"Quasi" science wins Nobel: crystal prize

Positively asymmetric

Until the morning of the 8th April 1982, crystals were regular. Repetitive. Symmetric. But, a chance discovery by Danny Shechtman then working in the laboratories of National Bureau of Standards in Gaithersburg, Maryland, now the National Institute of Standards and Technology, NIST, changed all that, although acceptance of what would become known as quasicrystals did not happen quite so instantaneously. After many years of mockery, ostracism, and job changes, the materials-shattering discovery by the Israeli has finally and fully been recognised with the award of the 2011 Nobel Prize for Chemistry.

It was in 1784 almost two centuries before Shechtman's discovery that Abbé Haüy suggested that periodic repetition might explain the regular and reproducible shapes of crystals. Ever since, long-range order and translation symmetry were inextricably linked to crystallinity. The textbook definition commonly reads as follows: A crystal is a substance in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating three-dimensional pattern.

The allowed symmetries have been well catalogued and specifically preclude fivefold symmetry. Just as pentagons cannot tessellate on a flat surface, so a crystal could not have translational symmetry if it were somehow to have fivefold symmetry, or indeed any multiple of fivefold...tenfold, say...

Intermetallic symmetry

On that fateful morning in 1982, Shechtman was studying aluminium alloys using transmission electron microscopy, X-ray diffraction and neutron diffraction. In run after run with his instruments nothing was amiss, until electron diffraction run number 1725, alongside which Shechtman wrote "10 fold ???" in his lab-book. Run #1725 displayed a forbidden tenfold symmetry. Further runs in which Shechtman rotated his sample allowed him to identify fivefold symmetry axes as well as three- and two-fold axes. The sample also had icosahedral symmetry.

When Shechtman revealed his findings to colleagues he was met with ridicule. His 1984 paper in Physical Review Letters elicited the attention of twice Nobel laureate Linus Pauling denounced the findings. But, over the years, the evidence mounted as other scientists discovered they could reproduce these forbidden symmetries in materials that ultimately became known as quasicrystals. Crystalline, solids in which there is local regularity but none of the translational symmetry of conventional crystals.

To mathematician Roger Penrose of Oxford University the discovery of such fivefold quasicrystals was not such a surprise, there was precedence in his work on mathematical objects that form tessellating patterns - Penrose tiles - that do not repeat and he has pointed to the inspirational work of 16th Century astronomer Johannes Kepler who recorded aperiodic tilings. Of course, much has been made since the Nobel Prize award to an Israeli scientist of the beautiful and deliberately asymmetric patterns of Moorish art.

Accepting quasicrystals

Today we can define a quasicrystal as a material with long-range order in a diffraction experiment but lacking translational periodicity and numerous examples of been found since Shechtman's work in the early 1980s. However, there may have been prior art. Given that it was known previously that crystals do not need to be periodic in three-dimensions because there can be periodic 3D distortions that do not fit the underlying parent lattice, it is no surprise that quasicrystals were inferred in the structure of cold-worked metals as early as 1927.

Crystal structure refinement for quasicrystals has been continuously improving since the 1980s. Today, analysis of decagonal quasicrystals approaches the refinement available in studies of "conventional" periodic crystals.

Shechtman's first quasicrystals were synthetic intermetallic materials and hundreds have now been studied. However, aside from dendrimer liquid crystals, star copolymers and self-assembled nanoparticles there remains a dearth of other types of quasicrystals in the literature. This is surprising given the potential for unique and potentially useful properties that might be exhibited by such materials. The aperiodicity endows quasicrystals with unusual transport properties and very low surface energies. Thermal and electronic transport is, of course, inhibited by the aperiodicity as periodicity is usually required to carry energy in the form of phonons and Bloch waves through regular crystalline materials; quasicrystals instead have some of the characteristics of glasses, yet their low surface energy makes them corrosion- and adhesion-resistant as well as giving them a low coefficient of friction.

The views represented in this article are solely those of the author and do not necessarily represent those of John Wiley and Sons, Ltd.