry. When something is symmetrical, it has parts that match each other. For instance, humans appear to be symmetrical on the outside: we have two hands, two legs, two eyes, and so on (of course, no one is perfectly symmetrical and our internal organs are also not symmetrical). In fact, most animals appear to be symmetrical on the outside: you could divide their body into two mirroring images that are similar. But this is just one type of symmetry. Rotational symmetry is a property of a shape to be symmetrical after being rotated to a certain degree angle. For instance, if you look at a roundabout road sign, it has a three-fold rotational symmetry: its appearance is identical in three different orientations.

With crystals, you can have two-fold, three-fold, four-fold, and six-fold rotational symmetry ─ but never five. Up until recently, the five-fold symmetry in crystals was strictly forbidden, it just couldn’t happen. Then Shechtman came along.

“All Hell Broke Loose”

In 1982, Shechtman was on a sabbatical at the U.S. National Bureau of Standards in Washington. At some point, he looked at a rapidly cooled mix of aluminium and manganese and thought that something was just not right. What he saw was something that could not be, according to what was known at the time: atoms arranged in a five-fold rotational symmetry.

Even he couldn’t believe it at first. For two years, he checked and double-checked that everything was correct, and in the end, managed to publish a paper. Then, he says, “all hell broke loose”.

The notebook of Dan Shechtman dating the discovery of quasicrystals to 8 April 1982.
The notebook of Dan Shechtman dating the discovery of quasicrystals to 8 April 1982. Photo/Credits: Iowa State University / Dan Schechtman / Nobel Prize.

Of course, Shechtman was aware of what he was saying. The definition for a crystal, as was presented at the time, was wrong (or at least incomplete). But it’s not like the finding came out of nowhere. In the 1960s, mathematicians had figured out that you could fill up a plane with aperiodic tiling, arrangements that are ordered but not periodic (they don’t have a repeating pattern), offering a tantalising suggestion that something like this could also show up in nature. In 1981, crystallographer Alan Lindsay Mackay predicted the existence of such structures. Another 1981 paper pointed out the possibility of a non-periodic quasicrystals.

Still, five-fold symmetry in crystals was still a fringe idea when Shechtman published his paper. The paper triggered a frantic race for other chemists to produce and observe the same type of structure. Some were successful and praised Shechtman, naming the structure “quasicrystals” and publishing several papers. But others were less thrilled.

A Story of Disagreement and Adversity

Many saw Shechtman’s work as something that could not be true and must be explained somehow through experimental error or some kind of misjudgement.

The head of Shechtman’s own research group gave him a textbook on crystallography and suggested that he read it. A few days later, the same researcher asked Shechtman to leave the group and not bring more “disgrace”, forcing Shechtman to find another research group. People laughed at him, Shechtman recalls. But the most vocal opponent of this work was Linus Pauling.

Pauling had two Nobels (one for chemistry, one for peace), and he was one of the most famous scientists of the day. He told everyone who wanted to listen that Shechtman was wrong. “There is no such thing as quasicrystals, only quasi-scientists.” Even as other researchers were reproducing the findings, Pauling was so influential (and the idea of a quasicrystal was so revolutionary) that quasicrystals were regarded with skepticism by many researchers.

A quasiperiodic crystal (quasicrystal) is a structure that is ordered but not periodic.
A quasiperiodic crystal (quasicrystal) is a structure that is ordered but not periodic. Here, silver deposition on an aluminium-palladium-manganese (Al-Pd-Mn) quasicrystal surface. Photo/Credits: J. W. Evans, Wiki Commons.

Time (and intense scientific effort) proved Shechtman right (and Pauling wrong) in this debate. In 1992, the International Union of Crystallography altered its definition of a crystal in a way that addresses the quasicrystal issue, and in 2011, Shechtman was awarded the Nobel Prize in Chemistry for the discovery of quasicrystals. In 2018, the first naturally-occurring quasicrystal was discovered. “His discovery was extremely controversial,” said the Nobel Committee at the Royal Swedish Academy of Sciences. “However, his battle eventually forced scientists to reconsider their conception of the very nature of matter.”

The Nobel Committee at the Royal Swedish Academy of Sciences said that “his discovery was extremely controversial,” but that his work “eventually forced scientists to reconsider their conception of the very nature of matter.”

Dan Shechtman’s work forced us to rethink not only what we think about crystals, but also what we think about matter itself. His work through adversity helped us understand a whole new class of materials, with far-reaching implications. Nowadays, hundreds of man-made quasicrystals have been reported and confirmed. Many quasicrystals have applications in materials science, being used in LEDs, engines, aviation, and heat insulation.

Andrei Mihai

Andrei is a science communicator and a PhD candidate in geophysics. He co-founded ZME Science, where he tries to make science accessible and interesting to everyone and has written over 2.000 pieces on various topics – though he generally prefers writing about physics and the environment. Andrei tries to blend two of the things he loves (science and good stories) to make the world a better place – one article at a time.