The STEM Chicksmas Day Five: Quasicrystals

For the 12 Days of “The STEM Chicksmas” we’re highlighting 12 scientists who have contributed something innovative and exciting to their field. It is the season of giving, and these brilliant minds have given incredible gifts to the scientific community! This year we’re looking at 12 Nobel Prize winners from the past 15 years in the fields of Physics, Chemistry, and Physiology or Medicine.

Day Five: The 2011 Nobel Prize in Chemistry.

The STEM Chicksmas Nobel Prize 2011 Chemistry
Source: Nobel Prize Summary and Nobel Prize Popular Information

There are two broad types of solids: amorphous and crystalline. In an amorphous solid like quartz or rubber, the molecules are randomly arranged. In a crystalline solid, the atoms are arranged in a pattern that stretches across the entire solid. An example of this is table salt. If you were to look at salt on the atomic level, you would see that each sodium and chloride ion is arranged at a specific distance from each other and in a certain pattern. If you looked in any direction, you would see that this pattern repeats for infinity (or until the edge of the crystal, or if you hit a defect). Up until the 1990s, the requirement for something to be crystalline was for this pattern to be regular and repeating. That means that if you took a small part of the crystal called the unit cell and slid that in any direction, it would superimpose over the atoms there. This is called translational symmetry. Another way of thinking about it is that you can build the crystal up in every direction by attaching the unit cells together at the edge. Crystals can also be classified by their rotational symmetry—that is, how many times you can turn it and still have the same structure.

Only certain degrees of rotational symmetry are possible in crystal lattices: 2, 3, 4, or 6. Degrees of 5 or ones higher than 6 are not allowed. A simple explanation for this is that they cannot be space filling. As an exercise, take a piece of paper and a pen. Try to draw a lattice made up of pentagons that are all the same size. You’ll quickly see that you can’t—there will always be a gap. (Also if you try this, please share the pictures with us!)

So when Dan Shechtman, winner of the 2011 Nobel Prize in Chemistry, discovered a crystal that seemed to have fivefold symmetry in the early 80s, he was stumped. Crystals can have their structures determined by a process called x-ray crystallography. In this process, high intensity light is shined on a crystal. The crystal diffracts the light, and gives a pattern of bright spots that are associated with the structure of the crystal. This “diffraction pattern” can be then analyzed to figure out the shape of the crystal. Shechtman’s diffraction pattern suggested his crystal had five- or tenfold rotational symmetry. He repeated the process a few times, assuming that either his crystal sample was bad or that he was looking at the pattern incorrectly, but each time he got the same result. He eventually published his work and it was very controversial. His supervisor kicked him out of the lab group. He was told to “read a textbook.” Nobel Prize winner Linus Pauling offered him coauthorship on a paper that would contradict his original work by claiming the samples were, in fact, not good enough. (Pauling ended up spending several years trying to explain the problem Shechtman’s crystal presented.)

Eventually Shechtman realized his crystal was not just fivefold symmetric, but icosahedral. An icosahedron is a polygon with 5 triangular faces. The neat thing about icosahedrons is that if you look at them in 6 dimensional space using matrix math, they have transformational symmetry, just like normal crystals! They also found that even though they didn’t have transformational symmetry or long range order in 3D space, there was underlying symmetry. The golden ratio appears over and over again in quasicrystals—the ratio between the distance between two atoms can be represented with the golden ratio. So even while Shechtman’s crystals, which we now call quasicrystals, did not have typical geometric order, they instead had mathematical order. This led to the definition of crystals being changed in 1992 to “any solid having an essentially discrete diffraction diagram.” That means quasicrystals really are crystalline! But we still call the quasicrystals out of convention and because they’re still a little weird.

Shechtman’s discovery is cool for a few different reasons. One, he totally changed the way crystals are considered and shook up the paradigm of the time. Two, he stuck to his theory and believed in his work, even when everyone was telling him he was wrong. Three, quasicrystals have since been discovered in certain types of steel and in a mineral found in a Russian river. Without Shechtman’s work these discoveries would have been overlooked as errors.  The discovery of quasicrystals shows us that sometimes, we can be smarter than the textbook and maybe even a Nobel Prize winner.

Read more at the Nobel Prize website or check out the winning paper here.


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