Quasicrystals: The Impossible Atomic Structures That Won a Nobel Prize

The Diffraction Pattern That Should Not Exist

On April 8, 1982, Israeli metallurgist Dan Shechtman stared at an electron diffraction pattern from a rapidly cooled aluminum-manganese alloy and wrote in his notebook: "10 fold???" The pattern showed tenfold rotational symmetry — a sharp, clear diffraction pattern characteristic of a highly ordered structure. The problem was categorical: crystallography had established since the 19th century that crystals can only have 2-, 3-, 4-, or 6-fold rotational symmetry. Tenfold symmetry was structurally impossible in a periodic crystal. Shechtman's colleagues assumed he was wrong. His lab director suggested he return a crystallography textbook. He was eventually asked to leave his research group.

Why Tenfold Symmetry Was "Impossible"

Classical crystallography defines a crystal as a solid whose atoms are arranged in a periodic lattice — a pattern that repeats exactly through space. The allowed rotational symmetries of such lattices are constrained by a fundamental geometric requirement: the pattern must tile space without gaps or overlaps. Try to tile a floor with regular pentagons and you will find it impossible — the angles leave gaps. This is why fivefold and tenfold rotational symmetry was excluded from the list of crystallographically allowed symmetries. The constraint was not empirical but mathematical.

Shechtman's diffraction pattern implied icosahedral symmetry — 6 fivefold axes, 10 threefold axes, and 15 twofold axes. This is the symmetry of a soccer ball and of the icosahedron, one of Plato's five regular solids. It had never been observed in a crystalline material.

Quasiperiodic Order

The resolution came through a concept that mathematician Roger Penrose had already developed on purely theoretical grounds: aperiodic tilings. Penrose demonstrated in 1974 that two specially shaped tiles (now called Penrose tiles) can fill a plane completely without gaps and without ever repeating — the pattern is ordered, with long-range correlations, but it never becomes periodic. The key insight is that long-range order does not require periodicity.

Shechtman's aluminum-manganese alloy was not a crystal in the classical sense. Its atoms were arranged in a quasiperiodic structure — ordered at every scale but never repeating. The new class of solids became known as quasicrystals. A formal definition was established: quasicrystals display long-range quasiperiodic translational order and non-crystallographic rotational symmetry.

Structure and Properties of Quasicrystals

The Scientific Resistance

Shechtman's findings, submitted for publication in 1984, were initially rejected. When finally published in Physical Review Letters in November 1984 — alongside a theoretical paper by Dov Levine and Paul Steinhardt explaining the quasiperiodic framework — they generated immediate controversy. Linus Pauling, arguably the most renowned chemist of the 20th century and two-time Nobel laureate, became the most prominent skeptic. Pauling argued persistently until his death in 1994 that Shechtman's "quasicrystals" were actually twinned crystals — intergrown regular crystals that produced misleading symmetry artifacts. The scientific community gradually converged on Shechtman's interpretation as more quasicrystalline materials were discovered and higher-resolution techniques confirmed the quasiperiodic structure.

Natural Quasicrystals

For decades, quasicrystals were exclusively laboratory-made materials. In 2009, geologist Luca Bindi and Princeton physicist Paul Steinhardt identified the first natural quasicrystal in a mineral sample from the Khatyrka meteorite, which originated in the outer asteroid belt. The sample contained icosahedrite — a naturally occurring quasicrystalline phase of aluminum, copper, and iron. A 2011 expedition to the Koryak Mountains of Chukotka, Russia, where the meteorite fragments had been found, confirmed the extraterrestrial origin of the quasicrystalline material through oxygen isotope analysis. Natural quasicrystals had apparently formed 4.5 billion years ago in the early solar system.

Applications of Quasicrystals

• Non-stick coatings — quasicrystalline coatings have been developed for cookware, though their brittleness limits commercial uptake
• Thermal barriers — low thermal conductivity makes certain quasicrystals useful in heat-resistant coatings
• Surgical instruments — hardness and low friction tested for cutting-tool applications
• Hydrogen storage — some quasicrystalline alloys absorb hydrogen efficiently, relevant to fuel cell research
• Structural reinforcement — quasicrystalline precipitates in aluminum alloys improve strength and corrosion resistance

The Nobel Prize

In 2011, the Royal Swedish Academy of Sciences awarded the Nobel Prize in Chemistry to Dan Shechtman "for the discovery of quasicrystals." The prize was awarded to Shechtman alone — a solo award relatively rare in modern science, reflecting the singular nature of his original observation and the extraordinary professional resistance he overcame. The discovery changed the fundamental definition of a crystal: the International Union of Crystallography revised its official definition in 1992 to include any solid with a discrete diffraction diagram, eliminating the periodic requirement that had defined crystallography for over a century.