The finding for which this year’s Chemistry Nobel was awarded earlier today was sufficiently unexpected and counter to the orthodoxy of the time that today’s prize winner was tossed out of his own research group for reporting it. His 1982 discovery has to do with how atoms are organized in solid matter, and is based on observations made with electron microscopy. Daniel Shechtman’s imagery…

…showed that the atoms in his crystal were packed in a pattern that could not be repeated. Such a pattern was considered just as impossible as creating a football using only six-cornered polygons, when a sphere needs both five- and six-cornered polygons. His discovery was extremely controversial.

The matter that matters is now called “Quasicrystal” in which the arrangement of atoms follows a definable mathematical pattern, but the pattern is not repeated. There are aspects of this patterning seen in the ancient concept of the “Golden Mean” as well as in medieval Islamic mosaics, which provide for a lot of analogies and pretty language in explaining what this stuff is.

“There can be no such creature” is what Shechtman wrote in his lab notebook when he first observed the patterns that do not repeat themselves using electron diffraction. The solid he was examining was a mixture of aluminum and manganese that had been rapidly cooled from molten to solid state. The pattern he was looking at was a diffraction pattern with a ten-fold symmetry.

You will remember diffraction patterns from High School physics. When energy waves (light, waves on water, sound, etc.) pass through a substance that blocks its path or absorbes it in some places and not others, the energy waves that get through interact in a manner that depends on a few different variables including the nature of the gaps through which it passed. Different diffraction patterns indicate different arrangements of matter.

Shechtman was using electron diffraction to observe the structure of the cooled metal when he came up with this pattern:

Notice the ten medium size dots surrounding and equidistant to the larger dot. This does not look like anything spectacular but it is. If you were a birder this would be like looking through the binoculars at a distant crow and when it comes into focus it has three wings. If you were reading a Tom Clancey book, this would be like finding the main characters to be all liberal pacifists. Maybe this is a little like some of the neutrinos arriving early?

There are expectations based on empirical data as well as theory, and apparently having a 10-fold diffraction pattern in this sort of material is not in the lookup tables of diffracting patterns nor is it otherwise expected. So when Shechtman’s colleagues heard of his work, they may have been thinking of Lowell and his Martian Canals: He sees these things but they are not there.

But why is this unexpected?

Atoms are organized in crystals in repeated patterns that have symmetry. The details of the symmetry vary but you can think of them like what you get when you fold paper using a repeated pattern of squares or triangles. At any point in time you can rotate the paper and the pattern returns: Four repetitions if you’ve made a square, three if you’ve made a triangle, etc.

With atoms, it was thought that the only symmetries that worked were those where atoms of a particular element ended up equidistant from each other Compare for example the following two patterns:

The upper pattern shows six fold symmetry, and the atoms that make up the symmetry are equidistant. The lower pattern shows five fold symmetry. The atoms here are not equidistant. Some of the atoms are closer than others. In the case of Shechtman’s diffraction pattern, there was 10-fold symmetry, which like the 5-fold symmetry was considered impossible.

Once a pattern is established, that pattern repeats itself at larger scales. So, for instance, if you have a crystal with a cubic shape, and you break it up into bits allowing it to reveal its inner crystallines pattern, you still get cubes. In the case of Shechtman’s 10-fold pattern, when you pull back and observe it at a larger scale, you get a 5-fold pattern. Like 10-fold patterns, 5-fold patterns were considered impossible. Not only was Shechtman’s symmetry not the same at different scales, but an impossible pattern yields to another impossible pattern at the larger scale. (Well, I suppose there is a certain symmetry to this.)

At first Shechtman’s results were interpreted by other experts in the field as a simple mistake that only an idiot would make. They told Shechtman that he was observing a “double crystal” and mixing up his observations. One snarky colleague gave him a school textbook on crystals implying that he should brush up on his basics. A manuscript Shechtman sent to the *Journal of Applied Physics* was sent back unopened.

Over time, using his personal connections to a grad school colleague and, in turn, his colleague’s connections, Shechtman got his work looked at more closely by other crystal experts, who concurred that the results were both a) real and b) impossible. Finally, in 1984, a paper coauthored by Shechtman and those experts (John Cahn, Denis Gratias and his schoolmate Ilan Blech) was published in *Physical Review Letters*. The world of crystallography was stunned, and the single most important pillar of dogma of the science of crystals … all crystals consist of repeating periodic patterns … was under serious question.

There are several interesting lessons in that Odyssey of Shechtman. One, don’t discount your personal and professional relationship, or the cultural aspects of scientific networks. A pure, scientific, or even “skeptical” view of Shechtman’s work failed. Shechtman needed to get someone to look at his results on blind trust that there could be something there, rather than approaching it from what was known to be very well established fact. On the other hand, it must be remembered that 99.99% of the time that a scientist gets an email from someone telling them that the basic tenets of their science are wrong, it is some crazy guy who sees things in rocks. But not this time. Ultimately, this is a case of science being conservative, which is usually appropriate, but learning something new. The turnaround time between nobody knowing this thing and key scientists getting it in print was only a couple of years.

But, Shechtman’s 1984 paper did not change everyone’s mind instantly. It was met with a combination of disdain, criticism, and uneasiness. Over time, other crystallographers started noticing that they had seen similar things but had used the old “It’s a twin crystal” brushoff to ignore their results. Over time, not only did various other researchers rediscover their own cases like Shechtman’s, but others as well that were also impossible, such as 8- and 12-fold symmetries.

There’s a lesson there too: If you want to be the one to win the Nobel Prize, *be the one that notices when you’ve made the Nobel Prize-winning discovery!!!!*

But what does it all mean?

Well, prior to Shechtman’s empirical discovery of what was to become known as Quasicrystals, mathematicians were messing around with a concept called aperiodic mosaics (or aperiodic patterns). Early on this concept was applied, literally, to mosaics, but eventually to atoms. The math behind aperiodic mosaics was mainly solved by Roger Penrose, a British mathematician, in the 1970s. Later, a crystallographer, Alan Mackay, applied the concept of aperiodic mosaics to atoms using a theoretical model in which he came up with a 10-fold symmetry in a diffraction study of a large scale crystal model (but not actual crystals).

Mackay’s theoretical Quasicrystal and Shechtman’s observed 10-fold symmetry were connected by Paul Steinhardt and Dov Levine, two physicists. You see, when Shechtman’s *Physical Review Letters* paper — the one he finally got published — was under review, Steinhardt got a look at it. Being already familiar with Mackay’s Quasicrystal model, he put two and two together. Just over a month after Shechtman’s paper came out, Steinhardt and Levine put out their own paper linking the observations and coining the term Quasicrystal.

And the rest is history.

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The information used to compile this post comes from the Nobel Prize site. Photo, graphics provided by Nobel.